11institutetext: 1 Max-Planck-Institut für Astronomie, Königstuhl 17, 69117
Heidelberg, Germany
2 Sandia National Laboratories, Livermore, California 94550, USA
3 European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The
Netherlands
4 Mullard Space Science Laboratory, University College London, Holmbury St
Mary, Dorking, Surrey RH5 6NT, UK
5 Aurora Technology B.V., Zwarteweg 39, 2201 AA Noordwijk, The Netherlands
6 Airbus Defence & Space SAS, Toulouse, France
7 ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo,
28692 Villanueva de la Cañada, Madrid, Spain
8 Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo,
s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692
Madrid, Spain
9 Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität
Heidelberg, Mönchhofstr. 12-14, 69120 Heidelberg, Germany
10 SYRTE, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université,
LNE, 61 avenue de l’Observatoire 75014 Paris, France
11 INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino
Torinese (TO), Italy
12 Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-
UB), Martí i Franquès 1, 08028 Barcelona, Spain
13 Institut d’Estudis Espacials de Catalunya (IEEC), Carrer Gran Capitá 2-4,
08034 Barcelona, Spain
14 Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748
Garching, Germany
15 University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität,
Scheinerstr. 1, 81679 Munich, Germany
16 Departament de Física Quàntica i Astrofísica (FQA), Universitat de
Barcelona (UB), Martí i Franquès 1, E-08028 Barcelona, Spain
17 Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405,
Orsay, France
18 Institute of Cosmology and Gravitation, University of Portsmouth,
Portsmouth PO1 3FX, UK
19 Institut für Theoretische Physik, University of Heidelberg, Philosophenweg
16, 69120 Heidelberg, Germany
20 Dipartimento di Fisica e Astronomia ”Augusto Righi” - Alma Mater Studiorum
Universitá di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
21 INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via
Piero Gobetti 93/3, 40129 Bologna, Italy
22 INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
23 Dipartimento di Fisica, Universitá di Genova, Via Dodecaneso 33, 16146,
Genova, Italy
24 INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy
25 Department of Physics ”E. Pancini”, University Federico II, Via Cinthia 6,
80126, Napoli, Italy
26 INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131
Napoli, Italy
27 Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP,
Rua das Estrelas, PT4150-762 Porto, Portugal
28 Dipartimento di Fisica, Universitá degli Studi di Torino, Via P. Giuria 1,
10125 Torino, Italy
29 INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
30 INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
31 Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of
Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
32 Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra
(Barcelona), Spain
33 INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio
Catone, Italy
34 INFN section of Naples, Via Cinthia 6, 80126, Napoli, Italy
35 Dipartimento di Fisica e Astronomia ”Augusto Righi” - Alma Mater Studiorum
Universitá di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
36 Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue
Edouard Belin, 31401 Toulouse Cedex 9, France
37 Institut national de physique nucléaire et de physique des particules, 3
rue Michel-Ange, 75794 Paris Cédex 16, France
38 Institute for Astronomy, University of Edinburgh, Royal Observatory,
Blackford Hill, Edinburgh EH9 3HJ, UK
39 Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy,
University of Manchester, Oxford Road, Manchester M13 9PL, UK
40 European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma,
Italy
41 University of Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR
5822, 69622 Villeurbanne, France
42 Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique
Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix,
Switzerland
43 Departamento de Física, Faculdade de Ciências, Universidade de Lisboa,
Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
44 Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências,
Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
45 Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290
Versoix, Switzerland
46 INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del
Cavaliere, 100, 00100 Roma, Italy
47 INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
48 Université Paris-Saclay, Université Paris Cité, CEA, CNRS, Astrophysique,
Instrumentation et Modélisation Paris-Saclay, 91191 Gif-sur-Yvette, France
49 INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143
Trieste, Italy
50 Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
51 Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029
Blindern, 0315 Oslo, Norway
52 Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The
Netherlands
53 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak
Grove Drive, Pasadena, CA, 91109, USA
54 von Hoerner & Sulger GmbH, SchloßPlatz 8, 68723 Schwetzingen, Germany
55 Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
56 Cosmic Dawn Center (DAWN), Denmark
57 Université de Genève, Département de Physique Théorique and Centre for
Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
58 Department of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
59 Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of
Helsinki, Helsinki, Finland
60 NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk
4, 7991PD, Dwingeloo, The Netherlands
61 Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71,
53121 Bonn, Germany
62 Department of Physics, Institute for Computational Cosmology, Durham
University, South Road, DH1 3LE, UK
63 Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris,
France
64 Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014, Paris,
France
65 Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université,
98 bis boulevard Arago, 75014 Paris, France
66 CEA Saclay, DFR/IRFU, Service d’Astrophysique, Bat. 709, 91191 Gif-sur-
Yvette, France
67 Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700
AV Groningen, The Netherlands
68 Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191, Gif-
sur-Yvette, France
69 Space Science Data Center, Italian Space Agency, via del Politecnico snc,
00133 Roma, Italy
70 Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov,
077125, Romania
71 Dipartimento di Fisica e Astronomia ”G. Galilei”, Universitá di Padova, Via
Marzolo 8, 35131 Padova, Italy
72 Dipartimento di Fisica e Astronomia, Universitá di Bologna, Via Gobetti
93/2, 40129 Bologna, Italy
73 Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-
Universität München, Scheinerstrasse 1, 81679 München, Germany
74 Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008,
Santiago, Chile
75 Institut de Ciencies de l’Espai (IEEC-CSIC), Campus UAB, Carrer de Can
Magrans, s/n Cerdanyola del Vallés, 08193 Barcelona, Spain
76 Centre for Electronic Imaging, Open University, Walton Hall, Milton Keynes,
MK7 6AA, UK
77 Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
(CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
78 Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências,
Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
79 Universidad Politécnica de Cartagena, Departamento de Electrónica y
Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
80 Institut de Recherche en Astrophysique et Planétologie (IRAP), Université
de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
81 INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
82 Infrared Processing and Analysis Center, California Institute of
Technology, Pasadena, CA 91125, USA
83 IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2,
34151 Trieste, Italy
84 INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
85 Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, 38204, San
Cristóbal de La Laguna, Tenerife, Spain
86 Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin
katu 2, 00014 University of Helsinki, Finland
87 Dipartimento di Fisica ”Aldo Pontremoli”, Universitá degli Studi di Milano,
Via Celoria 16, 20133 Milano, Italy
88 INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
89 Junia, EPA department, 41 Bd Vauban, 59800 Lille, France
90 Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid,
Spain
91 CERCA/ISO, Department of Physics, Case Western Reserve University, 10900
Euclid Avenue, Cleveland, OH 44106, USA
92 Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL,
CNRS, Sorbonne Université, 75005 Paris, France
93 Observatoire de Paris, Université PSL, Sorbonne Université, LERMA, 750
Paris, France
94 Astrophysics Group, Blackett Laboratory, Imperial College London, London
SW7 2AZ, UK
95 SISSA, International School for Advanced Studies, Via Bonomea 265, 34136
Trieste TS, Italy
96 INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
97 Dipartimento di Fisica e Scienze della Terra, Universitá degli Studi di
Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
98 Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe
Saragat 1, 44122 Ferrara, Italy
99 NASA Ames Research Center, Moffett Field, CA 94035, USA
100 Kavli Institute for Particle Astrophysics & Cosmology (KIPAC), Stanford
University, Stanford, CA 94305, USA
101 INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna,
Italy
102 Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire
Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France
103 Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH
Aachen University, 52056 Aachen, Germany
104 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive,
Honolulu, HI 96822, USA
105 Department of Physics & Astronomy, University of California Irvine, Irvine
CA 92697, USA
106 University of Lyon, UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico
Fermi, 69622 Villeurbanne, France
107 Canada-France-Hawaii Telescope, 65-1238 Mamalahoa Hwy, Kamuela, HI 96743,
USA
108 Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
109 Department of Astronomy & Physics and Institute for Computational
Astrophysics, Saint Mary’s University, 923 Robie Street, Halifax, Nova Scotia,
B3H 3C3, Canada
110 Dipartimento di Fisica, Universitá degli studi di Genova, and INFN-Sezione
di Genova, via Dodecaneso 33, 16146, Genova, Italy
111 Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical
Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780
Bochum, Germany
112 Department of Physics and Astronomy, Vesilinnantie 5, 20014 University of
Turku, Finland
113 AIM, CEA, CNRS, Université Paris-Saclay, Université de Paris, 91191 Gif-
sur-Yvette, France
114 Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin 69627
Villeurbanne Cedex, France
115 Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2,
00185 Roma, Italy
116 University of Applied Sciences and Arts of Northwestern Switzerland,
School of Engineering, 5210 Windisch, Switzerland
117 INFN-Sezione di Roma, Piazzale Aldo Moro, 2 - c/o Dipartimento di Fisica,
Edificio G. Marconi, 00185 Roma, Italy
118 Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762
Porto, Portugal
119 Zentrum für Astronomie, Universität Heidelberg, Philosophenweg 12, 69120
Heidelberg, Germany
120 Dipartimento di Fisica - Sezione di Astronomia, Universitá di Trieste, Via
Tiepolo 11, 34131 Trieste, Italy
121 Department of Mathematics and Physics E. De Giorgi, University of Salento,
Via per Arnesano, CP-I93, 73100, Lecce, Italy
122 INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per
Arnesano, 73100, Lecce, Italy
123 INFN, Sezione di Lecce, Via per Arnesano, CP-193, 73100, Lecce, Italy
124 Institute for Computational Science, University of Zurich,
Winterthurerstrasse 190, 8057 Zurich, Switzerland
125 Université St Joseph; Faculty of Sciences, Beirut, Lebanon
126 Department of Astrophysical Sciences, Peyton Hall, Princeton University,
Princeton, NJ 08544, USA

#  Euclid preparation. XXIX. Water ice in spacecraft part I:
The physics of ice formation and contamination

Euclid Collaboration: M. Schirmer0000-0003-2568-99941<EMAIL_ADDRESS>K.
Thürmer0000-0002-3078-73722 B. Bras3 M. Cropper0000-0003-4571-94684 J. Martin-
Fleitas5 Y. Goueffon6 R. Kohley7 A. Mora0000-0002-1922-85298 M. Portaluppi3 G.
D. Racca3 A. D. Short3 S. Szmolka3 L. M. Gaspar Venancio3 M. Altmann9,10 Z.
Balog0000-0003-1748-29269 U. Bastian0000-0002-8667-17159 M.
Biermann0000-0002-5791-90569 D. Busonero0000-0002-3903-707611 C.
Fabricius0000-0003-2639-137212,13 F. Grupp14,15 C.
Jordi0000-0001-5495-960212,16,13 W. Löffler9 A. Sagristà
Sellés0000-0001-6191-20289 N. Aghanim17 A. Amara18 L.
Amendola0000-0002-0835-233X19 M. Baldi0000-0003-4145-194320,21,22 C.
Bodendorf14 D. Bonino11 E. Branchini23,24 M. Brescia0000-0001-9506-568025,26
J. Brinchmann0000-0003-4359-879727 S. Camera0000-0003-3399-357428,29,11 G. P.
Candini4 V. Capobianco0000-0002-3309-769211 C. Carbone0000-0003-0125-356330 J.
Carretero0000-0002-3130-020431,32 M. Castellano0000-0001-9875-826333 S.
Cavuoti0000-0002-3787-419626,34 A. Cimatti35 R.
Cledassou0000-0002-8313-223036,37 G. Congedo0000-0003-2508-004638 C. J.
Conselice39 L. Conversi0000-0002-6710-847640,7 Y. Copin0000-0002-5317-751841
L. Corcione0000-0002-6497-588111 F. Courbin0000-0003-0758-651042 A. Da
Silva0000-0002-6385-160943,44 H. Degaudenzi0000-0002-5887-679945 A. M. Di
Giorgio46 J. Dinis44,43 F. Dubath0000-0002-6533-281045 X. Dupac7 S.
Dusini0000-0002-1128-066447 S. Farrens0000-0002-9594-938748 S. Ferriol41 M.
Frailis0000-0002-7400-213549 E. Franceschi0000-0002-0585-659121 M.
Fumana0000-0001-6787-595030 S. Galeotta0000-0002-3748-511549 B.
Garilli0000-0001-7455-875030 W. Gillard0000-0003-4744-974850 B.
Gillis0000-0002-4478-127038 C. Giocoli0000-0002-9590-796121,22 S. V. H.
Haugan0000-0001-9648-726051 H. Hoekstra0000-0002-0641-323152 W. Holmes53 F.
Hormuth54 A. Hornstrup0000-0002-3363-093655,56 K. Jahnke0000-0003-3804-21371
S. Kermiche0000-0002-0302-573550 A. Kiessling0000-0002-2590-127353 M.
Kilbinger0000-0001-9513-713848 T. Kitching0000-0002-4061-45984 M.
Kunz0000-0002-3052-739457 H. Kurki-Suonio0000-0002-4618-306358,59 S.
Ligori0000-0003-4172-460611 P. B. Lilje0000-0003-4324-779451 I. Lloro60 E.
Maiorano0000-0003-2593-435521 O. Mansutti0000-0001-5758-465849 O.
Marggraf0000-0001-7242-385261 K. Markovic0000-0001-6764-073X53 F.
Marulli0000-0002-8850-030320,21,22 R. Massey0000-0002-6085-378062 E.
Medinaceli0000-0002-4040-778321 S. Mei0000-0002-2849-559X63 Y. Mellier64,65,66
M. Meneghetti0000-0003-1225-708421,22 E. Merlin0000-0001-6870-890033 G.
Meylan42 M. Moresco0000-0002-7616-713620,21 L.
Moscardini0000-0002-3473-671620,21,22 E. Munari0000-0002-1751-594649 R.
Nakajima61 S.-M. Niemi3 J. W. Nightingale0000-0002-8987-740162 T. Nutma67,52
C. Padilla0000-0001-7951-016631 S. Paltani45 F. Pasian49 V. Pettorino48 S.
Pires68 G. Polenta0000-0003-4067-919669 M. Poncet36 L. A. Popa70 F.
Raison0000-0002-7819-691814 A. Renzi0000-0001-9856-197071,47 J. Rhodes53 G.
Riccio26 E. Romelli0000-0003-3069-922249 M. Roncarelli21 E. Rossetti72 R.
Saglia0000-0003-0378-703273,14 D. Sapone0000-0001-7089-450374 B. Sartoris73,49
P. Schneider61 A. Secroun0000-0003-0505-371050 G. Seidel0000-0003-2907-353X1
S. Serrano13,75 C. Sirignano0000-0002-0995-714671,47 G.
Sirri0000-0003-2626-285322 J. Skottfelt0000-0003-1310-828376 L.
Stanco0000-0002-9706-510447 P. Tallada-Crespí0000-0002-1336-832877,32 A. N.
Taylor38 I. Tereno43,78 R. Toledo-Moreo0000-0002-2997-485979 I.
Tutusaus0000-0002-3199-039980 E. A. Valentijn67 L.
Valenziano0000-0002-1170-010421,81 T. Vassallo0000-0001-6512-635849 Y.
Wang0000-0002-4749-298482 J. Weller0000-0002-8282-201073,14 A.
Zacchei0000-0003-0396-119249,83 J. Zoubian50 S. Andreon0000-0002-2041-878484
S. Bardelli0000-0002-8900-029821 P. Battaglia21 E. Bozzo0000-0002-8201-152545
C. Colodro-Conde85 M. Farina46 J. Graciá-Carpio14 E.
Keihänen0000-0003-1804-771586 V. Lindholm0000-0003-2317-547158,59 D.
Maino87,30,88 N. Mauri0000-0001-8196-154835,22 N. Morisset45 V. Scottez64,89
M. Tenti0000-0002-4254-590181 E. Zucca0000-0002-5845-813221 Y.
Akrami0000-0002-2407-795690,91,92,93,94 C.
Baccigalupi0000-0002-8211-163095,83,49,96 M.
Ballardini0000-0003-4481-355997,98,21 A. Biviano0000-0002-0857-073249,83 A.
Blanchard0000-0001-8555-900380 A. S. Borlaff0000-0003-3249-443199,100 C.
Burigana0000-0002-3005-5796101,81 R. Cabanac0000-0001-6679-260080 A.
Cappi21,102 C. S. Carvalho78 S. Casas0000-0002-4751-5138103 G.
Castignani0000-0001-6831-068720,21 T. Castro0000-0002-6292-322849,96,83 K. C.
Chambers0000-0001-6965-7789104 A. R. Cooray0000-0002-3892-0190105 J. Coupon45
H. M. Courtois0000-0003-0509-1776106 J.-G. Cuby0000-0002-8767-1442107,108 S.
Davini24 G. De Lucia0000-0002-6220-910449 G. Desprez109 S. Di
Domizio0000-0003-2863-5895110 H. Dole17 J. A. Escartin14 S.
Escoffier0000-0002-2847-749850 I. Ferrero0000-0002-1295-113251 L. Gabarra71,47
K. Ganga0000-0001-8159-820863 J. Garcia-Bellido0000-0002-9370-836090 K.
George0000-0002-1734-845515 F. Giacomini0000-0002-3129-281422 G.
Gozaliasl0000-0002-0236-919X58 H. Hildebrandt0000-0002-9814-3338111 J. J. E.
Kajava0000-0002-3010-8333112 V. Kansal113 C. C. Kirkpatrick86 L.
Legrand0000-0003-0610-525257 P. Liebing4 A. Loureiro0000-0002-4371-087638,94
G. Maggio49 M. Magliocchetti46 G. Mainetti114 R.
Maoli0000-0002-6065-3025115,33 S. Marcin116 M.
Martinelli0000-0002-6943-773233,117 N. Martinet0000-0003-2786-7790108 C. J. A.
P. Martins0000-0002-4886-9261118,27 S. Matthew38 M. Maturi19,119 L.
Maurin0000-0002-8406-085717 R. B. Metcalf0000-0003-3167-257420 P.
Monaco120,49,96,83 G. Morgante21 S. Nadathur0000-0001-9070-310218 A. A.
Nucita121,122,123 L. Patrizii22 J. E. Pollack66 V. Popa70 D.
Potter0000-0002-0757-5195124 M. Pöntinen0000-0001-5442-253058 A. G.
Sánchez0000-0003-1198-831X14 Z. Sakr0000-0002-4823-3757125,19,80 A.
Schneider0000-0001-7055-8104124 M. Sereno0000-0003-0302-032521,22 A.
Shulevski0000-0002-1827-046952,67 P. Simon61 J. Steinwagner14 R.
Teyssier0000-0001-7689-0933126 J. Valiviita0000-0001-6225-369358,59

