# Observations of Forbush Decreases of cosmic ray electrons and positrons with
the Dark Matter Particle Explorer

Francesca Alemanno  Gran Sasso Science Institute (GSSI), Via Iacobucci 2,
I-67100 L Aquila, Italy  Istituto Nazionale di Fisica Nucleare (INFN) -
Laboratori Nazionali del Gran Sasso, I-67100 Assergi, L Aquila, Italy  Qi An
State Key Laboratory of Particle Detection and Electronics, University of
Science and Technology of China, Hefei 230026, China  Department of Modern
Physics, University of Science and Technology of China, Hefei 230026, China
Philipp Azzarello  Department of Nuclear and Particle Physics, University of
Geneva, CH-1211, Switzerland  Felicia Carla Tiziana Barbato  Gran Sasso
Science Institute (GSSI), Via Iacobucci 2, I-67100 L Aquila, Italy  Istituto
Nazionale di Fisica Nucleare (INFN) - Laboratori Nazionali del Gran Sasso,
I-67100 Assergi, L Aquila, Italy  Paolo Bernardini  Dipartimento di Matematica
e Fisica E. De Giorgi, Università del Salento, I-73100, Lecce, Italy  Istituto
Nazionale di Fisica Nucleare (INFN) - Sezione di Lecce, I-73100, Lecce, Italy
XiaoJun Bi  University of Chinese Academy of Sciences, Yuquan Road 19A,
Beijing 100049, China  Particle Astrophysics Division, Institute of High
Energy Physics, Chinese Academy of Sciences, Beijing 100049, China  MingSheng
Cai  Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  School of
Astronomy and Space Science, University of Science and Technology of China,
Hefei 230026, China  Elisabetta Casilli  Dipartimento di Matematica e Fisica
E. De Giorgi, Università del Salento, I-73100, Lecce, Italy  Istituto
Nazionale di Fisica Nucleare (INFN) - Sezione di Lecce, I-73100, Lecce, Italy
Enrico Catanzani  Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di
Perugia, I-06123 Perugia, Italy  Jin Chang  Key Laboratory of Dark Matter and
Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing 210023, China  School of Astronomy and Space Science, University of
Science and Technology of China, Hefei 230026, China  DengYi Chen  Key
Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, Nanjing 210023, China  JunLing Chen  Institute of
Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  ZhanFang
Chen  Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  School of
Astronomy and Space Science, University of Science and Technology of China,
Hefei 230026, China  MingYang Cui  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  TianShu Cui  National Space Science Center, Chinese Academy of
Sciences, Nanertiao 1, Zhongguancun, Haidian district, Beijing 100190, China
YuXing Cui  Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  School of
Astronomy and Space Science, University of Science and Technology of China,
Hefei 230026, China  HaoTing Dai  State Key Laboratory of Particle Detection
and Electronics, University of Science and Technology of China, Hefei 230026,
China  Department of Modern Physics, University of Science and Technology of
China, Hefei 230026, China  Antonio De Benedittis  Dipartimento di Matematica
e Fisica E. De Giorgi, Università del Salento, I-73100, Lecce, Italy  Istituto
Nazionale di Fisica Nucleare (INFN) - Sezione di Lecce, I-73100, Lecce, Italy
Ivan De Mitri  Gran Sasso Science Institute (GSSI), Via Iacobucci 2, I-67100 L
Aquila, Italy  Istituto Nazionale di Fisica Nucleare (INFN) - Laboratori
Nazionali del Gran Sasso, I-67100 Assergi, L Aquila, Italy  Francesco de Palma
Dipartimento di Matematica e Fisica E. De Giorgi, Università del Salento,
I-73100, Lecce, Italy  Istituto Nazionale di Fisica Nucleare (INFN) - Sezione
di Lecce, I-73100, Lecce, Italy  Maksym Deliyergiyev  Department of Nuclear
and Particle Physics, University of Geneva, CH-1211, Switzerland  Margherita
Di Santo  Gran Sasso Science Institute (GSSI), Via Iacobucci 2, I-67100 L
Aquila, Italy  Istituto Nazionale di Fisica Nucleare (INFN) - Laboratori
Nazionali del Gran Sasso, I-67100 Assergi, L Aquila, Italy  Qi Ding  Key
Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, Nanjing 210023, China  School of Astronomy and
Space Science, University of Science and Technology of China, Hefei 230026,
China  TieKuang Dong  Key Laboratory of Dark Matter and Space Astronomy,
Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023,
China  ZhenXing Dong  National Space Science Center, Chinese Academy of
Sciences, Nanertiao 1, Zhongguancun, Haidian district, Beijing 100190, China
Giacinto Donvito  Istituto Nazionale di Fisica Nucleare, Sezione di Bari, via
Orabona 4, I-70126 Bari, Italy  David Droz  Department of Nuclear and Particle
Physics, University of Geneva, CH-1211, Switzerland  JingLai Duan  Institute
of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  KaiKai
Duan  Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  Domenico
D’Urso  [  Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di Perugia,
I-06123 Perugia, Italy  RuiRui Fan  Particle Astrophysics Division, Institute
of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
YiZhong Fan  Key Laboratory of Dark Matter and Space Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China
School of Astronomy and Space Science, University of Science and Technology of
China, Hefei 230026, China  Fang Fang  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  Kun Fang  Particle Astrophysics
Division, Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing 100049, China  ChangQing Feng  State Key Laboratory of Particle
Detection and Electronics, University of Science and Technology of China,
Hefei 230026, China  Department of Modern Physics, University of Science and
Technology of China, Hefei 230026, China  LeiFeng  Key Laboratory of Dark
Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of
Sciences, Nanjing 210023, China  Piergiorgio Fusco  Istituto Nazionale di
Fisica Nucleare, Sezione di Bari, via Orabona 4, I-70126 Bari, Italy
Dipartimento di Fisica M. Merlin, dell’Università e del Politecnico di Bari,
via Amendola 173, I-70126 Bari, Italy  Min Gao  Particle Astrophysics
Division, Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing 100049, China  Fabio Gargano  Istituto Nazionale di Fisica Nucleare,
Sezione di Bari, via Orabona 4, I-70126 Bari, Italy  Ke Gong  Particle
Astrophysics Division, Institute of High Energy Physics, Chinese Academy of
Sciences, Beijing 100049, China  YiZhong Gong  Key Laboratory of Dark Matter
and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing 210023, China  DongYa Guo  Particle Astrophysics Division, Institute
of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
JianHua Guo  Key Laboratory of Dark Matter and Space Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China
School of Astronomy and Space Science, University of Science and Technology of
China, Hefei 230026, China  ShuangXue Han  National Space Science Center,
Chinese Academy of Sciences, Nanertiao 1, Zhongguancun, Haidian district,
Beijing 100190, China  YiMing Hu  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  GuangShun Huang  State Key Laboratory of Particle Detection and
Electronics, University of Science and Technology of China, Hefei 230026,
China  Department of Modern Physics, University of Science and Technology of
China, Hefei 230026, China  XiaoYuan Huang  Key Laboratory of Dark Matter and
Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing 210023, China  School of Astronomy and Space Science, University of
Science and Technology of China, Hefei 230026, China  YongYi Huang  Key
Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, Nanjing 210023, China  Maria Ionica  Istituto
Nazionale di Fisica Nucleare (INFN) - Sezione di Perugia, I-06123 Perugia,
Italy  Wei Jiang  Key Laboratory of Dark Matter and Space Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China  Jie
Kong  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou
730000, China  Andrii Kotenko  Department of Nuclear and Particle Physics,
University of Geneva, CH-1211, Switzerland  Dimitrios Kyratzis  Gran Sasso
Science Institute (GSSI), Via Iacobucci 2, I-67100 L Aquila, Italy  Istituto
Nazionale di Fisica Nucleare (INFN) - Laboratori Nazionali del Gran Sasso,
I-67100 Assergi, L Aquila, Italy  S. Li  [  Key Laboratory of Dark Matter and
Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing 210023, China  ShiJun Lei  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  WenHao Li  Key Laboratory of Dark Matter and Space Astronomy,
Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023,
China  School of Astronomy and Space Science, University of Science and
Technology of China, Hefei 230026, China  WeiLiang Li  National Space Science
Center, Chinese Academy of Sciences, Nanertiao 1, Zhongguancun, Haidian
district, Beijing 100190, China  Xiang Li  Key Laboratory of Dark Matter and
Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing 210023, China  School of Astronomy and Space Science, University of
Science and Technology of China, Hefei 230026, China  XianQiang Li  National
Space Science Center, Chinese Academy of Sciences, Nanertiao 1, Zhongguancun,
Haidian district, Beijing 100190, China  YaoMing Liang  National Space Science
Center, Chinese Academy of Sciences, Nanertiao 1, Zhongguancun, Haidian
district, Beijing 100190, China  ChengMing Liu  State Key Laboratory of
Particle Detection and Electronics, University of Science and Technology of
China, Hefei 230026, China  Department of Modern Physics, University of
Science and Technology of China, Hefei 230026, China  Hao Liu  Key Laboratory
of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese
Academy of Sciences, Nanjing 210023, China  Jie Liu  Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  ShuBin Liu  State
Key Laboratory of Particle Detection and Electronics, University of Science
and Technology of China, Hefei 230026, China  Department of Modern Physics,
University of Science and Technology of China, Hefei 230026, China  Yang Liu
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  Francesco
Loparco  Istituto Nazionale di Fisica Nucleare, Sezione di Bari, via Orabona
4, I-70126 Bari, Italy  Dipartimento di Fisica M. Merlin, dell’Università e
del Politecnico di Bari, via Amendola 173, I-70126 Bari, Italy  ChuanNing Luo
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  School of
Astronomy and Space Science, University of Science and Technology of China,
Hefei 230026, China  Miao Ma  National Space Science Center, Chinese Academy
of Sciences, Nanertiao 1, Zhongguancun, Haidian district, Beijing 100190,
China  PengXiong Ma  Key Laboratory of Dark Matter and Space Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China  Tao
Ma  Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  XiaoYong Ma
National Space Science Center, Chinese Academy of Sciences, Nanertiao 1,
