Model of space charge(s) and its connection to the photon rate in - PowerPoint PPT Presentation

Model of space charge(s) and its connection to the photon rate in LArTPC Xiao Luo (Yale, UCSB), Flavio Cavanna (FNAL) ProtoDUNE DRA meeting April 17 th 2019

The origin - ionization charges Electrons are the LArTPC signal, but our model focus the invisible ions (e.g. Ar 2 + )

The story starts with ions (space charges)... Large detector, equilibrium Cathode Cathode Ar 2+ Ar 2+ Ar 2+ Ar 2+ Ar 2+ Ar + E Ar + e- Ar + e- Ar + Ar 2+ Ar 2+ Ar 2+ Ar 2+ Ar + e- ~ hour dx Ar + e- Ar 2+ Ar 2+ Ar 2+ e- e- Ar 2+ Ar 2+ x E Ar 2+ Anode Anode z Ion transport eq. Considering the flux only in 1-D at equilibrium: 3

Simplest case – ionization only Parameters: Cosmic muon rate : 13kHz n pair - rate of (e - , I + ) pairs after initial recombination: 1.9e9 [m -3 s -1 ] Ion mobility : 8e-8 [m 2 V -1 s -1 ] Ion velocity (E=500V/cm): 4e-3 [m/s] Ar 2+ Vs X n + [m -3 ] E field Vs X E [V/m] 1.2 × 10 12 70000 1.0 × 10 12 [E A ,E C ] = [-25%, +43%] 65000 8.0 × 10 11 60000 6.0 × 10 11 55000 50000 4.0 × 10 11 45000 2.0 × 10 11 40000 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Drift X [m] Drift X [m]

Add e- attachment: e - + X -> X - e- at attach achmen ment to impu mpurity y (e. (e.g. H 2 O) O): 𝑓 9 + 𝐼 < 𝑃 → 𝐼 < 𝑃 9 Parameters: Atta. (to H 2 O) Rate: k A [H2O]= 1.4 x 10 -15 [m 3 s -1 ] H 2 O Concentration: c[H 2 O] = 3ppt Lifetime: 6ms. E field Vs X E [V/m] H 2 O - Vs X n - [m -3 ] 70000 65000 4 × 10 11 Ionization only 60000 Attachment 3 × 10 11 + Attachement 55000 50000 2 × 10 11 45000 1 × 10 11 40000 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Drift X [m] Drift X [m]

Add Mutual Neutralization Cathode New process we incorporate in our model: Ar 2+ Ar 2+ Ar 2+ Ar 2+ Ar 2+ Mutual Neutralization (MN) O 2- A + 𝐼 < 𝑃 9 → 𝐵𝑠 ∗ + 𝐼 < 𝑃 𝐵𝑠 Ar 2+ O 2- Ar 2+ Ar 2+ Ar 2+ < < → 2𝐵𝑠 + 𝛿 + 𝐼 < 𝑃 Ar 2+ Ar 2+ Ar 2+ O 2- Assume each time MN happens, O 2- O 2- Ar 2+ Ar 2+ generating 1 VUV photon O 2- O 2- O 2- O 2- O 2- O 2- Anode Parameters asso. with this process: MN rate constant: k MN = 2.8e-13 [m 3 /s] 𝑙 EF 𝑜 9 𝑜 A Photon generation rate is

Mutual Neutralization cont. Ar 2+ Vs X n + [m -3 ] E field Vs X E (V/m) 1.2 × 10 12 Ionization only 70000 + Attachement Ionization only 65000 1.0 × 10 12 + Mutual Neutralization + Attachement 60000 8.0 × 10 11 + Mutual Neutralization 55000 6.0 × 10 11 50000 4.0 × 10 11 45000 2.0 × 10 11 40000 0.5 1.0 1.5 2.0 2.5 3.0 3.5 X[m] X[m] 0.5 1.0 1.5 2.0 2.5 3.0 3.5 H 2 O - Vs X [m -3 s -1 ] 𝛿 Vs X n - [m -3 ] 6 × 10 8 4 × 10 11 5 × 10 8 Attachment 3 × 10 11 + Mutual Neutralization 4 × 10 8 𝐽 A + 𝐽 9 → γ 3 × 10 8 2 × 10 11 2 × 10 8 1 × 10 11 1 × 10 8 X[m] 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 X[m] Drift X (m) Drift X (m)

