RADON REDUCTION SYSTEM FOR LZ DARK MATTER EXPERIMENT · 2018. 11. 22. · 136 Xe l Det. + Sur. +...

14
RADON REDUCTION SYSTEM FOR LZ DARK MATTER EXPERIMENT Maris Arthurs On behalf of the Michigan DM Group 16-July-2018 DMSS by the University at Albany, SUNY

Transcript of RADON REDUCTION SYSTEM FOR LZ DARK MATTER EXPERIMENT · 2018. 11. 22. · 136 Xe l Det. + Sur. +...

Page 1: RADON REDUCTION SYSTEM FOR LZ DARK MATTER EXPERIMENT · 2018. 11. 22. · 136 Xe l Det. + Sur. + Env. 0 2 4 6 8 10 222Rn specific activity [µBq/kg] 1 1.5 2 2.5 3 3.5 ×10−48] 2

RADON REDUCTION SYSTEM FOR LZ DARK MATTER EXPERIMENT

Maris ArthursOn behalf of the Michigan DM Group

16-July-2018

DMSS by the University at Albany, SUNY

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Radon—Where From & Why Bad ?2

¨  222Rn is a decay product of 238U that is everywhere¤  τRn = 5.516 day (mean lifetime)

¨  Radioactive noble gas with chemistry similar to xenon

¨  Dissolves in liquid xenon (LXe) and isn’t removed with hot gas purifying getters

¨  222Rn continuously emanates from detector components

¨  Decay products of 222Rn can mimic Dark Matter signals¤  β-decay of 214Pb can end up in the WIMP ROI and

survive the S2/S1 discrimination cut.

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Radon—Largest Background Source in LZ3

¨  The highest scenario assumes no reduction in emanation rate at LZ operating temperatures, 175K¨  222Rn emanation rates from warm cables and feedthroughs of LZ detector components estimated to

be in 8.3-20 mBq range

0 50 100 150 200Electronic recoil energy [keV]

10�6

10�5

10�4

Rate

[cou

nts/k

g/da

y/ke

V]

Solar n

222Rn

220Rn

85Kr

136Xe

Total

Det. + Sur. + Env.

0 2 4 6 8 10Bq/kg]µRn specific activity [222

1

1.5

2

2.5

3

3.548−10×]2

[cm

2W

IMP-

nucl

eon

cros

s sec

tion

at 4

0 G

eV/c

low estim

ate

projectedhigh estim

ate

highest estimate

LZ sensitivity (1000 live days)

Projected limit (90% CL one-sided)

High and low correspond +1σ and -1σ of all 222Rn screening measurements, respectively.

The background spectra in the 5.6 ton fiducial volume of the LZ LXe TPC for single scatter events

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In-line Radon Reduction System for LZ 4

q  N = τRn A (= 5.516 d * 1 mBq) = 476 Rn atoms (steady-state population)

q  Sequestration of atoms in activated carbon trap until most 222Rn nuclei decay¤  Analogous to gas chromatography:

v(Xe)/ v(Rn) (-85 C) ≈ 1000¨  In order to obtain removal of 90%,

sequestration time must be greater than ln(10)∙ τRn = 12.7 days

The LZ goal is to reduce 222Rn background of the warm section (cables and feedthroughs) below 1 mBq, about an order of magnitude reduction from current estimates, 8.3-20mBq.

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Michigan Radon Reduction R&D5

¨  1: SAES high temperature gas purification getter

¨  2: Gas flow meter¨  3: Emanation chamber

with 238U ores¨  4: Radon source (Pylon

source (103.6 kBq))¨  5: Cryostat with charcoal

trap¨  6: RAD7 radon detector¨  7: In-house radon detector

1

2

3

4

567

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Different Activated Charcoals Tested6

Charcoal Density (g/cm3) Surface area (m2/g) Spec. activity���(mBq/kg)

Price ($/kg)

Calgon OVC 4x8 0.45 1,100 53.6 ± 1.3 6

Shirasagi 0.45 1,240 101 ± 8 27

Saratech 0.60 1,340 1.71 ± 0.20 35

Saratach (HNO3) 0.60 1,340 0.51 ± 0.09 135

CarboAct 0.28 1,000 0.23 ± 0.19 15,000

Sara

tech

Carb

oAct

Shira

sagi

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Elution Curves for Ar in a 0.1l Trap at 293K7

¨  222Rn adsorption characteristics on various charcoals were studied in N2, Ar, and Xe carrier gases.

