# Efficacy of a magnetic shield against a Vlasov-Poisson plasma

## TL;DR

This paper investigates the effectiveness of a magnetic shield in preventing plasma penetration using a simplified Vlasov-Poisson model, analyzing plasma confinement under combined magnetic and external fields.

## Contribution

It introduces a mathematical model to study magnetic shielding efficacy against plasma intrusion in a half-space setting.

## Key findings

- Magnetic field effectively prevents plasma entry into the protected region.
- Balance between magnetic and external fields determines confinement success.
- Model provides insights into magnetic shielding mechanisms for plasma control.

## Abstract

The aim of the paper is to test on a simple model how impenetrable may be a magnetic shield. We study the time evolution of a single species positive plasma, confined in the half-space $x_1>0$. The confinement is the result of a balance between a magnetic field and an external field, both singular at $x_1=0$; the magnetic field forbids the entrance of plasma particles in the region $x_1 \leq 0$, whereas the external field attracts the plasma particles towards $x_1=0$. The plasma has finite total charge and velocities distributed with a Maxwell-Boltzmann law.