arXiv subjects

Silvia Caprino

Publications and source records attributed to Silvia Caprino.

6 recordsLinked to original sources

arXiv2019

Time evolution of a Vlasov-Poisson plasma with different species and infinite mass in $\mathbb{R}^3$

We study existence and uniqueness of the solution to the Vlasov-Poisson system describing a plasma constituted by different species evolving in $\mathbb{R}^3$, whose particles interact via the Coulomb potential. The species can have both positive or negative charge. It is assumed that initially the particles are distributed according to a spatial density with a power-law decay in space, allowing for unbounded mass, and an exponential decay in velocities given by a Maxwell-Boltzmann law, extending a result obtained by the same authors, which was restricted to finite total mass.

math-ph↗

arXiv2019

Efficacy of a magnetic shield against a Vlasov-Poisson plasma

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.

math-ph↗

arXiv2018

The Vlasov-Poisson equation in $\mathbb{R}^3$ with infinite charge and velocities

We consider the Vlasov-Poisson equation in $\mathbb{R}^3$ with initial data which are not $L^1$ in space and have unbounded support in the velocities. Assuming for the density a slight decay in space and a strong decay in velocities, we prove existence and uniqueness of the solution, thus generalizing the analogous result given in [5] for data compactly supported in the velocities.

math-ph↗

arXiv2017

On the magnetic shield for a Vlasov-Poisson plasma

We study the screening of a bounded body $Γ$ 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 $Γ$. 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 $Γ$. 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.

math-ph↗

arXiv2016

A Vlasov-Poisson plasma with unbounded mass and velocities confined in a cylinder by a magnetic mirror

We study the time evolution of a single species positive plasma, confined in a cylinder and having infinite charge. We extend the result of a previous work by the same authors, for a plasma density having compact support in the velocities, to the case of a density having unbounded support and gaussian decay in the velocities.

math.AP↗

arXiv2011

On the attractive plasma-charge system in 2-d

We study a positively charged Vlasov-Poisson plasma in which N negative point charges are immersed. The attractiveness of the system forces us to consider a possibly unbounded plasma density near the charges. We prove the existence of a global in time solution, assuming a suitable initial distribution of the velocities of the plasma particles. Uniqueness remains unsolved.

math.AP↗