1. Diego González-Díaz (GSI-Darmstadt) A. Berezutskiy (SPSPU-Saint Petersburg), G. Kornakov (USC-Santiago de Compostela), M. Ciobanu (GSI-Darmstadt), J. Wang (Tsinghua U.-Beijing)

2. Some references used in this talk [1a] H. Alvarez Pol et al., 'A large area timing RPC prototype for ion collisions in the HADES spectrometer', NIM A, 535(2004)277. [2a] A. Akindinov et al., 'RPC with low-resistive phosphate glass electrodes as a candidate for CBM TOF', NIM A, 572(2007)676. [3a] J. Wang et al., paper in preparation. [4a] L. Lopes et al., 'Ceramic high-rate RPCs', Nuclear Physics B (Proc. Suppl.), 158(2006)66. [5a] D. Gonzalez-Diaz et al., 'The effect of temperature on the rate capability of glass timing RPCs', NIM A, 555(2005)72. [6a] A. Ammosov et al., talk at XIII CBM collaboration meeting, Darmstadt, Germany. [7a] L. Nauman et al., talk at XIV CBM collaboration meeting, Split, Croatia. [1] A. Mangiarotti et al., 'On the deterministic and stochastic solution of Space-Charge models and their impact in high resolution timing' talk at RPC Workshop Seoul, 2005. [2] G. Chiodini et al., 'Characterization with a Nitrogen laser of a small size RPC', NIM A 572(2007)173. [3] A. Colucci et al., 'Measurement of drift velocity and amplification coefficient in C 2 H 2 F 4 -isobutane mixtures for avalanche-operated resistive-plate counters', NIM A, 425(1999)84. [4] W. Riegler et al., 'Detector physics and simulations of resistive plate chambers', 500(2003)144. [5] E. Basurto et al., 'Time-resolved measurement of electron swarm coefficients in tetrafluoretane (R134a)', Proc. to 28 th ICPIG, Prague, 2007. [6] P. Fonte, V. Peskov, 'High resolution TOF with RPCs', NIM A, 477(2002)17. [7] P. Fonte et al., 'High-resolution RPCs for large TOF systems', NIM A, 449(2000)295. [8] A. Akindinov et al. 'Latest results on the performance of the multigap resistive plate chamber used for the ALICE TOF', NIM A 533(2004)74. [9] G. Aielli et al., 'Performance of a large-size RPC equipped with the final front-end electronics at X5-GIF irradiation facility', NIM A 456(2000)77. [10] S. An et al., 'A 20 ps timing device—A Multigap Resistive Plate Chamber with 24 gas gaps', NIM A 594(2008)39. [11] A. Blanco et al., 'In-beam measurements of the HADES-TOF RPC wall', NIM A 602(2009)691. [12] W. Riegler, D. Burgarth, 'Signal propagation, termination, crosstalk and losses in resistive plate chambers', NIM A 481(2002)130. [13] T. Heubrandtner et al., NIM A 489(2002)439.

3. Talk layout CBM at FAIR-Darmstadt. RPC working principle. Rate capability of various prototypes. Avalanche simulation. Induction simulation. Cross-talk and FEE simulation. Comparison with data.

4. FAIR (Facility for Antiproton and Ion Research)

5. L.V. Bravina et al., Phys. Rev. C60 (1999) 044905 Au+Au collisions up to 11 AGeV: exploring properties of dense hadronic (resonance) matter in the vicinity of the phase transition E. Bratkovskaya, W. Cassing The CBM physics goal at SIS-100 This T-μ B phase-space region has been measured before (AGS, SPS). Idea: take advantage of the new technologies and focus on rare observables (open charm, di- leptons, hyper-nuclei, multi-strange hyperons, J/Ψ, Ψ')

6. Dipole magnet The Compressed Baryonic Matter Experiment Ring Imaging Cherenkov Detector Transition Radiation Detectors Resistive Plate Chambers (TOF) Electro- magnetic Calorimeter Silicon Tracking Stations Tracking Detector Muon detection System Projectile Spectator Detector (Calorimeter) Vertex Detector

7. The CBM-TOF wall. Design requirements ● Overall time resolution (including start time) σ T = 80 ps. ● Occupancy < 5 % for Au-Au central collisions at E=25 GeV/A. ● Space resolution ≤ 5 mm x 5 mm. ● Efficiency > 95 %. ● Pile-up < 5%. ● Rate capability = 20 kHz/cm 2. ● Multi-hit capability (low cross-talk). ● Compact and low consuming electronics (~65.000 electronic channels). ● Multi-strip design in the outer region, due to the very low occupancies. Why? -> Why not?. If electrically possible it is mechanically much more easy.

