Relativistic Vlasov-Maxwell System Research Articles

Global existence for the relativistic Vlasov-Maxwell system with nearly neutral initial data

Global classical solutions to the initial value problem for the relativistic Vlasov-Maxwell equations are obtained in three space dimensions. The initial distribution of the various species may be large, provided that the total positive charge nearly cancels the total negative charge.

The classical limit of the relativistic Vlasov-Maxwell system

Solutions of the relativistic Vlasov-Maxwell system of partial differential equations are considered in three space dimensions. The speed of light,c, appears as a parameter in this system. For smooth Cauchy data, classical solutions are shown to exist on a time interval that is independent ofc. Then, using an integral representation for the electric and magnetic fields due to Glassey and Strauss [6], conditions are given under which solutions of the relativistic Vlasov-Maxwell system converge in pointwise sense to solutions of the non-relativistic Vlasov-Poisson system at the asymptotic rate of 1/c, asc tends to infinity.

Relativistic plasma half-space with an external magnetic field

The boundary value problem involving a magnetized plasma half-space confined by a perfectly reflecting interface is solved using the relativistic Vlasov–Maxwell system. The external field is assumed to be constant and along the normal of the boundary, and only the linear responses to obliquely incident vacuum waves are considered. When the incidence is normal, only a pair of purely transversal modes, similar to the ordinary and extraordinary modes of the infinite systems, can be excited. When the incidence is oblique, two additional hybrid p and s modes may exist, which are decoupled into the longitudinal and transversal parts only when there is no external field. The p mode vanishes if the field at the boundary, B(0), is in the plane of incidence, and the s mode is zero if B(0) is in the plane which is perpendicular to both the interface and the plane of incidence. Reflection, transmission, and absorption coefficients are calculated for the case of normal incidence.

Concentrating solutions of the relativistic Vlasov–Maxwell system

We study smooth, global-in-time, spherically-symmetric solutions of the relativistic Vlasov–Poisson system that possess arbitrarily large charge densities and electric fields. In particular, we construct solutions that describe a thin shell of equally charged particles concentrating arbitrarily close to the origin and which give rise to charge densities and electric fields as large as one desires at some finite time. We show that these solutions exist even for arbitrarily small initial data or any desired mass. In the latter case, the time at which solutions concentrate can also be made arbitrarily large. As the constructed solutions are spherically-symmetric, they also satisfy the relativistic Vlasov–Maxwell system and thus our results apply to the latter system as well.