murrae-mail<EMAIL_ADDRESS>schultee-mail: DennySchulte@uni-
muenster.de murra2New address: Physics Department, Columbia University, New
York, USA

11institutetext: Institut für Kernphysik, Westfälische Wilhelms-Universität
Münster, Münster, Germany

# Design, construction and commissioning of a high-flow radon removal system
for XENONnT

M. Murramunster, murra,murra2  D. Schultemunster, schulte  C. Huhmannmunster
C. Weinheimermunster

###### Abstract

A high-flow radon removal system based on cryogenic distillation was developed
and constructed to reduce radon-induced backgrounds in liquid xenon detectors
for rare event searches such as XENONnT. A continuous purification of the
XENONnT liquid xenon inventory of
$8.4\text{\,}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{s}$ at
process flows up to 71 kg/h (200 slpm) is required to achieve a radon
reduction by a factor two for radon sources inside the detector. To reach such
high flows, the distillation column’s design features liquid xenon inlet and
outlets along with novel custom-made bath-type heat exchangers with high
liquefaction capabilities. The distillation process was designed using a
modification of the McCabe-Thiele approach without a bottom product
extraction. The thermodynamic concept is based on a Clausius-Rankine cooling
cycle with phase-changing medium, in this case the xenon itself. To
drastically reduce the external cooling power requirements, an energy
efficient heat pump concept was developed applying a custom-made four cylinder
magnetically-coupled piston pump as compressor. The distillation system was
operated at thermodynamically stable conditions at a process flow of $91\pm
2.\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$ (($258\pm 6$) slpm), 30%
over design. With this flow, a [222]Rn activity concentration $<1\,\upmu$Bq/kg
is expected inside the XENONnT detector given the measured radon source
distribution.

###### Keywords:

radon removal cryogenic distillation heat exchanger piston pump

††journal: Eur. Phys. J. C

##  I Introduction

Liquid xenon (LXe) is a well-established target material for rare event
searches a ; b ; c ; d ; e ; f ; g ; h . For XENONnT, located underground at
the Laboratori Nazionali del Gran Sasso (LNGS), with 8.4 tonnes of xenon,
[222]Rn is the main source of background for the dark matter WIMP search b ,
while the radioactives [219]Rn and [220]Rn are less critical due to their
short half-life. Radon is continuously emanated from the detector materials
into the target material xenon. Its half-life of $3.8\text{\,}\mathrm{d}$
allows for a homogeneous mixing within the active detection volume. The beta
decay of [214]Pb within the [222]Rn decay chain cannot be tagged by time
coincidences and thus, creates leakage events into the dark matter region of
interest. Therefore, radon should be avoided in the first place as much as
possible by dedicated material screening and selection Eman1 ; Eman2 .
Emanation measurements reveal the location of different radon sources in the
global detector system including the cryostat, but also the adjacent xenon
handling systems like cryogenic and purification systems.

This makes it possible to create a radon reduction strategy with an online
radon removal system (RRS). Such a system can be based on a charcoal tower xm
; lz  or, in the case of XENONnT, based on a cryogenic distillation tower
making use of the difference in vapor pressure between xenon and radon. Radon,
as the less volatile component compared to xenon, will accumulate within the
liquid xenon at the bottom of the distillation tower. Here, it is trapped
until disintegration. Thus, no extraction of the enriched xenon is required
making the operation xenon-loss-free.

Due to the large detector mass, a large xenon process flow is required for the
RRS to reach reduction factors inside the detector of a factor two and above.
Therefore, the XENONnT RRS features liquid xenon inlet and outlet flows
requiring a special thermodynamic concept. This is based on a heat-pump
cooling concept realized with radon-free heat exchangers and a compressor. The
design, construction and the thermodynamic commissioning of this novel high-
flow radon removal system for XENONnT is presented in this work. The radon
removal performance is published in RAD  using XENONnT directly as a radon
source and monitor.

In section II, a radon removal strategy based on the XENONnT radon source
distribution is developed. From this, the required design parameters for a
radon distillation system can be derived. The design of the distillation tower
is explained in section III based on a modified McCabe-Thiele method without
bottom product extraction. Section IV shows the thermodynamic concept based on
a Clausius-Rankine cycle as well as the full experimental setup including
different key components. The thermodynamic commissioning through an internal
liquid xenon bypass valve is presented in section V followed by a conclusion
in section VI.

##  II Radon removal strategy

A radon removal strategy can be defined based on the radon source distribution
within the global system. A simplified version is visualized in figure 1
including a detector with gaseous (GXe) and liquid phase as well as a radon
removal system.

Figure 1: Simplified scheme for a radon removal strategy. Different radon
sources (type 1a, type 1b, type 2) with regard to their location within the
global system have to be considered and are indicated by their production rate
$k_{\mathrm{1a}}$, $k_{\mathrm{1b}}$ and $k_{\mathrm{2}}$.

The radon emanation sources are divided in two types of sources, depending of
their position in the global detector system with respect to the RRS: Sources
that are labeled as type 1 are being emanated and flushed directly into the
detector before reaching the removal system. They are subdivided into sources
directly inside the LXe (type 1a) and sources within the GXe phase (type 1b)
indicated as $k_{\mathrm{1a}}$ and $k_{\mathrm{1b}}$ in figure 1,
respectively. A radon source between the detector and the RRS is referred to
as type 2. Consequently, type 2 radon is going into the RRS before reaching
the LXe inside the detector ($k_{\mathrm{2}}$).

The removal strategy is split in two ways: Firstly, radon is removed by
continuously extracting a LXe flow from the detector, purify it with the RRS,
and feed radon-depleted LXe back. Secondly, radon is removed by extracting
xenon from the GXe phase before entering the detector’s LXe phase. This way,
type 1b sources can be converted into type 2 sources going directly to the
RRS. The extraction efficiency for this process is defined as $\epsilon$.

The change in the number of radon particles inside the detector’s LXe volume
over time $\frac{dN(t)}{dt}$ can be expressed by the following differential
equation taking all in-going and out-going radon atoms into account:

$\displaystyle\frac{dN(t)}{dt}=$ $\displaystyle\hskip
2.84526ptk_{\mathrm{1a}}+(1-\epsilon)k_{\mathrm{1b}}$
$\displaystyle-\lambda_{\mathrm{Rn}}\cdot N(t)-f\cdot N(t)$ (1)
$\displaystyle+\frac{k_{2}+\epsilon k_{\mathrm{1b}}+f\cdot
N(t)}{R_{\mathrm{RRS}}}.$

Here, $\lambda_{\mathrm{Rn}}\cdot N(t)$ denotes the decay of [222]Rn with its
decay constant
$\lambda_{\mathrm{Rn}}=$0.18\text{\,}\mathrm{1}\mathrm{/}\mathrm{d}$$ and
$f\cdot N(t)$ describes the effective radon particle flux leaving the
detector. The effective circulation rate $f$ depends on the purification flow
$F_{\mathrm{Xe}}$ as well as on the total amount of the xenon inventory
$m_{\mathrm{Xe}}$ and is defined as

$f=\frac{F_{\mathrm{Xe}}}{m_{\mathrm{Xe}}}=\frac{1}{\tau_{\textrm{ex}}},$ (2)

with $\tau_{\textrm{ex}}$ being the detector’s LXe volume exchange time. The
number of radon atoms that are not removed by the RRS are given by the last
term of equation (II) and depends on the RRS’s reduction factor
$R_{\mathrm{RRS}}$. It is defined as the ratio of the radon concentration at
the inlet feed $c_{\mathrm{F}}$ and at the purified outlet $c_{\mathrm{D}}$
with

$R_{\mathrm{RRS}}\equiv\frac{c_{\mathrm{F}}}{c_{\mathrm{D}}}.$ (3)

Furthermore, $R_{\mathrm{RRS}}$ is assumed to be constant and independent from
the radon concentration.

Equation (II) can be solved for the starting condition $N(t=0)=N_{0}$, where
$N_{0}$ is the number of radon atoms before starting the removal:

$N(t)=\frac{K}{\Lambda}+\left(N_{0}-\frac{K}{\Lambda}\right)\cdot
e^{-\Lambda\cdot t},$ (4)

with

$K=k_{\mathrm{1a}}+(1-\epsilon)k_{\mathrm{1b}}+\frac{k_{2}+\epsilon
k_{\mathrm{1b}}}{R_{\mathrm{RRS}}},$ (5)

and

$\Lambda=\left(\lambda_{\mathrm{Rn}}+f\cdot\left(1-\frac{1}{R_{\mathrm{RRS}}}\right)\right).$
(6)

For infinitely large times, equation (4) simplifies to the equilibrium
relation

$\displaystyle N_{\mathrm{equi}}$
$\displaystyle\overset{t\to\infty}{=}\frac{K}{\Lambda}=\frac{k_{\mathrm{1a}}+(1-\epsilon)k_{\mathrm{1b}}+\frac{k_{2}+\epsilon
k_{\mathrm{1b}}}{R_{\mathrm{RRS}}}}{\lambda_{\mathrm{Rn}}+f\cdot(1-\frac{1}{R_{\mathrm{RRS}}})}$
(7)
$\displaystyle\overset{R_{\mathrm{RRS}}\to\infty}{=}\frac{1}{\lambda_{\mathrm{Rn}}+f}\cdot{(k_{\mathrm{1a}}+(1-\epsilon)k_{\mathrm{1b}})},$
(8)

where the last step assumes an infinite reduction power $R_{\mathrm{RRS}}$.
This shows that a perfect RRS can fully remove radon emanated directly by type
2 sources as well as type 1b sources converted into type 2. The effective flow
$f$ is limiting the reduction of type 1 sources. The reduction inside the
detector’s LXe volume can be defined as

