1. Diego González-Díaz (GSI-Darmstadt) GSI, 10-02-09

2. acknowledgements A. Berezutskiy (SPSPU-Saint Petersburg) G. Kornakov (USC-Santiago de Compostela), J. Wang (Tsinghua U.-Beijing) and the CBM-TOF collaboration

3. This is a talk about how to deal with signal coupling in highly inhomogeneous HF environments, electrically long and very long, not properly matched and with an arbitrary number of parallel conductors. This topic generally takes a full book, so I will try to focus on theoretical results that may be of immediate applicability and on experimental results from non- optimized and optimized detectors.

4. why?

5. Dipole magnet The Compressed Baryonic Matter Experiment Ring Imaging Cherenkov Detector Transition Radiation Detectors Resistive Plate Chambers (TOF), more than 150m 2, more than 100m 2 require of strip-based coverage Electro- magnetic Calorimeter Silicon Tracking Stations Projectile Spectator Detector (Calorimeter) Vertex Detector

6. huge cross-talk observed for timing RPCs with double-strip read-out 80-90% cross-talk levels cluster size: 1.8-1.9 !!! A. Blanco et al. NIM A 485(2002)328

7. but really... why?

8. definitions used here Pad: set of 1+1(ref) conductors electrically small Strip: set of 1+1(ref) conductors electrically large Double-Strip: set of 2+1(ref) conductors electrically large Multi-Strip: set of N+1(ref) conductors electrically large This definition leads to: pad strip mirror electrode not counting Multi-Pad: set of N+1(ref) conductors electrically small narrow-gap RPCs wide-gap RPCs

9. some of the geometries chosen by the creative RPC developers ALICE-LHC V -V STAR-RHIC V -V V HADES-SIS -V FOPI-SIS -V V all these schemes are equivalent regarding the underlying avalanche dynamics... but the RPC is also a strip- line, a fact that is manifested after the avalanche current has been induced. And all these strip-lines have a completely different electrical behavior. -V V V V S. An et al., NIM A 594(2008)39 ! HV filtering scheme is omitted

10. pad readout pad D w h CgCg inductionsignal collection R in CgCg if R in C g << 1/(α*v drift ) reasonable for typical narrow- gap RPCs at 1cm 2 scale R in taking the average signal and neglecting edge effects

11. 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 e,sat that is left as a free parameter. 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 e (t) ~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 We use the following 'popular' model the parameters of the mixture are derived from recent measurements of Urquijo et al. (see poster session) and HEED for the initial ionization pad

12. q induced, prompt [pC] q induced, total [pC] simulated measured Eff = 74% Eff = 60% Eff = 38% measured simulated n e,sat = 4.0 10 7 (for E=100 kV/cm) q induced, prompt [pC] assuming space-charge saturation at 4-gap 0.3 mm RPC standard mixture Data from: P. Fonte, V. Peskov, NIM A, 477(2002)17. P. Fonte et al., NIM A, 449(2000)295. MC results. Prompt charge distributions for 'pad-type' detectors pad 1-gap 0.3 mm RPC standard mixture

13. MC results. Efficiency and resolution for 'pad-type' detectors

14. to the authors knowledge nobody has ever attempted a MC simulation of an 'electrically long RPC' fine so far why? till here one can find more than a handful of similar simulations by various different groups, always able to capture the experimental observations.

15. single-strip readout strip D h w transmission and signal collection induction R in C g,L L o,L x z y

16. single-strip readout (with losses) strip R in C g,L L o,L log N e (t) toto t threshold ~ x 2/Texp(D/Λ) GLGL RLRL At a given frequency signals attenuate in a transmission line as: ? equivalent threshold ! they have little effect for glass and Cu electrodes as long as tan(δ)<=0.001

17. T. Heubrandtner et al. NIM A 489(2002)439 We use formulas from: extrapolated analytically to an N-gap situation and based on the Ramo theorem wide-strip limit h << w strip cross-section for HADES-like geometry this yields signal induction even for an avalanche produced in the neighbor strip (charge sharing) double-strip double-strip readout (signal induction) same polarity opposite polarity! D h w x z y

18. double-strip double-strip readout (transmission and signal collection) single-strip parameters double-strip parameters 0 high frequency dispersive term low frequency term / 'double-pad' limit It can be proved with some simple algebra that i ct has zero charge when integrated over all reflections

19. double-strip double-strip (simulations) input: signal induced from an avalanche produced at the cathode + FEE response signal transmitted normalized to the induced signal cross-talk signal normalized to the signal transmitted in the main strip A. Blanco et al. NIM A 485(2002)328 prototype 2002!