¨  Vastly different transition times for various charcoal types.

¨  By measuring the 218Po spectra after 222Rn injection, elution curves were obtained using the chromatographic plate model—the charcoal trap is divided into stages of equal volume where the gas and charcoal are in equilibrium.

0 100 200 300 400 500 600Time, (min)

0

100

200

300

400

500

600

700

Po21

8 Pe

ak A

rea

Saratech

OVC (4x8), Calgon

Shirasagi, G2x4/6-1n = 2.8

n = 47

n = 4.9

Figure 5: Examples of elution curves, fitted to function (2) (solid lines), of218Po measured in Ar carrier gas at 295 K where n is the number of theoreticalstages.

volume in which equilibrium can always exist between the gasand the charcoal. For a short pulse of 222Rn introduced into thecharcoal bed layer the elution curve is

y

� t⌧

�=↵n

n

(n � 1)!� t⌧

�n�1

e

�n

t

⌧ , (2)

where ↵ is the amplitude of the radon spike input, ⌧ is theaverage breakthrough time of 222Rn in a carrier gas, and n is thenumber of theoretical stages.

The ⌧-value is given by the linear relation [6]

⌧ =k

a

m

f

, (3)

where k

a

is the dynamic adsorption coe�cient in l/g, m is themass of the adsorbent in g, and f is the mass flow rate in slpm.

The ⌧-values for 222Rn in N2, Ar and Xe gases and the n-values were obtained from fits of the elution curves and arepresented with total uncertanties (�⌧2=�2

stat

+�2sys

) in Table 3.The n-values are presented with statistical uncertanties derivedfrom the elution curve fits.

The average breakthrough times of 222Rn measured in Ar car-rier gas in all charcoals are greater than in N2 gas measured inthe same charcoals. The longest average breakthrough times of222Rn both in N2 and Ar carrier gases were measured in CalgonOVC 4x8 and Saratech. The total uncertainties were about 5%.The systematic uncertainties were due to small fluctuations inthe flow rate and gas pressure in the system. The ⌧-values in Arand N2 in Calgon OVC 4x8 and Saratech charcoals increasedwith increasing gas pressure.

The ⌧-values for 222Rn in Xe measured in Saratech aregreater than in Carboact. The ⌧-values for regular Saratech andHNO3 etched Saratech are consistent within statistical and sys-tematic uncertainties. The ⌧-values in Xe gas in Carboact andShirasagi decrease as the gas flow rate increases by a factor of

CarrierG

asC

harcoalType⌧(m

in)n

295K

273K

263K

253K

190K

295K

273K

263K

253K

190K

N2

(2slpm

)

Calgon

OV

C4x8

(50g,1

Atm

A)

174.0±7.5419±19

712±311123±50

�4.7±0.1

5.4±0.25.5±0.2

5.6±0.2�

Saratech(70

g,1A

tmA

)189±8

444±20709±31

1152±50�

46±152±1

62±261±1

�Shirasagi(45

g,1A

tmA

)123±6

309±15490±23

825±39�

3.10±0.023.3±0.1

3.5±0.13.7±0.1

�A

r(2

slpm)

Calgon

OV

C4x8

(50g,1

Atm

A)

210±9505±23

825±361037±47

�5.0±0.2

5.0±0.25.4±0.3

6.2±0.4�

Saratech(70

g,1A

tmA

)189±9

520±24844±38

1371±62�

47±152±1

58±271±2

�Shirasagi(45

g,1A

tmA

)117±6

366±17613±31

1015±57�

3.3±0.13.0±0.1

3.1±0.13.0±0.1

�X

e(0.5

slpm)

CarboA

ct(241g,1

Atm

A)

246±14329±18

407±22563±31

992±548.3±0.5

8.6±0.210.3±1.0

5.9±0.15.60±0.04

Saratech(650

g,1.6A

tmA

)612±32

800±421270±67

1651±883800±200

138±2132±1

142±1142±10

142±9Etched

Saratech(650

g,1.6A

tmA

)623±33

882±471216±64

1788±953840±200

117±3132±5

116±5140±11

139±3Shirasagi(45

g,1A

tmA

)46±3

63±485±5

109±7193±12

6.0±0.15.70±0.04

5.50±0.055.7±0.1

4.2±0.1X

e(2

slpm)

Shirasagi(45g,1

Atm

A)

13.8±0.114±1

20±129±2

50±32.90±0.04

2.90±0.042.00±0.02

3.0±0.12.30±0.04

Table3:The

average222R

nbreakthrough

timesand

numberoftheoreticalstagesin

varioustypesofcharcoalsmeasured

inN

2 ,Arand

Xe

carriergases.