Zhongguancun, Haidian district, Beijing 100190, China  Giovanni Marsella  [
Dipartimento di Matematica e Fisica E. De Giorgi, Università del Salento,
I-73100, Lecce, Italy  Istituto Nazionale di Fisica Nucleare (INFN) - Sezione
di Lecce, I-73100, Lecce, Italy  Mario Nicola Mazziotta  Istituto Nazionale di
Fisica Nucleare, Sezione di Bari, via Orabona 4, I-70126 Bari, Italy  Dan Mo
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  XiaoYang Niu  Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  Xu Pan  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  School of Astronomy and Space Science, University of Science
and Technology of China, Hefei 230026, China  Andrea Parenti  Gran Sasso
Science Institute (GSSI), Via Iacobucci 2, I-67100 L Aquila, Italy  Istituto
Nazionale di Fisica Nucleare (INFN) - Laboratori Nazionali del Gran Sasso,
I-67100 Assergi, L Aquila, Italy  WenXi Peng  Particle Astrophysics Division,
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049,
China  XiaoYan Peng  Key Laboratory of Dark Matter and Space Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China
Chiara Perrina  [  Department of Nuclear and Particle Physics, University of
Geneva, CH-1211, Switzerland  Rui Qiao  Particle Astrophysics Division,
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049,
China  JiaNing Rao  National Space Science Center, Chinese Academy of
Sciences, Nanertiao 1, Zhongguancun, Haidian district, Beijing 100190, China
Arshia Ruina  Department of Nuclear and Particle Physics, University of
Geneva, CH-1211, Switzerland  MariaMunoz Salinas  Department of Nuclear and
Particle Physics, University of Geneva, CH-1211, Switzerland  Zhi Shangguan
National Space Science Center, Chinese Academy of Sciences, Nanertiao 1,
Zhongguancun, Haidian district, Beijing 100190, China  WeiHua Shen  National
Space Science Center, Chinese Academy of Sciences, Nanertiao 1, Zhongguancun,
Haidian district, Beijing 100190, China  ZhaoQiang Shen  Key Laboratory of
Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy
of Sciences, Nanjing 210023, China  ZhongTao Shen  State Key Laboratory of
Particle Detection and Electronics, University of Science and Technology of
China, Hefei 230026, China  Department of Modern Physics, University of
Science and Technology of China, Hefei 230026, China  Leandro Silveri  Gran
Sasso Science Institute (GSSI), Via Iacobucci 2, I-67100 L Aquila, Italy
Istituto Nazionale di Fisica Nucleare (INFN) - Laboratori Nazionali del Gran
Sasso, I-67100 Assergi, L Aquila, Italy  JingXing Song  National Space Science
Center, Chinese Academy of Sciences, Nanertiao 1, Zhongguancun, Haidian
district, Beijing 100190, China  Mikhail Stolpovskiy  Department of Nuclear
and Particle Physics, University of Geneva, CH-1211, Switzerland  Hong Su
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  Meng Su  Department of Physics and Laboratory for Space Research, the
University of Hong Kong, Pok Fu Lam, Hong Kong SAR, China  HaoRan Sun  State
Key Laboratory of Particle Detection and Electronics, University of Science
and Technology of China, Hefei 230026, China  Department of Modern Physics,
University of Science and Technology of China, Hefei 230026, China  ZhiYu Sun
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  Antonio Surdo  Istituto Nazionale di Fisica Nucleare (INFN) - Sezione
di Lecce, I-73100, Lecce, Italy  XueJian Teng  National Space Science Center,
Chinese Academy of Sciences, Nanertiao 1, Zhongguancun, Haidian district,
Beijing 100190, China  Andrii Tykhonov  Department of Nuclear and Particle
Physics, University of Geneva, CH-1211, Switzerland  JinZhou Wang  Particle
Astrophysics Division, Institute of High Energy Physics, Chinese Academy of
Sciences, Beijing 100049, China  LianGuo Wang  National Space Science Center,
Chinese Academy of Sciences, Nanertiao 1, Zhongguancun, Haidian district,
Beijing 100190, China  Shen Wang  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  ShuXin Wang  Key Laboratory of Dark Matter and Space Astronomy,
Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023,
China  School of Astronomy and Space Science, University of Science and
Technology of China, Hefei 230026, China  XiaoLian Wang  State Key Laboratory
of Particle Detection and Electronics, University of Science and Technology of
China, Hefei 230026, China  Department of Modern Physics, University of
Science and Technology of China, Hefei 230026, China  Ying Wang  State Key
Laboratory of Particle Detection and Electronics, University of Science and
Technology of China, Hefei 230026, China  Department of Modern Physics,
University of Science and Technology of China, Hefei 230026, China  YanFang
Wang  State Key Laboratory of Particle Detection and Electronics, University
of Science and Technology of China, Hefei 230026, China  Department of Modern
Physics, University of Science and Technology of China, Hefei 230026, China
YuanZhu Wang  Key Laboratory of Dark Matter and Space Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China
DaMing Wei  Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  School of
Astronomy and Space Science, University of Science and Technology of China,
Hefei 230026, China  JiaJu Wei  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  YiFeng Wei  State Key Laboratory of Particle Detection and
Electronics, University of Science and Technology of China, Hefei 230026,
China  Department of Modern Physics, University of Science and Technology of
China, Hefei 230026, China  Di Wu  Particle Astrophysics Division, Institute
of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
Jian Wu  Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  School of
Astronomy and Space Science, University of Science and Technology of China,
Hefei 230026, China  LiBo Wu  Gran Sasso Science Institute (GSSI), Via
Iacobucci 2, I-67100 L Aquila, Italy  Istituto Nazionale di Fisica Nucleare
(INFN) - Laboratori Nazionali del Gran Sasso, I-67100 Assergi, L Aquila, Italy
Sha Sha Wu  National Space Science Center, Chinese Academy of Sciences,
Nanertiao 1, Zhongguancun, Haidian district, Beijing 100190, China  Xin Wu
Department of Nuclear and Particle Physics, University of Geneva, CH-1211,
Switzerland  ZiQing Xia  Key Laboratory of Dark Matter and Space Astronomy,
Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023,
China  EnHeng Xu  State Key Laboratory of Particle Detection and Electronics,
University of Science and Technology of China, Hefei 230026, China  Department
of Modern Physics, University of Science and Technology of China, Hefei
230026, China  HaiTao Xu  National Space Science Center, Chinese Academy of
Sciences, Nanertiao 1, Zhongguancun, Haidian district, Beijing 100190, China
ZhiHui Xu  Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  School of
Astronomy and Space Science, University of Science and Technology of China,
Hefei 230026, China  ZunLei Xu  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  GuoFeng Xue  National Space Science Center, Chinese Academy of
Sciences, Nanertiao 1, Zhongguancun, Haidian district, Beijing 100190, China
ZiZong Xu  State Key Laboratory of Particle Detection and Electronics,
University of Science and Technology of China, Hefei 230026, China  Department
of Modern Physics, University of Science and Technology of China, Hefei
230026, China  HaiBo Yang  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  PengYang  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  YaQing Yang  Institute of
Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  Hui Jun
Yao  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  YuHong Yu  Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  GuanWen Yuan  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  School of Astronomy and Space Science, University of Science
and Technology of China, Hefei 230026, China  Qiang Yuan  Key Laboratory of
Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy
of Sciences, Nanjing 210023, China  School of Astronomy and Space Science,
University of Science and Technology of China, Hefei 230026, China  Chuan Yue
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  JingJing Zang
School of Physics and Electronic Engineering, Linyi University, Linyi 276000,
China.  Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  ShengXia
Zhang  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou
730000, China  WenZhang Zhang  National Space Science Center, Chinese Academy
of Sciences, Nanertiao 1, Zhongguancun, Haidian district, Beijing 100190,
China  Yan Zhang  Key Laboratory of Dark Matter and Space Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China  Yi
Zhang  Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, China  School of
Astronomy and Space Science, University of Science and Technology of China,
Hefei 230026, China  YongJie Zhang  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  YunLong Zhang  State Key
Laboratory of Particle Detection and Electronics, University of Science and
Technology of China, Hefei 230026, China  Department of Modern Physics,
University of Science and Technology of China, Hefei 230026, China  YaPeng
Zhang  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou
730000, China  YongQiang Zhang  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  ZhiYong Zhang  State Key Laboratory of Particle Detection and
Electronics, University of Science and Technology of China, Hefei 230026,
China  Department of Modern Physics, University of Science and Technology of
China, Hefei 230026, China  Zhe Zhang  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  Cong Zhao)  State Key Laboratory of Particle Detection and
Electronics, University of Science and Technology of China, Hefei 230026,
China  Department of Modern Physics, University of Science and Technology of
China, Hefei 230026, China  HongYun Zhao  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  XunFeng Zhao  National Space
Science Center, Chinese Academy of Sciences, Nanertiao 1, Zhongguancun,
Haidian district, Beijing 100190, China  ChangYi Zhou  National Space Science
Center, Chinese Academy of Sciences, Nanertiao 1, Zhongguancun, Haidian
district, Beijing 100190, China  Yan Zhu  National Space Science Center,
Chinese Academy of Sciences, Nanertiao 1, Zhongguancun, Haidian district,
Beijing 100190, China  Wei Chen  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  Li Feng  Key Laboratory of Dark Matter and Space Astronomy,
Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023,
China  Xi Luo  Shandong Institute of Advanced Technology, 250100 Jinan, China
ChengRui Zhu  Key Laboratory of Dark Matter and Space Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China

