Diego González-Díaz (GSI-Darmstadt)




       Santiago, 05-02-09
This is a talk about how to deal with signal coupling
in   highly    inhomogeneous      HF     environments,
electrically ...
definitions used
                                                               mirror electrode
                         ...
Some of the geometries chosen by the creative RPC developers

             HADES-SIS                          FOPI-SIS    ...
pad
                                     pad structure

             taking the average signal and neglecting edge effects...
How to create a simple avalanche model

     We follow the following 'popular' model

• The stochastic solution of the ava...
MC results. Prompt charge distributions
                       for 'pad-type' detectors
               4-gap 0.3 mm RPC st...
MC results. Efficiency and resolution for
         'pad-type' detectors
fine so far

till here one can find more than a handful of similar
simulations by various different groups, always able to...
strip
                           single-strip (loss-less)

            induction                                          ...
strip
                                single-strip (with losses)

At a given frequency signals attenuate in a transmission...
strip
single-strip (HADES TOF-wall)



               - area 8m2, end-cap, 2244 channels
               - cell lengths D =...
double-strip
             double-strip (signal induction)
strip cross-section for HADES-like geometry
          wide-strip...
double-strip
double-strip (transmission and signal collection)
                                                           ...
double-strip
        double-strip (simulations)

                            input:
                            signal ind...
double-strip
double-strip (measurements)



            unfortunately very little information is published
            on ...
double-strip
             double-strip (optimization)

fraction of cross-talk Fct:
-continuous lines: APLAC
-dashed-lines:...
double-strip
double-strip (optimization)
multi-strip
                               multi-strip

A literal solution to the TL equations
in an N-conductor MTL is of...
multi-strip




but how can we know if the TL theory works after all?

A comparison simulation-data for the cross-talk lev...
multi-strip
Far-end cross-talk in mockup RPC (23cm)



                                          signal injected
         ...
multi-strip
        Near-end cross-talk in FOPI 'mini'
             multi-strip RPC (20cm)
           HV   HV cathode
Glas...
multi-strip




most prominent examples of an a
priori   cross-talk   optimization
procedure as obtained in a recent
beam-...
multi-strip
       30cm-long differential and ~matched
                    multi-strip
experimental conditions:
~mips from...
multi-strip
         100cm-long shielded multi-strip
experimental conditions:
~mips from p-Pb reactions at 3.1 GeV, low
ra...
multi-strip
100cm-long shielded multi-strip

    time resolution for double-hits




   double-hit no any of 3rdneighbors
...
multi-strip
        100cm-long shielded multi-strip

           time resolution for double-hits
tails
summary



• We performed various simulations and in-beam measurements of Timing
RPCs in multi-strip configuration. Contra...
acknowledgements




 A. Berezutskiy (SPSPU-Saint Petersburg)
G. Kornakov (USC-Santiago de Compostela),
       M. Ciobanu ...
D Gonzalez Diaz  Optimization Mstip R P Cs
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D Gonzalez Diaz Optimization Mstip R P Cs