$r(R_{\mathrm{RRS}},f,\epsilon)\equiv\frac{N_{\mathrm{equi}}(R_{\mathrm{RRS}}=1,f,\epsilon)}{N_{\mathrm{equi}}(R_{\mathrm{RRS}},f,\epsilon)}.$
(9)

For a highly efficient RRS ($R_{\mathrm{RRS}}\to\infty$) one finds

$r(R_{\mathrm{RRS}}\to\infty,f,\epsilon)=\frac{\lambda_{\mathrm{Rn}}+f}{\lambda_{\mathrm{Rn}}}\cdot\frac{k_{\mathrm{tot}}}{k_{\mathrm{1a}}+(1-\epsilon)k_{\mathrm{1b}}},$
(10)

with $k_{\mathrm{tot}}=k_{\mathrm{1a}}+k_{\mathrm{1b}}+k_{\mathrm{2}}$.
Equation (10) is valid for the combined LXe and GXe modes. The individual
reduction capabilities $r_{\mathrm{LXe}}$ for the LXe only extraction ($f>0$,
$\epsilon=0$) and $r_{\mathrm{GXe}}$ for the GXe only extraction ($f=0$,
$\epsilon>0$) are given by

$\displaystyle r_{\mathrm{LXe}}$
$\displaystyle=r(R_{\mathrm{RRS}}\to\infty,f,\epsilon=0)$ (11)
$\displaystyle=\frac{\lambda_{\mathrm{Rn}}+f}{\lambda_{\mathrm{Rn}}}\cdot\frac{k_{\mathrm{tot}}}{k_{\mathrm{1a}}+k_{\mathrm{1b}}},$

and

$\displaystyle r_{\mathrm{GXe}}$
$\displaystyle=r(R_{\mathrm{RRS}}\to\infty,f=0,\epsilon)$ (12)
$\displaystyle=\frac{k_{\mathrm{tot}}}{k_{\mathrm{1a}}+(1-\epsilon)k_{\mathrm{1b}}}.$

For systems like XENONnT with $(k_{\mathrm{1a}}+k_{\mathrm{1b}})\gg
k_{\mathrm{2}}$, a reduction $r$ inside the detector by a factor two can be
reached for $f=\lambda_{\mathrm{Rn}}$, i.e. the RRS’s purification flow needs
to exchange a detector’s LXe inventory with a time constant of
$\tau_{\textrm{ex}}=$5.5\text{\,}\mathrm{d}$$. In the case of XENONnT, this
translates to $62\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$
($175\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$) for a xenon inventory
of $8.4\text{\,}\mathrm{t}$ and defines the required performance of the RRS
for XENONnT.

A further boost in reduction can be achieved by converting type 1b into type 2
sources, the GXe mode. An ideal extraction ($\epsilon=1$) yields a maximum
reduction factor $r$ of $2\cdot\frac{k_{\mathrm{tot}}}{k_{\mathrm{1a}}}$
assuming $f=\lambda_{\mathrm{Rn}}$.

In the following, the expected radon reduction within the XENONnT detector is
evaluated: The dual-phase LXe Time Projection Chamber (LXe TPC) itself is
housed in a cryostat referred to as the inner vessel. In order to keep the
xenon of the detector system in a thermodynamic equilibrium, a cryogenic
system (CRY) is required. Here, two pulse tube refrigerators and an emergency
LN2 cooling tower are connected to the inner vessel via a cryopipe to balance
evaporated xenon due to external heat input by condensation. Two cable
feedthrough vessels (Cables) connected to the cryopipe contain high voltage
and signal cables of the PMTs inside the detector. Furthermore, two
purification systems are used to clean the xenon: LXe from the detector is
extracted and evaporated via a series of heat exchangers in order to be
purified from electronegative impurities with the help of a gas purification
system (GXe PUR). In parallel, a novel LXe purification loop (LXe PUR) allows
to circulate the xenon inventory once a day through LXe filters removing
electronegatives as well. While most of the xenon through the LXe PUR is
returned to the cryopipe and subsequently to the detector, a fraction is
guided to the RRS for radon reduction. All details about the XENONnT
subsystems are summarized in Ref. Instr .

The radon source locations in XENONnT are well known due to dedicated
emanation measurements Eman2 . The values for the different sources are
typically stated in units of a [222]Rn activity concentration per kilogram of
xenon and are summarized in table 1 assuming a $8.4\text{\,}\mathrm{t}$ xenon
inventory. Note that radon sources related to the RRS are only contributing to
the total budget when the RRS is in operation. During this operation, the LXe
fraction $\epsilon_{\mathrm{LP}}$ coming from the LXe PUR system into the RRS
is given by $F_{\mathrm{Xe}}=\epsilon_{\mathrm{LP}}\cdot G_{\mathrm{Xe}}$ with
the total LXe purification flow $G_{\mathrm{Xe}}$. Assuming a homogeneous
radon distribution inside the LXe flow, $\epsilon_{\mathrm{LP}}$ corresponds
to the fraction of the measured radon emanation from the LXe PUR in table 1
that contributes as a type 2 source. In the following,
$\epsilon_{\mathrm{LP}}$ was fixed to $0.2$ by design.

The CRY system and the Cables have separated extraction ports, and thus,
feature different extraction efficiencies $\epsilon_{\mathrm{CRY}}$ and
$\epsilon_{\mathrm{C}}$, respectively, contributing to equation II with

$\displaystyle\epsilon k_{\mathrm{1b}}$
$\displaystyle=\epsilon_{\mathrm{CRY}}k_{\mathrm{CRY}}+\epsilon_{\mathrm{C}}k_{\mathrm{C}},$
(13) $\displaystyle(1-\epsilon)k_{\mathrm{1b}}$
$\displaystyle=(1-\epsilon_{\mathrm{CRY}})k_{\mathrm{CRY}}+(1-\epsilon_{\mathrm{C}})k_{\mathrm{C}}.$
(14)

Table 1: Radon source distribution in XENONnT assuming a $8.4\text{\,}\mathrm{t}$ xenon inventory Eman2 . | System | Variable | Value [$\upmu$Bq/kg]
---|---|---|---
Type 1a | LXe TPC | $k_{\mathrm{TPC}}$ | 1.11
| Inner vessel | $k_{\mathrm{IV}}$ | 0.30
| GXe PUR | $k_{\mathrm{GP}}$ | 0.21
| LXe PUR | $k_{\mathrm{LP,I}}$ |  $(1-\epsilon_{\mathrm{LP}})\times$ 0.43
| RRS-outlet | $k_{\mathrm{RRS,I}}$ | 0.19
Type 1b | CRY | $k_{\mathrm{CRY}}$ | 1.36
| Cables | $k_{\mathrm{C}}$ | 0.85
Type 2 | RRS-inlet | $k_{\mathrm{RRS,II}}$ | 0.3
| LXe PUR | $k_{\mathrm{LP,II}}$ |  $\epsilon_{\mathrm{LP}}\times$ 0.43

The expected radon reduction in XENONnT for a LXe only ($\epsilon=0$) and a
LXe + GXe ($\epsilon>0$) mode is presented for different extraction
efficiencies $\epsilon_{\mathrm{CRY}}$ and $\epsilon_{\mathrm{C}}$ in figure 2
using units of $\upmu\mathrm{B}\mathrm{q}\mathrm{/}\mathrm{k}\mathrm{g}$
instead of number of radon atoms.

Figure 2: Expected radon reduction in XENONnT for the LXe only mode as well as
the LXe + GXe mode for $R_{\mathrm{RSS}}\gg 1$. For the LXe only mode, the
design purification speed of the RRS of
$71\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$ (200 slpm) is assumed.
For the LXe + GXe mode, a cable extraction efficiency of
$\epsilon_{\mathrm{C}}=1$ is assumed. The total reduction is shown for
extraction efficiencies of the CRY system of $\epsilon_{\mathrm{CRY}}=0.5$
(purple), $\epsilon_{\mathrm{CRY}}=0.75$ (black) and
$\epsilon_{\mathrm{CRY}}=1$ (red).

In XENON1T, a full extraction from Cables was found
($\epsilon_{\mathrm{C}}=1$), while the extraction from the CRY system
$\epsilon_{\mathrm{CRY}}$ was about $0.5$ mur ; OnlRAD . For XENONnT, the
extraction flow from the CRY system is enhanced from
$0.5\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$
($1.5\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$) to
$7.1\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$
($20\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$) to get a more
efficient extraction. For $\epsilon_{\mathrm{C}}=1$ and
$\epsilon_{\mathrm{CRY}}$ close to $1$, XENONnT can reach its projected
[222]Rn activity concentration of
$1\text{\,}\upmu\mathrm{B}\mathrm{q}\mathrm{/}\mathrm{k}\mathrm{g}$ with the
help of the novel radon removal system.