(Received June 1, 2019; Revised January 10, 2019)

###### Abstract

The Forbush Decrease (FD) represents the rapid decrease of the intensities of
charged particles accompanied with the coronal mass ejections (CMEs) or high-
speed streams from coronal holes. It has been mainly explored with ground-
based neutron monitors network which indirectly measure the integrated
intensities of all species of cosmic rays by counting secondary neutrons
produced from interaction between atmosphere atoms and cosmic rays. The space-
based experiments can resolve the species of particles but the energy ranges
are limited by the relative small acceptances except for the most abundant
particles like protons and helium. Therefore, the FD of cosmic ray electrons
and positrons have just been investigated by the PAMELA experiment in the low
energy range ($<5$ GeV) with limited statistics. In this paper, we study the
FD event occurred in September, 2017, with the electron and positron data
recorded by the Dark Matter Particle Explorer. The evolution of the FDs from 2
GeV to 20 GeV with a time resolution of 6 hours are given. We observe two
solar energetic particle events in the time profile of the intensity of cosmic
rays, the earlier and weak one has not been shown in the neutron monitor data.
Furthermore, both the amplitude and recovery time of fluxes of electrons and
positrons show clear energy-dependence, which is important in probing the
disturbances of the interplanetary environment by the coronal mass ejections.

Forbush effect, Cosmic rays, Solar coronal mass ejections

††journal: ApJL

Using natbib with AASTeX

Now at: ]Università di Sassari, Dipartimento di Chimica e Farmacia, I-07100,
Sassari, Italy

Now at: ]School of Physics and Optoelectronics Engineering, Anhui University,
Hefei 230601, China

Now at: ]Dipartimento di Fisica e Chimica “E. Segrè”, Università degli Studi
di Palermo, via delle Scienze ed. 17, I-90128 Palermo, Italy.