20. double-strip double-strip (comparison with data)

21. multi-strip A literal solution to the Transmission Line equations in an N-conductor Multi-TL is of questionable interest, although is a 'mere' algebraic problem. It is known that in general N modes travel in the structure at the same time. For the rest of the talk we have relied on the exact solution of the TL equations by APLAC (FDTD method) and little effort is done in an analytical understanding

22. multi-strip but how can we know if the TL theory works after all? A comparison simulation-data for the cross-talk levels extracted from RPC performance is a very indirect way to evaluate cross-talk. comparison at wave-form level was also done!

23. cathode 1 50 anode 1 50 cathode 2 50 anode 2 50 cathode 3 50 anode 3 50 cathode 4 50 anode 4 50 cathode 5 50 anode 5 50 far-end cross-talk in mockup RPC (23cm) signal injected with: t rise ~1ns t fall ~20ns multi-strip

24. 50 anode 0 50 anode 1 50.......... 50 anode 11 50 anode 12 50 cathode 50 anode 13 50 anode 14 50 anode 15 near-end cross-talk in FOPI 'mini' multi-strip RPC (20cm) multi-strip M. Kis, talk at this workshop signal injected with: t rise ~0.35ns t fall ~0.35ns

25. multi-strip selected example of an optimized read-out structure as obtained in a recent beam-time at GSI

26. multi-strip... experimental conditions: ~mips from p-Pb reactions at 3.1 GeV, low rates, trigger width = 2 cm (< strip width) long run. Very high statistics. 100cm-long shielded multi-strip 5x2 gaps R HV ~10MΩ/

27. no double hit double-hit in any of 1 st neighbors double-hit in any of 2 nd neighbors double-hit in any of 3rd neighbors 100cm-long shielded multi-strip multi-strip time resolution for double-hits

28. tails 100cm-long shielded multi-strip multi-strip time resolution for double-hits

29. summary We performed various simulations and in-beam measurements of Timing RPCs in multi-strip configuration. Contrary to previous very discouraging experience (Blanco, 2002) multi-strip configuration seems to be well suited for a multi-hit environment, if adequate 'a priori' optimization is provided. Cross-talk levels below 3% have been obtained, with a modest degradation of the time resolution down to 110 ps, affecting mainly the first neighbor. This resolution is partly affected by the poor statistics of multiple hits in the environment studied. There is yet room for further optimization.

30. Appendix

31. double-strip double-strip (optimization) fraction of cross-talk F ct : -continuous lines: APLAC -dashed-lines: 'literal' formula for the 2-strip case. a) original structure b) 10 mm inter-strip separation c) PCB cage d) PCB e) differential f) bipolar g) BW/10, optimized inter- strip separation, glass thickness and strip width. h) 0.5 mm glass. Shielding walls ideally grounded + optimized PCB

32. 30cm-long differential and ~matched multi-strip... C m =20 pF/m C diff =23 pF/m experimental conditions: ~mips from p-Pb reactions at 3.1 GeV, low rates, high resolution (~0.1 mm) tracking probability of pure cross-talk: 1-3% intrinsic strip profile is accessible! Z diff =80 Ω I. Deppner, talk at this workshop 8 gaps multi-strip

33. 35-cm long wide-strip, mirrored and shielded... Z c ~18 Ω BW=260 MHz R in =100 Ω F ct =11%little dispersive experimental conditions: ~mips from p-Pb reactions at 3.1 GeV, low rates, trigger width = 2 cm (< strip width) F ct =19% 'fine-tunning' inter-strip region dominated by trigger width probability of pure cross-talk: 1-3% Analysis with high resolution tracking on-going. transverse scan CgCg CmCm

34. MC results. Efficiency and resolution for 'pad-type' detectors

35. continuous line: data from Basurto et al. in pure Freon [5] α extrapolated to mixture by using Freon's partial pressure: α mixture = α Freon (E/f Freon ) f Freon v d directly taken from Freon (inspired on microscopic codes) v d,mixture = v d,Freon Parameters of the gas used for input: α * (effective Townsend coefficient), v d (drift velocity), n o (ionization density) HEED (from Lippmann[4]) n o [mm -1 ] little dependence with mixture! *purely phenomenological!

36. strip single-strip (HADES TOF-wall) - average time resolution: 70-75 ps - average efficiency: 95-99% - cluster size: 1.023 - cell lengths D = 13-80 cm D. Belver et al., NIM A 602(2009)687 A. Blanco et al., NIM A 602(2009)691 - area 8m 2, end-cap, 2244 channels A. Blanco, talk at this workshop Z c = 5 - 12Ω (depending on the cell width) T = 0.2 - 0.4 v = 0.57c - disturbing reflections dumped within 50ns built-in electronic dead-time