Space charge effects in liquid argon TPCs and ion mobility - - PowerPoint PPT Presentation

Space charge effects in liquid argon TPCs and ion mobility measurement

Roberto Santorelli CIEMAT – Madrid

On behalf of: J.M. Cela, P. Garcia Abia, R. Lopez Manzano, V. Pesudo, S. Quizhpi Salamea, L. Romero, E. Sanchez (CIEMAT)

• S. De Luise, M. Leyton, T. Lux (IFAE)

TAUP 2019 - Toyama Sep2019

Liquefied noble gas TPCs

• Very successful technology: affordable, scalable, large volumes
• DM, 0, oscillation…..

TAUP19-Toyama Sep2019 2

• Scintillation
• Ionization
• PSD, dE/dx
• PID, track reconstruction ….

Liquefied noble gas TPCs

• Very successful technology: affordable, scalable, large volumes
• DM, 0, oscillation…..
• However the electrons are “slow” ( 𝑛/𝑛s), the ions are extremely

slow!! Without taking into account the liquid motion:

𝑗~2 ∙ 10−4𝑑𝑛2𝑊−1𝑡−1 (T.H. Dey , T.J. Lewis , J. Phys. D: Appl. Phys. 1 (8) - 1968) 𝑗~1.6 ∙ 10−3𝑑𝑛2𝑊−1𝑡−1 (M. Torti , Proceedings of the Fourth International Conference on New Frontiers in Physics - 2015 ) At 𝐹𝑒=1 kV/cm, 𝑤𝑗~1.6 ∙ 10−5𝑛𝑛/𝑡 to be compared to 𝑤𝑓~2 𝑛𝑛/𝑡

• The electrons drift to the anode, the ions stay!

TAUP19-Toyama Sep2019 3

• Scintillation
• Ionization
• PSD, dE/dx
• PID, track reconstruction ….

Space charge

• 𝑤𝑗 ≪ 𝑤𝑓  𝑗 ≫ 𝑓
• The volume charges up positively since the ions stay in the target
• i depends on:
• Effect worsened by the ion feedback from the vapor volume in case of charge amplification
• L. Romero, R. Santorelli, B. Montes (CIEMAT)

Astropart.Phys. 92 (2017) 11-20

TAUP19-Toyama Sep2019 4

• Amount of ionization (event energy and rate)
• Ion velocity (𝐹𝑒 and mobility)
• Total drift length
• The electron drift in a positively charged volume (neutral target only when the field is off)

Ed A K Free ion Free electron

Field distortion, “Secondary”recombination and volume light emission

𝐹𝑒 =1 kV/cm

with 𝐹𝑒=1 kV/cm 𝑇𝑑𝑡 transverse area (far enough) whose crossing field lines end on one ion (all the lines emerging from the ion cross that section) 𝑇𝑑𝑡= 1.2 ∙ 10−7𝑛𝑛2 l=0 l=L l

5

“ Impact of the positive ion current on large size neutrino detectors and delayed photon emission” JINST 13 (2018) no.04, C04015

Electron and ion fluxes as 𝑘𝑗,𝑓(𝑚) = 𝑤𝑗,𝑓 𝑚 𝑗,𝑓 𝑚 𝑤𝑗,𝑓(𝑚) = 𝑗,𝑓𝐹𝑒 𝑚 The recombination rate is given by 𝑠(𝑚) = 𝑘𝑓 𝑚 𝑗 𝑚 𝑇𝑑𝑡(𝑚)  𝑠(𝑚) = 𝑘𝑓 𝑚 𝑘𝑗 𝑚

𝑟

𝑗𝐹2(𝑚) We can determine the recombination rate in LAr knowing the currents and the drift field. In a stationary state the density variation is null at any l: h − r l −

𝑒𝑘𝑗(𝑚) 𝑒𝑚 =0 𝑒𝑘𝑗 𝑚 𝑒𝑚

+ 𝑘𝑓 𝑚 𝑘𝑗 𝑚

𝑟

𝑗𝐹2(𝑚) =h h − r l + 𝑒𝑘𝑓(𝑚)

𝑒𝑚 =0

𝑒𝑘𝑓 𝑚

𝑒𝑚

− 𝑘𝑓 𝑚 𝑘𝑗 𝑚

𝑟

𝑗𝐹2(𝑚) =-h At the same time the variation of the drift field is determined by the charge density: 