Also at: ]Institute of Physics, Ecole Polytechnique Federale de Lausanne
(EPFL), CH-1015 Lausanne, Switzerland.

##  1 Introduction

Charged solar wind particles and the associated magnetic fields affect the
transportation of Galactic cosmic rays (GCRs) in the solar system. Violent
solar activities like coronal mass ejections (CMEs) generate high-intensity
particle flows moving at super-Aflven speed, which enhance the local
interplanetary magnetic field significantly. Such temporarily enhanced
magnetic fields would block the propagation of GCRs, what contributes to sharp
decreases of the GCRs fluxes, known as Forbush decreases (FDs; Forbush, 1937;
Hess & Demmelmair, 1937). The Forbush decrease is a universal phenomenon
within the heliosphere, which was also observed at other planets, e.g., the
Mars (Guo et al., 2018) and the interplanetary space far away from the Sun
(e.g., by Voyager 2 (Burlaga, 2015)).

Precise measurements of FDs will enable us to diagnose the propagation of GCRs
and their interplay with complex environment in the heliosphere. FDs of GCRs
have been extensively measured for decades with worldwide ground-based neutron
monitors (NMs) located at regions with different geomagnetic cutoff
rigidities. Compared with direct detection experiments, the NMs can only
reflect an integral variation of the incident particle intensities, with much
information of the compositions and precise energy-dependencies losing. In the
1960s, some balloon experiments (Peter Meyer, Rochus Vogt, 1961) measured FDs
of electrons and protons at MeV energies. However, the relatively poor energy
resolution, bad particle identification, and limited statistics hindered a
good understanding of FDs of various particle species. Recently, the PAMELA
experiment simultaneously measured FDs of protons, helium nuclei, and
electrons for the first time, and found important differences of the
properties of different particle species (Munini et al., 2018). Specifically,
the recovery time for electrons is faster than that for protons and helium
nuclei, which may be interpreted as a charge-sign-dependent drift pattern
between electrons and nuclei (Munini et al., 2018). However, due to its
relatively small geometry factor, the data statistics is limited (particularly
for electrons), and the energy-dependence of the FD characteristics remains
somehow ambiguous.

The Dark Matter Particle Explorer (DAMPE) is a space-borne detector for
observations of cosmic ray electrons and positrons (CREs), nuclei, and
$\gamma$-ray photons (Chang et al., 2017; DAMPE Collaboration et al., 2017; An
et al., 2019). The DAMPE is optimized for high-energy-resolution measurements
of CREs. Compared with other particle detectors in orbit, the DAMPE has two
unique advantages in the measurements of time-variations of CREs fluxes, 1)
the inclination angle of the orbit is 97 degrees (Chang et al., 2017), and
thus DAMPE can reach the Earth’s polar regions where GCRs are weakly affected
by the geomagnetic rigidity cutoff, and 2) the relatively large effective
geometry acceptance ($\sim 0.35$ m2sr) enables a more detailed study of the
fine time structures of FDs. Benefited from these two facts, in this work we
present the observations of FDs of CREs by DAMPE with unprecedented accuracy
and give solid evidence of energy-dependences for both the FD amplitude and
the recovery time.

This paper mainly focuses on a strong FD event occurred in September, 2017
when two shock-associated interplanetary coronal mass ejections (ICMEs) and a
ground level enhancement (GLE) were also detected by on-ground NMs. The solar
flares in September 2017 are very famous events. Based on the NM data,
Badruddin et al. (2019) presented 3-4 hours time-lagged correlation between
cosmic ray intensities and the geomagnetic activity indices. Hubert et al.
(2019) presented cosmic ray-induced neutron spectra during active solar event
leading to changes in the local cosmic ray spectrum (Forbush decreases and a
GLE). Meanwhile, by calculating the GCR spectral index of FDs, several
theoretical yield functions were verified in Livada & Mavromichalaki (2020)
and references therein. Chertok et al. (2018) analyzed space weather
disturbance and successfully estimated the scale of FD and geomagnetic storm.

##  2 DAMPE detector

The DAMPE satellite operates in a sun-synchronous orbit at 500 km altitude
with a period of 5673 seconds and an incline angle of 97 degrees that enables
the satellite to travel the area from 83 degrees north to 83 degrees south.
The detector system consists of four sub-detectors (Chang et al., 2017). At
the top is a plastic scintillator array detector (PSD) which measures the
ionization energy loss of charged particles and also acts as an anti-
coincidence veto detector for identification of photon candidates (Yu et al.,
2017). The instrument mounted below PSD is a silicon tungsten tracker (STK)
equipping with 12 layers of $121~{}\mu$m wide silicon strip sensors (Azzarello
et al., 2016). STK is designed to measure the trajectory and charge of a
charged particle and to convert $\gamma$-rays into $e^{+}e^{-}$ pairs. The
core detector of DAMPE is a Bismuth Germanate (BGO) calorimeter which has 32
radiation lengths thickness of BGO crystals, and is to measure the energy and
direction of a particle, to distinguish hadronic and electromagnetic particle
species, and also to provide the trigger for the Data Acquisition (DAQ) system
(Zhang et al., 2015). The dense and thick materials of the BGO provides an
excellent energy resolution for CREs, which is about 5% (2%) at $\sim 2$ (20)
GeV (Zhang et al., 2016). At the bottom is a neutron detector (NUD) which is
used to improve the capability of hadron-nuclei separation, since much more
neutrons are generated in hadronic shower. The on-orbit performance of each
sub-detector can be found elsewhere (Tykhonov et al., 2018; Ambrosi et al.,
2019; Ma et al., 2019; Tykhonov et al., 2019; Huang et al., 2020).

##  3 Data Analysis

We describe the time variation of the GCRs due to the CME event at two levels,
the counting rate from the T0 counts (a category of data acquisition trigger
with very loose threshold, see below for details) and the absolute fluxes of
CREs. The T0 counting rate measures the overall intensity of all species of
GCRs above 100MeV with averaged 48 minutes(half orbit period) time resolution,
that enabled DAMPE to discover fine structures of time profile of GCRs
intensity. Meanwhile, the absolute fluxes variations of CREs in dozens energy
intervals are simultaneously measured for the purpose of investigating the
energy dependence of the characteristics of FDs.

###  3.1 T0 counting rate

Figure 1: The 5-min averaged time profiles of the solar wind speed (panel
(a)), the standard deviation of the IMF vector (panel (b)), the averaged
strength of the IMF at 1 AU (panel (c)). Data in panel(a)(b)(c) are all from
the OMNI database(https://omniweb.gsfc.nasa.gov/form/omni_min.html). Panel(d)
shows the 47-min averaged temporal variation of T0 counting rate of DAMPE for
$4.76<L<5.57$ (Rate is normalized to averaged value in August 2017). Also
shown in the panel (d) is the OULU NM 10-min averaged relative counting rate
with respect to averaged value in August 2017 (data from
http://www01.nmdb.eu/nest/). The two vertical red lines indicate the arrival
times of the interplanetary shocks.