(Received; accepted)

Material outgassing in a vacuum leads to molecular contamination, a well-known
problem in spaceflight. Water is the most common contaminant in cryogenic
spacecraft, altering numerous properties of optical systems. Too much ice
means that Euclid’s calibration requirements cannot be met anymore. Euclid
must then be thermally decontaminated, which is a month-long risky operation.
We need to understand how ice affects our data to build adequate calibration
and survey plans. A comprehensive analysis in the context of an astrophysical
space survey has not been done before.

In this paper we look at other spacecraft with well-documented outgassing
records. We then review the formation of thin ice films, and find that for
Euclid a mix of amorphous and crystalline ices is expected. Their surface
topography – and thus optical properties – depend on the competing energetic
needs of the substrate-water and the water-water interfaces, and they are hard
to predict with current theories. We illustrate that with scanning-tunnelling
and atomic-force microscope images of thin ice films.

Sophisticated tools exist to compute contamination rates, and we must
understand their underlying physical principles and uncertainties. We find
considerable knowledge errors on the diffusion and sublimation coefficients,
limiting the accuracy of outgassing estimates. We developed a water transport
model to compute contamination rates in Euclid, and find agreement with
industry estimates within the uncertainties. Tests of the Euclid flight
hardware in space simulators did not pick up significant contamination
signals, but they were also not geared towards this purpose; our in-flight
calibration observations will be much more sensitive.

To derive a calibration and decontamination strategy, we need to understand
the link between the amount of ice in the optics and its effect on the data.
There is little research about this, possibly because other spacecraft can
decontaminate more easily, quenching the need for a deeper understanding. In
our second paper, we quantify the impact of iced optics on Euclid’s data.

###### Key Words.:

Space vehicles, Space vehicles: instruments, Telescopes, Molecular processes,
Solid state: volatile

##  1 Introduction

Euclid will survey 15 000 deg2 of extragalactic sky (Euclid Collaboration:
Scaramella et al., 2022) during its nominal six-year mission (Laureijs et al.,
2011; Racca et al., 2016). To achieve its cosmology science goals with
measurements of weak lensing and galaxy clustering, Euclid must maintain
pristine image quality, and a relative spectrophotometric flux accuracy of
about $1\%$ in its optical and near-infrared (NIR) channels. Euclid will
observe from the Sun-Earth Lagrange point L2, which offers exceptional thermal
stability and a well-known space environment.

Yet, even at L2 Euclid will degrade over time due to space weathering.
Radiation damage, dust, and meteoroid111The IAU discouraged the use of the
term ‘micrometeoroid’ beginning in 2017. Dust particles are smaller than 30
$\mathrm{\SIUnitSymbolMicro m}$, and meteoroids are larger. impacts will
degrade protective thermal blankets and their efficacy (Engelhart et al.,
2017; Plis et al., 2019), which can change the electronical and optical
performance. Detectors directly suffer from radiation that increases the
charge transfer inefficiency of charge-coupled devices (CCDs; Massey et al.,
2014), and they may decrease the quantum efficiency of some photo-diode
architectures (Sun et al., 2020; Crouzet et al., 2020). Dust and meteoroids
increase the scattering and transmission loss of optical elements through
surface pitting (Rodmann et al., 2019; McElwain et al., 2023); ionising
radiation has a similar effect on optical surfaces, although on smaller
physical scales (Roussel et al., 2016; Simonetto et al., 2020). These
environmental factors are well known at L2. Euclid’s calibration program is
well suited to account and correct for them, yielding accurate and consistent
survey data. Atomic oxygen, the prime cause for spacecraft degradation in low-
Earth orbits (Banks et al., 2003; Palusinski et al., 2009; Samwel, 2014), is
fortunately not a problem at L2.

However, space weathering is not the only adversary. Ongoing contamination
also degrades the performance of optics, solar panels, thermal control, and
other sub-systems (e.g. Green, 2001; Zhao et al., 2009; Smith et al., 2012;
Hui et al., 2022). We distinguish between particulate and molecular
contamination, with the latter being composed of volatile (for example H2O and
CO) and non-volatile substances, such as polymers. In this paper, we mostly
focus on molecular contamination by water ice. In terms of prevention and
minimisation of contamination, Euclid is the best-designed spacecraft by the
European Space Agency (ESA) to date. Water from material outgassing is
expected to be the only relevant source of contamination, possibly forming
thin ice films on optical surfaces throughout the mission.

On ground, contamination is an inherent part of construction and launch, and
subject to contamination control plans (Kimoto, 2017; Luey et al., 2018; Patel
et al., 2019; Abeel et al., 2022). In the vacuum of space, contamination is
driven by material outgassing (Chiggiato, 2020). Quartz crystal microbalances
(QCMs) can be used to detect surface contamination down to a few $10^{-9}$ g
cm-2 (Dirri, 2016). In the case of water, this corresponds to a molecular
monolayer with a $10\%$ filling factor. Solar System exploration missions
require additional decontamination prior to launch to preserve the pristine
states of the bodies they visit, and those of any samples returned to Earth
(Willson et al., 2018; Chan et al., 2020).

Even though spacecraft materials can be degassed (baked out) to reduce
outgassing, water and other trace materials are recaptured until launch, on
timescales of days (Scialdone, 1993) and down to seconds (Postberg et al.,
2009). The outgassing rate depends, among other factors, on the material’s
molecular structure, chemical composition, surface finish, coatings,
temperature, and mass and mobility of the dissolved contaminants. Outgassing
rates for spacecraft materials are usually determined at room temperature, and
must be extrapolated to cryogenic conditions. This extrapolation is highly
uncertain due to the considerable dependence of diffusion and sublimation
coefficients on temperature. Nano-scale restructuring processes in the
materials during cool-down also play a role. Accurate contamination forecasts
are therefore hard and require considerable effort well beyond the scope of
this paper (e.g. Brieda et al., 2022, for the James Webb Space Telescope;
JWST).

To counter contamination, temperatures in many spacecraft can be increased
locally – for example for a single lens – or globally to sublime volatile
contaminants. A global decontamination, however, implies a major thermal shock
to the spacecraft; it may alter electronic and optical properties, and may
even lead to additional contamination (e.g. Haemmerle & Gerhard, 2006; Liebing
et al., 2018). In the case of Euclid, on-board heating power is insufficient
for a full decontamination; partial Sun exposure of the external telescope
baffle is required, implying further risks. A full decontamination cycle for
Euclid lasts about one month, including warm-up, cool-down, and recalibration,
and only $1-2$ days are spent at maximum temperature to allow the sublimates
to find their way out of the spacecraft. Given a mission duration of six
years, this is a very costly procedure.

Volatile and non-volatile molecular contamination has caused throughput losses
of 20% and more in some Earth-observation satellites, posing a substantial
challenge for accurate and consistent long-term environmental and climate
monitoring. To this end, the Global Space-Based Intercalibration System
(GSICS; Goldberg et al., 2011) has established terrestrial and bright
celestial targets as a reference, used by numerous Earth-observation
satellites for cross-calibration and correction. Yet surprisingly, little is
known about the effect of iced optics on astrophysical observations. Perhaps
this is because local decontamination comes as an easy fix in many spacecraft,
readily and frequently applied whenever necessary, or because their
calibration requirements are more relaxed; we give examples in Sect. 2 and
links to to other works in Appendix A. Euclid, however, cannot heat individual
optical elements alone, nor does it carry internal QCMs to monitor
contamination directly. To maintain a spectrophotometric accuracy of 1%
throughout its lifetime, Euclid has to rely on its own survey and self-
calibration data. In this way, we can detect and correct for water ice until a
decontamination is required.

In this context we need to understand (1) the physical properties of thin ice
films, (2) their surface topography, (3) their formation on optical
substrates, and (4) their temporal evolution in space conditions. We also need
to investigate the outgassing and sublimation fluxes in Euclid, and how
accurately they can be known in advance. These points are addressed in the
present paper. We present a comprehensive analysis of ice contamination in
spacecraft from the bottom-up perspective. This has allowed us to capture,
understand, and counter Euclid’s response to ice contamination. In Sect. 2 we
summarise the molecular contamination experienced by other spacecraft,
building a picture of what Euclid might encounter. In Sect. 3 we review the
types of water ice that exist in a vacuum at cryogenic temperatures, how they
transform into each other, and how their structure depends on the wetting
properties of the substrates. In Sect. 4 we review the physics of diffusion,
sublimation, and adsorption of water molecules. We also built a simple
transport model to estimate the water exchange between surfaces, and thus the
contamination rate in Euclid’s payload module (PLM). In Sect. 5 we present
results about outgassing from Euclid’s thermal vacuum tests, and we conclude
in Sect. 6.

In our second paper we investigate the optical properties of thin ice films
and their impact on the spectrophotometric data taken by Euclid. Specifically,
we look at absorption, interference, scattering, polarisation, apodisation,
and phase shifts, with each uniquely influencing Euclid’s spectrophotometric
data. We have developed strategies to detect, monitor, and – if possible –
correct for these effects. Only then are we in a position to determine how
much ice Euclid can tolerate on its optics to achieve its cosmological
science, and when a decontamination is in order.

##  2 Lessons learnt from other spacecraft

Material outgassing (Chiggiato, 2020) has troubled spacecraft already in the
Mercury, Gemini and Apollo programs (Leger & Bricker, 1972). Numerous
experiments were dedicated to it, such as on the Mir space station (Wilkes &
Zwiener, 1999), the Midcourse Space Experiment (MSX, Uy et al., 1998), and the
International Space Station (Palusinski et al., 2009).

Astrophysical spacecraft have added further insight into contamination and its
impressively broad spectrum of effects. Solar System exploration missions are
particularly useful, often carrying pressure sensors and mass spectrometers to
analyse the interplanetary gas and dust, and thus also the spacecraft’s own
outgassing constituents. In this section, we summarise the lessons learnt from
some missions with a well-documented outgassing record. These are of great
importance for our preparation of suitable calibration and decontamination
plans. Appendix A has a list of references and short summaries for a larger
number of astrophysical and Earth-observation satellites.

###  2.1 Multi-layer insulation (MLI) thermal blankets

Spacecraft have both hot and cold sides, in particular in the inner Solar
System, and are wrapped in MLI (Cepeda-Rizo et al., 2021) blankets to ensure
stable operating temperatures. Further thermal shielding may be needed
internally to accommodate instrument needs, for example in Euclid the Near
Infrared Spectrometer and Photometer (NISP, Maciaszek et al., 2016) has its
own blanket.

MLI consist of multiple – often ten or more – thin sheets of a high-
performance polymer such as Kapton – a polyimide – coated with aluminium or
gold (Fig. 1). Outer layers may be carbon charged to suppress optical
straylight (‘black Kapton’; used for NISP). The individual MLI sheets are
physically separated by a thin netting to minimise contact and thus thermal
conductivity. To avoid rupture due to the rapid depressurisation during
launch, the MLI may have venting holes or is perforated.

Similar to other polymers, Kapton – in particular its amorphous versions – can
trap large amounts of water due to its high gas solubility (e.g. Yang et al.,
1985; Sharma et al., 2018); the dissolved water then also has great mobility
(Chiggiato, 2020). After degassing at $125^{\circ}$ C for 24 h in a vacuum,
Kapton quickly recaptures $0.6$–$0.7$% of its initial total mass in terms of
water, during 24 h at $20^{\circ}$ C and in 55% relative humidity (see the
National Aeronautics and Space Administration’s outgassing
database222https://outgassing.nasa.gov/). Further water intake appears to be
stopped after this period (Scialdone, 1993). Due to its common application in
spacecraft, MLI is arguably the most important source of water contamination;
it may also release other contaminants due to space weathering (Chen et al.,
2016). Venting perforations – if present – facilitate contamination further,
and the MLI may not deplete even after a decade in space (see below).

