KLAUS DEHMELTEIC TRACKING R&D MEETING

FEBRUARY, 2015

Charge Division Concepts

February 09, 2015Klaus Dehmelt

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Klaus Dehmelt

MicroPattern Gas Detectors MPGD

February 09, 2015

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MPGD need narrow pads/strips/… for good position resolution cathode

Klaus Dehmelt

Dividing Charge

February 09, 2015

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MPGD vs MWPC

Why Divide Charge?

February 09, 2015Klaus Dehmelt

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Channel count vs point resolution Single strip/pad/… has famous -resolution

Wide strips -> less resolution Narrow strips -> better resolution but higher channel

count: $$$, data size, support, heat, … s = 100/50 mm require ~ 350/175 mm pitch: Narrow!

Charge distributed over more than one strip will increase resolution via c.o.g. method and at the same time allows for wide(r) strips COMPASS GEMs have 400 mm pitch and s ≈ 50 mm

How to distribute charge?

Klaus Dehmelt

Charge Distribution

February 09, 2015

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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 CF4 is rather immune against blow-up

Proportional wire: made use of charge division

Klaus Dehmelt

Charge Distribution

February 09, 2015

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Generalize charge division on to 2-D: let charge cloud disperse while inducing charge on strips

Klaus Dehmelt

Charge Distribution

February 09, 2015

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Equiv. circuit with intermediate resistive anode

Resistive anode foil

Signal pickup pads

Current generators

Pad amplifier

Klaus Dehmelt

Charge Dispersion with Telegraph-Equation

February 09, 2015

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Small inductance and negligible leakage current reduces equation to

Extend to 2-D

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Charge Dispersion in 2-D

February 09, 2015

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Solution to

is

and more realistic

Klaus Dehmelt

Charge Dispersion in 2-D

February 09, 2015

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For rectangular pads integrate charge over any pad shape area to obtain charge “seen” (induced) on that pad

with

Klaus Dehmelt

Detector Effects

February 09, 2015

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Klaus Dehmelt

Detector Effects

February 09, 2015

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L(t), R(t), and A(t) have to be convoluted into I(t)

Klaus Dehmelt

Simulation of Single Charge Cluster

February 09, 2015

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Convolution of detector effects (analytically)

Includes rise timelongit. diffusioncharge preamp.

rise and fall time

I(t)1

2Trise

exp 2a2 / 2 at erf t Trise 2a

2

1

exp 2b2 / 2 bt erf t Trise 2b

2

1

exp 2a2 / 2 a t Trise erf t 2Trise 2a

2

1

exp 2b2 / 2 b t Trise erf t 2Trise 2b

2

1

exp 2a2 / 2 at erf t 2a

2

erf

t Trise 2a

2

exp 2b2 / 2 bt erf t 2b

2

erf

t Trise 2b

2

a 1 tf ; b 1 tf 1 tr

Klaus Dehmelt

Simulation of Single Charge Cluster

February 09, 2015

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Convolution of detector effects (analytically)

Klaus Dehmelt

Simulation of Single Charge Cluster

February 09, 2015

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Convolution of detector effects and charge dispersion via numerical convolution

[

] = QI(t)

I(t)1

2Trise

exp 2a2 / 2 at erf t Trise 2a

2

1

exp 2b2 / 2 bt erf t Trise 2b

2

1

exp 2a2 / 2 a t Trise erf t 2Trise 2a

2

1

exp 2b2 / 2 b t Trise erf t 2Trise 2b

2

1

exp 2a2 / 2 at erf t 2a

2

erf

t Trise 2a

2

exp 2b2 / 2 bt erf t 2b

2

erf

t Trise 2b

2

Klaus Dehmelt

Simulation of Single Charge Cluster

February 09, 2015

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Numerical convolution

Klaus Dehmelt

To Be Continued

February 09, 2015

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Strategy Charge cloud at random (x0, y0) with random width ( s

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/…

⊝

Klaus Dehmelt

To Be Continued

February 09, 2015

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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 (s<10 mm) on precision moveable table (mm-precision) -> verify readout properties

Once verified, place readout board into RICH-prototype and go for yet another test-beam campaign, preferably FTBF

February 09, 2015Klaus Dehmelt 19

Additional info

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Charge Distribution Simulation

February 09, 2015

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Telegrapher’s Equation (Oliver Heaviside 1880) with Maxwell’s equations and ideal transmission line concept

Klaus Dehmelt

Charge Distribution Simulation

February 09, 2015

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Wave equation with velocity

Klaus Dehmelt

Charge Distribution Simulation

February 09, 2015

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In reality one has also internal wire resistance (R) and leakage of current (G) to ground

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Convolute All

February 09, 2015

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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

Klaus Dehmelt

Convolute All

February 09, 2015

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How is convolution defined?

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Convolution

February 09, 2015

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Klaus Dehmelt

Convolution: Excursion

February 09, 2015

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We all worked with convolutions already Impulse response of an inhomogeneous differential

equation

Green’s function