During the on-orbit operation of DAMPE, the housekeeping system records GCRs
trigger counts every 4 seconds (named T0 trigger count) for the purpose of
monitoring the health of detectors. T0 is a low threshold hit signal acting as
the timing reference to decide to start an event data taking. Based on Geant4
simulation, GCRs with kinematic energy above 100MeV can satisfy the T0 trigger
logic. Due to T0 does not record information of particle species, its counting
rate only reflects the overall intensity of all kinds of GCRs above 100MeV. On
DAMPE’s orbit, the T0 counting rate changes from several hundred Hz near the
equator to several thousand Hz at poles. We would like to compare the DAMPE T0
counting rate with the NM data. Since the NMs are fixed on the surface of the
Earth, and DAMPE keeps moving along its orbit, we select the T0 counting rate
in a narrow region with specific MacIlwain L-parameter values (Walt, 2005) in
there geomagnetic cutoff rigidity is assumed to be a constant. For the OULU NM
we adopt in the comparison, we find that for $4.76<L<5.57$ the averaged cutoff
rigidity is $R_{c}\approx 0.81$ GV which is similar with that of the OULU
station. The panel (d) of Figure 1 shows the time evolutions (normalized to
the average values in August, 2017) of the DAMPE T0 rate (red) and the OULU NM
rate (blue) in September, 2017. A 27 days long-term shallow change of the T0
rate has been subtracted through dividing the rate by a smooth polynomial
fitting form to the T0 counts from August 23 to September 24 after abandoning
the FD time range. Also shown in Figure 1 are 5-min averaged time profiles of
the solar wind speed (panel (a)), the standard deviation of the interplanetary
magnetic field (IMF) vector (panel (b)), and the average strength of the IMF
(panel (c)). Two vertical lines label the arrival times111Data from the CfA
Interplanetary Shock Database: www.caf.harvard.edu of two interplanetary
shocks, at 23:02 UT, September 6, 2017 and 22:28 UT, September 7, 2018.

From the T0 counting rate, we can clearly identify two solar energetic
particle (SEP) events. The first one with smaller amplitude reached the Earth
$10-11$ hours before the interplanetary shock wave and lasted for about 20
hours. However, the NM data (from OULU and others) did not show such a rising
for this event (see panel (d) of Figure 1). The reason of the difference
between NMs and the direct measurements is unclear yet. To a certain extent,
DAMPE is not blocked by the atmosphere and is more sensitive to low-energy
particles than NM stations. The other possible reason is the anisotropy of
SEPs which may lead to missing of the detection by NMs. We also investigate
the time profiles of the T0 counts at high latitudes (with $L>4.11$) in both
southern and northern hemispheres, and such intensity enhancements are both
observed. About 89 hours after the arrival of the second shock (during the
recovery phase of the FD), the T0 counting rate further shows a sudden and big
jump (increased by 2 orders of magnitude), which indicates the arrival of the
second SEP event. At that moment the OULU NM also observed a GLE event with
several percents increase of the counting rate. The big difference of the SEP
amplitudes between DAMPE and OULU is again a reflection that NMs are only
sensitive to high enough energy particles.

During SEPs passbying the Earth (UT 0906-23:02 to 0910-16:03) the fluxes of
energetic particles are so high that the detector cannot operate in the normal
status any more with significant and random shifts of the pedestals of the
electronics. Thus the science data taken in this period has been excluded in
the current analysis.

###  3.2 CRE fluxes

For the purpose of this study, about 60 days of the DAMPE data, in total 300
million events, recorded in August and September 2017 are analyzed. To make
sure the detector operates with good condition, the data recorded when DAMPE
passes through the South Atlantic Anomaly (SAA) region are excluded.

We apply a series of selection criteria to filter a clean sample of CREs. The
purpose is to suppress the background cosmic rays as much as possible while
keeping a sufficiently high CRE efficiency. The first step of the pre-
selections is to require that the BGO bar with the maximum deposited energy in
each layer is not at the edge of the BGO calorimeter, which can make sure that
most of the shower energies are recorded by the calorimeter and a good energy
resolution is guaranteed. Then a very similar track selection and evaluation
strategy as described in Xu et al. (2018) is adopted to identify the tracks of
events. Specifically, the STK track should be a long track crossing all layers
of STK and matches the BGO track, and the CRE should deposit most energy
within a 5mm cylinder around the track. Once the track is determined, the
charge of the particle can be obtained via the charge reconstruction algorithm
(Dong et al., 2019). Here we require that the charge number measured by PSD
should be less than 1.7, which can reject $Z\geq 2$ nuclei up to a level of
$99\%$. Finally, to eliminate secondary particles generated in the atmosphere,
the minimum energy at each geomagnetic latitude is required to exceed 1.2
times of the vertical rigidity cutoff (VRC; Smart & Shea, 2005).

The pre-selections can already strongly exclude heavy nuclei from the sample.
However, there is still heavy contamination from protons and also helium
nuclei. Based on the shower development in the calorimeter, a particle
identification (PID) variable is constructed.

${\rm PID}=F(E)[\log({\rm RMS}_{r})\sin\theta+\log({\rm RMS}_{l})\cos\theta]$

where, $F(E)$ is energy decoupling polynomial, $\theta$ is coordinate rotation
angle, ${\rm RMS}_{r}$ and ${\rm RMS}_{l}$ are functions describing radial
shower shape and longitudinal shower shape respectively.

The background contamination can then be estimated through a fitting with
Monte Carlo (MC) templates in each energy bin, as illustrated in Figure 2. The
background contamination is estimated to be $2\%\sim 8\%$ for events with
deposited energies between 2 GeV and 20 GeV. Below 2 GeV, the granularity of
the calorimeter does not allow us to efficiently identify CREs from nuclei.
Since the low energy particles are modulated by solar winds, their fluxes show
slight and continuous variations with time. We thus estimate the background in
each time bin. It is found that the hadronic background varies by $\sim 6\%$
at 2 GeV and $\sim 1\%$ at 20 GeV. After the pre-selections and the PID
procedure, the CRE candidate events are divided into 25 logarithmically even
energy bins from 2 GeV to 20 GeV and 240 time bins (6 hours each). The
statistical errors in two-dimensional bins are about $2\%$ at 5 GeV and $\sim
8\%$ at 20 GeV.

Figure 2: Distributions of the PID variable for deposited energy bin $4.83$
GeV$<E<5.25$ GeV. The best-fit MC templates are also shown for comparison.
Setting the PID selection value of $<2$ results in a background contamination
of $\sim 8\%$.

Due to the shielding effect of the geomagnetic field, primary GCRs can only be
detected when their rigidities are larger than the cutoff rigidity. A
threshold of $1.2\times$VRC is adopted to minimize such an effect. Since the
VRC varies with locations of the detector, the effective exposure time thus
changes with particle rigidity/energy. In each energy bin and time bin, the
exposure time is calculated via summarizing the time when the satellite
travels in the regions with VRC values smaller than 1/1.2 of the lower edge of
the energy bin, with an additional subtraction of the dead time of the DAQ
system and the time when DAMPE passes through the SAA region or under the
calibration operations. On average the effective exposure time is about $80\%$
of the total time for energies above 15 GeV, which gradually decreases to
$\sim 30\%$ at 2 GeV.