𝑒𝐹𝑒(𝑚) 𝑒𝑚

= 𝑟 ∙ 𝑗 𝑚 − 𝑟 ∙ 𝑓 𝑚 𝑗>> 𝑓

𝑒𝐹𝑒(𝑚) 𝑒𝑚

=

2𝑟

𝑗 𝑘𝑗 These are three coupled differential equations with three functions (𝑘𝑓, 𝑘𝑗, 𝐹𝑒) and a variable l Boundary conditions • 𝐹𝑒 0 = 𝐹𝐵

• 𝑘𝑓 𝑀 = 0
• 𝑘𝑗 0 = 𝐻𝐽 ∙ 𝑘𝑓 0

TAUP19-Toyama Sep2019 6

Mathematical framework

(h constant ionization rate)

2

d d d

𝐹𝑒 𝑚 = 𝑟 𝑗 ℎ𝑚2 + 2𝑘𝑗 0 𝑚 + 𝐹2

A

The field variation is a function of l The cathode voltage necessary to obtain a given field can be calculated integrating the drift field The field is minimum at 0 (𝐹𝑒 𝑀 = 𝐹𝐵) and maximum at the cathode The secondary recombination probability is equal to the fraction of the surface S(l) spanned the filed lines ending on the anode with respect to the total anode (cathode) area. Field variation, cathode voltage and secondary recombination probability can be calculated knowing the constant ionization rate, the field at the anode and ion gain 𝐻𝑗

• L. Romero, R. Santorelli, B. Montes (CIEMAT) Astropart.Phys. 92 (2017) 11-20

TAUP19-Toyama Sep2019 7

Mathematical framework - II

𝑊 𝑚 = 𝐹𝑒 𝑚 𝑒𝑚

𝑀

𝑄 𝑚 = 𝑇(𝑚) 𝑇(0) = 𝐹(0) 𝐹(𝑚) = 𝐹𝐵 𝑟 𝑗 ℎ𝑚2 + 2𝑘𝑗 0 𝑚 + 𝐹2

A

COMSOL Multiphysics Electrostatics and Transport of Diluted Species modules 1 × 1 × 1 m3 box filled with liquid Argon, 100 kV between the top and the bottom surface.

Finite element analysis

TAUP19-Toyama Sep2019 8

Space charge calculation

TAUP19-Toyama Sep2019 9

 Underground:

• “Dominant” contribution from 39Ar (~1 Bq/kg or ~1.4 kBq/m3)
• Q-value of 565 keV, 1/3 mean energy, One decay 8e3 pairs,
• Mean deposited energy 263 MeV/m3/s, h0 ~ 1.1e7 pairs/m3/s

 Surface:

• Dominant contribution from muons (168 muons/m2/s)
• Minimum ionizing energy:

𝑒𝐹 𝑒𝑚 ≈ 1.5 𝑁𝑓𝑊 𝑑𝑛2 𝑕

• Mean deposited energy  35 GeV/m3/s, h0  1.5e9 pairs/m3/s

𝑤𝑗~10 𝑛𝑛/𝑡 to be compared to 𝑤𝑓~2 𝑛/𝑛𝑡 (𝐹𝑒=1 kV/cm)

• Drift velocity:

…up to 12 m !

• Drift distance:
• “Ion yield”:

10

Underground case L=12 m

TAUP19-Toyama Sep2019 10

Surface case L=6 m

TAUP19-Toyama Sep2019 11

Experimental aspects

• Electron lifetime defined as: 1

 = 1 𝐵 + 1 𝑆 𝐵≪ 𝑆, 𝐵 ≫ 𝑆, 𝐵𝑆

• Independent measurement of the impurity concentration?

Purity monitor

• Drift field dependence?
• Light emission

TAUP19-Toyama Sep2019 12

Free ion Free electron h Uncorrelated Light production  ms scale? 10% secondary recombination probability gives 1e8 photons/m3/s produced Evidences from MicroBooNE/ProtoDUNE-SP?

Caveat

• The ionization rate is not constant and not uniform
• The LAr volume is NOT in steady state (negligible for

electrons but not for the ions)

• Corrections given by the recirculation system and by the

convection motions

• A detailed simulation of the liquid motion needed
• Average correction map complicated but possible, how

about event by event?