  1. 1. Diego González-Díaz (GSI-Darmstadt) Santiago, 05-02-09
  2. 2. 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.
  3. 3. definitions used mirror electrode not counting Pad: set of 1+1(ref) conductors electrically small Multi-Pad: set of N+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 For narrow-gap RPCs this definition leads to: pad strip vp c t rise vpc t rise D< = < 5 cm D≥ = ≥ 5 cm f c 2 0.35 f c 2 0.35
  4. 4. Some of the geometries chosen by the creative RPC developers HADES-SIS FOPI-SIS ALICE-LHC -V -V V V -V -V STAR-RHIC -V -V V V V ! all these schemes are equivalent -V regarding the underlying avalanche dynamics... but the RPC is also a strip- V line, a fact that is manifested after the -V avalanche current has been induced. And all these strip-lines have a completely V different electrical behavior. S. An et al., NIM A 594(2008)39 HV filtering scheme is omitted
  5. 5. pad pad structure taking the average signal and neglecting edge effects induction signal collection t '−t t 1 Cg α *v 1 iind (t ) = imeas (t ) = vdrift q ∫ exp[ + α * vdrift t ' ] dt ' t vdrift q e drift g C gap gC gap 0 RinC g if RinCg << 1/(α*vdrift) imeas (t ) ≅ iind (t ) reasonable for Rin typical narrow- iind (t ) gap RPCs at 1cm2 scale D h Cg Cg Rin w imeas (t )
  6. 6. How to create a simple avalanche model We follow the following 'popular' model • The stochastic solution of the avalanche Raether limit 8.7 equation is given by a simple Furry law (non- space-charge equilibrium effects are not included). regime ~7.5 • Avalanche evolution under strong space- log10 Ne(t) ~7 charge regime is characterized by no exponential-growth threshold effective multiplication. The growth stops regime when the avalanche reaches a certain number of carriers called here ne,sat that is left as a ~2 free parameter. exponential-fluctuation regime • The amplifier is assumed to be slow enough 0 to be sensitive to the signal charge and not to to tmeas t its amplitude. We work, for convenience, with a threshold in charge units Qth. avalanche Furry-type fluctuations the parameters of the mixture are derived from recent measurements of Urquijo et al (see poster session) and HEED for the initial ionization
  7. 7. MC results. Prompt charge distributions for 'pad-type' detectors 4-gap 0.3 mm RPC standard mixture 1-gap 0.3 mm RPC standard mixture Eff = 74% Eff = 60% Eff = 38% simulated simulated measured qinduced, prompt [pC] qinduced, prompt [pC] measured assuming space-charge saturation at ne,sat= 4.0 107 (for E=100 kV/cm) Data from: P. Fonte, V. Peskov, NIM A, 477(2002)17. P. Fonte et al., NIM A, 449(2000)295. qinduced, total [pC]
  8. 8. MC results. Efficiency and resolution for 'pad-type' detectors
  9. 9. fine so far till here one can find more than a handful of similar simulations by various different groups, always able to capture the experimental observations. to the authors knowledge nobody has ever attempted a MC simulation of an 'electrically long RPC' why?
  10. 10. strip single-strip (loss-less) induction transmission and signal collection 1 Cg 1 Τ Cg y iind (t ) ≅ vd q N e ( t ) imeas (t ) ≅ vd q N e (t − av ) + ∑ g C gap g 2 C gap v reflections L0,L 1 2Z c Zc = v= T= C g ,L L0,L ⋅ C g ,L Z c + Rin iind (t ) imeas (t ) Lo,L D Cg,L h Rin w z y x − iind (t )
  11. 11. strip single-strip (with losses) At a given frequency signals attenuate in a transmission line as: D − have little effect for glass and Cu Λ( f ) ≈e electrodes as long as tan(δ)<=0.001 equivalent threshold ! ? 1 R (f) ≈ L + Z c GL ( f ) Λ( f ) Zc ~ x 2/Texp(D/Λ) log Ne(t) threshold iind (t ) Lo,L RL imeas (t ) to t Cg,L GL Rin − iind (t )
  12. 12. strip single-strip (HADES TOF-wall) - area 8m2, end-cap, 2244 channels - cell lengths D = 13-80 cm Zc = 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 - average time resolution: 70-75 ps - average efficiency: 95-99% - cluster size: 1.023 D. Belver et al., NIM A 602(2009)687 A. Blanco et al., NIM A 602(2009)691 A. Blanco, talk at this workshop
