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 Scintillation Ionization PSD, dE/dx PID, track reconstruction …. • DM, 0 , oscillation….. TAUP19-Toyama Sep2019 2
Liquefied noble gas TPCs • Very successful technology: affordable, scalable, large volumes Scintillation Ionization PSD, dE/dx PID, track reconstruction …. • DM, 0 , oscillation….. • However the electrons are “slow” ( 𝑛 / 𝑛 s), the ions are extremely slow!! Without taking into account the liquid motion: 𝑗 ~2 ∙ 10 −4 𝑑𝑛 2 𝑊 −1 𝑡 −1 (T.H. Dey , T.J. Lewis , J. Phys. D: Appl. Phys. 1 (8) - 1968) 𝑗 ~1.6 ∙ 10 −3 𝑑𝑛 2 𝑊 −1 𝑡 −1 (M. Torti , Proceedings of the Fourth International Conference on New Frontiers in Physics - 2015 ) At 𝐹 𝑒 =1 kV/cm, 𝑤 𝑗 ~1.6 ∙ 10 −5 𝑛𝑛 / 𝑡 to be compared to 𝑤 𝑓 ~2 𝑛𝑛 / 𝑡 • The electrons drift to the anode, the ions stay! TAUP19-Toyama Sep2019 3
Space charge 𝑤 𝑗 ≪ 𝑤 𝑓 𝑗 ≫ 𝑓 • • The volume charges up positively since the ions stay in the target i depends on: • Amount of ionization (event energy and rate) Ion velocity ( 𝐹 𝑒 and mobility) Total drift length • 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 • The electron drift in a positively charged volume (neutral target only when the field is off) TAUP19-Toyama Sep2019 4
Field distortion, “Secondary”recombination and volume light emission A l=0 𝐹 𝑒 = 1 kV/cm E d l Free ion Free electron l=L K 𝑇 𝑑𝑡 transverse area (far enough) whose “ Impact of the positive ion current on large size crossing field lines end on one ion (all the neutrino detectors and delayed photon lines emerging from the ion cross that section) emission” 𝑇 𝑑𝑡 = 1.2 ∙ 10 −7 𝑛𝑛 2 with 𝐹 𝑒 =1 kV/cm JINST 13 (2018) no.04, C04015 5
Mathematical framework Electron and ion fluxes as 𝑘 𝑗,𝑓 (𝑚) = 𝑤 𝑗,𝑓 𝑚 𝑗,𝑓 𝑚 𝑤 𝑗,𝑓 (𝑚) = 𝑗,𝑓 𝐹 𝑒 𝑚 𝑟 The recombination rate is given by 𝑠(𝑚) = 𝑘 𝑓 𝑚 𝑗 𝑚 𝑇 𝑑𝑡 (𝑚) 𝑠(𝑚) = 𝑘 𝑓 𝑚 𝑘 𝑗 𝑚 𝑗 𝐹 2 (𝑚) d 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: 𝑒𝑘 𝑗 (𝑚) 𝑒𝑘 𝑗 𝑚 𝑟 h − r l − + 𝑘 𝑓 𝑚 𝑘 𝑗 𝑚 𝑒𝑚 =0 𝑗 𝐹 2 (𝑚) =h 𝑒𝑚 (h constant ionization rate) d h − r l + 𝑒𝑘 𝑓 (𝑚) 𝑒𝑘 𝑓 𝑚 𝑟 − 𝑘 𝑓 𝑚 𝑘 𝑗 𝑚 𝑒𝑚 =0 𝑗 𝐹 2 (𝑚) =-h 𝑒𝑚 d At the same time the variation of the drift field is determined by 𝑒𝐹 𝑒 (𝑚) 𝑒𝐹 𝑒 (𝑚) 2𝑟 2 the charge density: = 𝑟 ∙ 𝑗 𝑚 − 𝑟 ∙ 𝑓 𝑚 𝑗 >> 𝑓 = 𝑗 𝑘 𝑗 𝑒𝑚 𝑒𝑚 These are three coupled differential equations with three functions ( 𝑘 𝑓 , 𝑘 𝑗 , 𝐹 𝑒 ) and a variable l Boundary conditions • 𝐹 𝑒 0 = 𝐹 𝐵 • 𝑘 𝑓 𝑀 = 0 𝑘 𝑗 0 = 𝐻 𝐽 ∙ 𝑘 𝑓 0 • TAUP19-Toyama Sep2019 6