##  III Modified McCabe-Thiele method without bottom product extraction

The radon removal system for XENONnT is based on a cryogenic distillation
column where the removal concept is based on trapping [222]Rn in the liquid
xenon reservoir in the bottom of the system until it decays. This is possible
due to its comparable short half-life of
$T_{1/2}\,=\,$3.8\text{\,}\mathrm{d}$$. As consequence, there is no extraction
of contaminant enriched xenon as it is required for krypton or argon
distillation Pa ; Xma ; Kr1 ; Kr2 , and thus radon removal is a xenon-loss
free operation. This requires a modification of the McCabe-Thiele method Mc ,
a general approach to design such a distillation system. The modified approach
is derived in this work.

In a single distillation stage with a static gas-liquid xenon interface at
equilibrium, the size of the radon depletion in the gaseous xenon is described
by the relative volatility $\alpha$ deduced from Raoult’s law. It is the ratio
between the vapor pressure of the noble gas contaminant radon
$P_{\mathrm{Rn}}$ and the one of xenon $P_{\mathrm{Xe}}$:

$\displaystyle\alpha=\frac{P_{\mathrm{Rn}}}{P_{\mathrm{Xe}}}=0.1\ \ \
\text{at}\ \ \
$-98\text{\,}\mathrm{\SIUnitSymbolCelsius}$\text{\,\cite[cite]{\@@bibref{Authors
Phrase1YearPhrase2}{NST}{\@@citephrase{(}}{\@@citephrase{)}}}}.$ (15)

Measurements were performed in a boil-off experiment with a single-stage setup
br  yielding a radon depletion factor greater 4 in the gaseous phase,
depending on the extraction flow, to verify the concept of relative volatility
for radon concentrations on the order of
${10}^{-25}\text{\,}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}$
($\mathcal{O}$($\upmu$Bq/kg)).

In order to achieve larger separation factors, a distillation plant is made of
a series of theoretical plates111One theoretical plate equals one distillation
stage. to successively reduce the impurities. The McCabe-Thiele method is
applied to compute the number of required plates $n_{\mathrm{TP}}$ to achieve
the desired concentration at the purified outlet. In this method, the column
is separated in three parts, namely the feeding section, where the raw xenon
gas is injected to the tower, the rectifying section, where the less volatile
component, here the contaminant radon, is depleted and the stripping section,
where the less volatile contaminant is enriched. This is depicted in figure 3
along with relevant xenon flows and radon concentrations for each section.

Figure 3: Scheme of a multi-stage distillation tower with n plates, where the
less volatile component is the contaminant (green dots). The incoming flow F
with the contamination concentration $c_{\mathrm{F}}$ in the feeding section
is enriched in the stripping section below to a contamination concentration
$c_{\mathrm{B}}$ in the reboiler. In the case of radon, it is trapped inside
the reboiler until it decays, and therefore, no bottom product extraction is
required ($B=0$). In the rectifying section, above the feed, the contamination
is depleted to a concentration $c_{\mathrm{D}}$ in the output flow $D$ at the
top condenser. Furthermore, the liquid flows $L$, $L^{\prime}$ and gaseous
flows $V$, $V^{\prime}$ of the related sections are shown. The factor $q$
indicates if the feed is gaseous ($q=0$) or liquid ($q=1$).

Starting from the reboiler stage in the stripping section at the bottom, the
liquid xenon is evaporated and a gaseous stream flows upwards at a flow rate
of $V^{\prime}$. Assuming that the vapor will condense on Plate 1, the
generated liquid phase on this stage will have the same composition as the
vapor from the reboiler stage, and will therefore have a lower concentration
of the contaminant compared to the starting mixture due to the lower
volatility. By repeating this procedure for several stages, the fraction of
the contaminant in the xenon will successively decrease.

At the top, the concentration of the contaminant is at its minimum. While a
part of the vapor is liquefied with the help of the top condenser and fed back
to the column with a flow rate $L$, a fraction of the gas is removed as
purified xenon at a flow rate $D$. The ratio between the flows $L$ and $D$ is
defined as the reflux ratio $R$. In the same manner, a second ratio
$R^{\prime}$ can be found at the bottom. However, since no xenon is extracted
at the bottom ($B=0$), the same flow that is entering the reboiler as liquid
needs to be evaporated again. Therefore, $R^{\prime}$ becomes infinity:

$R=\frac{L}{D}\qquad\textrm{and}\qquad R^{\prime}=\lim_{B\to
0}\frac{V^{\prime}}{B}=\infty.$ (16)

The stripping section and the rectifying section are connected by the feeding
section, where xenon is injected at a flow rate $F$. It is added to either the
up-streaming vapour $V$ in the rectifying section or to the down-streaming
liquid flow $L^{\prime}$. This depends on the state of the injected matter
(gaseous or liquid), denoted by the caloric factor

$q=(L^{\prime}-L)/F.$ (17)

For the following calculations a saturated liquid feed at the boiling point
$(q=1)$ is assumed. As consequence, the injected xenon is added to the down-
streaming liquid flow $L^{\prime}$. In the McCabe-Thiele diagram, the
concentrations of the less volatile noble gas in the gaseous xenon phase
($y_{\mathrm{Rn}}$) and in the liquid xenon phase ($x_{\mathrm{Rn}}$) are
plotted against each other in an equilibrium diagram. For constant temperature
and pressure, the system drifts to equilibrium based on the concept of vapor
pressure as described above. For each local concentration
$x_{\mathrm{Rn}}=(1-x_{\mathrm{Xe}})$ of the contaminant in the liquid phase,
there is a certain equilibrium concentration $y_{\mathrm{Rn}}$ in the vapor
phase. For very low concentrations with $x_{\mathrm{Rn}}\cdot(\alpha-1)\ll 1$
this relation can be expressed by

$y_{\mathrm{Rn}}=\frac{\alpha\cdot x_{\mathrm{Rn}}}{1+(\alpha-1)\cdot
x_{\mathrm{Rn}}}\approx\alpha\cdot x_{\mathrm{Rn}}.$ (18)

In the diagram, this is called the equilibrium line.

Due to active heating from the bottom and cooling from the top, the upward
gaseous ($V,V^{\prime}$) and downward liquid ($L,L^{\prime}$) flows are
created along the column and as consequence, the equilibrium inside the system
is disturbed due to the mass flow. As a result of that, the actual
concentration of the contaminant in the gaseous phase related to the
concentration in the liquid phase is described by operation lines for each of
the three sections. Between the equilibrium line and operation lines a forcing
concentration gradient is ensured, driving the system toward the equilibrium
via mass transfer between the ascended gaseous stream and the descended liquid
stream.

During stable operation, the incoming xenon feed flow $F$ requires to be equal
to the outgoing xenon flow $D$ yielding the total mass balance

$F=D.$ (19)

Combining the flows with the different concentrations of the less volatile
noble gas radon inside the xenon in the feed $c_{F}$, in the top $c_{D}$ and
in the bottom $c_{B}$, equation (19) can be expressed in terms of the number
of contaminant atoms. In this work, the radon particle decay inside the
reboiler needs to be taken into account to ensure particle mass balance:

$F\cdot c_{F}=D\cdot c_{D}+c_{B}\cdot\lambda_{\mathrm{Rn}}\cdot
m_{\mathrm{Xe,reb}}.$ (20)

Here,
$\lambda_{\mathrm{Rn}}\,=\,$7.55\text{\times}{10}^{-03}\text{\,}{\mathrm{h}}^{-1}$$
denotes the decay constant of [222]Rn and $m_{\mathrm{Xe,reb}}$ is the liquid
xenon mass inside the reboiler. The last term effectively describes an out-
going mass flow of radon particles from the system by decay and is the
equivalent to an out-going offgas mass flow in the standard McCabe-Thiele
approach, e.g. for krypton mur . The decay of radon particles in the other
parts of the distillation system can be neglected due to the short residence
time compared to the decay time.

When fixing $F$, $c_{F}$, and $c_{D}$ by design, the mass of radon particles
in the reboiler $c_{B}\cdot m_{\mathrm{Xe,reb}}$ requires to be calculated
with above equations in order to conserve the particle mass balance:

$c_{B}\cdot m_{\mathrm{Xe,reb}}=\frac{c_{F}\cdot F-c_{D}\cdot
D}{\lambda_{\mathrm{Rn}}}.$ (21)

For the calculation of the McCabe-Thiele diagram, either the concentration
$c_{B}$ or the mass in the reboiler $m_{\mathrm{Xe,reb}}$ has to be fixed by
design.

For each of the three sections in the system, a particle balance can be
formulated using the respective flows in the sections. From these, the three
operation lines can be obtained:

$\displaystyle\textrm{Stripping line:}\,\,y_{\mathrm{Rn}}$
$\displaystyle=x_{\mathrm{Rn}}-\frac{c_{B}\cdot\lambda_{\mathrm{Rn}}\cdot
m_{\mathrm{Xe,reb}}}{L^{\prime}},$ (22) $\displaystyle\textrm{Rectifying
line:}\,\,y_{\mathrm{Rn}}$ $\displaystyle=\frac{R}{R+1}\cdot
x_{\mathrm{Rn}}+\frac{c_{D}}{R+1},$ (23) $\displaystyle\textrm{Feeding
line:}\,\,y_{\mathrm{Rn}}$ $\displaystyle=\frac{q}{q-1}\cdot
x_{\mathrm{Rn}}-\frac{c_{F}}{q-1}.$ (24)

More details for the derivation of the operation lines can be found in Ref.
mur .