For completeness, we note that MLI is not the only possible carrier of water
and other contaminants in spacecraft. Noteworthy are honeycomb structures
(Epstein & Ruth, 1993), often comprising an aluminium core with carbon-fibre
reinforced polymers (CFRP) that – depending on their design – might trap a
considerable volume of water.

While water is the most frequent contaminant, other substances such as
carbonates may be more troublesome for specific instruments. For Euclid, water
is expected to cause $90$–$95$% of the overall transmission loss due to
molecular and particulate contamination. We concentrate on water from Sect. 3
onwards, with a short excursion in Sect. 4.6.4 where we address contamination
from Euclid’s hydrazine thrusters.

Figure 1: Structure of a MLI thermal blanket, the main source of water
contamination in spacecraft. Figure credit: John Rossie of Aerospace
Educational Development Program (AEDP), CC BY-SA 2.5 license

###  2.2 Hubble Space Telescope

In its early years, the Hubble Space Telescope (HST) carried the Wide Field
and Planetary Camera WFPC1, and its successor WFPC2. Both cameras suffered
greatly from contamination in the UV (MacKenty et al., 1993; Holtzman et al.,
1995). Photopolymerisation was the cause for the heavy non-volatile
contamination of WFPC1 (Tveekrem et al., 1996; Lallo, 2012), and the
reservoirs of these contaminants depleted within 3 years. WFPC2 was
contaminated mostly by water, resulting in typical flux losses of 1% day-1 at
wavelengths 170–215 nm. It was thermally decontaminated on average every 28
days between 1993 until at least 2001 (Baggett et al., 2001). The
contamination rate slowly decreased by a factor of 2 during this time, and
later on WFPC2 was decontaminated every 49 days (Gonzaga et al., 2010).

WFPC2 contamination estimates at wavelengths $\lambda>600$ nm have poor
signal-to-noise ratio (S/N), since WFPC2’s UV science cases required
decontamination before flux losses became evident at longer wavelengths. In
the F555W filter – corresponding to the blue end of Euclid’s IE passband – the
mean flux loss between 1993 and 1998 was $1.2\pm 0.3$% month-1 (Baggett &
Gonzaga, 1998). More complex wavelength dependencies were found at longer
wavelengths, partially attributed to different contaminants and their
intrinsic diffusion-sublimation timescales.

The Wide-Field Camera 3 (WFC3), installed in 2009, has a throughput loss of up
to 0.3% year-1 in the ultraviolet and visible (UVIS) channel, not attributed
to contamination (Shanahan et al., 2017). The infrared (IR) channel loses
about 0.1% year-1, likely due to photopolymerisation of contaminants (Bohlin &
Deustua, 2019). More details about HST contamination and control can be found
in Clampin (1992), Baggett et al. (1996), and Baggett & Gonzaga (1998).

###  2.3 ACIS / Chandra

The Chandra X-ray observatory has been operated since 1999. Since the
detectors in the Advanced CCD Imaging Spectrometer (ACIS) are sensitive to
optical wavelengths, an optical blocking filter (OBF) is used. Plucinsky et
al. (2018) show that the optical thickness at X-ray wavelengths has been
monotonically increasing – and slowly stabilising – during the first seven to
eight years of the mission, due to contamination of the OBF. In 2010, a phase
of increasingly rapid contamination began that is still ongoing at different
speeds for different atomic species (Plucinsky et al., 2020).

Plucinsky et al. (2018) argue that the initial stabilisation could be due to
depletion of the contaminants’ reservoirs, while the observed acceleration
beginning a decade later came as a surprise. Plausibly, radiation damage
(Engelhart et al., 2017; Plis et al., 2019) or mechanical dust and meteoroid
breakdown of the MLI led to an increase in internal temperatures, activating
outgassing sources that were dormant previously. The steep temperature
dependence of sublimation and diffusion (Sect. 4) supports this scenario. The
slow-down in contamination since 2017 can be explained by the near depletion
of the contaminants, by an increased sublimation from the OBF due to higher
temperatures, or both.

The atomic composition of the contaminants is available from their X-ray
absorption edges. The dominant species is carbon, followed by oxygen and
fluorine. Their deposition rate and spatial distribution has changed over
time, indicating that multiple contamination sources are at play.
Contamination has been active in Chandra for almost two decades.

Similar contamination effects have been observed in the X-ray Multi-Mirror
Mission’s (XMM-Newton) European Photon Imaging Camera Metal Oxide Semi-
conductor cameras (EPIC-MOS), and also the Reflection Grating Spectrometer
(RGS; Plucinsky et al., 2012). More details are given in the official
calibration release
documents333https://xmmweb.esac.esa.int/docs/documents/CAL-SRN-0390-2-2.pdf
https://xmmweb.esac.esa.int/docs/documents/CAL-SRN-0305-1-0.pdf
https://xmmweb.esac.esa.int/docs/documents/CAL-SRN-0314-1-0.pdf.

###  2.4 Cassini

####  2.4.1 Cosmic Dust Analyzer (CDA)

Cassini launched in 1997 and reached Saturn in 2004. It carried the Cosmic
Dust Analyzer (CDA), which measured mass, speed, direction, and chemical
composition of cations. The latter were extracted from the gas and plasma
cloud created by the impact of particles on a rhodium target plate, liberating
contaminants as well (Postberg et al., 2009).

During Cassini’s cruise phase, the CDA was contaminated by rocket exhaust
fumes, outgassing, Solar wind, and the interplanetary medium. Beginning in
2000, after Cassini’s last inner Solar System fly-bys, the CDA was
decontaminated by heating the target plate to 370 K for 8 h every few months.
This removed volatile contaminants such as hydrocarbons and water ice.

Postberg et al. (2009) identified H+ and C+ as the dominant contaminants with
O+ at lower levels, but they could not unambiguously locate their origin.
Direct hydrocarbon contamination of the target plate has been considered
unlikely. Plausibly, hydrocarbons elsewhere in the spacecraft were photolysed
by the UV background, and the broken-down constituents formed an amorphous,
non-volatile carbon-rich layer on the target plate. This particular
contaminant likely formed prior to 2000 while Cassini was still in the inner
Solar System. Any halogen contaminants, such as Cl- and F-, remained
undetected since they were propelled away from the detector. Contamination in
the CDA mass spectra was taken into account until the end of the mission in
2017 (e.g. Altobelli et al., 2016).

####  2.4.2 Narrow Angle Camera (NAC)

Cassini’s NAC was decontaminated at $30^{\circ}$ C every six months for 14 h
during the cruise phase. Until the Jupiter fly-by in late 2000, the NAC
detector was kept warm at $0^{\circ}$ C to minimise radiation damage by means
of continuous annealing (Dale & Marshall, 1991; Holmes-Siedle et al., 1991;
Bassler, 2010). Contamination was absent in the Jupiter images taken with a
detector temperature of $-90^{\circ}$ C, but in 2001 a considerable haze
appeared (Fig. 2). It contained about 30% of the total flux at 827 nm and 80%
of the flux at 316 nm.

This was surprising because the haze manifested within a few days after a
decontamination. The main difference to the earlier 12 decontamination cycles
was that the latest one heated the NAC from $-90^{\circ}$ C to $+30^{\circ}$
C, whereas all prior cycles went from $0^{\circ}$ C to $+30^{\circ}$ C. We
know from Earth-orbiting satellites that shadow passages can release
considerable amounts of water and particulates (see also Sect. 2.7), due to
rapidly changing temperatures and related mechanical stresses; this is known
as ‘orbital thermo-cycling’. Haemmerle & Gerhard (2006) argue that a similar
effect caused the NAC contamination, concluding that a decontamination can
cause contamination if executed too quickly.

To recover NAC it had to be decontaminated twice: Once during a careful slow
heating for seven days to $-7^{\circ}$ C, which removed most of the haze that
was likely due to water vapour. A remaining haze in the UV images was cleared
by a another seven day decontamination to $+4^{\circ}$ C, probably due to very
small particulates or molecular contamination other than water. Similarly,
reoccurring contamination events were observed with the optical navigation
camera onboard STARDUST (Bhaskaran et al., 2004).

Figure 2: Effect of ice on the point-spread function (PSF). Left panel:
Cassini / NAC image of the star Maia (Pleiades) taken in the broadband CL1/GRN
filter ($\lambda_{\rm eff}=568$ nm) before the contamination event. Middle
panel: Bright star $\alpha$ PsA in the same filter, after the contamination
event. Right panel: Colour image of Maia in filter combinations UV2/UV3
($\lambda_{\rm eff}=316$ nm; blue), CL1/GRN (green), and IR2/IR1
($\lambda_{\rm eff}=827$ nm; red), showing the chromaticity of molecular
scattering. Figure credit: Adapted from Haemmerle & Gerhard (2006).

###  2.5 XMM-Newton Optical Monitor

Similar to Chandra, the X-ray Multi-mirror Mission (XMM-Newton) has
experienced considerable molecular contamination of its X-ray imaging and
spectroscopy cameras (Schartel et al., 2022). The most likely contaminants are
hydrocarbons, and other contaminants are suspected as well. Their origin is
not well understood, and contamination has continuously increased over 22
years since launch.

Of particular interest to us is the Optical Monitor (OM), observing in the
180–700 nm range (Mason et al., 2001). The in-orbit commissioning of the OM
showed a chromatic throughput loss of 16% to 56% compared to pre-launch
expectations, with the largest losses occurring in the UV (Kirsch et al.,
2005; Schartel et al., 2022). This contamination is attributed to non-volatile
hydrocarbons, as the OM detector is kept at 300 K, and the entire optics at
290 K (Stramaccioni et al., 2000); surface contamination by water does not
persist in a vacuum at these temperatures (Sect. 4.3).

Contamination of the OM has increased since, in parallel to an expected
degradation of the detector’s photocathode, which causes additional throughput
losses up to 2.8% year-1 (Kirsch et al., 2005). Notably, the OM’s point-spread
function (PSF) appears
unaffected444https://xmmweb.esac.esa.int/docs/documents/CAL-TN-0019.pdf by the
increasing contamination, and a chromatic aureole from scattering as in the
contaminated Cassini NAC images (Fig. 2) seems absent. Therefore, absorption
by organic non-volatile contaminants is the most likely explanation for the
observed throughput loss. The UV/Optical telescope (UVOT) onboard the Swift
Gamma-ray observatory inherited the OM design with improved contamination
control (Roming et al., 2005), and has shown little impact from contamination
since (Poole et al., 2008; Breeveld et al., 2010; Kuin et al., 2015).

###  2.6 Genesis

Genesis was a sample return mission probing the Solar wind, exposing ultra-
clean sample containers for 850 days at Lagrange point L1. The containers were
purged with dry nitrogen from assembly until launch to minimise on-ground
contamination. Upon their recovery, the containers showed pervasive stains
from material outgassing, composed of H, C, N, O, Si, and F. The root
contaminants were not identified, but plausibly contained hydrocarbon,
siloxane, and fluorocarbon components that were either vacuum pyrolysed, or
polymerised by the UV background, or both (Burnett et al., 2005; Calaway et
al., 2006); for the effect of UV-photofixation of contaminants, see also
Roussel et al. (2016). As for the possible sources, Burnett et al. (2005) list
among others seals and locking elements, the electroplated gold concentrator,
sealants and greases, residual films from pre-flight storage containers or
processing, and residue from anodisation processing.

###  2.7 Midcourse Space Experiment (MSX)

MSX was launched in 1996 into a Sun-synchronous orbit at 903 km altitude and
inclination of $None$, carrying a total of ten contamination monitoring
instruments; among others a neutral mass spectrometer (NMS) and a total
pressure sensor (TPS) to analyse its gaseous surroundings, and five QCMs to
investigate film depositions on external and internal surfaces (Uy et al.,
1998). MSX was operated for 12 years.

The NMS data show a pressure decrease with time $t$ as $t^{-1}$ for the first
few days, then slowing down to approximately $t^{-0.5}$ over the next six
months (Uy et al., 2003), which corresponds to a $1/{\rm e}$ decay time of
$t_{\rm e}=45$ days. The TPS data shows a $t^{-0.6}$ dependence ($t_{\rm
e}=30$ days) over the first six months. This pressure evolution is attributed
to the sublimation of superficial water ice, followed by diffusion and
sublimation of absorbed water.

After the end of its initial ten month cryogenic phase, the MSX was inclined
on a yearly basis by $None$ towards the Sun to heat its baffle and primary
mirror (Uy et al., 1998). Even after six years, these Sun exposure tests were
always accompanied by a $100$-fold increase in TPS water vapour pressure from
the sudden illumination of MLI that otherwise remained in the shadow; the
pressure peaks even increased with every repetition of this test. Uy et al.
(2003) conclude that the MLI acts as a deep water reservoir and continuous
source of contamination over many years, and that it is difficult to deplete.
The MLI was also found to react very quickly to even small changes in the
solar illumination angle. Uy et al. (2003) and Wood et al. (2003) also report
numerous high-pressure transients unrelated to changes in solar exposure.
These could be caused by rupturing, meteoroid impacts, and stress-release
events due to orbital thermo-cycling, and are evidenced by an increasing
particle density in the spacecraft’s local environment (orbital degradation).

The QCM results are described by Wood et al. (2003). During the initial, ten
month long cryogenic phase, the contamination layers grew up to 16 nm thick,
depending on which parts of the spacecraft were in the QCMs’ field of view.
The internal QCM showed the highest contamination, mostly from Ar – used as a
cryogen – and O, whereas H2O and CO2 were not detected. During the baffle’s
Sun-exposure tests following the cryogenic phase, up to 20 nm of water were
deposited on the internal QCM, indicating that the cold baffles had trapped
considerable amounts of water. The water began to evaporate noticeably once
the QCM was heated to 150 K, and was gone once 165 K were exceeded. Of the
external QCMs, the ones facing the solar panels showed the highest rate of
contamination during the first two years of the mission, followed by
incomplete sublimation over the next three years, indicating the presence of
non-volatile contaminants.

Figure 3: Pressure around Rosetta due to water outgassing, showing that
spacecraft travel for many years in their own gas cloud. Initially, desorption
from surfaces is the dominant source, and in this case detected for up to 200
days after launch. Diffusion-sublimation then supports the cloud for years
after, with a pedestal from decomposition due to UV- and particle radiation.
The outgassing rate appears fairly independent of heliocentric distance.
Typical interplanetary pressure is a few $10^{-12}$ mbar and below. Figure
reproduced from Schläppi et al. (2010).

###  2.8 ROSINA / Rosetta

Rosetta carried the Rosetta Orbiter Spectrometer for Ion and Neutral Analysis
(ROSINA), consisting of two mass spectrometers (RTOF and DFMS), and the Comet
Pressure Sensor (COPS). Rosetta was launched in 2004 and arrived at comet P67
in 2014. ROSINA was active during extended periods of the cruise phase and two
asteroid fly-bys, in particular also to understand contamination by outgassing
(Schläppi et al., 2010).

