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