In the following, the McCabe-Thiele diagram for the RRS for XENONnT is
discussed. The system was designed for a feed flow of
$F\,=\,$71\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$$ (200 slpm). As
described in section II, an initial activity concentration of
$c^{\prime}_{F}=$4.25\text{\,}\upmu\mathrm{B}\mathrm{q}\mathrm{/}\mathrm{k}\mathrm{g}$$
is expected. This can be converted into a radon-in-xenon concentration of
$c_{F}=$4.4\text{\times}{10}^{-25}\text{\,}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}$$
via

$c_{F}=\frac{M_{\mathrm{Xe}}}{\lambda_{\mathrm{Rn}}\cdot N_{\mathrm{A}}}\cdot
c^{\prime}_{F}=$1.04\text{\times}{10}^{-25}\text{\,}\frac{mol}{mol}\frac{kg}{\upmu
Bq}$\cdot c^{\prime}_{F},$ (25)

with
$M_{\mathrm{Xe}}=$131.3\text{\,}\mathrm{g}\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}$$
being the xenon molar mass,
$\lambda_{\mathrm{Rn}}=$2.098\text{\times}{10}^{-6}\text{\,}\mathrm{1}\mathrm{/}\mathrm{s}$$
being the [222]Rn decay constant, and $N_{\mathrm{A}}$ being the Avogadro
number.

In order to meet at least the requirements for a factor two reduction as
derived in section II, a depletion of a factor $100$ at the top and an
enrichment of a factor $1000$ at the bottom with respect to the feed
concentration were chosen. Since the removal is based solely on the [222]Rn
decay, the RRS requires to have a large enrichment factor between inlet and
bottom part. This allows to reduce the required xenon inventory inside the RRS
system while avoiding back contamination from the highly enriched bottom. It
follows
$c_{D}=$4.4\text{\times}{10}^{-27}\text{\,}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}$$
and
$c_{B}=$4.4\text{\times}{10}^{-22}\text{\,}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}$$.
The reflux ratio $R$ determines the amount of xenon that needs to be re-
liquefied and send back to the column and is therefore directly proportional
to the required cooling power at the top condenser. For high purification
flows and large $R$, this cooling can start to become an issue. Therefore, a
minimal reflux ratio $R_{\mathrm{min}}$ has to be estimated for the radon
column design to minimize the needed cooling power. The Underwood equation Mc
can be utilized to calculate the reflux ratio that results in the operation
line with minimal slope:

$R_{\mathrm{min}}=\frac{1}{\alpha-1}\cdot\left(\frac{c_{D}}{c_{F}}-\alpha\cdot\left(\frac{1-c_{D}}{1-c_{F}}\right)\right)=0.1.$
(26)

Several McCabe-Thiele diagrams for a liquid feed ($q=1$) and the given
concentrations above were constructed with varying reflux ratios starting with
$R=0.1$ up to $R=5$. For $R<0.1$ no diagrams can be constructed since the
rectifying line starts to go below the equilibrium line and no stages can be
drawn anymore. For $R=0.11$ a total number of 16 stages is required to meet
the desired purity level. The number of stages decreases with increasing $R$
up to $R=0.5$. Here, 7 theoretical stages can be drawn. With further increase
of the reflux, the number of stages can be reduced to 6 for $R=5.0$. The
reduction by one stage between $R=0.5$ and $R=5.0$ would require a ten times
higher cooling power at the top condenser. Therefore, a reflux ratio of
$R=0.5$ was chosen for the design also allowing for larger feed flows in the
future. All other required parameters to create the diagram for the chosen
reflux ratio are summarized in table 2.

Table 2: Input parameters for McCabe-Thiele diagram of the XENONnT RRS. Section | Parameter
---|---
Feeding | $c_{F}=$4.4\text{\times}{10}^{-25}\text{\,}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}$$
|
$F=$71\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$\,($200\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$)$
| $q=1$
Stripping | $c_{B}=$4.4\text{\times}{10}^{-22}\text{\,}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}$$
| $B=$0\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$$
|
$L^{\prime}=$106\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$\,($300\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$)$
|
$V^{\prime}=$106\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$\,($300\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$)$
| $R^{\prime}=\infty$
| $m_{\mathrm{Xe,reb}}=$9.4\text{\,}\mathrm{k}\mathrm{g}$$
Rectifying | $c_{D}=$4.4\text{\times}{10}^{-27}\text{\,}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}$$
|
$D=$71\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$\,($200\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$)$
|
$L=$35\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$\,($100\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$)$
|
$V=$106\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$\,($300\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$)$
| $R=0.5$

The resulting McCabe-Thiele diagram is visualized in figure 4. The solid
purple equilibrium line in contrast to the case of a more volatile component
like krypton is below the operation lines due to $\alpha\,=\,$0.1$$. The
stripping line from the bottom part, where in this case radon is enriched, is
indicated by the light blue dashed line, while the rectifying line from the
top, where radon is depleted, is drawn as red dotted line. The operation lines
are intersected by the gray dash dotted feed line, which is a vertical line
due to $q\,=\,1$. In contrast to krypton, the concentration $c_{B}$ in the
liquid, visualized for better understanding by the green dotted vertical line,
is located at the right border of the diagram. The concentration $c_{D}$ in
the gas, drawn as dark blue dotted horizontal line, is located at the left
border. Consequently, the bottom of the distillation column corresponds to the
right and the top to the left part of the diagram. In total, 7 theoretical
stages can be drawn, where 4 stages below and 3 stages above the feed section
are required to achieve the desired enrichment and depletion factors of $1000$
and $100$, respectively.

Figure 4:  McCabe-Thiele diagram for a radon distillation system with R = 0.5:
The equilibrium line (solid purple) is below the stripping line (dashed light
blue), and the rectifying line (dotted red). The operation lines are
intersected by the feed line (dash dotted gray), which is a vertical line due
to $q=1$. One vertical line (dotted green) represents the concentration
$c_{B}$, while the horizontal line (dotted dark blue) gives the concentration
$c_{D}$. The bottom of the column corresponds to the right and the top of the
system to the left part of the diagram.

From the experimental point of view, a series of multiple physically connected
single distillation stages is not practical. For this reason, a structured
packing material inside a package tube is utilized, featuring a large surface
for good liquid-gas exchange through the full height of the tower. The height-
equivalent of one theoretical plate (HETP) denotes the amount of required
packing material to realize one distillation stage. Together with the number
of plates $n_{\mathrm{TP}}$ derived from the McCabe-Thiele diagram, the total
height $h$ of the package tube can be calculated:

$h=\mathrm{HETP}\cdot n_{\mathrm{TP}}.$ (27)

Here, one stage is intrinsically given by the reboiler combined with the top
condenser. Thus, six theoretical plates have to be considered for the package
tube. The HETP value of the used packing material is unknown. However, tests
at XENON100 with a distillation column for krypton in inverse mode OnlRAD
give an upper limit for the HETP value of $27.5\text{\,}\mathrm{c}\mathrm{m}$
mur . A similar packing material from the same company, but with larger
diameter is used for the radon distillation plant of XENONnT. Taking the upper
limit, a maximum height of $165\text{\,}\mathrm{c}\mathrm{m}$ is calculated
for 6 stages for the new package tube.

##  IV The Radon Removal System

The cooling concept as well as the experimental realization of the RRS is
described in this section. The design parameters used for the McCabe-Thiele
diagram in section III define the requirements in terms of flows, cooling and
heating power. In order to reach the large target flow of
$F=$71\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$$
($200\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$), the RRS is operated
with LXe inlet and outlet. This is possible due to the novel LXe purification
system in XENONnT, where a LXe fraction is diverted into the RRS. The
returning radon-depleted LXe is then mixed back into the LXe circuit before
entering the cryostat. The total required cooling and heating powers can be
derived from the involved flows in the design.

At the top condenser, a cooling power of about
$1\text{\,}\mathrm{k}\mathrm{W}$ is required to guarantee the reflux ratio of
$R=0.5$ resulting in a liquefaction flow of
$L=$35\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$$
($100\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$) k . The radon-
depleted GXe xenon flow of
$D=$71\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$$
($200\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$) extracted at the top
condenser has to be liquefied again before it can be returned to the LXe
purification circuit. This requires an additional cooling power of about
$2\text{\,}\mathrm{k}\mathrm{W}$, leading to a total required cooling power of
$3\text{\,}\mathrm{k}\mathrm{W}$. Additionally, a heating power of about
$3\text{\,}\mathrm{k}\mathrm{W}$ at the reboiler is required to create the
evaporation flow
$V^{\prime}=$106\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$$
($300\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$) to establish a stable
distillation process across the package tube.

For the cooling, either an industrial cooling machine or liquid nitrogen (LN2)
can be used. However, industrial solutions were not readily available for our
application and would have to be customized for our purposes. Furthermore,
often the customer does not have full control over the components used and the
manufacturing processes applied by the company. The selection of high purity
material and manufacturing following standards of ultra-high vacuum components
are key requirements for the RRS. Therefore, it was decided to use LN2 and to
develop a custom-made cooling solution. Furthermore, LN2 provides a simple
cooling mechanism, is cost-efficient and has low-maintenance requirements in
the long term perspective compared to industrial cooling machines. It further
gives the possibility to scale up in terms of supplied cooling power at a
later stage. The XENONnT infrastructure features a 30 tonne LN2 tank
underground already, serving several other subsystems. To reach
$3\text{\,}\mathrm{k}\mathrm{W}$ of cooling, a LN2 consumption of
$1300\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{d}$ is required taking
only the LN2 phase change into account with an enthalpy of evaporation $\Delta
H_{\mathrm{vap}}^{\mathrm{N}_{2}}$ of
$199\text{\,}\mathrm{k}\mathrm{J}\mathrm{/}\mathrm{k}\mathrm{g}$ at
$77\text{\,}\mathrm{K}$ for LN2.

