Preliminary Study of Electron Emission for Use in the PIC Portion of MAFIA

This memorandum summarizes a study undertaken to apply the program MAFIA to the modeling of an electron gun in a traveling wave tube (TWT). The basic problem is to emit particles from the cathode in the proper manner. The electrons are emitted with the classical Maxwell-Boltzmann (M-B) energy distribution; and for a small patch of emitting surface; the distribution with angle obeys Lambert's law. This states that the current density drops off as the cosine of the angle from the normal. The motivation for the work is to extend the analysis beyond that which has been done using older codes. Some existing programs use the Child-Langmuir, or 3/2 power law, for the description of the gun. This means the current varies as the 3/2 power of the anode voltage. The proportionality constant is termed the perveance of the gun. This is limited, however, since the 3/2 variation is only an approximation. Also, if the cathode is near saturation, the 3/2 law definitely will not hold. In most of the older codes, the electron beam is decomposed into current tubes, which imply laminar flow in the beam; even though experiments show the flow to be turbulent. Also, the proper inclusion of noise in the beam is not possible. These older methods of calculation do, however, give reasonable values for parameters of the electron beam and the overall gun, and these values will be used as the starting point for a more precise particle-in-cell (PIC) calculation. To minimize the time needed for a given computer run, all beams will use the same number of particles in a simulation. This is accomplished by varying the mass and charge of the emitted particles (macroparticles) in a certain manner, to be consistent with the desired beam current.