The initial desorption of water from Rosetta’s surfaces had a $1/{\rm e}$
decay time of 30 days and could be detected for the first 200 days of the
mission (Fig. 3). Once this source depleted, diffusion-sublimation became the
dominant source in both DFMS and COPS data. After three years, the pressure
around Rosetta had stabilised at $3\times 10^{-11}$ mbar. For comparison, the
typical pressure in interplanetary space at these heliocentric distances is
considered to be a few $10^{-12}$ mbar (Postberg et al., 2009) and below. The
mass spectrometers did not have any direct line of sight to structural parts
of the spacecraft, whereas the pressure sensor had a nearly full solid-angle
field of view. Schläppi et al. (2010) show that the pressure sensors and mass
spectrometers reacted mostly to return flux from self-scattering. In other
words, Rosetta did travel in its own gas cloud, dense enough such that
backscattering caused contamination elsewhere on the spacecraft.

Similar to MSX, ROSINA found the gas pressure to be highly dependent on the
spacecraft’s Sun attitude (Schläppi et al., 2010). This was noticed during the
asteroid fly-bys, when Rosetta was reoriented to keep the target in sight and
to protect some instruments from direct Sun exposure. The sudden illumination
of structural parts that had been in the shadow for years resulted in the
pressure exceeding $10^{-8}$ mbar within a few tens of seconds after a
reorientation. Likewise, the chemical composition of the gas phase changed, an
effect that was also observed after the switch-on of previously dormant
instruments.

Outgassing from suddenly exposed, previously unilluminated components can
cause a considerable acceleration of the spacecraft. For example, when OSIRIS-
REx exposed its sample-return capsule to the Sun on its outbound journey, the
acceleration exceeded that by Solar radiation pressure by one order of
magnitude (Sandford et al., 2020).

Schläppi et al. (2010) report 146 different chemical constituents in the
ROSINA outgassing data, from hydrocarbons, PAHs, C-O, N-O and C-O compounds to
S, F, and Cl. The dominant species detected by DFMS are H2O, followed by CO, N
and CO2. Hydrocarbon compounds may originate from polycarbonates (structural
parts) and solvents, nitrogen-bearing compounds from adhesives, epoxies,
coatings, and structural parts. Halogens point at brazing and lubricants,
structure and tapes. Curiously, the RTOF spectra were dominated by F followed
by H2O. The high fluorine detection has been explained by a F-bearing
lubricant used in the antenna, which is Sun-lit and closer to RTOF than to
DFMS – neither of which has direct lines of sight to the spacecraft. Again,
this shows that contaminants evaporated into space can re-contaminate the
spacecraft elsewhere through backscattering (see also Bieler et al., 2016).
Schläppi et al. (2010) estimate that several hundred grams of nonmetallic
material and water outgas every year from Rosetta.

Figure 4: Throughput loss for Gaia’s telescopes since the beginning of
operations. Initially, a rapid loss of $0.06$ mag day-1 was observed. A total
of six decontaminations (indicated by vertical lines) were required over 2.6
years to reach a nearly stable state. Minor discontinuities in the data are
artefacts due to an incremental calibration strategy.

###  2.9 Gaia

Gaia is similar to Euclid, in the sense that it is a wide-field astrophysical
survey mission. Its mirrors and telescope structure are made of silicon
carbide (SiC; Bougoin & Lavenac, 2011), as are Euclid’s (Bougoin et al.,
2019). SiC is known for its high strength, hardness, thermal conductivity, and
low thermal expansion. Gaia had an industry forecast of very low water
contamination. However, water heavily contaminated the optical system, leading
to early and rapid transmission loss that required prompt decontamination
(Fig. 4). A total of six decontaminations were needed over 2.6 years to reach
a quasi-stable state (see also Gaia Collaboration: Prusti et al., 2016). As of
now, no clear consensus has been achieved about the nature and origin of the
contamination. Possibly, there is a contamination path from the service module
(SVM) to the PLM, even though the two are separated by a single-layer
insulation (SLI, as is the case for Euclid, see Figs. 18 and 19 in the
Appendix). Contamination is spatially and temporally variable across Gaia’s
focal planes, and it appears to have switched between Gaia’s two mirror
systems (Riello et al., 2021). We note that the Gaia PLM is fully covered in
MLI, very close to the optical surfaces555Photo of the MLI wrapping the Gaia
optics and structure..

Gaia carries internal laser interferometers to monitor its optical alignment.
One of the most important lessons for Euclid is that Gaia’s SiC structure did
not exactly resume its previous alignment after a decontamination. Moreover,
slow and continuous focus drifts are seen over years after the last
decontamination (Mora et al., 2016). This implies that a decontamination of
Euclid requires a careful check of the PSF calibration.

Being $10$–$20$ K warmer than Euclid, water in Gaia’s MLI is more mobile and
the outgassing rate considerably higher (see Sect. 4), but it is not at all
clear whether this can explain Gaia’s initial high transmission loss. Higher
temperatures also mean higher sublimation fluxes, beneficial if the ice is
located already on optical surfaces, but detrimental if located on – or still
in – other surfaces from where it can contaminate optics. Given Gaia’s
completely different design, we cannot conclude whether Euclid’s lower
temperature puts it at an advantage or disadvantage compared to Gaia, and on
what timescales. Euclid’s design benefited considerably from the Gaia
experience.

###  2.10 Take-home points

The main contamination lessons are: (i) water is the most common contaminant
for spacecraft operating in or near cryogenic conditions; it is found on – and
in – numerous materials, with MLI being the most important reservoir due to
its large area and high solubility of water in it; (ii) contamination
reservoirs deplete very slowly, and in the worst case will be active during
Euclid’s entire life; (iii) contamination rates, chemical composition, and
location are time variable, given the depletion of some reservoirs and the
activation of others, for example due to temperature changes; (iv) spacecraft
travel in their own gas cloud with sufficient gas pressure for backscattering,
that is molecules evaporating into outer space can recontaminate the
spacecraft elsewhere; (v) the chemical composition of the gas cloud is
spatially variable, with water being dominant on the shadow side, and
decomposed substances at the spacecraft’s Sun-illuminated side; (vi) the
pressure and chemical composition of the gas cloud respond within seconds to
small changes in the spacecraft’s Sun attitude and to instrument operations
such as a switch-on; (vii) water re-absorption on ground is both hard to avoid
despite cleaning and degassing efforts, and hard to track for estimates of the
absolute amount of water re-absorbed; (viii) hydrocarbons and non-volatile
organic compounds can considerably reduce the optical throughput by means of
absorption.

Figure 5: Schematic view of optical surfaces in Euclid. The telescope cavity
contains M1, M2 and the baffle, and the instrument cavity (box) the remainder
of the PLM. Figure credit: D. Filleul, Airbus Defence and Space. A high-
resolution 3D rendering of the instrument cavity and a photograph of the real
flight hardware are shown in Figs. 16 and 17. Table 1: Temperatures of PLM
elements for nominal operating conditions, a ‘warm’ comparison case, and for
decontamination mode.

Common path | $T_{\rm nominal}$ | $T_{\rm warm}$ | $T_{\rm decont.}$
---|---|---|---
M1 | 117 K | 123 K | 220 K
M2 | 104 K | 111 K | 289 K
FoM1 | 123 K | 128 K | 220 K
FoM2 | 122 K | 126 K | 221 K
M3 | 122 K | 129 K | 220 K
Dichroic | 122 K | 126 K | 221 K
NISP path |  |  |
Corrector lens | 130 K | 131 K | 218 K
Filter / Grism | 133 K | 133 K | 206 K
Camera lenses | 132 K | 132 K | 204 K
Detector | 95 K | 95 K | 200 K
VIS path |  |  |
FoM3 | 118 K | 123 K | 220 K
Detector | 152 K | 156 K | 270 K
Structural |  |  |
Baffle | 100 K | 108 K | 205 K
PLM baseplate | 120 K | 125 K | 207 K
666The order of the components is as they appear in the optical paths towards
NISP and VIS (see Fig. 5). Here ‘M’ stands for mirrors with optical power,
‘FoM’ for flat folding mirrors, and ‘L’ for lenses inside NISP. Temperatures
were taken from the PLM critical design review thermal analysis report.
Accurate operational values will only be known after launch and may deviate by
a few kelvin from the ones tabulated here. We note that the VIS detectors are
considerably warmer than their surrounding, whereas the NISP detectors are
colder, which determines their contamination experience.

###  2.11 Pertinent technical details about Euclid

For better understanding of the remainder of this paper, we provide here some
technical details of Euclid’s PLM. A schematic layout of the optical
configuration – a three-mirror anastigmat Korsch design (Korsch, 1977) – is
shown in Fig. 5; more details are given in Venancio et al. (2014). Mirrors M1,
M2, and M3 are powered mirrors, whereas FoM1 to FoM3 are flat. The dichroic
plate separates the near-infrared from the optical wavelengths for
simultaneous observations with VIS and NISP.

The silver coatings on mirrors M1, M2, M3 and FoM3 have additional layers for
chemical and physical protection. The designs of these protective layers were
not disclosed to us. Usually, they are complex, see for example Sheikh et al.
(2008) for the Kepler Space Telescope, and also Garoli et al. (2020). The top-
most layer is of great importance for the formation and structure of ice
films, as we discuss next in Sect. 3. The entire layer stack is relevant for
the optical properties of contaminating ice films, which we will show in our
second paper.

The folding mirrors FoM1 and FoM2 have a high-performance dielectric coating
stack including layers of gold, to provide a wavelength cut-off below $0.42$
$\mathrm{\SIUnitSymbolMicro m}$. More details about the stacks were not
disclosed by industry. The dichroic element and the NISP filters have
alternating layers of Nb2O5 and SiO2. The coatings on the fused silica NISP
lenses might include TiO2. Jointly, the mirrors and the dichroic plate provide
a complex chromatic selection function that defines the passbands – and out-
of-band blocking – for the VIS and NISP instruments (for details, see Euclid
Collaboration: Schirmer et al., 2022).

Relevant for ice formation are also the in-flight temperatures of the optical
and structural elements in the PLM. An estimate of the expected temperatures
is given in Table 1. Exact values are difficult to predict from thermal
modelling, and the actual temperatures might deviate by a few kelvin. Small
changes in temperature may have a large impact on contamination, as we show in
Sect. 4. To this end, we use a ‘warm’ case for comparison. The warm case is
not realistic; it is a part of the thermal analysis, showing that Euclid’s
temperature control systems can keep the spacecraft within operational limits
even in unusual conditions.

##  3 Water ice types in spacecraft conditions

The rest of this paper focuses on the effects of water, the most common – and
for Euclid– most important contaminant. Water shows complex behaviour in its
solid and liquid phases. This is attributed to four hydrogen bonds available
to a water molecule to connect to its neighbours, and the two lone electron
pairs of oxygen forcing the molecule into its bent shape. A water molecule is
0.28 nm in size. Depending on temperature and pressure, water can form at
least 20 different types of ice (Gasser et al., 2021; Rosu-Finsen et al.,
2023).

The formation and structure of thin water ice films on nanometer and
micrometer scales has been very actively researched (see Salzmann, 2019, for a
review). However, to the best of our knowledge, this has never been studied in
the context of contamination of astrophysical observatories. Given Euclid’s
extraordinary calibration requirements, we need to understand ice evolution at
a molecular level and how the numerous related physical processes lead to
measurable effects in Euclid data.

In Sects. 3.1 to 3.4, we introduce the various types of ice forming in
spacecraft, that is in a high vacuum and for very low deposition rates. In
laboratory experiments, thin ice films are usually deposited with $0.01$–$100$
nm min-1. Even the lowest rate of 0.01 nm min-1 is 2–4 orders of magnitude (or
more) higher than what Euclid might experience in flight (Sect. 4.6). Yet for
example $0.1$ nm min-1 are well applicable, since the latent heat released by
adsorption of water molecules is rapidly dissipated in bulk ice (Brown et al.,
1996), and eventually in the substrate before the next molecules are
deposited. The thickness of laboratory ice films ranges from a few Å – that is
incomplete monolayers – to several $\mathrm{\SIUnitSymbolMicro m}$. In Sects.
3.5 and 3.6 we review how the surface topography of the ice depends on the
substrate.

Studies of molecular contamination in the material sciences and by industry
usually parameterise thin-film deposits in units of surface density; likewise
for deposition, condensation, and sublimation fluxes. For our purposes, we
parameterise ice films in terms of their thickness, which is more directly
linked to their optical properties that we study in our second paper. For
practical purposes we approximate that $1\,{\rm nm}\propto 1\times 10^{-7}$ g
cm-2.

The scanning tunnelling microscope (STM) and atomic force microscope (AFM)
data of ice surfaces shown in this section are available upon informal
request. The surface-height profiles are encoded in ASCII x,y,z format.

Figure 6: Typical structure of high-density (left panel) and low-density
(right panel) amorphous ice. Red dots represent the oxygen atoms, and small
white circles the hydrogen atoms. Hydrogen bonds are indicated by dashed
lines. Coherent structures are absent. Figure adapted from Belosludov et al.
(2008); see also He et al. (2019).

###  3.1 Amorphous ice ($T\lesssim 120$ K)

Amorphous or non-crystalline ice, also called amorphous solid water or
vitreous ice, is characterised by the absence of coherent crystal structures
down to scales of individual water molecules. In a vacuum, it exists in three
states, with the two coldest ones being highly porous at a molecular level
(Fig. 6). For reviews about amorphous ices see for example Limmer & Chandler
(2014), He et al. (2019), and Cao (2021).

####  3.1.1 High-density amorphous ice Iah ($T<30$ K)

High-density amorphous ice Iah 777The 19 known types of ice are labelled with
Roman Numerals I to XIX. Ice types in spacecraft are all variants of type I.
forms when water vapour is deposited at temperatures below $T=30$ K
(Jenniskens & Blake, 1994). It has a typical density of $1.15$ g cm-3 (Cao,
2021) and has the least structured state of all ice types. Between $30$–$70$
K, one of the hydrogen bonds in ice Iah breaks, irreversibly transforming ice
Iah into low-density, amorphous ice Ial on timescales of a day (Schriver-
Mazzuoli et al., 2000).

Ice Iah will not be found in Euclid because temperatures are above 80 K (see
Table 1). It may be present in other spacecraft such as the James Webb Space
Telescope, where temperatures reach below 40 K (Lightsey et al., 2012; Wright
et al., 2015).

Figure 7: Comparison of crystalline and amorphous ice topography. Left panel:
STM image of a polycrystalline ice film, average thickness 6 nm, grown at 145
K on Pt(111). Surface steps of bilayer height (0.37 nm) are easily resolved.
Right panel: Same, for a 6 nm thick amorphous ice film grown at 100 K on
Pt(111), revealing high surface roughness at nanometer scales. Two surface
steps are visible in the otherwise atomically flat Pt(111) substrate,
replicated by the amorphous ice film. Data originally taken by Thürmer &
Bartelt (2008).

####  3.1.2 Low density amorphous ice Ial ($30\,K\lesssim T\lesssim 120$ K)

Low density amorphous ice Ial is created by vapour deposition between 30 K and
$110$ to $120$ K, the upper limit depending on the deposition rate (Sect.
3.3). The density of ice Ial is $0.94$ g cm-3, neglecting variations in
porosity. Porosity itself is parameterised by the internal surface area per
mass, and for Ial is typically $150$–$500$ m2 g-1 (Mitlin & Leung, 2002). Ice
Ial can be thought of as an open network of water molecules, where all pores
are directly connected to the top surface (He et al., 2019), independent of
the thickness of the ice. The top surface of ice Ial is very rough at the
nanometer scale when compared to crystalline ice (Fig. 7). The large surface
area of amorphous ice facilitates astrochemical processes (Watanabe & Kouchi,
2008; Gudipati & Castillo-Rogez, 2013).