### Cooling Concept

An energy-efficient cooling concept for the RRS was designed, as shown in
figure 5, to drastically reduce the LN2 consumption. In this concept, the
reboiler acts as a bath-type Xe-Xe heat exchanger (HE) with a top and bottom
vessel, both thermally connected with copper: Cooling energy stored in the
radon-enriched LXe inside the top reboiler vessel is used to provide
$2\text{\,}\mathrm{k}\mathrm{W}$ of cooling power for the radon-depleted GXe
liquefaction process inside the bottom reboiler vessel. Like that, in
parallel, the LXe in the top reboiler vessel is evaporated and the required
electrical power to establish the evaporation flow $V^{\prime}$ is reduced to
$1\text{\,}\mathrm{k}\mathrm{W}$ heating power. Making use of this cooling
concept reduces the LN2 consumption to
$430\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{d}$ applied at the top
condenser to create the desired reflux. However, in order to make the reboiler
HE work, a temperature difference between the two xenon phases needs to be
established such that heat can be transferred from the bottom to the top
reboiler vessel. Therefore, the concept further utilizes a heat-pump, or
compressor, that extracts radon-depleted GXe from the top condenser and
compresses it into the reboiler bottom vessel. Furthermore, two commercial
GXe-GXe HE are applied to bring the extracted GXe for the compression process
to room temperature and to pre-cool the returning compressed GXe. A spiral is
immersed in the LXe of the top reboiler vessel to even further cool the
compressed GXe before it enters the bottom reboiler vessel. After liquefaction
in the bottom reboiler vessel, the radon depleted LXe is returned to the LXe
purification circuit. A LXe bypass valve was installed to connect the RRS
outlet directly with the inlet to allow for performance tests independent from
the global XENONnT system.

The thermodynamic concept can be described by a left turning Clausius-Rankine
cycle with a phase-changing cooling medium, in this case the xenon itself.
Beside the four usual steps of evaporation
(\raisebox{-0.8pt}{4}⃝$\rightarrow$\raisebox{-0.8pt}{1}⃝), compression
(\raisebox{-0.8pt}{1}⃝$\rightarrow$\raisebox{-0.8pt}{2}⃝), condensation
(\raisebox{-0.8pt}{2}⃝$\rightarrow$\raisebox{-0.8pt}{3}⃝) and expansion
(\raisebox{-0.8pt}{3}⃝$\rightarrow$\raisebox{-0.8pt}{4}⃝), the thermodynamic
cycle of the RRS illustrated in figure 5 features multiple intermediate states
of heat transfer making the cycle more complex. The different states are
summarized in table 3. A p-H- and a T-S-diagram to describe the cycle are
presented in figure 8 of section V using data from the RRS’s performance
tests.

Table 3: States of the Clausius-Rankine cycle for the RRS cooling concept.  State |  | Description
---|---|---
\raisebox{-0.3pt}{\scriptsize{1a}}⃝ | evaporation | LXe evaporation in top reboiler
\raisebox{-0.3pt}{\scriptsize{1b}}⃝ |  | GXe extraction
\raisebox{-0.3pt}{\scriptsize{1c}}⃝ |  | GXe HE warm-up
\raisebox{-0.3pt}{\scriptsize{1d}}⃝ |  | 4MP inlet
\raisebox{-0.3pt}{\scriptsize{2a}}⃝ | compression | 4MP outlet
\raisebox{-0.3pt}{\scriptsize{2b}}⃝ |  | GXe HE pre-cooling
\raisebox{-0.3pt}{\scriptsize{2c}}⃝ |  | GXe spiral pre-cooling
\raisebox{-0.3pt}{\scriptsize{3}}⃝ | condensation | Liquefaction in bottom reboiler
\raisebox{-0.3pt}{\scriptsize{4}}⃝ | expansion | Internal bypass
Figure 5: Layout of the radon distillation system. The four main components
are the top condenser, the reboiler, the package tube and the compressor. The
cooling concept is based on a Clausius-Rankine cooling cycle with phase-
changing cooling medium indicated by the numbers (1) to (4).

### Experimental Setup

The four main components of the RRS for XENONnT are the top condenser, the
reboiler, the package tube and the compressor. Additionally, auxiliary
components are used to warm up and pre-cool the GXe in the cycle. The
experimental setup is described in the following. The full radon removal
system was first constructed at the University of Münster as shown in figure
6. Later, it was partially disassembled, shipped and installed inside the top
floor of the XENONnT service building. The system’s total height is
$3.8\text{\,}\mathrm{m}$ constrained by the floor height inside top floor. In
order to monitor the RRS during operation, the entire system is equipped with
32 Resistance Temperature Detectors (RTDs) (Honeywell HEL-705), four silicon
diodes (Lakeshore DT670D-CU), 13 pressure sensors (Wika WU20), four
differential pressure sensors (Baratron 226A), and a vacuum pressure sensor
(Thyracont VSM77DL), all controlled by a Programmable Automation Controller
(PAC) from General Electric (GE RX3i) on the hardware side and Cimplicity
SCADA (Supervisory Control And Data Acquisition) on the software side in the
private front-end network of XENONnT.

Furthermore, to minimize external heat inputs, the inlet and outlet LXe tubes
connecting the RRS to the LXe Purification system as well as the full
distillation system are encapsulated in an insulation vacuum. The top
condenser insulation chamber features a diameter of 650 mm and a height of 658
mm, the reboiler vessel a diameter of 750 mm and a height of 758 mm and the
two-component package tube vessels a diameter of 300 mm and a height of 712 mm
each.

Figure 6: Radon removal system fully installed at University of Münster before
shipping to LNGS (left) and related CAD drawing (right). The four key
components top condenser, package tube, reboiler and four-cylinder
magnetically-coupled piston pump are visible.

#### Package Tube

The package tube extending into the top condenser insulation vessel as well as
into the reboiler vacuum chamber has a total height of
$1900\text{\,}\mathrm{m}\mathrm{m}$ and is made of three segments: The bottom
segment that connects to the reboiler is a stainless steel tube with a height
of 920 mm and diameter of $200\text{\,}\mathrm{m}\mathrm{m}$. A custom-
modified Conflat (CF) flange at its top features two feedthroughs for GXe and
LXe feed tubes. In order to spread the incoming LXe around the whole package
diameter equally, a distributor is connected to the LXe feedthrough on the
inside. The top segment is a stainless steel bellow with eight windings, a
wall thickness of 0.2 mm and a nominal operation pressure of 4 bar that
connects to the top condenser. It is used to compensate thermal shrinkage and
expansion when cooling down the system from room temperature to liquid xenon
temperature or vice versa. Eight package segments (Sulzer PDX) of
$178\text{\,}\mathrm{m}\mathrm{m}$ height and
$200\text{\,}\mathrm{m}\mathrm{m}$ diameter each were inserted into the two
stainless steel tubes, five in the bottom tube and three in the top tube,
leading to a total package height of $1420\text{\,}\mathrm{m}\mathrm{m}$.
Furthermore, liquid xenon pneumatic flow controlled valves (Thermomess) at the
liquid inlet and outlet are used to regulate the flow-rate through the system
during operation within the global system.

#### Top Condenser

The top condenser described in detail in Ref. k  with a diameter of
$300\text{\,}\mathrm{m}\mathrm{m}$ is composed of two vessels: A cooling
vessel using liquid nitrogen on top and a xenon liquefaction vessel below.
Aluminum spacers keep the distance between the heat exchanger and the
surrounding insulation vessel. In order to reduce the heat transfer via
conduction between the inner vessels and the insulation chamber, these spacers
are equipped with preimpregnated fibre plates. Additionally, the vacuum-
insulated gas lines of the inlet and outlet for the xenon as well as the
nitrogen are guided through the insulation chamber via bellow-based
feedthroughs.

For the cooling vessel at the top, the nitrogen supply line is given by a 1/2”
tube, the exhaust line by a 1” tube. A total of $7.1\text{\,}\mathrm{l}$ LN2
can be filled. The vessel inside is equipped with baffle plates at the inlet
and at the outlet preventing the nitrogen to bypass the system. Additionally,
to increase the heat transfer surface, six oxygen-free high conductivity
copper fins are mounted on the ground of the vessel.

The ground flange of the vessel, acting as the thermal connection to the
liquefaction vessel, is given by a stainless steel blank flange of
$27\text{\,}\mathrm{m}\mathrm{m}$ thickness with helicoflex-type sealing faces
on both sides. Here, advanced gaskets (HTMS CSI) based on a copper-coated
helical spring with the capability to recover from thermal deformations are
used.

