1. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 1 M.A. Fernandez-Morales, J.A. Garzón, D. González-Díaz

2. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 2 R&D in high rate / large area tRPCs. D. Gonzalez-Diaz et al., Nuclear Physics B (Proc. Suppl.) 158(2006)111 lines obtained with the functional dependence also used in:

3. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 3. DC model (CBM goal) R&D in high rate / large area tRPCs (DC model scaling).

4. The DC model works reasonably well when the RPC reached a stationary situation. What happens before?

5. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 5 Transient behaviour in RPCs (I). E. Cerron Zeballos et al., NIM A 367(1995)388, also I. Crotty et al. NIM A 337(1994)370 (Asymmetric 8 mm RPC)

6. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 6 Transient behaviour in RPCs (II). P. Colrain, E. Polycarpo et al., NIM 456(2000)62 0.66 mm-4 gap RPC

7. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 7 Transient behaviour in RPCs (III). D. Gonzalez-Diaz et al., Nuclear Physics B (Proc. Suppl.) 158(2006)111 0.3 mm-4 gap RPC

8. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 8 Transient behaviour in RPCs (IV) M. M. Fraga et al., NIM 419(1998)485 transient time depends on rate!

9. What did we do?

10. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 10 Experimental setup X-ray tube glass (1.8mm) gap (0.3 mm) Cu electrode goniometer (0.1 deg precission) mylar window Cu absorbers RPC (3.5x3.5 cm 2 ) (standard timing mixture)

11. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 11 transients of the current in the circuit transient with flux increased transient with flux decreased no transients

12. Part I. Characterization of the electrical properties of glass

13. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 13 Measurement of the glass electric properties guard ring The response function of glass φ(t) can be expressed as: Fisica de dielectricos, J.M. Albella. J.M. Martinez, Barcelona 1984

14. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 14 Some basic relations (I) Most materials can be described as RC circuits with C->C *( ω): being: ε S : the permittivity of the material when it is 'relaxed' (t-> ∞ ), or 'static'. ε ∞ : the permittivity of the material at high frequency (short times), before relaxation takes place. RIm[C( ω)] Re[C( ω)]

15. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 15 Some basic relations(II) Some ways of describing the relaxation process in soda-lime/window glass: Experimental procedure: in order to rule out electrode-related effects we followed H.E. Taylor systematic approach, and so different experimental configurations were tested: Different electrode materials (Au, Ag, Cu). Different electrode technologies (tape, polymer, acetate, evaporation). Different electrode contact (welded, by presion). With and without guard ring. Only the consistent data is shown in the following ! M. M. Fraga et al., NIM 419(1998)485 (simple RC circuit) 1. 2. 3. Distribution of relaxation times dN/d τ=sech(1/2τ)dτ Taylor, H.E., J. Soc. Glass. Tech. 41(1957)350.

16. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 16 Dependence of the response function on voltage (I)

17. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 17 Dependence of the response function on voltage (II) For voltages up to 1 kV (higher voltage drops have little practical implication in the tRPC response) we conclude that the window glass of the kind used here is highly ohmic, and its response function is fairly independent on voltage. T=27 o C

18. Part II. Characterization of the RPC behaviour at high rates.

19. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 19 Experimental setup X-ray tube RPC (3.5x3.5 cm 2 ) (standard timing mixture) glass (1.8mm) gap (0.3 mm) Cu electrode goniometer (0.1 deg precision) mylar window Cu absorbers

20. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 20 X-ray tube characteristics Energy spectrum for HV = 50 kV (maximum) The X-ray response can be considered as instantaneous at the time scale we are interested in: determined through the current response of a diode operated in reverse bias voltage. =12 keV energy determined with TeCd detector

21. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 21 Experimental setup. Orientation respect to the X-rays direction of incidence (I) A illuminated ~A A illuminated ~A/2 A illuminated =A Parameters: P glass, P gas

22. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 22 region B region A Experimental setup. Orientation respect to the X-rays direction of incidence (II) working point

23. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 23 -> At low rates, the dependence of the average total charge with the applied field in the space-charge regime is well described by a straight line: MC description. Modeling the RPC behaviour R = resistance Φ = flux [Hz/cm 2 ] A = illuminated RPC area r = Φ A = rate [Hz] G. Aielli et al. NIM A 508(2001)6 [2 mm RPC] G. Carboni et al. NIM A 498(2003)135 [2 mm RPC] D. González-Díaz et al. NIM A 555(2005)72 [0. 3 mm RPC] At high rates, and once the DC/stationary situation is reached, the total charge is affected by the field drop caused in the glass itself:

24. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 24 The area of influence of an avalanche is approximated by A cell : M. Abbrescia NIM A 533(2004)7 MC description. Modeling the electric response (I) In the MC, the situation is described by analogy with a random shot noise generator in parallel with the gap capacitance. The current measurable in the external circuit is given by: where the first term gives the current induced instantaneously by each new avalanche and the second is the current induced due to the instantaneous voltage across the glass. Fisica de dielectricos, J.M. Albella, J.M. Martinez, Barcelona 1984 D. Gonzalez-Diaz et al., Nuclear Physics B (Proc. Suppl.) 158(2006)111

25. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 25 C ∞ denotes the RPC capacitance at high frequencies ( ω=1-10 9 GHz), readily accessible from the C ∞ of glass with an LCR analyzer (here: ε r = 7-8) and C S is the RPC capacitance at low frequencies, which is more difficult to access and is the one actually responsible for the relaxation process. Going from a glass response of the type φ(t)=exp(-t/ τ ) β to the RPC response function has sizeable technical difficulties, since non-analytical Fourier Transforms are involved. The following method will be used instead: the response function is assumed to be a simple exponential with τ= RC s, and C s is left as a free parameter: The first term is a bit complicated to compute numerically but, as far as average values are concerned, it can be replaced by: MC description. Modeling the electric response (II)

26. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 26 Consistency criteria of the MC Under the assumption of linearity between total charge and voltage, the following relations are fulfilled in the DC limit : (therefore, in the DC limit: i = ΔV/R)

27. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 27 Constraining aΦ and V th parameters in the DC limit

28. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 28 DC limit! Results from the MC Δ Δ Δ Δ

29. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 29 MC and data after fitting (only C S is a free parameter)

30. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 30 MC and data after fitting (only C S is a free parameter). Zoom

31. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 31 Expected behaviour of the total charge from MC

32. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 32 stabilization time needed for charge is totally different when starting and stopping illumination Transients in current and charge. MC and data

33. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 33 Time scale of transients stabilization of the current in the external circuit does not mean stabilization of the RPC! t eq,I(ΔV) = equilibration time: time at 65% of the DC value of I (ΔV)

34. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 34 Conclusions A MC devised to describe transient effects in RPCs based on a previous code (D. Gonzalez-Diaz, Nucl. Phys. B(Proc. Supl.), 158(2006)111) has been introduced showing a reasonable description of data. A simple RC circuit was assumed, because of the much more simplified situation, but it was illustrated how a detailed comparison would require indeed to introduce the response function through the generalized R(ω)C( ω ) circuit. It has been shown that Cu tape electrodes and both Au, Ag evaporated electrodes provide a consistent determination on the glass response function, being highly independent on the voltage up to 1kV. Ag acetate and polymer provided discrepancies of a factor 2, and visible instabilities in the polymer case. It was shown how the transient times for current stabilization are different from the transient times for charge stabilization (driven by the stabilization of the voltage across the glass). In particular it is shown how, naturally, the stabilization time (both for current and charge) depends mainly on the primary rate whenever irradiation starts, and depends mainly on the relaxation time whenever it stops.

35. Appendix

36. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 36 Loosely relevant parameters The shape of the charge distribution does not seem to have any influence (chequed with a Poissonian distribution). The influence of the A cell is also small (here A cell = 0.3 mm 2 ) as long as it does not result in a single shot of magnitude comparable to the maximum voltage drop ΔV=V-V th : This is also consistent with the simple derivation of the equilibration time from: D. Gonzalez-Diaz et al., Nuclear Physics B (Proc. Suppl.) 158(2006)111

37. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 37 Determination of the flux over the RPC saturation due to the voltage drop in the glass extrapolation to high fluxes I X-ray tube [nA] Φ dosimiter [Hz/cm 2 ] checked that the proportionality between tube current and the primary flux exists Φ RPC : observed flux with RPC Φ dosimiter : observed flux determined with a comercial dosimiter.

38. Diego González Díaz - Gesselschaft fur Schwerionenforschung (GSI) 38 Fit to the absorption curves