The CRE flux in the $i$th energy bin and $j$th time bin can be calculated as

$\Phi_{i,j}=\frac{N_{i,j}(1-f_{i,j})}{A_{i}\eta_{i,j}\Delta T_{j}\Delta
E_{i}},$ (1)

where $N_{i,j}$, $f_{i,j}$, and $\eta_{i,j}$ represent the number of CRE
candidates, the fraction of the background contamination, and the trigger
efficiency, $A_{i}$ is the effective acceptance of the detector, $\Delta
T_{j}$ is the live time, and $\Delta E_{i}$ is the width of the energy bin. In
this analysis we focus on the relative fluxes of CREs in a time scale of two
months, and therefore the absolute efficiences are not crucial.

The dominating systematic uncertainty of the relative flux ratio measurements
comes from the stability of efficiencies. An extensive study of the efficiency
variations have been performed in this analysis. As shown in Ambrosi et al.
(2019), the major calibration parameters, including the pedestals, dynode
ratios, electronics gains, MIP energies etc., are very stable after the
temperature correction (with variations $<1.5$% per year). Therefore the
detection efficiency change within one month is expected to be very small
($0.13\%$). On the other hand, due to the radiation damage and electronics
aging, the light yields of the BGO crystals and the gains of photomultipliers
are found to slightly decrease over time. Their impacts on the trigger
threshold of each BGO crystal are carefully calibrated, which show a decrease
of $\sim 1.25\%$ per year. We further investigate the impact of the trigger
efficiency from the potential bias of the energy scale through applying a
series of bias factors from $-5\%$ to $+5\%$ with a step of $1\%$ in the MC
simulation, and find that the change of trigger efficiency within 1 month is
also small ($0.5\%@2GeV,0.01\%@20GeV$). The other efficiency is the track
efficiency of the STK. Since we employ track selection at different moments of
2017, we estimate the corresponding stability of the tracking, using proton
flight data samples. Our results confirm the high stability of the tracking
efficiency, with the overall variations throughout the data taking period less
than $0.2\%$ per year.

In summary, the total systematic uncertainty of the relative detection and
selection efficiencies is about $0.53\%$, which is much smaller than the
statistical errors ($2\%\sim 8\%$).

##  4 Time Profiles of CRE fluxes

We calculate the CRE fluxes with a time bin width of 6 hours (about 4 orbits
for DAMPE). The flux of each bin is normalized to the average flux of August,
2017. The time profiles of 4 selected energy bins are shown in Figure 3. As we
have discussed in Sec. 3.1, the data from 18:00UT of September 9 to 12:00UT of
September 11 have been eliminated due to the strong impact from the energetic
particles from the SEP. The relative intensities averaged over 10 minutes from
the OULU NM222http://www01.nmdb.eu/nest/ are also plotted in Figure 3.

Figure 3: Time profiles of CRE fluxes in four energy bins from 00:00 UT of
September 1 to 00:00 UT of October 1, 2017. The error bars are summation of
statistical errors and systematic errors. In each plot, the T0 counting rates
for $4.76<L<5.57$ are shown in red and the OULU NM intensities are in blue.

Compared with the T0 rates, we do not find significant increase in the CRE
fluxes during first SEP event. One possible reason is that the data statistics
is limited, and the population of SEP above GeVs is not significant. The NM
data do not show the SEP event either. The physical interpretation of such
differences may need further studies.

Similar with the PAMELA experiment (Munini et al., 2018) we use the following
function

$\frac{\Phi(t)}{\Phi_{\rm
ref}}=1-A_{e}\exp\left(-\frac{t-t_{0}}{\tau}\right),$ (2)

to describe the amplitude and recovery behavior after the CRE fluxes reach the
valley. In the above equation, $\Phi_{\rm ref}$ is the reference flux of
August, 2017, $A_{e}$, $\tau$, and $t_{0}$ represent the decrease amplitude,
recovery time, and time of the minimum flux (or the start of recovery phase),
respectively. For this event, $t_{0}$ is fixed to be 13:30 UT of September 8,
2017. $A_{e}$ and $\tau$ parameters are fitted for each energy bin. The
fitting results of the 25 energy bins of $A_{e}$ and $\tau$ are shown in
Figure 4. Both $A_{e}$ and $\tau$ clearly show decreases with energy. An
exponential decay function, $p_{0}\exp(-E/p_{1})$, is adopted to fit the
energy-dependences of $A_{e}$ and $\tau$, resulting in $\chi^{2}/{\rm
ndf}=21.45/25$ and $\chi^{2}/{\rm ndf}=34.42/25$, respectively.

The amplitude can be well described by the exponential function. The fact that
the FD amplitudes become smaller for higher energies can be easily understood
as that high energy particles are less affected by the perturbed interstellar
environment by the CME. Consequently, the energy spectra should also vary with
time when an FD occurs (Belov et al., 2021), which are expected to be harder
during the FD. A single power-law fit to the energy spectrum between 4 and 20
GeV shows that the spectral index is about $2.85$ before the FD, $\sim 2.70$
when the fluxes reach the minimum, and becomes $2.85$ after the FD. The
energy-dependence of the recovery time is, however, more complicated than the
amplitude. It is interesting to compare the results obtained in this study
with that by PAMELA. In Munini et al. (2018), the PAMELA experiment gave the
energy-dependences of the recovery time for electrons, protons, and helium
nuclei, for rigidities from 0.6 GV to 10 GV. The qualitative behaviors of
recovery time for these three types of particles are similar, all show an
increase from 0.6 GV to 5 GV, although the specific values for electrons are
different from that for nuclei. At higher energies, the recovery time for
protons and helium nuclei decreases again. Due to the limited statistics, the
decreasing behavior of the electron recovery time has not been observed. The
DAMPE result shows clearly the decreasing behavior for the CRE recovery time
above 2 GeV, which may indicate that the peaks of the recovery time for all
particles are few GeV. We can further see from Figure 4 that at high energies,
the recovery time tends to be a constant rather than keeping on decreasing.
The recovery time for protons by PAMELA may also show such a flattening at
high energies (Munini et al., 2018). But the errors, both for PAMELA protons
and DAMPE CREs, are too large to clearly address this phenomenon.

Figure 4: The decease amplitude (panel (a)) and recovery time (panel (a))
versus energy. Red solid lines show the best-fits with an exponential function
$p_{0}\exp(-E/p_{1})$.

The ground NMs can also measure the energy-dependences of the FDs, although
the energy resolution is relatively poor and the energy threshold is
relatively high. As illustrated in Zhao & Zhang (2016), there are two types of
energy-dependences of the recovery time, one depends strongly on energies and
the other remains almost independent of energies. It has been conjected that
the orientations and topologies of the CMEs may result in such differences
(Zhao & Zhang, 2016). However, a reliable energy determination of the NMs is
difficult. For specific NM station, a typical median energy $E_{M}$ is defined
as the value below which cosmic rays contribute to one half of the counting
rate. The median energy can be estimated as a function of cutoff rigidity
$R_{c}$ as $E_{M}=0.0877R^{2}_{c}+0.154R_{c}+10.12$, where $E_{M}$ and $R_{c}$
are in units of GeV and GV (Jämsén et al., 2007). The median energy is $\sim
10$ GeV at the polar region and $\sim 20$ GeV at the equator. The full
behaviors of the recovery time in a wide energy range, especially for lower
energies, are thus difficult to be revealed by the NMs. The energy-dependence
or independence of the recovery time shown by NMs may be only a part of the
full energy-dependence. For the event we discuss here, the CME travels towards
the Earth. It should correspond to the Event 2 of Zhao & Zhang (2016), and the
recovery time is expected to be a constant. Our results do not support such an
expectation in general. However, the constant behavior may just be the
reflection of the flattening above $\sim 10$ GeV as shown in Figure 4. A more
complete modeling of the recovery time versus energies is necessary.