Amorphous ice is distinguished from crystalline ice by its large surface area
and by the high internal vapour pressure at highly curved surface elements
(Nachbar et al., 2018a, b). This enhances the sublimation flux by factors
2–100 compared to crystalline ice at the same temperature (Sect. 4.3.3). Yet
the absolute sublimation flux at temperatures where ice Ial can form is very
low (Sect. 4.3).

In Euclid, ice Ial can occur on the NISP detectors (95 K), the external baffle
(100 K), and the secondary mirror (M2; 104 K). It will remain amorphous during
the mission (Fig. 8). On the NISP detector, ice Ial would modulate the quantum
efficiency through interference effects (Holmes et al., 2016) and possibly
severely affect the pixel response non-uniformity (PRNU); we address these
effects in our second paper. Elsewhere in the PLM at $T\gtrsim 120$ K (Table
1), ice Ial would crystallise within a few days or weeks. However, these parts
of the PLM are usually not cold enough to form amorphous ice in the first
place.

####  3.1.3 Restrained amorphous ice Iar and onset of crystallisation
($120\,K\lesssim T\lesssim 160$ K)

When amorphous ice is heated to $120$–$140$ K, or water vapour deposited at
these temperatures at a high rate, surface reorganisation starts to collapse
the internal pores (Hessinger et al., 1996) and reduces the number of
‘dangling bonds’, that is unsatisfied OH bonds. The resulting modified state
is called restrained amorphous ice Iar; the transformation cannot be reversed
by means of cooling. At these temperatures, nanocrystals begin to form in the
amorphous phase through nucleation, and grow into crystalline clusters (Kouchi
et al., 1994; Nachbar et al., 2018a). For 3D simulations of the transition
process from amorphous ice to crystalline ice see He et al. (2019).

Amorphous ice is meta-stable with respect to crystallisation (Fig. 8). Even at
temperatures as low as $80$ K it will eventually anneal into stacking
disordered ice (Sect. 3.2.1), albeit on geological timescales. Depending on
the heating rate and deposition speed, crystallisation in laboratory
experiments is observed mostly between $120$–$160$ K (La Spisa et al., 2001;
Mitlin & Leung, 2002; Mastrapa et al., 2013; He et al., 2022). Amorphous
constituents in the crystalline phase are uncommon above $160$ K (Kuhs et al.,
2012), and do not survive $175$–$180$ K for more than a few hours.
Crystallisation cannot be reversed by cooling. Annealing of amorphous ice does
not necessarily result in the same crystalline structures as depositing water
at higher temperatures when crystalline ice forms directly (Hessinger & Pohl,
1996).

In Euclid, ice Iar will occur only intermittently when heating cold surfaces
covered with ice Ial to their decontamination temperature (Table 1).
Otherwise, it would crystallise on timescales of days to a few months.

Figure 8: Annealing time for amorphous ice Ial to reach different fractions of
crystallisation, using the Kouchi et al. (1994) formalism that is based on
kinetic theory of crystallisation. The shaded box shows the relevant time and
temperate ranges for Euclid. The crystallisation speed can be greatly
accelerated in the case of epitaxial growth on suitable substrates (Dohnálek
et al., 2000).

###  3.2 Crystalline ice

In crystalline water ice, the oxygen atoms of six water molecules connect via
hydrogen bonds to form corrugated hexagons. These hexagons merge into
extended, 2-dimensional corrugated bilayers, which can be stacked in two ways:
without rotation, forming cubic ice Ic, and by rotating every other bilayer by
$180^{\circ}$, forming hexagonal ice Ih (Fig. 9). The hexagonal stacking order
is energetically preferred over the cubic stacking order.

####  3.2.1 Stacking disordered ice Isd ($120\,K\lesssim T\lesssim 160$ K)

Cubic ice Ic was first described by König (1943) and wrongly thought to exist
at a macroscopic scale at $120$–$160$ K. It is now known that at these
temperatures the ice consists of cubic and hexagonal layers, interlaced in a
complex non-random fashion described as ‘stacking disordered ice’ Isd (Kuhs et
al., 2012). Pure cubic ice exists essentially only in nanocrystals and in ice
films a few nanometer thick (Kuhs et al., 2012; Thürmer & Nie, 2013; Malkin et
al., 2015; Nachbar et al., 2018a). At a macroscopic level, pure cubic ice was
created only recently by del Rosso et al. (2020).

Stacking disordered ice Isd is meta-stable and forms via vapour deposition
between $120$–$185$ K. There is a large number of crystal defects and stacking
faults in ice Isd, requiring specific energies to be healed (Hondoh, 2015): At
$T=130$ K, the least stable defects heal in about one week, whereas the
timescale of most other defects exceeds one year. At $140$ K, simple defects
heal in one day, and within 1 h at $150$ K. The transformation from ice Isd to
ice Ih speeds up considerably at $175$ K and above (Kuhs et al., 2012; Hondoh,
2015; del Rosso et al., 2020). Cubic sequences disappear within $1$ h when ice
Isd is heated to $210$ K, and they are essentially absent above $240$ K.

In Euclid, all mirrors are at or below $T=120$ K (Table 1). The transformation
of any ice Isd deposits to ice Ih is therefore negligible on mission
timescales.

Figure 9: Side views of four stacked corrugated bilayers of ice. The dots are
the oxygen atoms, connected by hydrogen bonds. Thicker dots are higher up in
the stack. The left panel shows cubic ice Ic. The right panel shows hexagonal
ice Ih, where every second bilayer is rotated by $180^{\circ}$ around its
surface normal axis; $h_{\rm ice}$ refers to the bilayer height. Figure
credit: Thürmer & Nie (2013). Figure 10: Growth of crystalline ice on
atomically flat Pt(111). The temperature and the mean film thickness are
indicated. Shown is the relative height of each film, as the absolute height
is difficult to assess for the thickest film that does not expose the
substrate anymore. Left panel: $2$–$3$ nm ($7$–$10$ layers) high, flat-top
crystallites appear in the wetting monolayer (dark blue), imaged with an STM.
Middle panel: Further deposition causes the crystallites to grow laterally and
overlap each other (STM). Right panel: A thick ice film that would not conduct
sufficient electricity anymore from the substrate to the tip of an STM; an AFM
was used instead. More details can be found in Thürmer & Bartelt (2008),
Thürmer & Nie (2013), and Thürmer et al. (2014), who also took these data. For
comparison, Euclid’s SiC mirrors have a typical surface roughness of
$0.9$–$1.1$ nm.

####  3.2.2 Hexagonal ice Ih ($T\gtrsim 120-185$ K)

Hexagonal ice Ih forms from ice Isd upon heating (Sect. 3.2.1), or via vapour
deposition at high rates ($\gtrsim 1$ nm s-1) at $T>185$ K. It can also form
by slow ($0.1$ nm min-1) vapour deposition at temperatures as low as $120$ K
in ultra-high vacuum ($p\sim 3\times 10^{-11}$ mbar; see Thürmer & Nie, 2013).
Once formed, ice Ih is stable against cooling at least down to $T=5$ K. Rosu-
Finsen et al. (2023) show that ice Ih can be mechanically transformed into a
previously unknown, medium-density amorphous ice; we do not consider this
further as this process does not happen in Euclid. On Earth, all naturally
occurring ice is hexagonal, apart from very cold high-altitude cirrus clouds,
where ice Ic may be found.

The physical properties of ices Ih, Isd, and Ic are similar (Bertie et al.,
1969; Kuhs et al., 2012; Mastrapa et al., 2013) for the purposes of the
current paper, so we do not distinguish between them. However, the optical
properties do show smaller differences in the refractive index (He et al.,
2022) that could be relevant for modelling effects in the data (see our second
paper).

###  3.3 Deposition rate and crystallinity

Whether vapour deposition initially leads to amorphous or crystalline ice
depends on temperature, film thickness, and deposition rate. The latent heat
released upon adsorption facilitates surface diffusion of water molecules and
thus their settlement into energetically preferred configurations. With very
high deposition rates, ice Ial is formed initially, but dissipation of the
latent heat is impeded by the low thermal conductivity of Ial (Cuppen et al.,
2022), and crystallisation occurs. See also He et al. (2022), Cao (2021),
Watanabe & Kouchi (2008), La Spisa et al. (2001), and Kouchi et al. (1994).

For low deposition rates and $T\gtrsim 120$ K, water molecules can settle into
crystalline structures before being disturbed by other incoming molecules
(Kouchi et al., 1994; Thürmer & Bartelt, 2008). At $105$–$120$ K, ice films
may be amorphous, crystalline, or a mixture of both. At $100$ K and below,
they are always amorphous even when grown very slowly ($0.1$ nm min-1; La
Spisa et al., 2001; Thürmer & Bartelt, 2008).

In Euclid, deposition rates are anticipated to be very low. We expect
crystalline ice at $T\gtrsim 120$ K, amorphous ice at $T\lesssim 110$ K, and a
mixture for the range $T\sim 110$–$120$ K.

###  3.4 Amorphisation through irradiation

Crystalline ice can be amorphised by proton, heavy ion, and UV irradiation,
which dissociate (photolyse) water molecules (Raut et al., 2008; Famá et al.,
2010; Rothard et al., 2017). The freed hydrogen atoms diffuse through the
crystal and recombine with the fragments of other dissociated molecules, thus
breaking down the crystalline structure. Irradiation experiments have shown
that amorphisation processes become effective only at $70$ K and below (Kouchi
& Kuroda, 1990; Mastrapa & Brown, 2006). Typical timescales range between one
year to several $10^{5}$ years, depending on environment and ice thickness
(see also Dartois et al., 2013, 2015).

Temperatures in the Euclid PLM are above 80 K. At L2, irradiation-induced
compaction and amorphisation of crystalline ice is negligible.

###  3.5 Wetting of surfaces and growth of ice films

So far we have reviewed ice types alone. We now shift our focus to the
substrate-water interface and its important influence on ice films growing on
a substrate.

####  3.5.1 Energetic needs of the substrate-water interface

In general, surface atoms of a clean solid do not have all their bonding
requirements fulfilled. Eventually, molecules in the surrounding gas phase are
adsorbed due to van der Waals forces, covalent binding or electrostatic
attraction, releasing latent heat in the process.

When water molecules adsorb on a substrate (‘wetting’), they settle into
energetically preferred locations determined by the surface’s topography and
electronic configuration. Above 40 K, water molecules have enough energy for
surface diffusion and form hydrogen bonds with neighbouring water molecules.
The topography of these superficial water structures depends on the energetic
needs of the substrate material; it can vary widely between 1D filaments,
isolated clusters surrounded by ‘dry’ substrate, and 2D contiguous films
(wetting monolayers). At higher temperatures, water molecules may partially
dissociate forming a mix of H, OH, and H2O. For a comprehensive introduction
and review see Hodgson & Haq (2009) and Björneholm et al. (2016).

Figure 11: Effect of the substrate on ice topography, for an average amount of
2.5 nm ice. Top panel: On Ni(111), a wetting bilayer (dark blue) is formed, in
which isolated crystallites grow in height that cover 15% of the surface area.
Middle panel: On Pt(111), crystallites quickly overgrow each other, forming a
contiguous film. The wetting monolayer (dark spots) is still exposed in a few
places. Bottom panel: Height profiles measured along the horizontal lines
shown in the upper panels. The standard deviation of the height distribution
for Ni(111) is ten times that of Pt(111). The profile of the Ni(111)
crystallites is convolved with the width of the STM’s scanning tip; in
reality, the walls of the crystallites are more vertical. To directly compare
the height profiles, we plot the absolute height above a substrate mean
reference, whereas in Fig. 10 we show the relative heights. The data for these
plots were taken by Thürmer et al. (2014), who also inspired this figure.

Once enough water is deposited for more than a monolayer (a wetting layer with
a thickness of one molecule), the energetic constraints of the substrate-water
interface need to be balanced with those of the water-water interface (Thürmer
et al., 2014; Lin et al., 2018; Maier, 2018). This results in a complex
restructuring of the water-substrate interface that depends on the substrate’s
lattice constant, structure, electronic needs, and how water molecules in
direct contact with the substrate orient themselves. The effects may reach
just a few layers into the ice, or well beyond 100 layers (25–40 nm
thickness). Density functional theory can predict these structures for a given
substrate, yet the case of water remains difficult (Tamijani et al., 2020).

####  3.5.2 Influence of the substrate on ice film topography

We now compare wetting layers on two atomically flat, close-packed, and
monocrystalline surfaces. We choose Pt(111) and Ni(111), two well-studied
surfaces that illustrate the strong influence of the substrate on the growing
ice films; the (111) tuple is the Miller index, describing the orientation of
the atomic lattice exposed at the surface.

On Pt(111), a contiguous monolayer is formed at first. Further deposition of
water results in $50$–$150$ nm wide crystallites surrounded by the monolayer.
The crystallites have flat-top surfaces and heights of $2$–$3$ nm ($7$–$10$
layers). Further deposition makes the crystallites grow mostly laterally and
coalesce with their neighbours, maintaining an intact wetting layer in
between. Eventually, all crystallites have merged, forming a contiguous
polycrystalline film (Fig. 10). Therein, crystallites overgrow each other,
leading to the preferential formation of hexagonal ice Ih at temperatures as
low as $115$–$140$ K (see Fig. 10, and Thürmer & Nie, 2013).

On Ni(111), instead of a monolayer, the wetting layer is two molecules thick
(bilayer). The emerging crystallites are much taller than those on Pt(111) and
have smaller diameters of $30-60$ nm. At a mean film thickness of 2.5 nm –
when on Pt(111) a continuous film has formed – the crystallites on Ni(111) are
still well isolated, covering just 15% of the surface (Fig. 11). This is
attributed to a larger driving force for dewetting, presumably due to a lower
surface energy of the wetting bilayer, or due to an increased energy of the
interface between the crystallites and Ni(111). There are no high-resolution
microscopy data for thicker films of ice on Ni(111) available at this point.
However, based on comparison with yet another close-packed metal surface,
Ru(0001), we predict with some confidence that the trend of ice films on
Ni(111) being much rougher than those of equal mean thickness on Pt(111), will
persist up to at least 100 molecular layers, if not indefinitely. The gas
adsorption experiments by Haq & Hodgson (2007) for Ru(0001) have revealed that
although the crystallites cover already 50% of the surface at a mean film
thickness of 2.5 nm, it takes about 90 layers for the ice to fully coalesce.
We thus infer that ice on Ni(111) will not coalesce for thicknesses up to at
least 100 layers and remain much rougher than on Pt(111).

Quoting Maier (2018): ‘On metal surfaces, the adsorption energy of water is
comparable to the hydrogen bond strength among water molecules. Therefore, the
delicate balance between competing water–water and the water–metal
interactions leads to a rich variety of structures that form at the interface
between water and seemingly simple, flat metal surfaces.’

