Relativistic Vlasov-Maxwell Research Articles

Relativistic electron beam acceleration by Compton scattering of extraordinary waves

Relativistic transport equations, which demonstrate that relativistic and nonrelativistic particle acceleration along and across a magnetic field and the generation of an electric field transverse to the magnetic field, are induced by nonlinear wave-particle scattering (nonlinear Landau and cyclotron damping) of almost perpendicularly propagating electromagnetic waves in a relativistic magnetized plasma were derived from the relativistic Vlasov-Maxwell equations. The relativistic transport equations show that electromagnetic waves can accelerate particles in the k″ direction (k″=k−k′). Simultaneously, an intense cross-field electric field, E0=B0×vd∕c, is generated via the dynamo effect owing to perpendicular particle drift to satisfy the generalized Ohm’s law, which means that this cross-field particle drift is identical to the E×B drift. On the basis of these equations, acceleration and heating of a relativistic electron beam due to nonlinear wave-particle scattering of electromagnetic waves in a magnetized plasma were investigated theoretically and numerically. Two electromagnetic waves interact nonlinearly with the relativistic electron beam, satisfying the resonance condition of ωk−ωk′−(k⊥−k⊥′)vd−(k∥−k∥′)vb≃mωce, where vb and vd are the parallel and perpendicular velocities of the relativistic electron beam, respectively, and ωce is the relativistic electron cyclotron frequency. The relativistic transport equations using the relativistic drifted Maxwellian momentum distribution function of the relativistic electron beam were derived and analyzed. It was verified numerically that extraordinary waves can accelerate the highly relativistic electron beam efficiently with βmec2≲1GeV, where β=(1−vb2∕c2)−1∕2.

Multipole Radiation in a Collisionless Gas Coupled to Electromagnetism or Scalar Gravitation

We consider the relativistic Vlasov-Maxwell and Vlasov-Nordstr\"om systems which describe large particle ensembles interacting by either electromagnetic fields or a relativistic scalar gravity model. For both systems we derive a radiation formula analogous to the Einstein quadrupole formula in general relativity.

The Relativistic Vlasov-Maxwell System in Two Space Dimensions: Part I

The motion of a collisionless plasma is modeled by the Vlasov‐Maxwell system. For the relativistic Vlasov‐Maxwell system in the plane with smooth initial data, bounds on particle speeds are derived. In an earlier work [10] it was shown that solutions remain smooth as long as particle speeds do not approach the speed of light. When these results are combined, it follows that solutions remain smooth for all time.

On Stationary Solutions of the Relativistic Vlasov-Maxwell System

We study stationary solutions of the relativistic Vlasov–Maxwell system of plasma physics which have a special form introduced (in the classical setting) by Rudykh, Sidorov and Sinitsy and establish their existence under suitable assumptions on the ansatz functions. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 667–677 (1997).

A low velocity approximation for the relativistic Vlasov‐Maxwell system

AbstractAn approximation for the relativistic Vlasov‐Maxwell (RVM) system of partial differential equations in the one‐space, two‐momenta case is proposed. The speed of light, c, appears as a parameter in this system. The approximation is obtained by modifying certain integral operators appearing in integral representations, due to Glassey and Strauss, of the electric and magnetic fields, and replaces the hyperbolic Maxwell system with one that is elliptic in nature (for each fixed t). Solutions of the modified problem are shown to converge in a pointwise sense to solutions of (RVM) at the asymptotic rate of 1/c2 as c tends to infinity.

An action principle for the relativistic Vlasov–Maxwell system

System actions for the relativistic Vlasov-Maxwell's equations are considered, both in covariant and Hamiltonian forms. The particle distribution function appears as a field to be varied in the action. We derive a Hermitean structure for the linearized system and a Poisson bracket structure for the full nonlinear system.

