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The Vlasov-Maxwell and Vlasov-Poisson systems of equations for a one-dimensional electron plasma are defined and discussed. A method for transforming a solution of one system which is periodic over a bounded or unbounded spatial interval to a similar solution of the other is constructed.
The subject of this dissertation is the numerical integration of the initial-value problem for the non-linear Vlasov equation. The Vlasov equation is used to describe the dynamics of a "collisionless", one-dimensional, classical electron gas confined between two perfectly reflecting boundaries. Only the long-range Coulomb interactions of the electrons are considered; effects associated with the discrete structure are neglected. The numerical results obtained for non-linear Landau damping compare well with similar results obtained by Knorr. A general statement of the results on stable initial conditions is: As the degree of non-linearity of the initial conditions is increased, the deviation from linear Landau damping appears sooner and is more severe. In some cases damping was observed to cease. Curves showing the time dependence of the damping decrement are derived and compared with predictions of non-linear theories. New results obtained in this study include the observation that for strongly non-linear cases, the damping of the electric field causes an initially Maxwellian fo (v, O) to develop a peak in the neighborhood of the phase velocity; strong growth of the second harmonic is seen after fo (v, t) develops such a peak. Also new in this study is the interpretation of the development of a certain class of strongly unstable initial conditions as approaching an inhomogeneous equilibrium.
In this study, properties of small-amplitude parallel and oblique whistler-mode waves are investigated for a wide range of plasma parameters by numerically solving the full electromagnetic Vlasov-dispersion equation. To investigate the cold-plasma and electrostatic approximations for the whistler mode, the results are compared with results obtained using these descriptions. For large wavelengths, the cold-plasma description is often accurate, while for short wavelengths and sufficiently oblique propagation, the electrostatic description is often accurate. The study demonstrates that in a Vlasov plasma the whistler mode near resonance has a group velocity more nearly parallel to the magnetic field than that predicted by cold-plasma theory.
Upper hybrid drift waves are found as a special solution to a Vlasov-Maxwell plasma which has a longitudinal electric field and a perpendicular uniform magnetic field. A single-species plasma with a constant-density mobile neutralizing background supports spatially varying disturbances that oscillate at the upper hybrid frequency. The general functional dependences of the electric field, the plasma number density, and the one-particle distribution function for the special case are found from more general Vlasov-Maxwell equations invariant under a Lie group point transformation. The one-particle distribution function for the plasma is a function of the Liouville invariant, which is the energy in the generalized Bernstein-Greene-Kruskal (BGK) reference frame, and the momentum in the drift direction.
The equations for the single-particle orbits in a nonneutral high density plasma in the presence of inhomogeneous crossed fields are obtained. Using these orbits, the linearized Vlasov equation is solved as an expansion in the orbital radii in the presence of inhomogeneities and density gradients. A model distribution function is introduced whose cold-fluid limit is exactly the same as that used in many previous studies of the cold-fluid equations. This model function is used to reduce the linearized Vlasov-Poisson equations to a second-order ordinary differential equation for the linearized electrostatic potential whose eigenvalue is the perturbation frequency.
Computer programs for solutions of Vlasov equations for plane, cylindrical, and spherical geometry
Vlasov equations studies and applications of statistical mechanics to plasma dynamics
Dielectric tensor in relativistic Vlasov plasma in electron cyclotron harmonic resonance region
Nonlinear study of Vlasov equation for distribution function for one-dimensional rarefied plasma
Nonlinear solution of Vlasov equation by velocity space polynomial expansion for plasma instability study
Theta pinch shock implosion calculations by computer simulation of collisionless ion Vlasov equation
Three-dimensional eigenmodes for collisionless electronic Vlasov plasma imbedded in magnetic field in electrostatic approximation, noting plasma stability
Fourier-Hermite solutions of Vlasov equations for electron motion against positive neutralizing background examined in linearized limit, noting Landau damping recovery
Time and space development equations for longitudinal and transverse modes in Vlasov plasma
Collisionless electron plasma dynamics in one dimension, investigating nonlinear Vlasov equation for Landau damping and instability
Fokker-Planck damping introduced into Fourier- Hermite representation of Vlasov equation produces Landau and Van Kampen treatments
Approximate integrodifferential equations determining ensemble mean and covariance of particle distribution function of Vlasov plasma, discussing incompressible Navier-Stokes turbulence
Two-body relaxation term in N-body self- gravitating gases of one and three dimensions and validity of Vlasov equation