##  5 Modeling of the CRE FDs

The Parker’s equation has been widely employed to describe the transport of
charged particles in the heliosphere (Parker, 1965). When the heliosphere has
been disturbed by CMEs and the associated shocks, FDs of GCR fluxes can occur.
This process can be modelled using the diffusion barrier model, which employs
a moving diffusion barrier with different diffusion and drift parameters from
those in the interplanetary space (Luo et al., 2018). The Parker’s transport
equation together with the diffusion barrier can be solved with the stochastic
differential equation method (Zhang, 1999; Strauss et al., 2011). We describe
the method of the modeling of FDs in detail in the Appendix.

Given proper parameters of the model, the FD behaviors of the DAMPE data can
be reproduced, as shown in Figure 5 for selected energy bands. We further
derive the recovery time at different energies using Eq.(2), and give the
results in Figure 6. We can see that the model prediction is in good agreement
with the data in the energy range of $2-20$ GeV. However, this model may not
explain precisely the detailed behaviors of the data at higher or lower
energies. The possible flattening at high energies, although higher precision
of the measurements is required to reach a conclusion, is not obvious in the
modeling. Also the model predicts longer recovery time at lower energies,
which may not explain the turnover at few GeV as indicated by the PAMELA and
DAMPE data. Further refinement or modification of the FD modeling is thus
necessary to fully account for the data.

Figure 5: Variations of the relative CRE fluxes from the DAMPE observations
(bars) and the FD model (lines). For visualization the results for different
energies are shifted downwards gradually with respect to the top one in each
panel. Figure 6: The recovery time of the model prediction compared with the
DAMPE data.

##  6 Conclusion

In this work we give a detailed study of the FDs of CREs associated with the
CME occurred in September, 2017 by the DAMPE detector. A weak SEP event has
been revealed through the T0 counting rate, while no unambiguous signal is
shown by on-ground NMs. Meanwhile the high-precision time evolutions of CRE
fluxes with a 6-hour time resolution have been obtained simultaneously. We
study the energy-dependences of the FD amplitudes and the recovery time, and
find that both decrease with energies. Together with the results of different
particle species measured by PAMELA, it may show that the recovery time of all
species of particles show an increase below a few GeV and a decrease at higher
energies. For energies above $\sim 10$ GeV, the recovery time may become
constant, which nevertheless requires more statistics to draw a firm
conclusion. These results would give very important implications in modeling
the propagation of GCRs in the heliosphere when there are disturbances from
CMEs.

This study also illustrates the importance of direct measurements of FDs of
various GCR species. Compared with the usually employed NM data, the direct
measurements have the advantages of excellent particle identification, very
good energy resolution, and much wider energy range coverage. More comparative
studies of various FD events for different particle species by DAMPE in future
are expected to further shed light on the understanding of the physics of
particle transportation in the interplanetary environment.

## Acknowledgments

The DAMPE mission is funded by the strategic priority science and technology
projects in space science of Chinese Academy of Sciences. In China the data
analysis is supported by the National Key Research and Development Program of
China (No. 2016YFA0400200), the National Natural Science Foundation of China
(Nos. 11773085, U1738207, 11722328, 41774185, U1738205, U1738128, 11851305,
11873021, U1631242), the strategic priority science and technology projects of
Chinese Academy of Sciences (No. XDA15051100), the 100 Talents Program of
Chinese Academy of Sciences, the Young Elite Scientists Sponsorship Program by
CAST (No. YESS20160196), and the Program for Innovative Talents and
Entrepreneur in Jiangsu. In Europe the activities and the data analysis are
supported by the Swiss National Science Foundation (SNSF), Switzerland; the
National Institute for Nuclear Physics (INFN), Italy.

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##  Appendix A The Parker’s transport equation

The Parker’s transport equation is written as (Parker, 1965)

$\displaystyle\frac{\partial f}{\partial t}$ $\displaystyle=$
$\displaystyle-~{}\left(\vec{V}_{\rm
sw}+\left\langle\vec{v}_{d}\right\rangle\right)\cdot\nabla f$ $\displaystyle+$
$\displaystyle\nabla\cdot\left(K^{(s)}\cdot\nabla f\right)$ $\displaystyle+$
$\displaystyle~{}\frac{1}{3}\left(\nabla\cdot\vec{V}_{\rm
sw}\right)\frac{\partial f}{\partial\ln p},$ (A2)

where $f(\vec{r},p,t)$ is the particle distribution function, $p$ is the
momentum, $\vec{V}_{\rm sw}$ is the latitude-dependent solar wind speed
(Potgieter et al., 2015; Luo et al., 2019),
$\left\langle\vec{v}_{d}\right\rangle$ is the pitch-angle averaged drift
velocity (Jokipii et al., 1977; Burger & Potgieter, 1989; Forman et al., 1974;
Engelbrecht & Burger, 2015) with the following form:

$\left\langle\vec{v}_{d}\right\rangle=\frac{pv}{3q}\nabla\times\frac{\vec{B}}{B^{2}},$
(A3)

where $q$ and $v$ are the charge and velocity of the GCR particle, and
$\vec{B}$ is the magnetic field inside the heliosphere. The last term of
Eq.(A) is the adiabatic energy loss. $K^{(s)}$ is the symmetric diffusion
tensor, given in the IMF aligned coordinates by

$K^{(s)}=\left(\begin{array}[]{ccc}\kappa_{\parallel}&0&0\\\
0&\kappa_{\perp\theta}&0\\\ 0&0&\kappa_{\perp r}\\\ \end{array}\right),$ (A4)

where $\kappa_{\parallel}$ is the parallel diffusion coefficient, and
$\kappa_{\perp r}$, $\kappa_{\perp\theta}$ are two perpendicular diffusion
coefficients in the radial and latitudinal directions. In our simulation, the
diffusion coefficients are expressed as (Luo et al., 2019)

$\displaystyle\kappa_{\parallel}=\kappa_{\parallel
0}\beta\frac{B_{0}}{B}\left(\frac{P}{P_{k}}\right)^{a}\left[1+\left(\frac{P}{P_{k}}\right)^{\frac{b-a}{c}}\right]^{c},$
(A5) $\displaystyle\kappa_{\perp r,\perp\theta}=(\kappa_{\perp r0,\perp\theta
0})\beta\frac{B_{0}}{B}\left(\frac{P}{P_{k}}\right)^{a}\left[1+\left(\frac{P}{P_{k}}\right)^{\frac{b-a}{c}}\right]^{c}.$
(A6)

Here, $\beta$ is the particle velocity in unit of the light speed, $B$ is the
magnitude of the local IMF with $B_{0}=1$ nT, $P$ is the rigidity,
$\kappa_{\parallel 0}$, $\kappa_{\perp r0}$, and $\kappa_{\perp\theta 0}$ are
constants, $P_{k}$, $a$, $b$, $c$ are free parameters which define the
rigidity dependence of these diffusion coefficients.

