Computation of Pierce electrodes for a relativistic high-current electron beam source
For an axisymmetric high-current electron beam source with plane field emission cathode accelenating field structures around stationary beams of high quality are computed. This is accomplished in two main steps. In the first step a sufficiently selfconsistent mathematical model for the electron flow and electric potential distribution in the region occupied by the beam is given. This model includes self-magnetic fields. It is determined by a system of simultaneous analytic differertial equations whose integration yields the shape of the beam border and a corresponding voltage and normal field distribution along this boundary. In the second step the potential is continued from this boundary into the space-charge-free region outside the beam. This involves solving a Cauchy initinl value problem for the Laplace equation. Since this equation is elliptic, the problem cannot be solved in a stable manner by a numerical algorithm which works in the real space of the coordinates only. By a method due to Garabedian stable results are obtained, however, in our case by extending the Cauchy data and the computational process for complex values of the coordinates. This computation finally yields a system of equipotentinl surfaces outside the beam which can practically be achieved as in Pierce systems by correspondingly shaped accelerating electrodes. (auth)
- Research Organization:
- Max-Planck-Institut fuer Plasmaphysik, Garching, Ger.
- NSA Number:
- NSA-29-016444
- OSTI ID:
- 4337234
- Journal Information:
- Particle Accel., v. 5, no. 3, pp. 171-177, Other Information: Orig. Receipt Date: 30-JUN-74
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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