Diego González-Díaz (GSI-Darmstadt) GSI, now R3B!

I am not going to show any result related to time resolution in this talk

How to create a simple avalanche model The stochastic solution of the avalanche equation is given by a simple Furry law (non- equilibrium effects are not included). Avalanche evolution under strong space- charge regime is characterized by no effective multiplication. The growth stops when the avalanche reaches a certain number of carriers called here N sat, electrons drift from there to the anode. The amplifier is assumed to be slow enough to be sensitive to the signal charge and not to its amplitude. We work, for convenience, with a threshold in charge units Q th. log 10 n electrons ~7 toto t space-charge regime exponential-growth regime ~7.5 t meas avalanche Furry-type fluctuations ~2 Raether limit 8.7 exponential-fluctuation regime threshold 0 simplifying assumptions

Parameters of the gas used as input: α-η (effective Townsend coefficient), v drift (drift velocity), n o (ionization density) Townsend coefficient and drift velocity obtained from the Nov09 paper from de Urquijo et al, measured in pure C 2 H 2 F 4. Partial-pressure scaling used (SF 6 electro-negativity neglected). Ionization density for mips in the standard mixture: n o =7.5cl/mm (HEED). Scaled to different energies and mixtures by using Bethe-Bloch with density effect. Cluster size =1 ~ equivalent to say that all electrons in the same cluster grow till a common maximum N sat. They are not treated independently.

Determination of the maximum number of electrons in the avalanche N sat. Space-Charge limit. fast charge [pC] Assumptions: - N sat is independent from the gap as long as it is close to 0.3mm. - N sat is proportional to the electric field. mixture: 98.5/0.5/1 HV=3.1 kV/gap gap=0.3mm 4 gaps

Efficiency for 'wide-pad' counters

Efficiency for 'wide-strip' counters

MC results. Prompt charge distributions for 'wide-strip' type detectors pedestal* = 225 FEE gain*= 90 FEE gain*= 110 pedestal* = 150 FEE gain*= 90 FEE gain*= 145 FEE gain from pulser measurements ~ FEE gain from FEE-paper ~ TSINGUA-0 (APRIL) USTC-I TSINGUA-II/III TSINGUA-I

Status of weighting field calculations (charge sharing) weighting-field calculation with analytical formula (assumes no inter-strip separation) very important for describing the inter-strip region fast and durty calculation with neBEM solver (Nayana Majumdar) very preliminary! the issue is here USTC-I due to obvious numerical uncertainty here, the value has been changed within 50%

Z c,I * = 22.5 Ω 17% cross-talk 1st 7.5% cross-talk 2nd Length=94 cm Z c,III * = 21 Ω USTC I cross-talk and transmission measured with a fast pulser injected at one end. Measured with 3GHz scope. 10% cross-talk 1st 4% cross-talk 2nd Length=52.5 cm USTC I outer 1 inner 1 outer 2 inner 2 50 outer 3 50 inner 3 50 outer 4 inner 4 50 outer5 inner 5 outer 6 inner 6 50 outer 3 outer 1 outer 2 outer 4 outer 5 outer 6 50 Z diff,I *~(Z c,out + Z c,in – 2Z m )/2=20 Ω Z diff,III *~(Z c,out + Z c,in – 2Z m )/2=21 Ω typical uni-polar RPC signal injected at the middle of the central electrode of the counter and read-out by RICE-FEE Status of signal transmission (cross-talk)

comparison with data 1- Generate avalanche 2-Calculate fraction of signal induced here and there. 3-Propagate all the signals. 4-Add-up cross-talk with the observed polarity. 5-Include line transmission and electronics response. 6-Determine efficiency and charge distributions. No final results are possible due to the need of precise weighting field calculations. Take the following as very preliminary

USTC-I low resolution (20 mm)high resolution (2 mm assumed) ?

Tsingua-II low resolution (20 mm) high resolution (2 mm assumed) 50 fC NEC needed to describe these points [!!] ? E w extrapolated from the one simulated for USTC-I with neBEM

Comparing neBEM with the analytical formula for the weighting field used so far analtycal formula for E z preliminary numerical estimate (neBEM) USTC-I Tsingua-II

typical plots worth looking at (not quantitatively here)

what is the analytical formula telling us? The analytical formula assumes that Space charge enters at higher values than the number of electrons at threshold level Nth: for strips for pads indeed the formula depends little on the value of N th. N is the total number of clusters Let's define: f=Nth/Nsat.

what is the analytical formula telling us? pads strips the analytical formula assumes that Space charge enters at higher values than the number of electrons at threshold level: N th <N sat. Lets define: f=0.5f~2 f~4f~15 f~20 Z det ~20 Ω little sensitivity to the threshold level very strong sensitivity to the threshold level

Conclusions Efficiency and charge distributions are reasonably well described (still some details must be fixed, pedestals: gain, gas mixture, etc). The low efficiency observed seems to be connected to the factor –f-. This factor tells us how much above of Space-Charge the threshold sits. More or less evidently, the conclusion is that the threshold was too high (100 fC, to be confirmed). Impedance matching brings –f- down by ~x2, a differential read-out should bring another factor x2, the threshold should be preferably on the order of Q th ~50fC (seems possible!). Very good agreement between APLAC and USTC-I regarding transmission measurements with fast pulser. Tsingua-I measurements were not done in a proper way, and accurate comparison is difficult. The calculation of the weighting field maps proves to be very critical. The analytical formula seems to be insufficient in between the strips. The proposal is to use the neBEM solver. Preliminary simulations show an overall good agreement, suggesting that we are in the good way, but fine tuning still needed.

Conclusions For the next counters one should focus on the electronics responsivity, i.e: minimum charge that can be discriminated. This number should be known before hand. There is no obvious problem with spacers for these counters, they seem to work as one expects.