Thürmer et al. (2014) conclude similarly: ‘Even for simple atomically flat
close-packed metal substrates, the question of how water wets is surprisingly
difficult. The delicate balance between optimising water-water bonding and
water-metal interaction, the effect of the metal lattice constant, and […] the
possibility of water dissociation, all contribute to a complexity that renders
predictions of water layer structure unfeasible. Density functional theory […]
is not yet able to find the lowest-energy configuration of a water layer on a
metal substrate reliably.’

###  3.6 Impossibility to predict ice topography for Euclid’s optical surfaces

For Euclid, the situation is exacerbated, as most coating materials have not
been disclosed to us by industry (see Sect. 2.11). Wetting experiments were
conducted for crystalline metal oxides such as Al2O3 (Tamijani et al., 2020)
and TiO2 (He et al., 2009), common optical coating materials. However, this
does not help us, even if these materials were actually used in Euclid.

First, the wetting process is highly dependent on the crystal planes (Miller
indices) exposed at the surface, which we do not know in general. Second,
vapour deposition of metal and semiconductor oxides generally results in
amorphous and polycrystalline films (Kazmerski, 2012) that are also not
atomically flat. Third, while the topography of a substrate is often
replicated in dense optical coating layers (Trost, 2015), this does not hold
for contaminating ice films. There, long-range forces from crystallisation and
the substrate-water interface control the topography on nano- and micrometer
scales, together with growth spirals over substrate-surface steps (Thürmer &
Bartelt, 2008) and shadowing effects during deposition (Labello, 2011).

###  3.7 Conclusions for ice in Euclid

##### NISP detectors, M2, and external baffle:

These are the only places where low-density amorphous ice may form. Only if
deposition occurs already during cool-down at $T\gtrsim 120$ K, crystalline
ice is expected, with a top amorphous layer from further contamination.

##### All other optical surfaces:

Polycrystalline ices Isd and Ih are expected. Their exact nano-scale
crystalline composition is not relevant for Euclid data. However, long-range
forces in polycrystalline ice films determine the surface topography on scales
of 100 nm and above, and may thus have a noticeable impact on optical
scattering and wavefront errors. These are difficult to model and predict, and
it is not a priori clear how amorphous and crystalline ices manifest in the
data. Crystalline ices have a narrow absorption line at 1.65
$\mathrm{\SIUnitSymbolMicro m}$ that would be detectable in heavier
contamination scenarios (see our second paper).

##### Internal and external processes:

Annealing and irradiation can break down the nanoscopic structure of ice
films. They are highly inefficient at $90$–$120$ K and can be ignored for
Euclid.

##### The structure of ices are mostly stable:

Ice films are predominantly modified by sublimation and further deposition.
Mechanical surface restructuring will occur from dust and meteoroid pitting on
M1 (Grün et al., 1985; Evans, 2000).

##### The topography of ice films cannot be predicted:

The energetic needs of the substrate-water interface and the water-water
interface are very complex. Also, we do not know the composition of the top-
most coating layer on most surfaces.

##  4 Contamination and decontamination modelling

A single thermal decontamination cycle for Euclid takes about 18 days, not
counting subsequent recalibrations. Estimates of the contamination rate are
thus of great interest for mission planning. Outgassing is driven by bulk
diffusion of dissolved molecules in a substrate, followed by their
sublimation. Our knowledge uncertainties of these processes limit the accuracy
of contamination models; an estimate of a single decontamination per year
could quickly become several per year, or none at all.

Sophisticated codes exist to compute outgassing and contamination rates (e.g.
Brieda & Laugharn, 2020; Zitouni & von Germersheim, 2020). They were applied
for example to compute the contamination of the JWST during its initial 180
days in flight, accounting for JWST’s complex unfolding sequence (Brieda et
al., 2022). In this section we aim much lower, developing an understanding of
the dynamics of molecular contamination to inform our calibration strategy. We
break down the contamination process into the underlying basic physics and
geometry, and develop a transport model for the water exchange between
surfaces in Euclid. The main result is shown in Table 2, listing estimated
contamination rates for the optical surfaces in Euclid. These are indicative
only and highly uncertain. To arrive at these values, we need sublimation and
condensation rates (Sects. 4.2 and 4.3), the vapour pressure from sublimed ice
in Euclid’s cavities (Sect. 4.4), the effect of geometry on the sublimation
and condensation rates between two surfaces facing each other (Sect. 4.5), and
lastly geometrical models of the PLM to compute the water exchange flux
between surfaces (Sect. 4.6). Finally, in Sect. 4.7 we provide an overview of
the thermal decontamination procedure.

Of equal interest is the impact of contamination on the data, which ultimately
drives how often we have to decontaminate Euclid. This will be addressed in
the second paper.

###  4.1 Methodologies

Here as in Sect. 3 we make extensive use of literature in the material
sciences, outside the astronomical context. For better understanding we
summarise basic measurement principles.

The water update of a material can be determined using dynamic gravimetric
vapour-sorption888The term ‘sorption’ refers to the uptake of a substance by
some material at (i) the material’s surface (adsorption), and (ii) by
integration into the material’s atomic structure (absorption), without
distinguishing between these processes. experiments, where a material is
exposed to various degrees of relative humidity (e.g. Sharma et al., 2018).
Fourier-transform infrared (FTIR) spectroscopy is another method to measure
the absorption or emission of water (e.g. Scherillo et al., 2014). These
experiments are typically conducted at room temperature or higher.

The surface- and bulk-diffusion coefficients can be determined from transport
models that describe the dynamic mass balance determined by sorption
experiments. An alternative is laser-induced thermal desorption (LIDT) coupled
with mass spectrometry, possibly using different isotopologues such as
H${}_{2}^{\,16}$O and H${}_{2}^{\,18}$O ice as in Brown & George (1996).

Different methodologies are available to measure sublimation and condensation
rates, that is the change of ice-film thickness. The change in mass can be
tracked by depositing ice films directly on cryogenic QCMs (e.g. Sack &
Baragiola, 1993). Alternatively, the film thickness is determined directly
using interference fringe counts in a reflected laser beam, or using FTIR
reflection-absorption spectroscopy, exploiting the very strong absorption line
of water ice at 3 $\mathrm{\SIUnitSymbolMicro m}$ (as e.g. in Ghesquière et
al., 2015); details about water-ice absorption are presented in our second
paper.

###  4.2 Diffusion

The first Fick law relates the diffusion flux, $\boldsymbol{j}_{\rm d}$, of
absorbed particles to the spatial gradient of their concentration, $c$ (see
also Chiggiato, 2020). In one dimension,

$j_{\rm d}(l,t)=-D\,\frac{\partial c(l,t)}{\partial l}\;,$ (1)

where $l$ and $t$ are space and time, respectively. The diffusion coefficient
$D$ is described by an Arrhenius-type law,

$D=D_{0}\,{\rm exp}\left(-\frac{E_{\rm d}}{k_{\rm B}\,T}\right)\;.$ (2)

Here, $D_{0}$ is the pre-exponential factor, $k_{\rm B}$ Boltzmann’s constant,
and $E_{\rm d}$ the diffusion activation energy. The constants $D_{0}$ and
$E_{\rm d}$ depend on mass of the absorbed molecules, their size, and on the
nanoscopic structure of the substrate. Using Kapton and ice as examples, we
show that $D$ is highly sensitive to these parameters:

In amorphous Kapton, $E_{\rm d}=0.2$ eV (Yang et al., 1985) and $D$ may vary
by a factor of 3 depending on the orientation of the polymers, the thickness
of Kapton, and the presence of aggregates (Yang et al., 1986). This, and the
absorption of water by Kapton, was further studied by Sharma et al. (2018),
who find $E_{\rm d}=0.3$–$0.4$ eV, and that $D$ can change by a factor of
$10$, depending on the addition of aggregates. We note that lowering $E_{\rm
d}$ from $0.40$ eV to $0.39$ eV at 120 K – a typical Euclid temperature –
increases $j_{\rm d}$ by a factor 2.6. Thus $j_{\rm d}$ is highly susceptible
to measurement errors of $E_{\rm d}$ and to the addition of aggregates.

Next, we consider the mobility of dissolved water molecules in ice. In
amorphous ice Ial, the porous structure greatly facilitates diffusion jumps of
water molecules, resulting in a low $E_{\rm d}=0.08$–$0.25$ eV (Ghesquière et
al., 2015). The mean-square displacement of a particle due to bulk diffusion
is given by

$\langle(\Delta l)^{2}\rangle=D\,t\,.$ (3)

Accordingly, and using the computations in Ghesquière et al. (2015), it would
take a water molecule $\sim$ 0.5 s to cross an amorphous ice film of 10 nm
thickness at 120 K. In crystalline ice Ih, this would take $120$ s. Brown &
George (1996) report even lower diffusion rates for ice Ih, finding $E_{\rm
d}=0.7$ eV at $160$ K. Using the Arrhenius law to compute the respective $D$
at 120 K, we find that bulk diffusion is essentially incapacitated (see also
Labello, 2011) in ice Ih in Euclid, at least on mission timescales.

This means that an existing film of amorphous ice on Kapton does not slow down
the diffusion flux $j_{\rm d}$ from Kapton at all, nor from any other
substrate in Euclid. Water molecules easily reach the top of the ice surface
where they eventually sublime, unless they get more permanently integrated
into the bulk amorphous ice. Therefore, amorphous ice films should grow
continuously by substrate diffusion from below and by deposition on top.

Contiguous crystalline ice films, on the other hand, act as an effective
diffusion barrier with $E_{\rm d}=0.7$ eV. Considering the lower sublimation
energy of water ($E_{\rm sub}=0.45$–$0.53$ eV, Sack & Baragiola, 1993; Feistel
& Wagner, 2007; Shakeel et al., 2018), any water flux emanating from a surface
contaminated with crystalline ice is due to sublimation of this ice, and not
due to substrate outgassing. Yet, efficient diffusion channels from the
substrate to the surface of the bulk ice could still exist, for example along
fault lines and domain walls in polycrystalline ice, or if the surface
roughness is very high – such as on Ni(111) – exposing large areas of thin
wetting layers (Sect. 3.5).

The take-home message is that estimates of the outgassing rates in a
spacecraft are highly uncertain at low temperatures: (i) They depend strongly
on the substrate’s nanoscopic structure and aggregates. (ii) Small temperature
changes of a few kelvin result in an order-of magnitude change in $j_{\rm d}$.
Temperatures of spacecraft sub-systems are difficult to estimate prior to
launch and may change over time due to radiation damage and mechanical erosion
of the insulation. (iii) Small measurement errors in $E_{\rm d}$ at the
percent level change $j_{\rm d}$ by a factor of a few. (iv) Outgassing
databases use measurements at room temperature because of the much higher
signal and simpler non-cryogenic experimental setup. Extrapolations down to
120 K span many orders of magnitude in $j_{\rm d}$ and ignore all
restructuring processes at a microscopic level and below that might occur
during cool-down from thermal contraction. For example, thermal stress-induced
micro-fractures likely caused the sudden contamination of Cassini / NAC (see
Sect. 2.4.2, and Haemmerle & Gerhard, 2006).

Accurate diffusion and outgassing forecasts for Euclid are therefore not
feasible. However, we can still build a sublimation model, knowing that
contiguous crystalline ice films act as effective diffusion barriers.
Therefore we adopt a ‘glacial’ scenario, in which all surfaces in Euclid are
already contaminated by crystalline ice films. The model shall be stationary,
that is we do not consider self-depletion by sublimation. Such a glacial
scenario could be the case immediately after launch, or after a long period
without decontamination, that is a worst-case scenario. We recall that
amorphous ice deposited at $120$ K crystallises within a few weeks to months
(Fig. 8).

We use this glacial model to forecast the change of ice thickness and the
amount of water escaping into space through the telescope front aperture.
Since the model ignores diffusion, it cannot forecast the contamination rate
of an initially uncontaminated spacecraft, nor the depletion times of the
various water reservoirs.

###  4.3 Sublimation-condensation rates

####  4.3.1 General approach with the Hertz–Knudsen equation

Deposition and sublimation happen simultaneously, and their rate is commonly
described by the Hertz-Knudsen equation from classical kinetic gas theory. In
the case of equal temperature $T$ of a substrate and its surrounding gas
phase, we have

$j_{\rm s}(T)=\sqrt{\frac{m}{2\pi\,k_{\rm
B}\,T}}\;\left[\sigma{\rm{}_{s}}\,p_{\rm
sat}(T)-\sigma{\rm{}_{c}}\,p(T)\right]\;.$ (4)

Here, $j_{\rm s}(T)$ is the sublimation flux (in kg m-2 s-1), $m$ the mass of
the subliming molecule, $p_{\rm sat}(T)$ the equilibrium saturation-vapour
pressure for which sublimation and deposition rates are equal, and $p(T)$ the
pressure in the gas phase. The sublimation and condensation coefficients,
$\sigma_{\rm s}$ and $\sigma_{\rm c}$, are the fractions of molecules that
sublime and re-condense (backscatter) upon reaching the surface; they are
difficult to determine accurately. Persad & Ward (2016) derive a quantum-
mechanical formulation for $j_{\rm s}(T)$, but its computation requires
knowledge of the local curvatures of the substrate-gas interface, which are
not known for ices on Euclid’s surfaces.

The back-scattering term $\sigma_{\rm c}\,p(T)$ accounts for sublimed
molecules that immediately redeposit again on the surface after collisions
with other sublimed water molecules in the vapour phase. This is negligible
for Euclid, where the mean free path length is thousands of kilometres (Sect.
4.4). Subliming molecules hit other surfaces and stick to them (Sect. 4.4)
before colliding with other molecules in the gas phase, and thus $\sigma_{\rm
c}\,p=0$ in Eq. (4).

Figure 12: Sublimation-flux models for amorphous and crystalline (hexagonal)
ice. Overlaid are various measurements. The model for amorphous ice is shown
up to 120 K by the dashed pink line; it is obtained by shifting the Murphy &
Koop (2005) curve by 3 K to lower temperatures.

####  4.3.2 Theoretical and empirical estimates for hexagonal ice

To evaluate Eq. (4) for a vacuum, we can replace $\sigma_{\rm s}\,p_{\rm
sat}(T)$ with the sublimation pressure $p_{\rm sub}(T)$. Wagner et al. (2011)
derive $p_{\rm sub}(T)$ for a planar surface of monocrystalline ice Ih based
on the thermodynamics of the sublimation zone, valid from 50 K to $T_{\rm
t}=273.16$ K,

$p_{\rm sub}(T)=p_{\rm
t}\,\exp\left[\mathcal{T}^{-1}\sum_{i=1}^{3}\,a_{i}\mathcal{T}^{b_{i}}\right]\;,$
(5)

where $\mathcal{T}=T/T_{\rm t}$, $p_{\rm t}=611.657$ Pa, and

$\displaystyle a_{1}$ $\displaystyle=-0.212\,144\,006\times 10^{2},$
$\displaystyle\hskip 14.22636ptb_{1}$ $\displaystyle=0.333\,333\,333\times
10^{-2},$ $\displaystyle a_{2}$ $\displaystyle=\;\;0.273\,203\,819\times
10^{2},$ $\displaystyle\hskip 14.22636ptb_{2}$
$\displaystyle=0.120\,666\,667\times 10^{1},$ $\displaystyle a_{3}$
$\displaystyle=-0.610\,598\,130\times 10^{1},$ $\displaystyle\hskip
14.22636ptb_{3}$ $\displaystyle=0.170\,333\,333\times 10^{1}.$

Frequently used is Murphy & Koop (2005), also based on thermodynamic
considerations. We rewrite their result as

$p_{\rm sub}(T)=\exp\left[c_{1}+c_{2}/\mathcal{T}+c_{3}\,{\rm
ln}\,(\mathcal{T})+c_{4}\,\mathcal{T}\right]\;{\rm Pa}$ (6)

with $c_{1}=29.3577$, $c_{2}=-20.9521$, $c_{3}=3.53068$, and $c_{4}=-1.98951$.
This agrees to within 0.3% with Wagner et al. (2011) in the 90–210 K range,
and hereafter we collectively refer to Eqs. (5) and (6) as the WMK models.