Attached to the thermal connection flange a copper plate of
$290\text{\,}\mathrm{m}\mathrm{m}$ diameter and
$20\text{\,}\mathrm{m}\mathrm{m}$ thickness extends into the
$220\text{\,}\mathrm{m}\mathrm{m}$ high xenon liquefaction vessel. Additional
$23$ copper fins mounted to the copper plate increase the heat transfer
surface in contact to the xenon to $0.76\text{\,}\mathrm{m}^{2}$.

By regulating the LN2 flow through the top vessel, variable cooling powers can
be achieved. Cooling power measurements in Ref. k  show a performance of
$3\text{\,}\mathrm{k}\mathrm{W}$ and beyond only limited by the available
heating power to balance the system. This is three times larger than the
required $1\text{\,}\mathrm{k}\mathrm{W}$ and gives the possibility to scale
up the process flow in the future. During these performance tests, a heat
exchanger efficiency of ($0.98\pm 0.03$) was computed.

#### Reboiler

Also the reboiler described in detail in Ref. k  with a diameter of
$500\text{\,}\mathrm{m}\mathrm{m}$ is composed of two vessels: The storage
vessel of the highly radon-enriched xenon on top and the xenon liquefaction
vessel below at the bottom.

The top storage vessel is open to the package tube via a CF200 flange. A total
of $46.5\text{\,}\mathrm{l}$ LXe can be stored in the 237 mm high top vessel.
Furthermore, six oxygen-free high conductivity copper fins increasing the heat
transfer surface in contact with the stored liquid are installed on the top
side of the connecting flange.

This connecting flange thermally connects and hermetically seals both
reservoirs. It is made of a $35\text{\,}\mathrm{m}\mathrm{m}$ thick copper
plate of $450\text{\,}\mathrm{m}\mathrm{m}$ diameter that was electron-welded
into the connecting flange to improve the heat transfer. In total, $79$ copper
fins are attached to the down-facing side of the copper plate extending into
the $200\text{\,}\mathrm{m}\mathrm{m}$ high liquefaction vessel in the bottom.
This increases the total condensation surface in the bottom vessel in contact
with the xenon to $2.2\text{\,}\mathrm{m}^{2}$. The liquefaction reservoir can
be filled with up to $19.6\text{\,}\mathrm{l}$ LXe limited by the length of
the copper fins. The bottom flange is funnel-shaped to collect the radon-
depleted LXe at a centered feed returning the liquid via a 1/2” stainless
steel tube to the global system.

Furthermore, a PID regulated heating system based on 12 1/2” heating
cartridges (WEMA S5105) connected to a programmable 3 kW power supply (Kniel
VE3PUI2) is used to balance the desired evaporation in the top reservoir as
well as the liquefaction in the bottom reservoir depending on the circulation
flow, the operation pressure and the applied cooling power at the top
condenser.

Following the heat transfer model in Ref. k  based on conservative
assumptions, an expected heat transfer between the two reservoirs of
$3293\text{\,}\mathrm{W}$ is expected for a pressures of
$2\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$ in the top and
$3.5\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$ in the bottom vessel. The
reboiler performance can only be tested with the RRS system fully constructed.
The results are presented in section V.

#### Compressor

The compressor is a four-cylinder magnetically-coupled piston pump based on a
prototype used for the XENON1T experiment BRW . It features particular
cleanliness and radiopurity to avoid contamination of the purified xenon.
Further improvements of its dead volume and flow path compared to the
prototype in combination with the usage of four pumps in parallel with a
smaller dimension allows to reach the required flows and compression for the
RRS design. A synchronized movement with a phase shift of the four pumps
results in an additional performance boost and guarantees a stable operation
of the RRS. The system features a flow meter (Brooks SLA5863) at its outlet,
where flows of up to $167\pm
3.\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$ ($474\pm
9.\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$) were measured during
commissioning at a xenon inlet pressure of
$2.1\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$ and a compression of $1.80\pm
0.06\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$. A detailed description of the
design and performance is given in Ref. l .

#### Auxiliary Components

Two commercial plate heat exchangers (EWT BE4-10x20) featuring 1/2” inlets and
outlets are installed in parallel between the column and the compressor to
warm-up and pre-cool the GXe.

The spiral immersed in the top reboiler vessel is a 1/2” stainless steel tube
with 4.25 windings and a total length of $3000\text{\,}\mathrm{m}\mathrm{m}$.

The LXe bypass valve (Thermomess) is specifically made for LXe applications
and has a diameter of 6 mm.

##  V Thermodynamic Performance

The top condenser and the compressor were tested stand-alone as described in
Ref. k  and Ref. l , respectively. The performance of the reboiler can only be
investigated with the full RRS system installed underground at LNGS. The
thermodynamic functionality and stability of the full RRS is presented in this
section. For this, the internal LXe bypass valve is used as the throttle
valve, expanding and feeding the LXe from the bottom reboiler vessel at a high
pressure to the LXe feed port of the package tube at a lower pressure. To
start the LXe circulation through the bypass valve, the RRS needs to be cooled
down, and both reboiler vessels have to be filled with LXe initially.

### Filling

In order to cool down the RRS from room temperature to about
$178\text{\,}\mathrm{K}$, the entire system is filled with
$3\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$ xenon. Then, the LN2 cooling at the
top condenser is activated, and the xenon starts to cool down. In the cooling
process, LXe droplets continuously form at the top and fall down into the
package tube, where they evaporate again. Like that, the top condenser,
package tube and top reboiler vessel can be cooled down from top to bottom
within $12\text{\,}\mathrm{h}$. Once the system is cold, GXe is continuously
injected into the package tube via the GXe feed port, is then liquefied at the
top condenser, and from there, rinsing down along the package tube into the
top reboiler vessel.

In the next step, xenon needs to be transferred into the bottom reboiler
vessel, to run the internal circulation. This bottom filling is the first test
to liquefy xenon with xenon in the reboiler system and is presented in figure
7(a): The top panel contains the relevant pressures for the filling process,
namely the column pressure PI510 (green), and the bottom reboiler pressure
PI530 (red). The middle panel shows the liquid level meter measurements DP540
(purple) based on differential pressure in the bottom reboiler vessel. The
bottom panel illustrates the flow FIC550 (light blue) created by the
compressor. Before a continous filling can be established, the bottom reboiler
vessel is pre-cooled as well by circulating GXe through the entire system. In
detail, cold GXe is extracted and warmed up using the GXe/GXe HE. The
compressor pushes the GXe back into the GXe/GXe HE where it is cooled down
again. The GXe enters the spiral to be even further cooled, and then enters
the bottom reboiler. From here, the GXe flows back into the package tube via
the fully opened bypass valve. This is done over the course of a few hours
from which only the relevant part for the filling process is included in
figure 7(a).

(a) Filling (b) Internal liquid circulation

Figure 7: RRS performance measurements: (a) Filling of the bottom reboiler
vessel. By closing the LXe bypass valve, the bottom reboiler pressure (PI530)
increases up to $2.84\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$ required to
liquefy the xenon gas flow (FIC550). The liquid level increase in the bottom
part is indicated by a differential pressure measurement (DP540). (b) Start of
internal liquid circulation of the RRS through the LXe bypass valve. The
required bottom reboiler pressure (PI530) for the liquefaction of the required
flow as well as the column pressure (PI510) are shown (top). Several
circulation flows (FIC550) were tested (bottom).

At $t=$0.4\text{\,}\mathrm{h}$$, the bypass valve is partially closed. This
results in a decrease of the flow FIC550 and an increase in the bottom
reboiler pressure PI530. After that, the compressor performance was raised and
the flow FIC550 and PI530 further increase. At $t=$2.1\text{\,}\mathrm{h}$$,
the bypass valve was fully closed leading to another flow reduction combined
with an increase of $\mathrm{PI}530$ until it reaches a maximum of
$2.84\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$ at $t=$2.6\text{\,}\mathrm{h}$$
and from here, staying constant. This is an indication for the first
liquefaction of the GXe using the LXe at the top as cooling medium. A pressure
difference of $0.84\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$ is required to
initiate the liquefaction process given the constant pressure of
PI510$=$2\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$$ in the column.

At $t=$3.05\text{\,}\mathrm{h}$$, the LXe in the bottom vessel reaches the
level meter $\mathrm{DP}540$. From here on, xenon was filled until
$t=$5.75\text{\,}\mathrm{h}$$ with flows of up to
$15\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$
($43\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$). The total amount
filled is
$\mathrm{DP}540=$15.2\text{\,}\mathrm{m}\mathrm{b}\mathrm{a}\mathrm{r}$$
corresponding to about $33.8\text{\,}\mathrm{k}\mathrm{g}$ of LXe.

After the filling, the compressor was stopped and the bottom reboiler was
isolated from the column to monitor the containment/stability over the course
of several hours before starting the circulation.

### Internal liquid circulation

The internal liquid circulation measurements including different flow values
are presented in figure 7(b): The top panel shows the column pressure PI510
(green), and the bottom reboiler pressure PI530 (red). The bottom panel
contains the flow FIC550 (light blue) induced by the compressor.

The process was started at $t=$0.35\text{\,}\mathrm{d}$$ by partially opening
the LXe bypass valve and starting the compressor. The pressure in the column
was kept constant at $\mathrm{PI}510=$2.00\pm
0.03\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$$ with the help of the PID
regulated heaters in the reboiler copper plate. Starting from
$t=$0.45\text{\,}\mathrm{d}$$, a pressure increase to $\mathrm{PI}530=$3.01\pm
0.05\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$$ in the bottom reboiler vessel
was required to fully liquefy the related xenon gas flow of $36\pm
1.\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$ ($103\pm
3.\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$) and to push the
generated LXe from the reboiler bottom $1.5\text{\,}\mathrm{m}$ upwards
through the bypass valve back into the package tube’s LXe feed port.

