Electrode shapes for spherical Pierce flow
Abstract
The problem of obtaining the electrode shapes to produce a conically converging proton beam that has constant current density over each spherical surface of convergence is treated in spherical coordinates. A cone is taken from the Langmuir and Blodgett solution for the region within, and at the edge of, the conically converging beam. A solution for the LaPlace equation, required for the region outside the beam, is in terms of a power series in r and the Legendre polynomials of cos phi V(r,phi)=(A sub n)(P sub n)r(n).
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1981
 Bibcode:
 1981STIN...8316686M
 Keywords:

 Convergence;
 Design Analysis;
 Electrodes;
 Proton Beams;
 Beam Injection;
 Laplace Equation;
 Least Squares Method;
 Legendre Functions;
 Power Series;
 Spherical Coordinates;
 Fluid Mechanics and Heat Transfer