The resulting sublimation fluxes $j_{\rm s}(T)$ are shown in Fig. 12,
expressed as a loss rate for the ice film thickness. But how accurate are
these theoretical models? The surface roughness of polycrystalline ice Ih
(Sect. 3) enlarges the effective surface area and increases the sublimation
flux. Surface roughness also means larger nano-scale surface curvatures, thus
higher internal vapour pressure (Andreas, 2007; Nachbar et al., 2018a, b) and
higher sublimation.

The WMK models are in very good agreement with the sublimation fluxes measured
by Woronowicz & Meadows (2012) at $T=120$–140 K to understand the effect of
ice on the thermal performance of the JWST sunshield. They also match the data
from Bryson et al. (1974), but only down to a temperature of 140 K, where the
sublimation flux begins to exceed the WMK models by factors 2–4. A similar
trend is seen in the data from Sack & Baragiola (1993), where for $T\leq 140$
K the measurements shortly after deposition999A clear statement is missing in
Sack & Baragiola (1993), but from their description we estimate about 15–90
min between deposition and measurement, depending on chosen deposition
temperature and thermal warm-up time. showed sublimation rates temporarily
increased by factors 2–5. This is explained by more volatile amorphous
constituents that have not yet annealed into a more stable crystalline form
upon heating the ice films to their desired temperature.

We note that the values measured by Sack & Baragiola (1993) systematically
exceed the WMK models by respective factors of 1.4 and 2.1 at $T=180$ K and
$T=140$ K (see Fig. 12). This is also seen in measurements done by ESA to
scale Euclid’s decontamination mode (Szmolka & Bras 2021, private
communication; red dots in Fig. 12). A first explanation is that the
measurements were done too soon after deposition, when the restrained
amorphous ice or stacking-disordered ice still experience considerable
annealing, in particular if the deposition rates were high (Sects. 3.1.3 and
3.3, and Sack & Baragiola, 1993; Pratte et al., 2006; Smith et al., 2011;
Rosu-Finsen et al., 2022). Indeed the measurements by Woronowicz & Meadows
(2012) showing lower sublimation fluxes were done over 40–60 h, compared to 15
min for Sack & Baragiola (1993); no information about this is given in Bryson
et al. (1974). A second explanation is that different coatings on the QCMs
affected the ices’ surface topography (Sect. 3.5) and thus altered the
sublimation flux. The QCM used by Sack & Baragiola (1993) was coated with
gold; the QCM101010A CrystalTek Cryo QCM,
https://crystaltekcorp.com/products/cqcm used by ESA for our tests was also
gold-plated; Woronowicz & Meadows (2012) did not comment on possible coatings
of their QCM. Sack & Baragiola (1993) accounted for this by including an
effective surface-area factor in their fit.

Sack & Baragiola (1993) fitted their measured sublimation flux (in molecules
m-2 s-1) with a semi-empirical model,

$\Phi_{\rm SB93}(T)=a\,T^{3.5}\;{\rm exp}\,\left(\frac{-E_{\rm sub}}{k_{\rm
B}\,T}\right)\;,$ (7)

where $a=1.82\times 10^{25}$ molecules m-2 s-1 K-3.5 is a constant prefactor.
The model is shown as the blue line in Fig. 12 for $E_{\rm sub}=0.45$ eV. We
note that changing $E_{\rm sub}$ to 0.46 eV makes this fit consistent with the
WMK models within 20% in the 120–160 K range. Considerable discrepancies below
120 K arise because $E_{\rm sub}$ is actually temperature-dependent: Feistel &
Wagner (2007) compute that the sublimation enthalpy $E_{\rm sub}$ decreases by
0.008 eV from 140 K to 90 K, which has a pronounced effect on the sublimation
curve. We conclude that Eq. (7) is less suitable to accurately describe
sublimation fluxes over a very large temperature range that extends below 120
K, and that the WMK models are preferred.

####  4.3.3 Estimates for amorphous ice

Amorphous ice can absorb large quantities of gas thanks to its porosity
(Talewar et al., 2019), making it an important constituent in the colder parts
of the Solar System (Guilbert-Lepoutre, 2012). Large amounts of gas can be
released when the pores of amorphous ice collapse during crystallisation. This
may enlarge the sublimation rate of amorphous ice by many orders of magnitude
down to 50 K (e.g. Notesco et al., 2003; Bar-Nun et al., 2007; Drobyshev et
al., 2007; Prialnik & Jewitt, 2022), a phenomenon referred to as ‘molecular
volcano’ (May et al., 2013) seen mostly in amorphous ice exceeding several
micrometer thickness. Even small fractions of a few percent of absorbed trace
gases can increase the sublimation rate of water substantially. This is not
relevant for Euclid, where ice films are expected to be thinner (Sect. 4.6)
and decontamination will occur sooner (second paper).

Sublimation measurements of pure amorphous ice at temperatures below 120 K are
difficult due to limited instrumental sensitivity. Kouchi (1987) show that the
saturation vapour pressure in amorphous ice depends strongly on the deposition
temperature and the rate of deposition, and estimate it to be 10–100 times
higher than in crystalline ice (see also Sack & Baragiola, 1993). More recent
work suggests that the sublimation flux of amorphous ice is enhanced by a
factor of ten or less compared to crystalline ice, once annealing effects
immediately after deposition have settled. Fraser et al. (2001) compute that
amorphous ice has a 4.7 times shorter half-life time compared to crystalline
ice at 120 K, increasing to 7.6 times at 90 K. Smith et al. (2011) measure the
desorption rates at 137–150 K for amorphous and crystalline ice. Using their
estimates of $E_{\rm sub}$ and ignoring its temperature dependence (Feistel &
Wagner, 2007), we extrapolate to lower temperatures and find that the
sublimation rate of amorphous ice increased by factors 3.3 and 5.1 at $T=120$
and 90 K, respectively. Nachbar et al. (2018b) find a factor 2–3 increase of
the saturation vapour pressure at 130 K for amorphous ice on flat gold and
copper substrates, with an upward trend towards lower temperatures.

Hence the sublimation flux of amorphous ice gradually increases over that of
crystalline ice for decreasing temperatures. Given the uncertainties just
outlined, we estimate the sublimation flux for amorphous ice by shifting the
WMK models – that is Eqs. (5) and (6) – by 3 K to lower temperatures,

$j_{\rm s}^{\;\rm amorph}(T)=j_{\rm s}^{\;\rm crystal}(T+3\,K)\;.$ (8)

This results in respective factors 8.4 and 3.4 enhancement of the sublimation
flux at 90 K and 120 K, and is shown by the dashed pink line in Fig. 12. We
assume that below $110$–$115$ K any ice deposits in Euclid are amorphous and
will remain amorphous (Fig. 8), applicable to M2, the external baffle, and the
NISP detectors, all of which are at $T<110$ K (see Table 1, and Sect. 3.1.2).

We summarise that the sublimation flux is a very steep function of temperature
(Fig. 12). Estimates for various PLM components are given in Table 3 using
Eqs. (6) and (8) for operational and decontamination temperatures. The actual
sublimation fluxes in Euclid might deviate by a factor of a few, depending on
the substrates and the in-flight temperatures.

###  4.4 Vapour pressure in Euclid cavities

The last information we need for our water transport model is whether the
pressure in the sublimate is negligible. Indeed, the molecules are in free
molecular flow, that is they travel along straight lines between point of
sublimation and point of adsorption without collision. This is shown as
follows.

The probability $f_{\rm stick}$ of a water molecule to adhere to an ice
surface upon impact – the ‘sticking coefficient’ – has been analysed by
Batista et al. (2005) and Gibson et al. (2011); see also Suliga et al. (2020).
Dependencies on kinetic energy, impact angle, surface topography, and
temperature can be safely ignored in Euclid conditions, resulting in high
values of $f_{\rm stick}=0.98$–$1.00$. This is because the energy transfer
from the impinging molecule to molecules of equal mass in the bulk ice is
maximal, and because the kinetic energy quickly dissipates in the bulk ice
(Brown et al., 1996). Thus the molecules are effectively removed from the gas
phase upon surface contact in Euclid. We adopt a conservative $f_{\rm
stick}=0.97$, measured at 120 K and $p=10^{-10}$ mbar by Brown et al. (1996).

To estimate the gas pressure and mean free path length, we approximate
Euclid’s telescope cavity with a cylinder (Table 4 and Fig. 21 in the
Appendix). We also assume that the cavity wall is in thermal equilibrium with
the gas phase – which is incorrect (Sect. 4.5) – but has no practical
implications for our deduction of the mean free path length. The wall of the
cylinder (Euclid’s external baffle) has a temperature of 100 K and its bottom
(PLM baseplate and M1) 120 K. All surfaces are assumed to be iced. Using Eqs.
(6) and (8), the total sublimation flux into the cylinder is $n_{\rm
sub}=3.24\times 10^{13}$ molecules s-1, 99.9% of which coming from the warmer
bottom. The escape fraction, $f_{\rm esc}$, through the front telescope
aperture on direct paths is 3.5% (Appendix D.6). We adopt a typical distance
of $s=1.0$ m, travelled by a water molecule before its adsorption, with a mean
velocity of $\langle v\rangle=374$ m s-1, that is the mean of the Maxwell-
Boltzmann distribution at 120 K. The number $N$ of molecules in the cylinder
at any time is then

$N=n_{\rm sub}\,\frac{s}{\langle v\rangle}\,(1-f_{\rm
esc})\,\sum_{k=0}^{\infty}\,(1-f_{\rm stick})^{k}=n_{\rm
sub}\,\frac{s}{\langle v\rangle}\,\frac{1-f_{\rm esc}}{f_{\rm stick}},$ (9)

where the rapidly converging sum represents the molecules that do not stick
after $k$ surface impacts. With these conditions we have $N=8.6\times 10^{10}$
molecules in the cylinder at any time. In an ideal gas, the pressure is then
$p=3.1\times 10^{-13}$ mbar and the mean free path length is $167\,000$ km,
using $0.28$ nm for the diameter of the water molecule. Therefore, the gas in
the telescope cavity is in free molecular flow; sublimed molecules travel in
straight lines from their point of sublimation to their point of impact, where
they stick.

The realisation of free molecular flow implies that the sublimate is not in
thermal equilibrium with the mechanical surfaces, and that its velocity
distribution is dominated by the processes in the surface-gas interface (Sect.
4.5). Any effects from the resulting non-Maxwellian velocity distribution are
negligible for the conclusion of free molecular flow.

Figure 13: Parametrisation of the sublimation geometry. The water flux is
emitted by the surface element ${\rm d}S$ and received at the surface element
${\rm d}A$. The blue vectors represent the respective surface normal vectors.
For details, see Sect. 4.5.

###  4.5 Computation of incident water flux

We consider the total flux $\Phi_{\rm tot}(T)$ of water molecules subliming
from a surface element ${\rm d}S$ (Fig. 13), in units of molecules m-2 s-1,

$\Phi_{\rm tot}(T)=m\,j_{\rm s}(T)\,.$ (10)

Here, $m=2.99\times 10^{-26}$ kg is the mass of a water molecule, and $j_{\rm
s}(T)$ is computed from Eqs. (4) and (6) for crystalline ice; for amorphous
ice, we use Eq. (8). The dependence of the emitted flux on the angle
$\theta_{\rm S}$ with respect to the surface normal is commonly described as
${\rm cos}\,\theta_{\rm S}$ (Knudsen cosine law, see also Greenwood, 2002).
Lower-resolution experimental data initially supported this, as was shown by
Bryson et al. (1974) for H2O and CO ice at Euclid temperatures and by Padowitz
& Sibener (1989) for NO ice. This is questionable though, given the complex
surface topography of ice (Sects. 3.5 and 3.6); newer experiments suggest
angular dependencies that are considerably more – or less – focused (Todorov &
Bloch, 2017, and references therein). Closely related to the violation of the
Knudsen cosine law is the fact that the velocity distribution of subliming
particles can be sub- or super-Maxwellian; this is a consequence of the
complex short- and long-range atomic forces at play in the desorption
processes and in the surface-gas interface (Kann & Skinner, 2016).

In the absence of experimental data providing more realistic angular and
velocity distributions for the sublimates in Euclid, we revert to the Knudsen
cosine law and assume that the sublimate and the cavity are in thermal
equilibrium. This and the free molecular flow established in Sect. 4.4 allow
us to treat the problem in analogy to the photon emission of a luminous
surface111111In principle, a code that computes the radiative heat exchange
between surfaces can also compute contamination, by replacing the photon flux
with the sublimation flux (as e.g. in Brieda et al., 2022)..

Accordingly, the flux $f$ (in molecules s-1) received by a surface element
${\rm d}A$ from the sublimating surface element ${\rm d}S$ is

$f(x,\theta,T)={\rm d}S\,\Phi_{0}(T)\,x^{-2}\,{\rm cos}\,\theta_{\rm S}\,{\rm
cos}\,\theta_{\rm A}\,{\rm d}A\,,$ (11)

where $\theta_{\rm S}$ and $\theta_{\rm A}$ are the respective angles to the
surface normal vectors, $x$ is the distance between the two surface elements,
and $\Phi_{0}(T)$ is the peak sublimation flux emitted at $\theta_{\rm S}=0$.
We compute $\Phi_{0}(T)$ by determining the total sublimation flux emitted by
the unit area into the hemisphere above,

$\Phi_{\rm
tot}(T)=\int\displaylimits_{0}^{2\pi}\int\displaylimits_{0}^{\pi/2}\,\Phi_{0}(T)\,{\rm
cos}\,\theta_{\rm S}\,{\rm sin}\,\theta_{\rm S}\,{\rm d}\theta_{\rm S}\,{\rm
d}\varphi=\pi\,\Phi_{0}(T)\;.$ (12)

Here, we assumed azimuthal symmetry in the angle $\varphi$.

###  4.6 Contamination forecasts

The telescope cavity consists of mirrors M1, M2, and the external telescope
baffle, and is directly exposed to open space at the telescope’s front
aperture. The instrument cavity is mounted on the PLM baseplate and is located
below M1, containing folding optics and the instruments (see Fig. 5). The
instrument cavity is connected to open space only through the bore hole in M1,
limiting the capability of water escape.