Add the Volume Recombination Cathode Ar 2+ Ar 2+ Ar 2+ Ar 2+ Ar 2+ New process that we incorporate in our model. Note the difference from the well-known initial recombination process Ar 2+ Ar 2+ Ar 2+ Ar 2+ Volume Recombination (VR) A + 𝑓 9 → 𝐵𝑠 ∗ → 2𝐵𝑠 + 𝛿 Ar 2+ Ar 2+ Ar 2+ e- 𝐵𝑠 < < Ar 2+ Ar 2+ Assume each time VR happens, E Ar 2+ generating 1 UVU photon Anode Parameters asso. with this process: VR rate constant: k R = 1.1e-10 m 3 /s Photon generation rate is 𝑙 J 𝑜 A 𝑜 K

Volume Recombination cont. Ar 2+ Vs X n + [m -3 ] E (V/m) E field Vs X Ionization only 1.2 × 10 12 70000 + Attachement Ionization only + Mutual Neutralization 1.0 × 10 12 65000 + Attachement + Volume Recombination + Mutual Neutralization 60000 8.0 × 10 11 + Volume Recombination 55000 6.0 × 10 11 50000 4.0 × 10 11 45000 2.0 × 10 11 40000 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 [m -3 s -1 ] H 2 O - Vs X 𝜹 Vs X n - [m -3 ] 7 × 10 8 4 × 10 11 Mutual Neutralization 6 × 10 8 Attachment Volume Recombination VR: Total 5 × 10 8 𝐽 A + 𝑓 9 → γ + Mutual Neutralization 3 × 10 11 + Volume Recombination 4 × 10 8 generates less γ 2 × 10 11 3 × 10 8 than MN. 2 × 10 8 1 × 10 11 1 × 10 8 X[m] 0.5 1.0 1.5 2.0 2.5 3.0 3.5 X[m] 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Use experimental observable to constrain the model parameters. Final E field Vs X Final solution (from our model) of photon E (V/m) production rate (the purple line) in the 65000 entire ProtoDUNE volume is: 6.3 X 10 10 Hz 60000 +32% 𝜹 rate Vs X 55000 [m -3 s -1 ] 7 × 10 8 50000 Mutual Neutralization 6 × 10 8 -17% Volume Recombination 45000 Total 5 × 10 8 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4 × 10 8 X [m] 3 × 10 8 Final solution (the red line) of E field has 2 × 10 8 E anode = 416 V/cm and E cathode = 662 V/cm. 1 × 10 8 This is a larger distortion comparing to the ProtoDUNE experimental measurements. 0.5 1.0 1.5 2.0 2.5 3.0 3.5 X [m]

Many parameters in our model are uncertain, next I will describe the impact of the size of the effect (mainly on the E field distortion and photon rate) by varying: • Cosmic flux or other ionization source (Ar 39 ) • Lifetime: attachment rate to impurity and impurity concentration • Ion mobility • E field central value

Cosmic flux/Ar39 ~ 10% seasonal variation of the cosmic flux. Ar39 beta decay is another source of the ionization charges (~1Bq/kg in natural Argon) – this add 0.5% of npair comparing to the cosmic at surface. Next I compare effect with standard cosmic flux to 10% higher cosmic flux.

