# A full electromagnetic Particle-In-Cell code to model collisionless plasmas in magnetic traps

## TL;DR

This paper presents a relativistic Particle-in-Cell code for simulating collisionless plasma behavior in magnetic traps under electron cyclotron resonance, demonstrating its application to plasma heating in a minimum-B trap configuration.

## Contribution

The work introduces a specialized PIC code tailored for ECR plasma heating in magnetic traps, combining analytical and numerical methods for complex plasma physics problems.

## Key findings

- Successful simulation of plasma heating in a minimum-B trap
- Identification of electron energy groups during ECR heating
- Validation of the PIC code for collisionless plasma modeling

## 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 multicharge ion sources. 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 $10$ $keV$.