Upper bound for the spacecharge limiting current of annular electron beams
Abstract
We report here on a twodimensional analytical calculation of an upper bound on the spacecharge limiting current for a relativistic electron beam in cylindrical geometry. Voronin and coworkers have previously obtained an analytical estimate for the maximum steadystate current that can be propagated in a solid, unneutralized electron beam which completely fills a drift tube immersed in an infinite magnetic guide field. We generalize their method to include annular beams of arbitrary thickness and length, specifying a rigorous upper bound on the limiting current in terms of an eigenvalue of Bessel' s differential equation and separated, homogeneous boundary conditions of the most general form. For the special cases of a thin solid beam in a drift tube of infinite length and a thin annular beam in a drift tube of finite length, we find closedform analytical expressions for the upper bound which are in good agreement with numerical solutions for the actual spacecharge limiting current.
 Publication:

Journal of Plasma Physics
 Pub Date:
 February 1980
 DOI:
 10.1017/S0022377800022194
 Bibcode:
 1980JPlPh..23..129G
 Keywords:

 Charge Distribution;
 Relativistic Electron Beams;
 Space Charge;
 Bessel Functions;
 Boundary Conditions;
 Boundary Value Problems;
 Current Regulators;
 Eigenvalues;
 Magnetic Fields;
 Microwave Equipment;
 Surface Geometry;
 Electronics and Electrical Engineering