E field Vs X E (V/m) Hard to observe the E field change induced by 65000 the cosmic flux seasonal change. Standard 60000 10 % higher cosmic flux 55000 10% higher cosmic flux -> 13% more photon rate. 50000 45000 [m -3 s -1 ] Photon rate Vs X Photon production Vs X 8 × 10 8 0.5 1.0 1.5 2.0 2.5 3.0 3.5 X [m] Ar 2+ Vs X n + [m -3 ] 6 × 10 8 Standard 10 % higher cosmic flux 1 × 10 12 4 × 10 8 Standard 8 × 10 11 10 % higher cosmic flux 6 × 10 11 2 × 10 8 4 × 10 11 2 × 10 11 0.5 1.0 1.5 2.0 2.5 3.0 3.5 X [m] 0.5 1.0 1.5 2.0 2.5 3.0 3.5 X [m]

Purity / k A dependence: Impurity concentration c[H2O] and e- attachment rate to impurity (k A ) always couple together in our differential equation - , this term also proportional to 1/ 𝜐 , where 𝜐 is the electron lifetime (a measureable quantity in the experiment) Intuitively, more impurities, more photons generated from the Mutual Neutralization. Prediction: effect negatively correlated with lifetime In this study, vary the product (c[H2O] * ka) from standard 6ms to 3ms, 2ms, 1.5ms

”purity” modifies the E field! E field Vs X E (V/m) 65000 lifetime E A E C E C /E 0 % ka ka * 2 60000 6ms 416 V/cm 662 V/cm [-17%,+32%] ka * 3 ka * 4 55000 3ms 437 V/cm 635 V/cm [-13%, +27%] 50000 2ms 452 V/cm 613 V/cm [-10%,+23%] 45000 597 V/cm [-7%,+19%] 1.5ms 463 V/cm 0.5 1.0 1.5 2.0 2.5 3.0 3.5 X [m] The data measurements of E field constrain the model to prefer shorter lifetime than 6ms.

”purity” modifies photon rate! Ar2+ density Vs X Decrease lifetime from 6ms to 2ms increase photon 1 × 10 12 rate by 90%. 8 × 10 11 decrease Comparing to SPE rate for different purity data samples are 6 × 10 11 lifetime on-going. 4 × 10 11 Photon rate Vs X [m -3 s -1 ] Photon production Vs X 1.5ms 2 × 10 11 1.4 × 10 9 ka 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ka * 2 1.2 × 10 9 2ms ka * 3 H2O- density Vs X 1.0 × 10 9 ka * 4 3ms 8.0 × 10 8 1 × 10 11 6ms 8 × 10 10 6.0 × 10 8 decrease 6 × 10 10 4.0 × 10 8 lifetime decrease 4 × 10 10 lifetime 2.0 × 10 8 2 × 10 10 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 X [m]

Ion mobility dependence: There could be a big uncertainty of the ion mobility. In the standard calculation we use 8x10 -8 [m 2 V -1 s -1 ] as Ar2+ mobility (this corresponds to 4x10 -3 m/s drift velocity at 500V/cm Field). Intuitively, increase the mobility will decrease the density of the ions, which decrease the photon generation rate. Prediction: effect negatively correlated with ion mobility In this study, compare the effect with x2 of the standard mobility for both positive and negative ions.

Comparing to slower ion mobility E field Vs X Ar2+ density Vs X Twice of the ion 65000 1 × 10 12 mobility: 60000 8 × 10 11 Standard Standard x2 ion mobility x2 ion mobility 6 × 10 11 55000 Decrease E field • 4 × 10 11 50000 distortion from [-17%, +32%] to 2 × 10 11 45000 [-9%,+19%]. 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 H2O- density Vs X Photon production Vs X Photon production Vs X 7 × 10 8 4 × 10 10 Decrease the • 6 × 10 8 photon rate by Standard 3 × 10 10 5 × 10 8 Standard 21%. x2 ion mobility x2 ion mobility 4 × 10 8 2 × 10 10 3 × 10 8 2 × 10 8 1 × 10 10 1 × 10 8 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5

E field dependence: higher E field, faster drift velocity, less ion densities, less photons. • higher E field, less initial recombination, more Ar 2+ , more photons • Changing E field leads to two competing processes, that decides final photon generation rate. For simplicity, ignore the gauss law for this study. Vary E field from 500 V/cm to 200 V/cm with 50V/cm step.