# On the magnetic shield for a Vlasov-Poisson plasma

## TL;DR

This paper investigates how a magnetic shield can prevent a charged plasma wind from reaching a bounded body, using models based on the Vlasov-Poisson equations, and demonstrates that particles cannot penetrate the shield under certain conditions.

## Contribution

The study introduces models of magnetic shielding for plasmas with different charge compositions and proves that particles are blocked from reaching the body, extending previous results to more general initial data.

## Key findings

- Particles cannot reach the bounded body under the magnetic shield.
- The magnetic field effectively prevents plasma penetration in the models studied.
- Results are improved for straight magnetic lines, representing an unbounded body.

## Abstract

We study the screening of a bounded body $\Gamma$ against the effect of a wind of charged particles, by means of a shield produced by a magnetic field which becomes infinite on the border of $\Gamma$. The charged wind is modeled by a Vlasov-Poisson plasma, the bounded body by a torus, and the external magnetic field is taken close to the border of $\Gamma$. We study two models: a plasma composed by different species with positive or negative charges, and finite total mass of each species, and another made of many species of the same sign, each having infinite mass. We investigate the time evolution of both systems, showing in particular that the plasma particles cannot reach the body. Finally we discuss possible extensions to more general initial data. We show also that when the magnetic lines are straight lines, (that imposes an unbounded body), the previous results can be improved.