This flow configuration was kept for three days to monitor the stability of
the RRS. Starting from $t=$3.3\text{\,}\mathrm{d}$$, the compressor
performance was successively increased to reach larger flows. Between
$$3.6\text{\,}\mathrm{d}$<t<$4.3\text{\,}\mathrm{d}$$, the RRS was performed
stably at a flow of $78\pm
1.\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$ ($219\pm
2.\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$), slightly above the
design target value. At $t=$4.52\text{\,}\mathrm{d}$$, a maximum operation
flow of $91\pm 2.\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$ ($258\pm
6.\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$) at
$\mathrm{PI}530=$3.25\pm 0.01\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$$ was
achieved. This is about $1.3$ times above the desired target flow and
sufficient for an efficient radon removal in XENONnT. All relevant FIC550 flow
values as well as reboiler bottom pressures PI530 are summarized in table 5.

Table 4: Temperature and pressure values of the intermediate states during internal liquid circulation at a flow of $91\pm 2.\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$ ($258\pm 6.\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$). In order to describe the full cycle, some values with (‡) are computed from measured values (†), or are based on assumptions (∗). State | T [K] | P [bar] | Part
---|---|---|---
\raisebox{-0.3pt}{\scriptsize{1a}}⃝ | 178.2‡ | 2.03† | Reboiler top
\raisebox{-0.3pt}{\scriptsize{1b}}⃝ | 181.3† | 2.03† | Top Condenser
\raisebox{-0.3pt}{\scriptsize{1c}}⃝ | 268.8† | 2.03† | GXe/GXe HE to 4MP
\raisebox{-0.3pt}{\scriptsize{1d}}⃝ | 285.2† | 1.58† | 4MP inlet
\raisebox{-0.3pt}{\scriptsize{2a}}⃝ | 299.9† | 3.77† | 4MP outlet
\raisebox{-0.3pt}{\scriptsize{2b}}⃝ | 218.1† | 3.77∗ | GXe/GXe HE to spiral
\raisebox{-0.3pt}{\scriptsize{2c}}⃝ | 196.7† | 3.25† | Spiral
\raisebox{-0.3pt}{\scriptsize{3}}⃝ | 188.5‡ | 3.25† | Reboiler bottom
\raisebox{-0.3pt}{\scriptsize{4}}⃝ | 178.2‡ | 2.03† | Internal Bypass

In the following, the maximum flow measurement is used to describe the
thermodynamic cycle. The temperature and pressure at each intermediate state
of the Clausius-Rankine cycle are summarized in table 4. All given pressure
values are measured, except for state \raisebox{-0.3pt}{\scriptsize{2b}}⃝,
where no pressure measurement is available. Therefore, this value is an
assumption. Furthermore, some temperature values were derived from the
measured pressure at a given state using the saturation properties. This is
specifically the case for RTDs in states with LXe, where the limited contact
between sensor and metal enclosure leads to temperature offsets towards warmer
values.

Values for the enthalpy $h$ and specific entropy $s$ are computed from the
temperature and pressure values at each state and are summarized in a $p$-$h$
diagram in figure 8(a) and a $T$-$s$ diagram in figure 8(b). In both diagrams,
the compression is highlighted in red, the condensation in green, the
expansion in purple, and the evaporation in light blue. Note that the
expansion (\raisebox{-0.8pt}{3}⃝$\rightarrow$\raisebox{-0.8pt}{4}⃝) through
the bypass valve (throttle) is an irreversible process. Therefore, the
enthalpy stays constant as indicated by the vertical purple line in figure
8(a), while the specific entropy increases as indicated by the purple line
with a small inclination, not visible in figure 8(b). This also shows that a
fraction of the initially saturated LXe evaporates during the expansion. The
distance from the saturated liquid curve to state \raisebox{-0.8pt}{4}⃝
indicates the related vapor quality $f_{\mathrm{vap}}$ which indicates the gas
fraction that is created. The remaining liquid fraction $f_{\mathrm{liq}}$ is
then given by $(1-f_{\mathrm{vap}})$. In reality, the throttle efficiency
$\epsilon_{\mathrm{thr}}$ is expected to be smaller than 1 depending on the
size of heat losses across the throttle. This can lead to an increase in
enthalpy between the states \raisebox{-0.8pt}{3}⃝ and \raisebox{-0.8pt}{4}⃝.

(a) $p$-$h$ diagram (b) $T$-$s$ diagram

Figure 8: The left-turning Clausius-Rankine cycle at a process flow of $91.3\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$ ($258\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$) with the four main states compression (red), condensation (green), expansion (purple), and evaporation (light blue) subdivided into intermediate states for a throttle efficiency $\epsilon_{\mathrm{thr}}=1$. The $p$-$h$-diagram (a) indicates also lines of equal vapor quality ($f_{\mathrm{vap}}$), isoterms and isentropic lines. The $T$-$s$-diagram (b) indicates also lines of equal vapor quality ($f_{\mathrm{vap}}$), as well as isobaric lines. The different states were computed using the $CoolProp$ library cool . Table 5: Parameters during internal liquid circulation. Measured variables are indicated with (†), while computed values are indicated by (‡). The value of $f_{\mathrm{liq}}$ is calculated for a perfect throttle $\epsilon_{\mathrm{thr}}=1$ (as shown in figure 8a), while $\epsilon_{\mathrm{thr}}$ is calculated using equation (35). ${F^{{\dagger}}}$ [kg/h] ([slpm]) | PI530† [bar] |  $Q_{\mathrm{B^{\prime}}}^{{\ddagger}}$ [W] |  $Q_{\mathrm{H}}^{{\dagger}}$ [W] | $f_{\mathrm{liq}}^{{\ddagger}}$ |  $\epsilon_{\mathrm{thr}}^{{\ddagger}}$ [$90\text{\,}\mathrm{\char 37\relax}$ C.L.]
---|---|---|---|---|---
0 | $2.87\pm 0.01$ | 0 | $1129\pm\,6$ | - | -
$33.6\pm 1.4$ ($95\pm 4$) | $3.05\pm 0.01$ |  $841\pm 36$ | $1086\pm 10$ | $0.9658\pm 0.0005$ | $>0.94$
$49.2\pm 1.8$ ($139\pm 5$) | $3.08\pm 0.01$ | $1230\pm 44$ | $1066\pm 12$ | $0.9649\pm 0.0005$ | $>0.94$
$55.6\pm 1.8$ ($157\pm 5$) | $3.10\pm 0.01$ | $1389\pm 45$ | $1067\pm 13$ | $0.9644\pm 0.0005$ | $>0.95$
$63.0\pm 1.8$ ($178\pm 5$) | $3.12\pm 0.01$ | $1574\pm 45$ | $1060\pm 13$ | $0.9638\pm 0.0005$ | $>0.95$
$68.7\pm 1.8$ ($194\pm 5$) | $3.14\pm 0.01$ | $1714\pm 44$ | $1060\pm\,8$ | $0.9632\pm 0.0005$ | $>0.96$
$77.5\pm 1.8$ ($219\pm 5$) | $3.20\pm 0.01$ | $1933\pm 44$ | $1048\pm 11$ | $0.9616\pm 0.0005$ | $>0.96$
$86.7\pm 1.8$ ($245\pm 5$) | $3.22\pm 0.01$ | $2162\pm 43$ | $1032\pm 12$ | $0.9611\pm 0.0005$ | $>0.96$
$91.3\pm 2.1$ ($258\pm 6$) | $3.25\pm 0.01$ | $2274\pm 52$ |  $991\pm 17$ | $0.9602\pm 0.0005$ | $>0.94$

The throttle efficiency is calculated in the following for the different flow
steps presented in table 5 to further evaluate the RRS performance. For small
heat losses across the bypass valve, the efficiency $\epsilon_{\mathrm{thr}}$
is expected to be close to $1$. The assumption is made that the throttle is
made of the LXe bypass valve including the stainless steel tubes from the
reboiler bottom vessel up to the LXe feed port. Furthermore, the external heat
input is expected to be constant during all measurements presented and can
therefore be neglected for the throttle efficiency calculations. The top
condenser’s cooling power $Q_{\mathrm{L}}$, and thus, the reflux liquid flow
$L$, was kept constant throughout all measurements. As described in section
IV, the additional electrical heating power $Q_{\mathrm{H}}$ is applied to the
reboiler copper plate to balance the LXe flow $L$ coming from the top
condenser. The presented values $Q_{\mathrm{H}}$ were measured once both LXe
levels inside the bottom reboiler part as well as inside the top part were
constant after a flow change.