8. In order to accommodate the different granularities as a function of the polar angle, five different regions were defined: ➔ Pad region (1): 2.0 x 2.0 cm 2 ( 27072 channels, ~10 m 2 ) ➔ Strip region (2): 2.0 x 12.5 cm 2 ( 3840 x 2 channels, ~10 m 2 ) ➔ Strip region (3): 2.0 x 25.0 cm 2 ( 5568 x 2 channels, ~30 m 2 ) ➔ Strip region (4): 2.0 x 50.0 cm 2 ( 6150 x 2 channels, ~60 m 2 ) ➔ Strip region (5): 2.0 x 100.0 cm 2 ( 2900 x 2 channels, ~60 m 2 ) TOTAL ( ~65000channels, ~170 m 2 ) RPC geometry in simulation (I)

9. A multi-gap RPC in general. Here a differential RPC ('a la' STAR), just for the sake of 'electrical elegance' R in standard PCB with read-out strips on one side HV insulator with V break >10-15 kV HV coating with R~100 MΩ/□ +V -V differential pre-amplifier at least 4 gas gaps (~0.3 mm thick) float glass particle *parameters not from STAR

10. More electrical schemes are (un)fortunately possible 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, and this 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 [10] ! HV filtering scheme is omitted

11. prompt (e-) component Slow (ion) component g/v e ~ 1 nsg/v i ~1 μs E=ΔV/g particle e - -I + How (we believe) is the avalanche produced? i th space-charge limitation E av ~E avalanche growth decreases! τ g ~ 1 s (glass relaxation time) see [4], for instance

12. A parentheses: rate capability of various CBM prototypes for small fluxes and in a simple DC-model see for instance: D. Gonzalez-Diaz et al. Nucl. Phys. B (Proc. Suppl.) 158(2006)111

13. A parentheses: rate capability and DC-model systematics In first order, it fits!

14. Back to the avalanche. 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. 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

15. 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!

16. Induction and weighting field E z t=2.5 mm w=22 mm HV read-out wide-pad limit t << w additionally when g<<t (typical situation) E z does not depend on the position –z- along the gap g=0.3 mm w s-s ~0 mm T. Heubrandtner et al. NIM A 489(2002)439 We use formulas from: problem: under-estimation of E z for large inter-strip separations

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

18. q induced, prompt [pC] q induced, total [pC] 1-gap 0.3 mm RPC standard mixture 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 Fonte, [6,7] MC results. Prompt charge distributions for 'wide-pad' type detectors

19. multi-strip detectors

20. First of all... what is a strip? In this talk: A strip is a read-out structure that must be described (due to the phenomena under study) like a transmission-line. In the simplest single-strip description, it is something characterized by 2 magnitudes: a transmission coefficient and a propagation velocity. This is a definition based on the electrical properties of the structure. In standard language: - strip: something read-out in two ends/something 'quite rectangular' - pad: something read-out in one end/something 'quite squared'

21. Induction + transmission + FEE. Sketch (I) induction 1 transmission 2 FEE response 3 multi-strip 4

22. Induction + transmission + FEE. Sketch (II) Five stages in order to get a predictive result Avalanche generation with the previous code. [->Comparison with eff vs V and fine-tune, if needed, of threshold value. This approach seems to be flexible enough.] Induction, based on analytical formulas from [13], extrapolated to multiple-gaps by using the effective series permittivity of the corresponding group of layers. Propagation based on HF simulator APLAC (http://web.awrcorp.com/Usa/Products/APLAC/).http://web.awrcorp.com/Usa/Products/APLAC/ [-> Validation of APLAC for the structure of interest with a pulse generator (nowadays we do not need this step anymore)] Termination and other circuit elements are included, together with FEE, simulated also with APLAC.

23. A 2-strip RPC as a loss-less transmission-line. Example (I) two different modes in the transmission line!. This causes 'modal dispersion' unless: true for homogeneous transmission lines! a 4-gap RPC seen as a transmission-line dominated by skin-effect: small for typical dimensions and rise-times very small, due to the presence of gas and glass for typical materials (glass) loss-less line! W. Riegler, D. Burgarth, NIMA 481(2002)130 [12] see if 1) 2)

24. for exponential signals low-frequency /small distance / non-dispersive limit high-frequency /large distance / dispersive limit small dispersion very large dispersion in general A 2-strip RPC as a loss-less transmission-line. Example (II) z o = position along the strip where the signal is induced see also [12] the 2 modes are fully decoupled

25. A 2-strip RPC as a loss-less transmission-line. Example (III) 2-strip geometry and signal taken from [12] injected signalcross-talk signal non-dispersive limit (z o =0) dispersive limit (z o ->∞) ->Continuous line is the exact analytical solution from [12]. ->Dashed and dotted lines are the numerical solution from APLAC used later in this work.