We use the standard Parker field to describe the IMF (Parker, 1958):

$\vec{B}(r,\theta)=\frac{AB_{\oplus}}{r^{2}}\left(\boldsymbol{e_{r}}-\frac{r\Omega\sin\theta}{V_{\rm
sm}}\boldsymbol{e_{\theta}}\right)\left[1-2H(\theta-\theta_{\rm cs})\right],$
(A7)

where $B_{\oplus}$ is the reference value at the earth position which we take
as the mean value of the last 13 months before the solar flare event, $A=\pm
1/{\sqrt{\left(1+\frac{\Omega^{2}}{\vec{V}_{\rm sw}^{2}}\right)}}$ with the
sign determining the polarity of the IMF, $\Omega$ is the angular velocity of
the Sun, $H(\theta-\theta_{\rm cs})$ is the Heaviside function and
$\theta_{\rm cs}$ determines the polar extent of the Heliospheric Current
Sheet (HCS). We model the HCS by the following analytical expression (Kota J,
Jokipii JR, 1983),

$\cot\theta_{\rm cs}=-\tan\alpha~{}\sin\phi^{*}.$ (A8)

Here, $\alpha$ is the HCS tilt angle which we also adopt as the mean value of
the last 13 months, $\phi^{*}=\phi+\frac{r\Omega}{V_{\rm sw}}$ with $\phi$
being the longitude angle of the current sheet surface. We do not consider the
phase of the co-rotating HCS.

The the magnitude of drift in the HCS can be specified as (Burger & Potgieter,
1989)

$v_{\rm HCS}=\frac{v}{6}\times\frac{4R_{g}}{r}\delta(\theta-\theta_{\rm cs}),$
(A9)

where $R_{g}$ is the gyroradius of the GCR particle and $v$ is the particle’s
speed. Following Luo et al. (2013) and Luo et al. (2017), we replace
$\delta(\theta-\theta_{\rm cs})$ with $r/(4R_{g})$ within the distance of
$(-2R_{g},2R_{g})$ to the HCS. By defining $\psi$ as the angle between the
local current sheet normal direction $\boldsymbol{n}$ and the
$-\boldsymbol{e_{\theta}}$ direction, the drift vector of the current sheet
can be written as

$\vec{V}_{\rm
cs}=\frac{v}{6}\left(\boldsymbol{e_{r}}\sin{\Phi}\cos\psi+\boldsymbol{e_{\theta}}\sin\psi+\boldsymbol{e_{\phi}}\cos\Phi\cos\psi\right),$
(A10)

with $\Phi$ being the IMF winding (spiral) angle.

##  Appendix B The diffusion barrier model

In our model, we use a 3D geometry profile to describe the propagating
diffusion barrier. The diffusion and drift coefficients inside the barrier are
expressed as

$\kappa^{\prime}_{\parallel,\perp,T}=\frac{\kappa_{\parallel,\perp,T}}{1+\rho
h(\theta)f(r)g(\phi)}.$ (B1)

In the above equation, $\kappa^{\prime}_{\parallel,\perp}$
($\kappa^{\prime}_{T}$) are the diffusion (drift) coefficients inside the
barrier, $\rho$ is a constant determining the reduction level of the diffusion
and drift coefficients, $h(\theta)$, $g(\phi)$, and $f(r)$ describe the
geometry of the diffusion barrier

$\displaystyle h(\theta)$ $\displaystyle=$ $\displaystyle
e^{-\left(\frac{\theta-\theta_{0}}{\theta_{\rm br}}\right)^{10}},$ (B2)
$\displaystyle g(\phi)$ $\displaystyle=$ $\displaystyle
e^{-\left(\frac{\phi}{\phi_{\rm br}}\right)^{10}},$ (B3) $\displaystyle f(r)$
$\displaystyle=$ $\displaystyle\left\\{\begin{array}[]{lc}1-\frac{r-r_{\rm
cen}}{r_{\rm a}},&r_{\rm cen}<r<r_{\rm sh}\\\ \frac{r-r_{\rm end}}{r_{\rm
b}},&r_{\rm end}<r\leq r_{\rm cen}\\\ 0,&{\rm otherwise}\end{array}\right..$
(B7)

Here, $\theta_{0}=\pi/2$ means that diffusion barrier hits the earth head on,
the parameters $\theta_{\rm br}$ and $\phi_{\rm br}$ denote the extensions of
the diffusion barrier along the $\boldsymbol{e_{\theta}}$ and
$\boldsymbol{e_{\phi}}$ directions, $r_{\rm sh}$, $r_{\rm cen}$, and $r_{\rm
end}$ are the radial distances of the front, center, and end locations of the
barrier, $r_{\rm a}=r_{\rm sh}-r_{\rm cen}$, $r_{\rm b}=r_{\rm cen}-r_{\rm
end}$ are widths of the leading and trailing paths of the barrier. In our
model, we assume $r_{\rm a}=0.5$ AU, $r_{\rm b}=0.3$ AU, $\theta_{\rm
br}=60^{\circ}$, $\phi_{\rm br}=180^{\circ}$. The velocity of the diffusion
barrier is adopted to be 1500 km/s, as given in the CME
list333https://cdaw.gsfc.nasa.gov/CME_list/.

##  Appendix C The stochastic differential equation method

Based on the Ito’s formula, the Parker’s equation can be solved numerically
with the stochastic differential equation (SDE) technique (Zhang, 1999;
Strauss et al., 2011), with

$\displaystyle d\vec{X}=\left(\nabla\cdot K^{(s)}-\vec{V_{\rm
sw}}-\left\langle\vec{v}_{d}\right\rangle\right)ds+\sum^{3}_{\sigma=1}\vec{\alpha}_{\sigma}dW_{\sigma}(s),$
(C1) $\displaystyle dp=\frac{p}{3}(\nabla\cdot\vec{V}_{\rm sw}\,ds),$ (C2)

where $dW_{\sigma}(s)$ is the Wiener process, which can be numerically
generated by the Gaussian random number, and
$\sum_{\sigma}{\alpha}_{\sigma}^{\mu}\alpha_{\sigma}^{\nu}=2\kappa^{\mu\nu}$.
The SDE method gives the time-dependent solution of Eq. (A) as (Zhang, 1999;
Luo et al., 2019)

$f(t,\vec{X},p)=\left\langle
f_{b}^{i}(t-\chi_{i},\vec{X}_{i},p_{i})\right\rangle.$ (C3)

$\left\langle f_{b}^{i}(t-\chi_{i},\vec{X}_{i},p_{i})\right\rangle$ is the
mean value for the pseudo-particles reaching the boundary
$(\vec{X}_{i},p_{i})$ at the first exit time $\chi_{i}$. In our calculation,
the local interstellar spectrum of electrons are adopted from Zhu et al.
(2021). The small fraction of positrons has been neglected.