An optimization algorithm for emission current density calculation

Nowadays studying of parameters of pulsed sources which produced electron beams is of great interest. For example these sources are used for target irradiation and surfaces treatment. Electron emission currents of pulsed sources are often space-charge limited. An iterative particle tracking method with so-called gun iteration is the most effective tool for simulations of beam dynamics for pulsed sources. Compared with the most popular particle-in-cell method, iterative method is more fast because of number of the required macroparticles for the particle-in-cell is significantly larger than the number of the macroparticles required for the iterative method. There are two main groups of methods for solving of the space charge limited emission problem which are usually use with iterative method. The methods of the first group based on application of Child or Langmuir one dimensional analitical solutions for planar, cylindrical and spherical cases. These methods are most commonly used because of its simplicity and low computations required. However, in the case of the curvilinear geometry of the emission surface application of these methods can lead to significant errors. The other group of methods for calculation the current density is based on the condition of vanishing the electric field at the emitter. This approaches allow us to solve the problem with the curvilinear shape of emission surface, but all methods of the second group required large amount of computations as compared with the first group methods. In this paper we propose a modification of the one method of this group, which allow us to reduce the amount of required computations for two-dimensional and axisymmetric problems. The space charge limited emission problem is formalized as the problem of multidimensional optimization. To solve this problem we propose an approach based on an approximation of the current density function as a polinomial fit and use the multidimensional modified Newton method. Refs 15. Figs 11. Table 1.