The LXe flow $L^{\prime}$ entering the top reboiler vessel is then given by

$L^{\prime}=L+qF,$ (28)

with $q=\epsilon_{\mathrm{thr}}\cdot f_{\mathrm{liq}}$. Due to the mass
balance in this location, it follows

$L^{\prime}=V^{\prime},$ (29)

with $V^{\prime}$ being the evaporated GXe leaving the top reboiler. The
related heat transfer can be further split into different contributions:

$\displaystyle Q_{L^{\prime}}$
$\displaystyle=Q_{L}+Q_{qF}=Q_{B^{\prime}}+Q_{H}+Q_{S}.$ (30)

Here, $Q_{qF}$ is the stored energy from the flow fraction $qF$,
$Q_{B^{\prime}}$ is the heat input transferred through the reboiler copper
plate from the bottom to the top part, and $Q_{S}$ is the heat input from the
spiral immersed in LXe of the top reboiler part. The different $Q$ terms are
given by

$\displaystyle Q_{L}$
$\displaystyle=\left.Q_{\mathrm{H}}\right|_{$0\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$}=const.,$
(31) $\displaystyle Q_{qF}$ $\displaystyle=\epsilon_{\mathrm{thr}}\cdot
f_{\mathrm{liq}}\cdot F\cdot\left.\Delta
H_{\mathrm{vap}}^{\mathrm{Xe}}\right|_{\mathrm{PI510}},$ (32) $\displaystyle
Q_{B^{\prime}}$ $\displaystyle=F\cdot\left.\Delta
H_{\mathrm{vap}}^{\mathrm{Xe}}\right|_{\mathrm{PI530}},$ (33) $\displaystyle
Q_{S}$ $\displaystyle=F\cdot c_{\mathrm{p}}\cdot\Delta T_{\mathrm{S}},$ (34)

Here,
$\left.Q_{\mathrm{H}}\right|_{$0\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$}$
is the applied heating power at zero flow $F$, $\left.\Delta
H_{\mathrm{vap}}^{\mathrm{Xe}}\right|_{\mathrm{PI510}}$ is the enthalpy of
evaporation for the given column pressure $\mathrm{PI510}$. The pressure in
the column was kept constant throughout all measurements at a value of
$\mathrm{PI510}=$2.00\pm 0.01\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$$.
$\left.\Delta H_{\mathrm{vap}}^{\mathrm{Xe}}\right|_{\mathrm{PI530}}$ is the
enthalpy of evaporation for the given pressure $\mathrm{PI530}$ in the bottom
reboiler part. Its value depends on the flow and the values are summarized in
table 5.The specific heat capacity of the GXe inside the spiral is given by
$c_{\mathrm{p}}$, while the temperature difference across the spiral is
$\Delta T_{\mathrm{S}}$. The applied heating power $Q_{H}$ is used to achieve
mass balance as described above and is measured for each given flow. Using
equations (29) to (34) and solving for the throttle efficiency
$\epsilon_{\mathrm{thr}}$ leads to

$\epsilon_{\mathrm{thr}}=\frac{F\cdot\left(\left.\Delta
H_{\mathrm{vap}}^{\mathrm{Xe}}\right|_{\mathrm{PI530}}+c_{\mathrm{p}}\cdot\Delta
T_{\mathrm{S}}\right)+\Delta Q_{H}}{f_{\mathrm{liq}}\cdot F\cdot\left.\Delta
H_{\mathrm{vap}}^{\mathrm{Xe}}\right|_{\mathrm{PI510}}},$ (35)

with $\Delta
Q_{H}=Q_{H}-\left.Q_{\mathrm{H}}\right|_{$0\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$}$.

The temperature difference $\Delta T_{\mathrm{S}}$ cannot be accurately
measured as the connection between the temperature sensors before and after
the spiral to the pipe introduce unknown systematics. This also does not allow
to determine the temperature at which the GXe enters the bottom reboiler.
However, following equation (35), the conservative assumption can be made that
the spiral has no effect ($c_{\mathrm{p}}\cdot\Delta T_{\mathrm{S}}=0$) and
that the GXe enters the reboiler at saturation temperature. This yields the
lowest value for the efficiency and a lower limit can be derived. Taking the
uncertainties for the measured flow, pressure and heating powers into account,
a throttle efficiency of
$\epsilon_{\mathrm{thr}}>0.94\left($90\text{\,}\mathrm{\char
37\relax}$\,\mathrm{C.L.}\right)$ is calculated for the maximum flow of
$F=$91.3\pm 2.1\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$($258\pm
6.\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$)$. The efficiency limits
for the remaining flows are summarized in table 5 and all yield similar
results close to one as expected for small heat losses across the bypass valve
and the connecting tubes.

The reboiler performance itself is investigated for the maximum flow. The flow
was fully liquefied exiting from the bottom reboiler vessel. This corresponds
to a heat transfer from the bottom to the top reboiler vessel through the
copper plate of

$\left.Q_{B^{\prime}}\right|_{$91\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$}=(2274\pm
52)\,\mathrm{W},$ (36)

with $\left.\Delta
H_{\mathrm{vap}}^{\mathrm{Xe}}\right|_{\mathrm{3.25\,bar}}=89.70$ kJ/kg NST
being the enthalpy of evaporation at the related pressure in the reboiler
bottom part. Note that also here the conservative assumption was made that
saturated GXe enters the reboiler for liquefaction after leaving the spiral.
The heating power at the given flow was measured to be

$\left.Q_{\mathrm{H}}\right|_{$91\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$}=$991\pm
17.\text{\,}\mathrm{W}$.$ (37)

This leads to a total heat transfer of

$\displaystyle\left.Q_{\mathrm{tot}}\right|_{$91\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$}=Q_{B^{\prime}}+Q_{\mathrm{H}}=$3265\pm
69.\text{\,}\mathrm{W}$.$ (38)

From the heat transfer model for the reboiler based on conservative
assumptions in Ref. k , a maximum total heat transfer of
$2627\text{\,}\mathrm{W}$ is expected for the given pressure of
PI$530=$3.25\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$$. The measured value is
about $1.25$ times larger, indicating that the liquefaction process is more
efficient than expected.

Finally, the coefficients of performance $COP_{\mathrm{R}}$ for the
refrigerator part and $COP_{\mathrm{HP}}$ for the heat pump part COP1  can be
derived from the p-h-diagram. A range for $0.94<\epsilon_{\mathrm{thr}}\leq 1$
is computed for the maximum flow:

$\displaystyle COP_{\mathrm{R}}$
$\displaystyle=\frac{h_{\mathrm{1a}}-h_{4}}{h_{\mathrm{2a}}-h_{\mathrm{1a}}}=4.10-4.36,$
(39) $\displaystyle COP_{\mathrm{HP}}$
$\displaystyle=\frac{|h_{3}-h_{\mathrm{2a}}|}{h_{\mathrm{2a}}-h_{\mathrm{1a}}}=5.36,$
(40)

with $h_{\mathrm{i}}$ being the enthalpy at each state. Traditional heat pumps
feature COP values of 2-5 COP , indicating that the RRS performance is on the
upper end, and thus, highly efficient.

##  VI Conclusion

A radon removal system based on cryogenic distillation was built to reduce the
radon background in XENONnT. The derived radon removal strategy based on the
radon source locations shows that a reduction by a factor two for type 1 radon
sources within the detector volume can be achieved for a process flow of
$62\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{h}$
($175\text{\,}\mathrm{s}\mathrm{l}\mathrm{p}\mathrm{m}$) given the
$8.4\text{\,}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{n}\mathrm{e}$ xenon
inventory. An additional factor two is expected when type 1b radon sources
from the detector’s GXe volume are extracted and converted into type 2 sources
before they can enter the detector’s LXe.

The distillation process was designed using the McCabe-Thiele method, where a
modification was needed: Instead of a physical xenon extraction flow at the
bottom that removes radon from the system, the radon decay itself was added as
an equivalent extraction flow. This makes it possible to describe the
distillation process, while conserving the required particle mass balance
inside the column. It was shown, that the energy efficient design based on a
Clausius-Rankine cycle with phase-changing cooling medium including a custom-
made heat pump drastically reduces the externally applied cooling power.

A first liquefaction of radon-depleted xenon in the bottom vessel of the
reboiler heat exchanger using the liquid xenon in the top vessel was achieved.
A heat transfer of $3265\pm 69.\text{\,}\mathrm{W}$ was demonstrated, a factor
1.25 larger than modeled in k . The system was operated in an internal liquid
circulation cycle using a LXe bypass valve. A stable flow of $(91\pm 2)$ kg/h
(($258\pm 6$) slpm) was achieved, a factor 1.3 larger than required by design.
In this test, the efficiency of our LXe bypass throttle valve was evaluated to
be $\epsilon_{\mathrm{thr}}>0.94\left($90\text{\,}\mathrm{\char
37\relax}$\,\mathrm{C.L.}\right)$.

The achieved process flow of the LXe extraction mode in combination with the
GXe extraction mode leads to an expected total radon reduction by a factor of
4.7. With an initial activity concentration of $4.25\,\upmu$Bq/kg in XENONnT,
a final [222]Rn activity concentration of $<1\,\upmu$Bq/kg is expected.

###### Acknowledgements.

We thank the XENON Collaboration and LNGS staff, especially D. Tatananni and
R. Corrieri, for supporting the installation of the system at LNGS. We thank
the group of M. Lindner at MPIK Heidelberg for determining the radon emanation
of all components of the removal system. We acknowledge the work of the
Precision Mechanical and the Electrical Workshop of the Institute for Nuclear
Physics at Münster University. The development of the system at Muenster
University has been supported by the German Ministery for Education and
Research BMBF (05A17PM2, 05A20PM1).

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