6

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ka—The Dynamic Adsorption Coefficient8

¨  ka-values for 222Rn range from 5-45 l/g in N2 and Ar carrier gases, while in Xe they are an order of magnitude lower, 0.5-3 l/g.

¨  For Xe as the carrier gas the ka-values in Saratech and etched (HNO3) Saratech consistent with Arrhenius law, however in CarboAct, violates it.

0 100 200 300 400 500 600Time, (min)

0

100

200

300

400

500

600

700

Po21

8 Pe

ak A

rea

Saratech

OVC (4x8), Calgon

Shirasagi, G2x4/6-1n = 2.8

n = 47

n = 4.9

Figure 5: Examples of elution curves, fitted to function (2) (solid lines), of218Po measured in Ar carrier gas at 295 K where n is the number of theoreticalstages.

volume in which equilibrium can always exist between the gasand the charcoal. For a short pulse of 222Rn introduced into thecharcoal bed layer the elution curve is

y

�t

�=↵n

n

(n � 1)!�

t

�n�1

e

�n

t

⌧ , (2)

where ↵ is the amplitude of the radon spike input, ⌧ is theaverage breakthrough time of 222Rn in a carrier gas, and n is thenumber of theoretical stages.

The ⌧-value is given by the linear relation [6]

⌧ =k

a

m

f

, (3)

where k

a

is the dynamic adsorption coe�cient in l/g, m is themass of the adsorbent in g, and f is the mass flow rate in slpm.

The ⌧-values for 222Rn in N2, Ar and Xe gases and the n-values were obtained from fits of the elution curves and arepresented with total uncertanties (�⌧2=�2

stat

+�2sys

) in Table 3.The n-values are presented with statistical uncertanties derivedfrom the elution curve fits.

The average breakthrough times of 222Rn measured in Ar car-rier gas in all charcoals are greater than in N2 gas measured inthe same charcoals. The longest average breakthrough times of222Rn both in N2 and Ar carrier gases were measured in CalgonOVC 4x8 and Saratech. The total uncertainties were about 5%.The systematic uncertainties were due to small fluctuations inthe flow rate and gas pressure in the system. The ⌧-values in Arand N2 in Calgon OVC 4x8 and Saratech charcoals increasedwith increasing gas pressure.

The ⌧-values for 222Rn in Xe measured in Saratech aregreater than in Carboact. The ⌧-values for regular Saratech andHNO3 etched Saratech are consistent within statistical and sys-tematic uncertainties. The ⌧-values in Xe gas in Carboact andShirasagi decrease as the gas flow rate increases by a factor of

CarrierG

asC

harcoalType⌧(m

in)n

295K

273K

263K

253K

190K

295K

273K

263K

253K

190K

N2

(2slpm

)

Calgon

OV

C4x8

(50g,1

Atm

A)

174.0±7.5419±19

712±311123±50

�4.7±0.1

5.4±0.25.5±0.2

5.6±0.2�

Saratech(70

g,1A

tmA

)189±8

444±20709±31

1152±50�

46±152±1

62±261±1

�Shirasagi(45

g,1A

tmA

)123±6

309±15490±23

825±39�

3.10±0.023.3±0.1

3.5±0.13.7±0.1

�A

r(2

slpm)

Calgon

OV

C4x8

(50g,1

Atm

A)

210±9505±23

825±361037±47

�5.0±0.2

5.0±0.25.4±0.3

6.2±0.4�

Saratech(70

g,1A

tmA

)189±9

520±24844±38

1371±62�

47±152±1

58±271±2

�Shirasagi(45

g,1A

tmA

)117±6

366±17613±31

1015±57�

3.3±0.13.0±0.1

3.1±0.13.0±0.1

�X

e(0.5

slpm)

CarboA

ct(241g,1

Atm

A)

