An efficient method to model thermal-velocity effects in beam optics analyzer

Summary form only given. Many electron guns with thermionic emission must take into account the effects of the spread in the particle velocities emitted from the cathode. Via Liouville's theorem, this distribution function is a constant of the particle motion. Therefore, if proper distribution of particle positions and velocities at the emitter can be prescribed then accurate nonlaminar, space-charge flows throughout the particle domain can be achieved. It has been verified experimentally this distribution of particles emitted from any point on the cathode is Gaussian. A good approximation of this phase-space-density distribution is the Maxwell-Boltzmann distribution that we can integrate to obtain the cumulative distributions of various quantities particularly the root mean square and the tangential mean of the emitter velocity. They can be linearized and used with the Monte Carlo method to provide the particle velocities at a given position on the cathode for specified numbers of launch angles and energies. This direct approach has worked well and accurately simulated the thermal-velocity effects in many cases in Beam Optics Analyzer (BOA). However, one weakness of this Direct Monte Carlo method is the use of the mean velocity tangential to the cathode. It helps to simplify the linearized equations but generates symmetric launch angles with respect to the normal. It requires at least three launch angles to satisfy the required statistics, and many more to produce compatible results to experiments. An improved approach has been implemented in BOA using the inverse cumulative distribution of the phase-space-density distribution function. This method allows low number of launch particles per site on the emitter and still meets the desired accuracy. Even with only one launch particle but by construction, it still satisfies the required statistics. We will present the simulation of a X-ray device, in which thermal-velocity effects are required. Numerical results will be compared and validated by experimental data.