Particle simulation of electron beams with self-consistent magnetic fields

The design of electron guns to produce very-high-perveance ultrarelativistic low-emittance electron beams for free electron lasers or electron-beam weapons requires electron gun design programs that solve for the self-magnetic field of the beam as well as the space-charge electric field. Most gun design codes solve only for the angular component of the self-magnetic field using a straightforward application of Ampere´s law. This paper reports on the development of an electron gun design code, Magun, which solves for all three components of self-magnetic field in a cylindrically symmetric system. As in other programs, the angular component is obtained from Ampere´s law; the axial and radial components are found from the angular component of the vector potential, which is obtained from a solution of the vector Poisson´s equation. Another feature of Magun is that the space-charge field is found by solving Poisson´s equation for the electrostatic potential on a deformable finite element mesh. A discussion of the advantages of this kind of program is followed by an exposition of the code´s algorithms. Finally, an application to the beam injector of the Experimental Test Accelerator (ETA) at the Lawrence Livermore National Laboratory is presented. Numerical and graphical results from our program will be compared with results from Lawrence Livermore´s computer code EBQ. Emphasis is placed on the behavior of the beam injector (or gun) at extraction grid drives close to the point where a virtual cathode is formed, which provides a particularly severe test of the code.