246±14329±18

407±22563±31

992±548.3±0.5

8.6±0.210.3±1.0

5.9±0.15.60±0.04

Saratech(650

g,1.6A

tmA

)612±32

800±421270±67

1651±883800±200

138±2132±1

142±1142±10

142±9Etched

Saratech(650

g,1.6A

tmA

)623±33

882±471216±64

1788±953840±200

117±3132±5

116±5140±11

139±3Shirasagi(45

g,1A

tmA

)46±3

63±485±5

109±7193±12

6.0±0.15.70±0.04

5.50±0.055.7±0.1

4.2±0.1X

e(2

slpm)

Shirasagi(45g,1

Atm

A)

13.8±0.114±1

20±129±2

50±32.90±0.04

2.90±0.042.00±0.02

3.0±0.12.30±0.04

Table3:The

average222R

nbreakthrough

timesand

numberoftheoreticalstagesin

varioustypesofcharcoalsmeasured

inN

2 ,Arand

Xe

carriergases.

6

Xe carrier gas

N2, Ar carrier gas

¨  τ, the average breakthrough time for radon is related to the absorption coefficient by , obtained from the fit of the elution curves.

¨  ka-values for N2 and Ar as a function of the inverse temperature of the trap follow Arrhenius law for the tested charcoals.

Different Ranges

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Adsorption of Xenon gas on Charcoal9

¨  Xe atoms have high polarizability and tend to occupy the charcoal adsorption sites much faster resulting in the short 222Rn breakthrough times.¤  Increases linear with decreasing

temperature¤  Increases only slightly with pressure

¨  Saratech adsorbs on average about 30% less Xe than CarboAct at atmospheric pressures .

¨  Adsorption of N2 and Ar gases was below detection limit of the scale, (below 20 g of charcoal)

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Building a Radon Trap 10

¨  Lowest achievable Rn concentration is limited by specific activity (s0) of charcoal

¨  Need 5 – 7 kg of etched Saratech to reduce Rn concentration from warm cables and feedthroughs at the output of the trap below 1 mBq

¨  Even though CarbAct has lowest s0, not most efficient trap material for low(ish) mass

Adsorbent mass, (kg)0 2 4 6 8 10 12 14

222R

n ou

tput

con

cent

ratio

n, (m

Bq)

0

1

2

3

4

5

6

7

8

Carboact (this work)Carboact (Rau et al.)Saratech (this work)

(a)

Adsorbent mass, (kg)0 2 4 6 8 10 12 14

222R

n ou

tput

con

cent

ratio

n, (m

Bq)

0

2

4

6

8

10

12

14

16

18

20

Carboact (this work)Carboact (Rau et al.)Saratech (this work)

(b)

Figure 10: 222Rn trap output concentration versus charcoal mass for input trapconcentrations of 8.3 mBq at 0.5 slpm (a), and 20 mBq at 2 slpm (b) fromthe LZ DM detector. The colored bands represent uncertainties, and the blackdashed lines represent the minimal 222Rn concentrations required for the LZDM experiment.

5. Acknowledgments

We acknowledge support of the US Department of En-ergy (DE-SC0015708), Lawrence Berkeley National Labora-tory (LBNL), Stanford Linear Accelerator Center (SLAC) andthe University of Michigan. We would like to thank ProfessorJacques Farine at Laurentian University for providing the rub-ber radon emanation standard and Professor Tom Shutt at SLACfor providing the radon counting hardware. We would like toacknowledge Eric Miller at South Dakota School of Mines andTechnology for performing the temperature dependence radonemanation rate calculations for the LZ components. We wouldalso like to thank the members of the LZ collaboration for manyinsightful discussions. Special thanks go to Professor Kimber-lee Kearfott at the Nuclear Engineering and Radiological Sci-

ences department of the University of Michigan for lending usthe Pylon radon source.

References

[1] D. S. Akerib et al., Results from a search for Dark Matter in the completeLUX exposure, Phys. Rev. Lett., 118 (2017) 021303.

[2] EXO-200 Collaboration, Search for Majorana neutrinos with the first twoyears of EXO-200 data, Nature, 510 (2014) 229–234.

[3] V. E. Guiseppe et al., The Status and Initial Results of the MAJORANADEMONSTRATOR experiment, arXiv:1708.07562, 2017.

[4] E. Aprile et al., Noble gas detectors, WILEY-VCH (2006) 1–363[5] Z. Wang et al., Large scale xenon purification using cryogenic distillation

for dark matter detectors, JINST 9 (2014) 1–14.[6] A. Pocar, Low background techniques and experimental challenges for

Borexino and Nylon Vessels, PhD thesis, Princeton university (2003) 1–267.