  13. 13. double-strip double-strip (signal induction) strip cross-section for HADES-like geometry wide-strip E ≅ 1 Cg limit h << w z iind (t ) = E z vdrift N e (t ) g C gap same polarity this yields signal induction even for an avalanche produced in the neighbor strip (charge sharing) opposite polarity! D We use formulas from: T. Heubrandtner et al. NIM A 489(2002)439 h z y w extrapolated analytically to an N-gap situation x
  14. 14. double-strip double-strip (transmission and signal collection) 0 Τ iind,v+ (t )+iind,v− (t ) Z m Rin iind,v− (t )−iind,v+ (t ) itr,meas(t )= + + ∑ 2 2 ( Zc + Rin )2 2 reflections y0 iind,v+ (t ) = iind (t − ) Z m Rin iind ,v − (t )+iind ,v + (t ) Τ iind ,v − (t ) −iind ,v + (t ) v + ∆v ict,meas (t ) = + + ∑ ( Z c + Rin ) 2 2 2 2 reflections y iind,v− (t ) = iind (t − 0 ) v − ∆v low frequency high frequency term / 'double pad'-limit dispersive term 1 −1 ∆v Lm,L C m, L v= v = L0,L (C g ,L +Cm,L ) , = − L0,L ⋅ C g ,L v L0,L C g ,L + Cm,L 2Z c T= L0,L Z m 1 ⎡ Lm,L C m, L ⎤ Z c + Rin L0,L Zc = , = ⎢ + ⎥ Zc = C g , L + C m, L Z c 2 ⎢ L0,L C g ,L + Cm,L ⎥ ⎣ ⎦ C g ,L It can be proved with some single strip double strip parameters simple algebra that ict has parameters zero charge when integrated over all reflections
  15. 15. double-strip double-strip (simulations) input: signal induced from an avalanche produced at the signal transmitted cathode + FEE response normalized to signal induced A. Blanco et al. NIM A 485(2002)328 cross-talk signal normalized to signal transmitted in main strip
  16. 16. double-strip double-strip (measurements) unfortunately very little information is published on detector cross-talk. In practice this work of 2002 is the only one so far performing a systematic study of cross-talk in narrow-gap RPCs 80-90% cross-talk levels cluster size: 1.8-1.9 !!!
  17. 17. double-strip double-strip (optimization) fraction of cross-talk Fct: -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
  18. 18. double-strip double-strip (optimization)
  19. 19. multi-strip multi-strip A literal solution to the TL equations in an N-conductor MTL 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 remaining part 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
  20. 20. 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!
  21. 21. multi-strip Far-end cross-talk in mockup RPC (23cm) signal injected with: trise~1ns tfall~20ns 50 anode 1 50 50 cathode 1 50 50 anode 2 50 50 cathode 2 50 50 anode 3 50 50 cathode 3 50 50 anode 4 50 50 cathode 4 50 50 anode 5 50 50 cathode 5 50
  22. 22. multi-strip Near-end cross-talk in FOPI 'mini' multi-strip RPC (20cm) HV HV cathode Glass z Spacers signal injected with: trise~0.35ns tfall~0.35ns cathode Multistrip anode M. Kis, talk at this workshop 50 anode 0 50 Y 50 anode 1 50 50 .......... 50 50 anode 11 50 50 anode 12 50 50 anode 13 50 50 anode 14 50 50 anode 15 50
  23. 23. multi-strip most prominent examples of an a priori cross-talk optimization procedure as obtained in a recent beam-time at GSI
  24. 24. multi-strip 30cm-long differential and ~matched multi-strip experimental conditions: ~mips from p-Pb reactions at 3.1 GeV, low rates, high resolution (~0.1 mm) tracking 8 gaps Cm=20 pF/m ... ... Cdiff=23 pF/m Zdiff=80 Ω intrinsic strip profile is accessible! probability of pure cross-talk: 1-3% I. Deppner, talk at this workshop
  25. 25. multi-strip 100cm-long shielded 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. ... ... 5x2 gaps
  26. 26. multi-strip 100cm-long shielded multi-strip time resolution for double-hits double-hit no any of 3rdneighbors double-hit in double 2st neighbors hit in any of 1 nd neighbors
  27. 27. multi-strip 100cm-long shielded multi-strip time resolution for double-hits tails
  28. 28. 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 appear to be well suited for a multi-hit environment, if adequate 'a priori' optimization is provided. Cross-talk levels below 3% and cluster sizes of the order of 1 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 physics environment studied. • There is yet room for further optimization.
  29. 29. acknowledgements A. Berezutskiy (SPSPU-Saint Petersburg) G. Kornakov (USC-Santiago de Compostela), M. Ciobanu (GSI-Darmstadt), J. Wang (Tsinghua U.-Beijing) and the CBM-TOF collaboration

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