Mathematical framework - II 𝑟 ℎ𝑚 2 + 2𝑘 𝑗 0 𝑚 + 𝐹 2 𝐹 𝑒 𝑚 = The field variation is a function of l 𝑗 A The field is minimum at 0 ( 𝐹 𝑒 𝑀 = 𝐹 𝐵 ) and maximum at the cathode 𝑀 The cathode voltage necessary to obtain a given 𝑊 𝑚 = 𝐹 𝑒 𝑚 𝑒𝑚 field can be calculated integrating the drift field 0 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. 𝑄 𝑚 = 𝑇(𝑚) 𝑇(0) = 𝐹(0) 𝐹 𝐵 𝐹(𝑚) = 𝑟 𝑗 ℎ𝑚 2 + 2𝑘 𝑗 0 𝑚 + 𝐹 2 A Field variation, cathode voltage and secondary recombination probability can be calculated knowing the constant ionization rate, the field at the anode and ion gain 𝐻 𝑗 L. Romero, R. Santorelli, B. Montes (CIEMAT) Astropart.Phys. 92 (2017) 11-20 TAUP19-Toyama Sep2019 7
Finite element analysis 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. TAUP19-Toyama Sep2019 8
Space charge calculation Drift velocity: 𝑤 𝑗 ~10 𝑛𝑛 / 𝑡 to be compared to 𝑤 𝑓 ~2 𝑛/𝑛𝑡 ( 𝐹 𝑒 =1 kV/cm) Drift distance: …up to 12 m ! “Ion yield”: Underground: • “Dominant” contribution from 39 Ar (~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/m 3 /s, h 0 ~ 1.1e7 pairs/m 3 /s Surface: Dominant contribution from muons ( 168 muons/m 2 /s) • 𝑁𝑓𝑊 𝑑𝑛 2 𝑒𝐹 𝑒𝑚 ≈ 1.5 • Minimum ionizing energy: Mean deposited energy 35 GeV/m 3 /s, h 0 1.5e9 pairs/m 3 /s • TAUP19-Toyama Sep2019 9
Underground case L=12 m 10 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 Free ion Uncorrelated Light h production Free electron ms scale? 10% secondary recombination probability gives 1e8 photons/m 3 /s produced Evidences from MicroBooNE/ProtoDUNE-SP? TAUP19-Toyama Sep2019 12
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
SETUP TAUP19-Toyama Sep2019 14
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 (log 10 ) V/m 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
Electric field magnitude (log 10 ) V/m Liquid Ar @ 87.3 K Needle: 3.1 kV • Plane: 0.95 kV • Shaping rings: ground • Wires: -3.03 kV • Height of liquid in chamber (2 mm below top shaping ring) Relative permittivity Ar gas Ar gas Ar liquid (293 K) (98 K) (87.3 K) ε r 1.000516 1.00155 1.49545 TAUP19-Toyama Sep2019 17
Field lines from tip of needle Liquid + gas Warm gas Cold gas
Preliminary results: warm/cold gas P=1.3 bar T=293 K P=1.3 bar T=98 K A = 3.0 kV V V K = -3.0 kV TAUP19-Toyama Sep2019 19
Preliminary results: warm/cold gas • Ions successfully produced at the anode and collected at the cathode • Two behaviors identified depending on the settings Spiky region Constant current region • 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 TAUP19-Toyama Sep2019 20
Preliminary results: LAr • 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? TAUP19-Toyama Sep2019 21
Conclusion: • 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 22
ありがとうございます。 ( Arigato gozaimasu) TAUP19-Toyama Sep2019 23
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