MicroBooNE Document 4708-v1

Wire Plane Analytic Calculations

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Document type:
Design or Technical Note
Submitted by:
Glenn Horton-Smith
Updated by:
Glenn Horton-Smith
Document Created:
17 Aug 2015, 11:50
Contents Revised:
17 Aug 2015, 11:50
Metadata Revised:
17 Aug 2015, 12:10
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Useful formulas for design of TPCs with multiple parallel wire planes are derived using an extension of conformal representation theory previously applied to single-grid ionization chambers. Expressions are given for the electric potential and field lines around the wires, the fraction of electrons collected by the wire planes, and the relation between wire plane voltages and asymptotic fields between planes.

Python code for calculating and plotting potentials is also provided. However, the equation for calculating the wire voltages from desired asymptotic fields turns out to be surprisingly simple, though not quite trivial.

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