26. Measurements of cross-talk with RPC mockup

27. cathode 1 50 anode 1 50 cathode 2 50 anode 2 50 cathode 3 50 anode 3 50 cathode 4 anode 4 50 cathode 5 50 anode 5 50 Cross-talk in an un-terminated line signal from BC420 scintillator (used as current generator)

28. 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 Cross-talk in a terminated line

29. Cross-talk and signal shape cross-talk constant, very independent from the signal shape low dispersion counter, typical working conditions, BW=260 MHz Take as a typical shape the one of an avalanche produced at the cathode Even for dispersive counters it is reasonable since most of the charge is coming from that region

30. Typical plots where to look at Transverse profile of the efficiency, with and w/o valid charge. Cross-talk probability. Integral and as a function of the charge in the main strip. Resolution when a second hit is present in the module. Cluster sizes (not shown here). Dependence with HV of the above observables (not shown here).

31. data

32. old 'reference' data

33. 1.6 m long wide-strip (P. Fonte et al., 2002) C g =514 pF/m C m =88 pF/m C m /C g =17% F ct =50% ! BW=1.5 GHz R in =50 Ω very dispersive! experimental conditions: Π, E=3.5 GeV, low rates, trigger width = 2 cm good agreement with MC avalanche F ct =40% 'fine-tunning' 80%-90% measured cross-talk levels reproduced Z c ~13 Ω transverse scan

34. new data

35. 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

36. 50-cm long wide-strip, mirrored and not shielded... probability of pure cross-talk: 1-3% similar cross-talk levels than in previous case experimental conditions: ~mips from p-Pb reactions at 3.1 GeV, low rates, trigger width = 2 cm (< strip width) BW=260 MHz R in =100 Ω Z det ~20 Ω C m =18 pF/m C g =276 pF/m dispersive C m /C g =6.5% F ct =11.5%

37. 30-cm long narrow strip, differential... C m =20 pF/m C diff =23 pF/m F ct =9% 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 dispersive transverse scan

38. 1-m long counter, 12-gap, mirrored and shielded... experimental conditions: ~mips from p-Pb reactions at 3.1 GeV, low rates, trigger width = 2 cm (< strip width) long run. Very high statistics.

39. The last point: cross-talk influence in the timing of a coincident (double) hit. A simple derivation. log[q(t)] t q th variations in base-line due to cross-talk variations in time at threshold due to cross-talk space-charge exponential regime

40. Cross-talk influence in timing (simple derivation) Assumptions: Within the same primary collision cross-talk extends up-to infinite time. It does not depend on position. Fluctuations in time of cross-talk signal are smaller than fluctuations coming from the avalanche charge distribution. Pick-up strips are separated by a typical distance bigger than the area of influence of the avalanche. Charge sharing during induction can be neglected!. Cross-talk is small, given by F ct. cross-talk is expected to affect timing when

41. 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 1-m long counter, 12-gap, mirrored and shielded

43. conclusions and outlook Multi-strip design at 1-m scale with acceptable cross- talk, small cluster size and small deterioration of time resolution seems doable. Further optimized structures based on simulations are on the way (F ct ~1%). Rate capability seems to be achievable. Stability tests already started. -> Detailed optimization based on physics performance soon to follow. Then we will know if cross-talk is 'high' or not. -> Comparisons between simulations and data will continue

44. Appendix

45. Multi-strip-MRPC (MMRPC) 1.1 mm Glass: ε=7.5, strip width = 1.64 mm, strip gap = 0.9 mm, strip length = 900 mm 1.1 mm 0.5 mm 0.22 mm copper (20 μm) 8 gaps The FOPI counter

46. Induction. Example FOPI case.

47. The FOPI counter (11 th strip) 50 anode 0 50 anode 1 50.......... 50 anode 11 50 anode 12 50 cathode 50 anode 13 50 anode 14 50 anode 15

48. The FOPI counter (9 th strip) 50 anode 0 50 anode 1 50.......... 50 anode 9 50 anode 10 50 cathode 50 anode 11 50 anode 12 50.......... 50

49. 50-cm long, mirrored and not shielded...

50. ~1-m long, non-mirrored and shielded...

51. several electrons (I) An ionizing particle at fixed energy creates an average number of ionizations n o randomly distributed along the gap, with each cluster having a (1/n e in cluster ) 2 probability to produce more than 1 electron. This is very easy to generate. Then each cluster can be made to fluctuate according to Furry law. HEED calculation