[7] A. Abe et al., Radon removal from gaseous xenon with activated charcoal,Nucl. Instrum. Meth. 661 (2012) 50–57.

[8] J. Golihtly, Characterization of a carbon radon filter and radon detection,Master thesis, Queen’s university, (2008) 1–108.

[9] D. S. Akerib et al., Projected WIMP sensitivity of the LUX-ZEPLIN (LZ)dark matter experiment, arXiv:1802.06039 [astro-ph.IM], 2018.

[10] T. Andersen, Development of systems for the Sudbury Neutrino Observa-tory, PhD thesis, University of Guelph (1997).

[11] A. Howard and W. Strange., Heavy-ion migration through argon and he-lium in weak electric fields, J. Appl. Phys. 69 (1991) 6248.

[12] C. Mitsuda et al., Development of super-high sensitivity radon detec-tor for the Super-Kamiokande detector, Nucl. Instrum. Meth. 497 (2003)414–428.

[13] F. Mamedov et al., Development of an ultra-sensitive radon detector forthe Super NEMO experiment, JINST. 6 (2011) 1–6.

[14] P. K. Hopke et al., The initial atmospheric behavior of radon decay prod-ucts, J. Rad. and Nucl. Chem., 203(2) (1996) 353–375.

[15] W. Rau and G. Heusser., 222Rn emanation measurements at extremely low

activities, Appl. Radiat. Isot. 53 (2000) 371–375.[16] RAD7 specification document, https://durridge.com/

documentation/RAD7%20Specifications.pdf, Last time accessed:2018-2-16.

[17] G. Bortels and P. Kollaers., Analytical function for fitting peaks in alpha-particle spectra from Si detectors, Appl. Radiat. Isot. 38(10) (1987) 831–837.

[18] K. P. Strong and D. M. Levins., Dynamic adsorption of radon on acti-vated carbon, Proceedings of the 15th DOE nuclear air cleaning confer-ence 10(19) (1978) 627–639.

[19] A. I. M. Keulemans et al., Gas Chromatography, New York, (1959) 1–234.

[20] A. Gross, Theoretical Surface Science:A Microscopic Perspective,Springer-Verlag, (2007).

[21] J. H. De Boer and S. Kruyer., The two-dimensional Van-Der Waals con-stants of molecules adsorbed on charcoal and graphite, Trans. of theFarad. Soc. 54 (1958) 540–547.

[22] D. Ruthven, Principles of adsorption and adsorption processes, Wiley,(1984).

[23] B. J. Mount et al., LUX-ZEPLIN (LZ) Technical Design Report,arXiv:1703.09144v1 [physics.ins-det], 2018.

10

Nin = 8.3 mBq, f = 0.5 SLPM

Nin = 20 mBq, f = 2 SLPM

Due to activity of the charcoalDue to Rn in GXe

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Conclusion & Acknowledgments11

¨  222Rn breakthrough times in N2 and Ar carrier gases are significantly longer than in Xe carrier gas.¤  This may be attributed to the lower polarizabilies of N2 and Ar compared to Xe

¨  Among the investigated charcoals, Saratech appears to be the most efficient 222Rn reduction material.¤  Chemical etching of Saratech with HNO3 acid reduced the intrinsic radioactivity (238U) by

about a factor of three.¤  Etching did not affect the 222Rn adsorption characteristics of Saratech making it a strong

candidate for a trap.¨  Published in NIM journal: A 903 (2018) 267–276

This work was supported by DOE

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12

Backup Slides

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218Po and 214Po peaks Radon spectrum (218Po and 214Po peaks)

9

6.12 MeV 7.83 MeV

¨  Fitted to this analytical function for alpha spectra from which the area of the peak can be determined.

13

Charcoal Specific activity(mBq/kg)

Price(US D/kg) References

Calgon OVC 4x8 53.6 ± 1.3 6 This workShirasagi G2x4/6-1 101.0 ± 8.0 27 This work

Saratech 1.71 ± 0.20 35 This workHNO3 etched Saratech 0.51 ± 0.09 135 This work

Carboact 0.23 ± 0.19 15,000 This workCarboact 0.33 ± 0.05 15,000 [32]

Table 2: Radon emanation screening from charcoals and their approximate prices in 2017. Uncertainties are statistical only and are reported at 68% C.L. Thesystematic uncertainty on the specific activity for the Calgon OVC is 8% due to the mass measurement.

