A Full Electromagnetic Particle-in-Cell Code To Model Collision-less Plasmas in Magnetic Traps

Abstract

A lot of plasma physics problems are not amenable to exact solutions due to many reasons. It is worth mentioning among them, for example, nonlinearity of the motion equations, variable coefficients or non lineal conditions on known or unknown borders. To solve these problems, different types of approximations which are combinations of analytical and numerical simulation methods are put into practice. The problem of plasma behavior in numerous varieties of a minimum-B magnetic trap where the plasma is heated under electron cyclotron resonance (ECR) conditions is the subject of numerical simulation studies. At present, the ECR minimum-B trap forms the principal part of the multi-charge ion sources. There are different numerical methods to model plasmas. Depending of both temperature and concentration, these can be classified in three main groups: fluid models, kinetic models and hybrid models. The fluid models are the most simple way to describe the plasma from macroscopic quantities, which are used for the study of highly collisional plasmas where the mean free path is much smaller than size of plasma (l_mfp > L) from the solution of the Boltzmann or Vlasov equation, respectively [2]. For kinetic simulations there are different method to solve the Boltzmann or Vlasov equation, being the Particle-In-Cell (PIC) codes one the most popular. The hybrid model combine both the fluid and kinetic models, treating some components of the system as a fluid, and others kinetically; which are used for the study of plasmas, may use the PIC method for the kinetic treatment of some species, while other species (that are Maxwellian) are simulated with a fluid model. In this work, a scheme of the relativistic Particle-in-Cell (PIC) code elaborated for an ECR plasma heating study in minimum-B traps is presented. For a PIC numerical simulation, the code is applied to an ECR plasma confined in a minimum-B trap formed by two current coils generating a mirror magnetic configuration and a hexapole permanent magnetic bars to suppress the MHD instabilities. The plasma is maintained in a cylindrical chamber excited at TE_111 mode by 2.45 GHz microwave power. In the obtained magnetostatic field, the ECR conditions are fulfilled on a closed surface of ellipsoidal type. Initially, a Maxwellian homogeneous plasma from ionic temperature of 2 eV being during 81.62 ns, that correspond to 200 cycles of microwaves with an amplitude in the electric field of 1 kV/cm is heated. The electron population can be divided conditionally into a cold group of energies smaller than 0.2 keV, a warm group whose energies are in a range of 3 − 10 keV and hot electrons whose energies are found higher than 10 keV.