1. KLAUS DEHMELT EIC TRACKING R&D MEETING FEBRUARY, 2015 Charge Division Concepts February 09, 2015 Klaus Dehmelt 1

2. MicroPattern Gas Detectors MPGD February 09, 2015 Klaus Dehmelt 2 MPGD need narrow pads/strips/… for good position resolution cathode

3. Dividing Charge February 09, 2015 Klaus Dehmelt 3 MPGD vs MWPC

4. Why Divide Charge? February 09, 2015 Klaus Dehmelt 4

5. Charge Distribution February 09, 2015 Klaus Dehmelt 5 Geometric charge division: increase size of charge cloud  Let charge cloud diffuse transversely -> gas with large(r) transverse diffusion coefficient  Maximize misalignment of GEM-holes  Introduce (small) incident angle  Tetrafluormethane CF 4 is rather immune against blow-up Proportional wire: made use of charge division

6. Charge Distribution February 09, 2015 Klaus Dehmelt 6 Generalize charge division on to 2-D: let charge cloud disperse while inducing charge on strips

7. Charge Distribution February 09, 2015 Klaus Dehmelt 7 Equiv. circuit with intermediate resistive anode Resistive anode foil Signal pickup pads Current generators Pad amplifier

8. Charge Dispersion with Telegraph-Equation February 09, 2015 Klaus Dehmelt 8

9. Charge Dispersion in 2-D February 09, 2015 Klaus Dehmelt 9 Solution to is and more realistic

10. Charge Dispersion in 2-D February 09, 2015 Klaus Dehmelt 10 For rectangular pads integrate charge over any pad shape area to obtain charge “seen” (induced) on that pad with

11. Detector Effects February 09, 2015 Klaus Dehmelt 11

12. Detector Effects February 09, 2015 Klaus Dehmelt 12 L(t), R(t), and A(t) have to be convoluted into I(t)

13. Simulation of Single Charge Cluster February 09, 2015 Klaus Dehmelt 13 Convolution of detector effects (analytically) Includes rise time longit. diffusion charge preamp. rise and fall time

14. Simulation of Single Charge Cluster February 09, 2015 Klaus Dehmelt 14 Convolution of detector effects (analytically)

15. Simulation of Single Charge Cluster February 09, 2015 Klaus Dehmelt 15

16. Simulation of Single Charge Cluster February 09, 2015 Klaus Dehmelt 16 Numerical convolution

17. To Be Continued February 09, 2015 Klaus Dehmelt 17 Strategy  Charge cloud at random (x 0, y 0 ) with random width (  specific to gas)  Place pads/strips/… with (x, y) boundaries and compare with dispersed, convoluted signal at any (x, y) after some time t  Basically limited to a finite number of pads/strips/…

18. To Be Continued February 09, 2015 Klaus Dehmelt 18 Strategy (contd.)  Find a set of best responding system(s)  Determine pad-response-function PRF (a measure of pad signal “amplitude” as a function of space point position relative to the pad)  Produce a corresponding readout board (resistive layer, pad/strip/… layout)  BNL has strongly focused X-ray source (  verify readout properties  Once verified, place readout board into RICH-prototype and go for yet another test-beam campaign, preferably FTBF

19. February 09, 2015 Klaus Dehmelt 19 Additional info

20. Charge Distribution Simulation February 09, 2015 Klaus Dehmelt 20 Telegrapher’s Equation (Oliver Heaviside 1880) with Maxwell’s equations and ideal transmission line concept

21. Charge Distribution Simulation February 09, 2015 Klaus Dehmelt 21

22. Charge Distribution Simulation February 09, 2015 Klaus Dehmelt 22 In reality one has also internal wire resistance (R) and leakage of current (G) to ground

23. Convolute All February 09, 2015 Klaus Dehmelt 23 With convolution one can calculate zero state response (i.e., response to input when system has zero initial conditions) of system to arbitrary input by using impulse response of system Impulse response of dynamic system is its output when presented with brief input signal, called impulse

24. Convolute All February 09, 2015 Klaus Dehmelt 24 How is convolution defined?

25. Convolution February 09, 2015 Klaus Dehmelt 25

26. Convolution: Excursion February 09, 2015 Klaus Dehmelt 26 We all worked with convolutions already  Impulse response of an inhomogeneous differential equation Green’s function