Figure 3: Schematic view of the ESC. The ancillary electronics is described inthe text.

was electrically isolated from the grounded stainless steel ves-sel. A high voltage (HV) divider was built to supply up to-6 kV [29]. The HV divider was physically separated froma charge sensitive preamplifier (CSP, Cremat, CR110) to pre-vent current leakage. The reverse voltage (-800 V) was appliedthrough the HV divider to the anode of the Si-PIN photodioderesulting in maximum collection e�ciency of 218Po ions. Thereverse voltage di↵erence between the cathode and the anodeof the Si-PIN photodiode was below the maximum allowed re-verse voltage (100 V) for this particular Si-PIN photodiode.The charge signals were sent from the cathode to the CSP fol-lowed by a shaping amplifier (SA, Tennelec, TC243) with ashaping time of 1 µs. These amplified pulses were subsequentlydigitized by a multi-channel analyzer (MCA8000D, Amptek).The detection sensitivity was measured for both the RAD7 andin-house detectors using the Pylon source. The detection sen-sitivity for RAD7 was found to agree with its specificationwithin statistical uncertainties for 218Po alpha-peaks [33] andwas (6.34±0.02)⇥10�3 cpm/Bq/m3. The detection sensitivityfor our in-house ESC detector was found to be greater than forRAD7. It was measured to be (21.80±0.06)⇥10�3 cpm/Bq/m3

for 218Po alpha-peaks. Furthermore, the in-house ESC detectorcan be operated at high gas pressures (⇡ 2 atm) while the oper-ating gas pressure for RAD7 is not recommended to exceed 1atm.

2.5. Slow control system

A slow control system was developed to monitor and controlthe important functions of the system. Parameters such as gaspressure, Novec-7100 fluid temperature, gas flow rates, char-coal temperature, Xe gas mass, room temperature, and roomhumidity were continuously monitored and recorded during op-erations. The values were archived in a SQL database anddisplayed on a remotely monitored webpage. Additional auto-matic control features were introduced to control the gas systemremotely. A liquid cryogenic control system was constructedfor the 222Rn breakthrough time measurements in Xe gas to fa-cilitate long term and safe measurements.

3. Experimental results and discussion

3.1. Measurements of

222Rn adsorption characteristics on var-

ious charcoals in N2, Ar, and Xe carrier gases

218Po and 214Po spectra were measured with time intervalsfrom 3 to 15 minutes after a 222Rn spike was injected into thecharcoal trap. Only 218Po was of interest since it is the firstprogeny decay product (”new radon”) of the 222Rn decay chain.The 218Po peaks were fitted with an analytical function for alphaparticle spectra where the integral-area of the peak was deter-mined according to [34]

f (x, µ,�, ⌫) =A

2⌫e

( x�µ⌫ +

�2⌫2

)er f c

✓ 1p2

x � µ�+�

�◆, (1)

where x is the channel number, A is the peak area, µ is themean of the Gaussian probability-density function, � is thestandard deviation and ⌫ is the parameter of the normalizedleft-sided exponential function. A typical radon daughter pulseheight spectrum is shown in Figure 4. Figure 5 displays exam-ples of elution curves measured in Ar carrier gas through threetypes of charcoals Calgon OVC 4x8, Shirasagi, and Saratech)contained in a 0.1 l trap at a temperature of 295 K and at atmo-spheric pressure.

The chromatographic plate model method [35, 36] was em-ployed in the data analysis for this paper. In this approach, acharcoal trap can be divided into a number of stages of equalvolume in which equilibrium can always exist between the gasand the charcoal. For a short pulse of 222Rn introduced into thecharcoal bed layer the elution curve is

5

Page 14: RADON REDUCTION SYSTEM FOR LZ DARK MATTER EXPERIMENT · 2018. 11. 22. · 136 Xe l Det. + Sur. + Env. 0 2 4 6 8 10 222Rn specific activity [µBq/kg] 1 1.5 2 2.5 3 3.5 ×10−48] 2

Arrhenius Law

¨  Describes the rate of chemical reactions¨  k: rate constant¨  Ea: activation energy (J)¨  kb: Boltzmann constant (J/K)¨  T: temperature (K)

14

a

b

Ek Tk Ae−

=