TAUP19-Toyama Sep2019 13

TAUP19-Toyama Sep2019 14

SETUP

Simulation in COMSOL

• Simulated static electric field using finite element analysis in

COMSOL and a simplified version of as-built geometry

• Finalized mesh uses 4.5M tetrahedral elements with varying sizes,

from 0.3 to 12.1 mm

• Tuned parameters element size, maximum element growth rate,

curvature factor and resolution of narrow regions

TAUP19-Toyama Sep2019 15

Electric field magnitude (log10)

Gas Ar @ 293 K, 1.3 bar

• Needle: 3.6 kV
• Plane: floating
• Shaping rings: -1.28 kV, -1.5 kV
• Wires: -2.8 kV

Gas Ar @ 98 K, 1.3 bar

• Needle: 2.8 kV
• Plane: 1.16 kV
• Shaping rings: ground
• Wires: -3.02 kV

TAUP19-Toyama Sep2019 16

V/m

Electric field magnitude (log10)

Liquid Ar @ 87.3 K

• Needle: 3.1 kV
• Plane: 0.95 kV
• Shaping rings: ground
• Wires: -3.03 kV

Ar gas (293 K) Ar gas (98 K) Ar liquid (87.3 K)

εr

1.000516 1.00155 1.49545

Height of liquid in chamber (2 mm below top shaping ring)

Relative permittivity

TAUP19-Toyama Sep2019 17

V/m

Field lines from tip of needle

Warm gas Cold gas Liquid + gas

Preliminary results: warm/cold gas

TAUP19-Toyama Sep2019 19

P=1.3 bar T=98 K P=1.3 bar T=293 K V

A= 3.0 kV

VK=-3.0 kV

• Ions successfully produced at the anode and collected at the cathode
• Two behaviors identified depending on the settings
• Sum of the currents < a few nA (no dispersion)
• Full ions collection on the cathode with constant currents possible in gas with the

proper settings

Preliminary results: warm/cold gas

TAUP19-Toyama Sep2019 20

Spiky region Constant current region

Preliminary results: LAr

TAUP19-Toyama Sep2019 21

• Liquid level between the two shaping rings (couple cm)
• Only spiky behavior, no constant current with all the configuration tested (even

at much higher voltages)

• Effect consistent with SC in liquid.
• Evidence of ion feedback from the gas?
• Ion mobility?

Conclusion:

TAUP19-Toyama Sep2019 22

• The electrons drift through the positive charges whose

density depends on the ion production rate, mobility and drift length

• We quantified the displacement of the reconstruction, the

recombination rate constant and the emission of light induced by the space charge

• A small prototype in laboratory can already reproduce

some of the effects

• A quantitative study of the ion feedback from the gas

and of the ion mobility is currently on-going

TAUP19-Toyama Sep2019 23

ありがとうございます。

(Arigato gozaimasu)

TAUP19-Toyama Sep2019 24

• Voltage difference between anode and cathode in order to generate

a 70 nA current from needle with gas at room temperature.

Characterization of the system: pressure effect

• HV increases to

compensate the gas density

• Current detected

TAUP19-Toyama Sep2019 25

Characterization of the system: Vacuum

• Chamber filled with argon at room

temperature at 1.2 bar.

• Collection of ~100%.
• V fixed (6 kV) → 2 kV (A) -3.5kV(K)

 Little (or no) impact of the initial vacuum

Ar/Xe scintillation light

Excitation e- + Ar  Ar* + e-

• Ar* + Ar  Arv*

2 Excimer formation (bound diatomic molecules in the exc. state)

• Arv*

2 + Ar  Ar2 * + Ar Relaxation

• Ar2

*  Ar + Ar + h Radiative de-exc.

and dissociation Ar

The superscript v is used to distinguish the vibrational excited states from the purely electronic excitations (Ar2

* with v=0)

Ionization e- + Ar  Ar+ + 2e-

• Ar+ + Ar + Ar  Ar+

2 + Ar Molecular ion

• Ar+

2 + e-  Ar** + Ar

Recombination

• Ar** + Ar  Ar* + Ar + heat Excimer

h

TAUP19-Toyama Sep2019 26

Underground case L=12 m

• Dominant contribution from 39Ar (~1 Bq/kg or ~1.4 kBq/m3)
• Q-value of 565 keV, 1/3 mean energy, One decay 8e3 pairs,
• Mean deposited energy 263 MeV/m3/s, h0 ~ 1.1e7 pairs/m3/s

𝐻𝑗 𝐻𝑗

TAUP19-Toyama Sep2019 27

L=12 m L=12 m

TAUP19-Toyama Sep2019 28

Underground case L=12 m

• Dominant contribution from muons (168 muons/m2/s)
• Minimum ionizing energy:

𝑒𝐹 𝑒𝑚 ≈ 1.5 𝑁𝑓𝑊 𝑑𝑛2 𝑕

• Mean deposited energy  35 GeV/m3/s, h0  1.5e9 pairs/m3/s

Surface case L=6 m

L=6 m L=6 m 𝐻𝑗 𝐻𝑗

TAUP19-Toyama Sep2019 29