####  4.6.1 Telescope cavity

In Appendix D we introduce a cylindrical model of the telescope cavity to
compute the contamination rates for M1 and M2 (see Table 2), using the
formalism developed earlier in this section. In this model, M1 can be
contaminated by ice subliming from the interior wall of the external baffle,
from M2, and from a ‘front ring’ that reduces the telescope aperture.
Likewise, M2 can be contaminated by sublimation from the baffle, from M1, and
from a ‘back ring’, that is the structural parts visible between M1 and the
baffle wall.

We compute the contamination for the nominal temperatures and the warm
comparison case (Table 1). In flight, temperatures are expected to stay within
a few kelvin of the nominal case.

The following are some of our findings for the nominal temperatures and the
glacial scenario: (i) 99.6% of the water escaping through the front aperture
is subliming from M1 and the back ring. (ii) 11% (6%) of the ice subliming
from the baffle (M1) escape the telescope cavity on direct paths, the rest
will redeposit. (iii) M1 slowly decontaminates at $-0.33$ nm month-1. Despite
being very cold, M2 will contaminate only slowly at $+0.13$ nm month-1. (iv)
The thickness variation of the ice on M1 and M2 is about 1% or less and thus
very uniform (Fig. 22).

Table 2: Total contamination rates for the nominal and warm case (Table 1).

Common to | ${\rm d}z/{\rm d}t\;(T_{\rm nominal})$ | ${\rm d}z/{\rm d}t\;(T_{\rm warm})$
---|---|---
VIS and NISP | [nm month-1] | [nm month-1]
| WMK | Sack+ (1993) | WMK
M1 | $-0.33$ | $-1.1$ | $-4.0$
M2 | $0.13$ | $+0.3$ | $+1.1$
FoM1 | $+0.08$ | $-0.16$ | $-14$
FoM2 | $+1.4$ | $+3.4$ | $+0.50$
M3 | $+1.4$ | $+3.4$ | $-25$
Dichroic | $+1.4$ | $+3.4$ | $+0.50$
NISP path |  |  |
NISP lenses | $-101$ | $-238$ | $-89$
Detector | $+9.9$ | $+27$ | $+22$
VIS path |  |  |
FoM3 | $+3.6$ | $+9.6$ | $+9.3$
Detector | $-44\,000$ | $-79\,000$ | $-122\,000$
121212Negative values mean that sublimation is more efficient than
condensation. We note that in most related technical publications, the
sublimation and condensation fluxes are given in units of g cm-2 s-1. For us
the optical effects are of interest, hence we parameterise contamination rates
as a change of ice thickness $z$.

####  4.6.2 Instrument cavity

In Appendix E we present a hemispherical model to compute contamination rates
in the instrument cavity (Table 2). In a hemispherical model, the flux of
water is incoming from the $2\pi$ sr solid angle above the point under
consideration and is independent of the hemisphere’s radius. For a simple
estimate we can thus ignore the much more complex geometry of the instrument
cavity (Figs. 16 and 17), as long as the solid angle is filled with emitting
surfaces at the same temperature.

For nominal operating temperatures and the glacial scenario we find: (i) If
the NISP optics are initially free of ice, then they will stay free of ice. A
surface in the NISP optics will effectively sublime 101 nm month-1 since it is
comparatively warm. (ii) The NISP optics can decontaminate themselves during
the time between launch and the arrival at Lagrange point L2, unless they get
initially contaminated with more than 100 nm per surface. (iii) The NISP
detectors will accumulate a substantial amount of 10 nm month-1, as they are
considerably colder than their environment. (iv) Any contamination on FoM1
will remain unchanged. (v) FoM2, M3, the dichroic, and in particular FoM3 will
accumulate ice. (vi) The VIS detector effectively decontaminates itself, as it
is much warmer than its environment. (vii) Actual contamination rates are
highly sensitive to temperature changes as small as $1$–$2$ K.

We note that the above statements about the NISP optics remaining free of ice
only hold if the optics are exposed to the instrument cavity. In the as-built
instrument this is not the case. The NISP optics, the filter wheel, and the
grism wheel are encapsulated in a SiC box that has very small venting holes,
only. NISP itself is wrapped in MLI (Fig. 17, effectively forming a closed
system with its own contamination dynamics.

####  4.6.3 Industry forecast by Airbus Defence and Space (ADS)

ADS has performed a molecular contamination analysis of the PLM, using 3D
geometric models and a distribution of various outgassing materials and
molecular species. The expected water contamination ranges from 0.1 nm month-1
for the telescope cavity, to 1 nm month-1 for the instrument cavity. This is
about the same order of magnitude as the water exchange from sublimation in
our stationary glacial model (see Table 2). We note that the ADS estimates are
subject to the same uncertainties as outlined in Sects. 4.2 and 4.3, and could
be a factor of a few (or more) higher or lower. More quantitative estimates
about the actual uncertainty cannot be made with the data at our hands.

####  4.6.4 Ammonia contamination from thruster firings

In this subsection we deviate shortly from water ice. Euclid carries 137.5 kg
of pure hydrazine propellant (N2H4), sufficient for a L2 halo-orbit insertion,
a six-year mission, a potential 1–2 year mission extension, and an end-of-life
insertion into a heliocentric graveyard orbit (Racca et al., 2016). Halo-orbit
correction manoeuvres are carried out every four weeks during a reserved 6 h
window (Euclid Collaboration: Scaramella et al., 2022). Thruster firings will
in general contaminate a spacecraft through expansion of the supersonic flow
in a vacuum (Chen et al., 2000; Dettleff & Grabe, 2011; Lee, 2017; Yarygin et
al., 2017). Some of Euclid’s hydrazine thrusters are shown in Fig. 20. Thales
Alenia Space – who built Euclid’s SVM – have modelled Euclid’s thruster
contamination and found it to be negligible, but no details could be
communicated that would allow us to independently verify their conclusions.
Therefore, here we make a simple worst-case estimate of the expected
contamination, and confirm that it is negligible.

Hydrazine is a monopropellant – that is it does not need an oxidiser – with
the following two reactions when pushed through the catalytic bed of a
thruster (Price & Evans, 1968; Makled & Belal, 2009),

$\displaystyle\ce{3N2H4->4NH3+N2}\;$ $\displaystyle\;\;{\rm and}$ (13)
$\displaystyle\ce{4NH3->2N2+6H2}\;.$ (14)

The first reaction is fast and exothermic and happens at the beginning of the
catalyst bed, whereas the second reaction is slow and endothermic and occurs
at the end of the catalyst bed. For thruster purposes the second reaction
should be suppressed, that is as much NH3 as possible should be preserved to
achieve a hot exhaust jet with high specific impulse (Pakdehi et al., 2019).
The fraction of unspent NH3 is controlled by the thruster design131313A
comparatively cold but very gas-rich stream emerges if most NH3 is spent, in
which case the catalytic chamber serves as a gas producer for various
different technical purposes..

Figure 14: Schematic view of the flow regime of a typical small chemical or
cold-gas thruster on a spacecraft, expanding into vacuum. The backflow might
contaminate the spacecraft. Figure credit: Dettleff & Grabe (2011).

x

Figure 15: Measured particle flux density across the flow of a cold-gas
thruster. Data taken from Dettleff & Grabe (2011). The red line shows our
piece-wise fit, symmetric around $\theta=0$, and extrapolated to the edges of
the $[-\pi,+\pi]$ range.

For the worst-case L2 halo-orbit correction manoeuvre we assume the following:
1 kg of hydrazine is used to achieve a velocity change of $\Delta v=0.5$ m
s-1, the latter being a worst-case assumption by Euclid’s flight-dynamics
team; all NH3 is preserved, that is a maximum of 1.42 kg of NH3 are produced;
and the entire rarefied backflow (Fig. 15) from the thruster’s jet gets
deposited uniformly on all Euclid surfaces.

To estimate the amount of NH3 that could contaminate Euclid, we must determine
the fraction of mass contained in the backflow. We digitised141414Using
WebPlotDigitizer (Rohatgi, 2022) the measurements in figure 28 of Dettleff &
Grabe (2011), showing the particle flux density in the supersonic flow, and
reproduce it in our Fig. 15. We then approximate the flow as

${\rm log_{10}}\,\left[\frac{p(\theta)}{1\,{\rm
m^{2}\,s}}\right]=\begin{cases}-2.30\,|\theta|+24.25\,,&{\rm
for}\;|\theta|\leq 0.75\,\pi\;\;($$)\\\ 18.85\,,&{\rm
for}\;0.75\,\pi<|\theta|<\pi\;.\end{cases}$

Here, $\theta$ is the ejection angle with respect to the nozzle’s axis and
$p(\theta)$ is the particle flux per area measured in ${\rm m}^{-2}\,{\rm
s}^{-1}$. Assuming radial symmetry around the nozzle’s ejection axis, we
integrate over the particle flux density and find that the backflow
($|\theta|>\pi/2$) contains 0.65% of the total mass ejected. This translates
to 9.2 g of NH3 in the backflow. We ignored any mass-segregation effects
(Price & Evans, 1968), that is NH3 and N2 are homogeneously distributed in the
flow.

Approximating Euclid with a cylinder of 4.5 m height and 3.1 m width, it would
have a surface area of 59 m2, of which 1.2 m2 are for the M1 mirror. Assuming
NH3 is uniformly distributed over this surface, M1 would then accumulate 0.19
g of NH3. Solid NH3 has a density of 0.9 g cm-3 at 100 K (Satorre et al.,
2013), similar to the density of crystalline water ice; the NH3 layer would be
169 nm thick. Brown & Bolina (2007) show that the desorption rate of solid NH3
in a vacuum at 100–120 K is 6–8 orders of magnitude higher than that of water
ice (see also Zhang & Paige, 2009). Hence this layer of NH3 would sublime in
about 4 h at 110 K (see also Fig. 12). That is consistent with Dawes et al.
(2007) and references therein, who report the occurrence of multilayer
desorption of NH3 at temperatures of 100 K and above. In reality, not all of
the backflow will deposit on Euclid, and only a very small fraction will enter
the telescope aperture that faces away from the thrusters’ nozzle axes (see
Fig. 20). Any NH3 deposits from orbit maintenance will have sublimed before
science operations resume.

N2 and H2 ices from hydrazine breakdown cannot form on Euclid due to its
comparatively high temperature. We have not considered unspent hydrazine,
which may constitute 1% of the mass in the exhaust (Chen et al., 2000), but we
note that hydrazine is dissociated by UV-photons with wavelengths shorter than
250 nm (Vaghjiani, 1993).

###  4.7 Decontamination procedure

The thermal decontamination scheme for Euclid foresees temperatures of
$140$–$270$ K, using heaters and partial Sun exposure. The thermal cycle alone
takes about 18 days. During the first three days, the spacecraft’s
decontamination heaters are turned on with full power demand. Because of
Euclid’s compact design, it can generate only a limited amount of heating
power from its on-board solar cells. Therefore, on the fourth day, the
telescope’s solar aspect angle151515The solar aspect angle is the angle
between Euclid’s viewing direction and the Sun. During routine operations it
is kept between $None$–$None$ to maximise thermal stability (Euclid
Collaboration: Scaramella et al., 2022). will be reduced to $None$. This
allows the external telescope baffle to reach a temperature of up to 200 K.
Only a small part of the baffle is directly exposed to the Sun, but since it
is made of aluminium, which conducts heat easily, the parts remaining in the
shadow will also decontaminate. The demanded heater power is reduced during
this time, acknowledging the reduced effective area of the solar panel.

The telescope stays at full decontamination power for two days. The
sublimation itself takes a few minutes only once maximum temperatures are
reached: 0.23 $\mathrm{\SIUnitSymbolMicro m}$ and 3.6
$\mathrm{\SIUnitSymbolMicro m}$ of ice sublime per second at 200 K and 220 K,
respectively. While the ice may evaporate rapidly, additional time is required
to give sublimates a chance to find their way out of the cavities and leave
the spacecraft. For example, according to our model only 6% of the water
molecules evaporating in the telescope cavity escape on direct paths, the rest
will undergo numerous redeposition and sublimation cycles before eventually
escaping. Furthermore, the high decontamination temperatures result in a
decreased sticking coefficient (Kossacki et al., 1999; Batista et al., 2005;
Gibson et al., 2011; Brieda et al., 2022) and a massively increased
evaporation rate. Consequently, the mean free path length might become
comparable to – or even smaller than – the size of the spacecraft, in which
case pressure effects would have to be taken into account for more accurate
evacuation-time estimates.

Six days after beginning of the decontamination, the spacecraft is restored to
a nominal solar aspect angle, and a controlled cool-down begins. The latter
takes approximately twelve days, keeping optical elements warmer than their
surroundings so that any water residuals can condense on colder surfaces. A
series of recalibration steps is executed as soon as the instruments have
reached operational temperatures. A possible optical realignment and further
on-sky recalibrations can only occur once the telescope optics are stable
again. The duration of a full decontamination cycle including all
recalibrations is expected to last up to 25 days and potentially longer.

We expect essentially all superficial ice to evacuate from the telescope
cavity during a full decontamination cycle. The situation for the instrument
cavity is different, as the opening to the telescope cavity is comparatively
small and the geometry of the instrument cavity complex. In particular in
NISP, which is mostly enclosed in MLI, water has reduced escape capabilities
and could eventually recontaminate the detector. Given a clear indication of
ice on the NISP detectors – for example modulated quantum efficiency, spectral
absorption or structures in the flat fields, as elaborated in Holmes et al.
(2016) and in our second paper – a partial decontamination only for NISP
detectors could be considered. This would mean a smaller thermal disturbance
to the telescope than a full decontamination, yet preliminary thermal
considerations indicate that 3–4 days would still be required.

Other than the NISP detectors, surgical decontamination of individual
components is not possible with Euclid, as the mounted optics and the PLM
baseplate are fully constructed in SiC (see also Fig. 16). Any heat applied
locally to an optical element would quickly propagate within the instrument
cavity to other areas due to the high thermal conductivity of SiC, thus
introducing a global thermal state change. Fine temperature control of optical
elements in Euclid is not possible, as most heater controllers operate in an
on-off fashion, providing full power when on.

To mitigate uncertainties in contamination, Euclid will undergo an immediate
post-launch thermal decontamination, being kept at 200–273 K for four days. We
expect that all water trapped on surfaces will desorb, and that a large
fraction of it evacuate the telescope and instrument cavities.

##  5 Results from thermal vacuum tests

###  5.1 Vacuum tests of the PLM

In 2021 the Euclid PLM underwent extensive vacuum tests for 60 days at a
pressure of $10^{-6}$ mbar, simulating space conditions in a vacuum chamber at
the Centre Spatial de Liège (CSL), Belgium. To cool down to its operational
temperatures, the PLM must see a colder object, provided by a liquid helium
shroud, which itself sits in a nitrogen shroud. Once the chamber was
evacuated, everything was kept at ambient temperature for 4.5 days for initial
outgassing of all components in the chamber. Euclid was then cooled down and
kept at operating temperatures for 30 days. Afterwards, a full decontamination
was run (11 days), followed by another cool-down to operating temperatures (9
days) before the final-warm-up.

Witness samples for non-volatile organic contaminants were placed inside the
PLM’s instrument and telescope cavities. These contaminants are heavier than
water and outgas at higher temperatures. No organic contamination could be