Simulations of various aspects of the PPS Various members of the collaboration, to be enumerated later

We Need to Know? Properties of the discharge – Voltage required – Current delivered – Development time – Decay time – Recovery time (deadtime) Properties of the device – Electric field distribution – Electric field uniformity in drift regions – Electric field intensity in discharge regions How to trigger the discharge – Minimum Number of electrons – Minimum Energy of the electrons How to produce the electrons – Energy loss from ions traversing the device – “Converters” Properties of the output pulses – Risetime – Decay time – Crosstalk

What to simulate Arriving particle spectrum Particle energy loss, multiple scattering Gas ionization Electric fields Output electrical signal Plasma discharge dynamics

Particle scattering Principal tool is GEANT4 – Widely used in nuclear physics – Gives event-by-event output for later analysis – Open source, easily available Example: 106 Ru (R. Varner)

106 Ru example

106 Ru Example

Electric Fields Y. Silver COMSOL has been the most used tool Examples:

Cell capacitance estimates

Electric Field Map Drift Region Dielectric 10  m  =10 Discharge (15 x 75  m) (1mm deep) 80 fF capacitance Sense (10 x 25  m) Applied HV (20 x 25  m) Resistive ( siemens/meter)

Modeling and simulation Initial geometry: two orthogonal copper strips separated by a 400 µm gas gap. One strip at ground, one at 1V. Initial strip dimensions: 1 cm X 1 mm X 25 µm. Initial two-strip capacitance: pF Incrementally changed dimensions Right: Electric potential plot of initial strip geometry

Capacitance v gas gap Right: Plot of capacitance vs. gas gap, keeping strip geometry constant Changed gas gap from 400 microns to 2000 microns, in 100 micron increments Data fitted with 4 th degree polynomial

Capacitance vs Electrode Width Right: capacitance plotted vs width of terminal electrode Width changed from 1 mm to 10 mm, in 1 mm increments

HV sensitivity of cells

Output electrical Signal Develop equivalent circuit Evaluate the circuit using SPICE to simulate the output pulse properties – Amplitude – Width – Ringing

Cell Schematic

Full Schematic

Plasma discharge Many approaches considered – None found to be practical or sufficient Possibilities – Fully dynamical (Y. Silver) Boltzmann equation Maxwell equation Atomic physics cross-sections Somewhat developed for Plasma Display Panels Expensive to run – Drift chamber models (C. Ferretti) CERN GARFIELD Electron production Gas amplification – Geiger counter models Semi-empirical – Require calibration “Rules of thumb”