Numerical modeling of axisymmetric electron beam devices using a coupled particle-finite element method

A coupled particle finite-element method is developed for the numerical resolution of the time-dependent relativistic Vlasov-Maxwell equations in axisymmetric geometries. The use of a conforming finite-element method for the Maxwell solver supplemented with a mass-lumping technique leads to an explicit system for the computation of the electromagnetic fields components. For the Vlasov solver, a fully vectorized algorithm is used for the location of the particles in an unstructured mesh made up with triangles. The numerical values of the electromagnetic fields radiated by a dipole are compared with the analytical solution. The whole Vlasov-Maxwell solver is tested on a simplified free-electron laser electron injector, designed for an RF-based free electron laser and the results are compared with those obtained with a finite-difference code. >

The virtual particle electromagnetic particle-mesh method

New types of current conserving particle-mesh algorithms for solving the coupled relativistic Vlasov-Maxwell set of equations are presented. They are derived using finite elements in both space and time. These new numerical schemes offer considerable advantages over the currently used finite difference PIC methods. They are charge and energy conserving, have good dispersive properties and are computationally fast. Their finite element derivations allow them to be applied to complex geometries more readily than their finite difference PIC counterparts. The local nature of their discrete equations is ideally suited to massively parallel computer architectures. In this paper, an outline of the general derivation is given. One and two dimensional cases are treated in some detail, and the extension to three dimensions is discussed. Procedures for lumping and noise reduction (using a transverse current adjustment - TCA), both of which result in substantial speedups, are outlined. The name “virtual particle” arises from an interpretation of the current assignment scheme.

Study of the starting current and frequency deviation of electrostatic gyromonotron

From relativistic linear Vlasov-Maxwell equations, the expressions of the starting current and frequency deviation of a electrostatic gyromonotron with a field distribution sink ‖ z are derived and the numerical calculation is carried out.

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.

Absence of shocks in an initially dilute collisionless plasma

The Cauchy Problem for the relativistic Vlasov-Maxwell equations is studied in three space dimensions. It is assumed that the initial data satisfy the required constraints and have compact support. If in addition the data have sufficiently smallC2 norm, then a uniqueC1 solution to this system is shown to exist on all of spacetime.

High velocity particles in a collisionless plasma

AbstractWe prove that smooth solutions of the relativistic Vlasov‐Maxwell equations exist for all time provided the kinetic energy density is uniformly bounded.

Singularity formation in a collisionless plasma could occur only at high velocities

The global existence problem is studied for regular solutions of the relativistic Vlasov-Maxwell equations. If it is assumed that the plasma density vanishes a priori for velocities near the speed of light, then regular solutions with arbitrary initial data exist in all of space and time. This assumption is either postulated for a solution or is arranged for all solutions through a modification of the equations themselves.

Self-Consistent Electromagnetic Waves in Relativistic Vlasov Plasmas

It is shown that the treatment of relativistic superluminous waves can be simplified by making a Lorentz transformation to a new frame in which the spatial variable no longer appears. Self-consistent solutions of the relativistic Vlasov-Maxwell equations can be constructed in the new frame. These solutions correspond to nonlinear traveling waves in a finite temperature plasma, and reduce to the usual linear results in the small-amplitude limit. A particular example is considered in which the nonlinear waves propagate through a relativistic Maxwellian plasma, and it is shown that pure transverse waves cannot exist in such a case, but that a coupled longitudinal field necessarily appears. For this case the nonlinear effects are evaluated correct to second order in the transverse field amplitude, thus obtaining a nonlinear dispersion relation and a measure of the coupling. In addition, solutions involving pure longitudinal waves can be found, and are also investigated. In limiting cases the results agree closely with previous calculations based on hydrodynamic models.

Initial-Value Problem for Relativistic Plasma Oscillations

The solution of the collisionless, relativistic Vlasov-Maxwell set of equations is given for the case where neither ambient electric nor magnetic fields are present and a smeared-out negative charge background preserves over-all space-charge neutrality with a relativistic proton plasma. The method of solution is based upon the eigenfunction expansion method invented by van Kampen. It is shown that, besides the relativistically modified modes of Case and Zelazny, there exists a new discrete set of modes whose phase velocities are greater than the speed of light in vacuo. The solution also exhibits the coupling of electrostatic and electromagnetic modes and the existence of complex phase velocities. This initial-value problem (or the problem with the electron and proton roles reversed) is of interest because of the existence of cosmic rays, relativistic electrons emitting synchrotron radiation in nonthermal radio sources, solar noise generation, where electron velocities may approach c (Bailey, 1951), and high-energy electrons in laboratory machines (Post, 1960). In these cases the nonrelativistic treatment is clearly inadequate.