Electrostatic field between non-concentric cylinders

Garcia, M

Lawrence Livermore National Laboratory

关键词: Lawrence Livermore National Laboratory;    Electrostatics;    Electron Beams;    Asymmetry;    42 Engineering;   

DOI  :  10.2172/15002373
RP-ID  :  UCRL-ID-137122
RP-ID  :  W-7405-ENG-48
RP-ID  :  15002373

美国|英语

来源: UNT Digital Library

【 摘 要 】

This report describes a closed-form solution to the electrostatic potential, and the electric field, between non-concentric cylinders, with the inner cylinder charged and the outer cylinder grounded. This problem is an abstraction of the situation of an electron beam within a drift tube. Capacitive and surface current probes on the inner wall of the outer cylinder are used to detect the asymmetry of the field when the beam is off center. The solution of this problem allows for a quantitative relationship between probe-array signals and beam deflection. probe-arrays of this type are called ''beam bugs'' at LLNL. The solution described here is suggested by the analysis presented in [3]. The essential point is that the 2D potential for a line source decreases along a radius as the logarithm of the distance. The non-concentric cylinder problem has a unique profile of this type for each ray from ({rho}, {sigma}) linking the inner cylinder at equipotential V{sub 2}, and the outer cylinder at equipotential 0.