Three-dimensional normal modes of a magnetized Vlasov plasma.
Three-dimensional eigenmodes for collisionless electronic Vlasov plasma imbedded in magnetic field in electrostatic approximation, noting plasma stability
PLASMA STABILITY↗
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Results for “Vlasov equation”
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Random phase approximation for a plasma in an external electric field.
Random phase approximation for plasma, establishing perturbed electron distribution in oscillating electric field
VLASOV EQUATION↗
Statistical frameworks for weak plasma turbulence.
Weakly turbulent spatially uniform ensemble of Vlasov plasmas, discussing time evolution of correlations due to collective interactions
PLASMA TURBULENCE↗
Initial-value problem for relativistic plasma oscillations.
Initial value problem for collisionless relativistic Vlasov-Maxwell equations, noting new plasma oscillation modes and various phase velocities
Lerche, I.↗
Nonlinear oscillations in a Vlasov-Maxwell plasma.
Vlasov-Maxwell equations solved for large amplitude oscillatory electric fields with uniform external magnetic field, considering initial plasma current
Davidson, R. C.↗
Electromagnetic plasma wave propagation along a magnetic field
The linearized response of a Vlasov plasma to the steady-state excitation of transverse plasma waves along an external magnetic field is examined. Assuming a delta-function excitation mechanism, and performing a detailed Vlasov-Maxwell equation analysis using Fourier-Laplace transforms, the plasma response is found to consist of three terms: a branch-cut term, a free-streaming term, and a dielectric-pole term. Also considered is the phenomenon of plasma wave echoes. The case of longitudinal electrostatic waves is extended to the case of transverse plasma waves that propagate along an external magnetic field. It is shown that a transverse echo results in lowest order only when one excitation is transverse and the other is longitudinal.
Olson, C. L.↗
Ordinary-mode electromagnetic instability in colliding plasma streams.
The instability of the electromagnetic linearly polarized mode propagating perpendicularly to the magnetic field is studied for a system composed of two colliding plasma streams, in each of which the electrons and ions are streaming at the same velocity. Using linearized Vlasov-Maxwell equations and allowing for anisotropic temperatures, it is found that in the presence of streaming ions the instability can occur in very low-beta plasmas. The plasma is increasingly susceptible to the electromagnetic instability with increasing values of beta, streaming velocity, temperature ratio of parallel to perpendicular electrons, and temperature ratio of perpendicular electrons to perpendicular ions.
Lee, K. F.↗
On the structure of the magnetotail current sheet.
A self-consistent tail current sheet model described by an exact analytic solution of the time-independent Vlasov-Maxwell equations is presented. The model has a 'slingshot' field configuration with field lines outside the plasma sheet slightly flared in the antisolar direction. It is pointed out that when the model parameters are adjusted to agree with the spatial variation along the tail the required thickness of the neutral sheet must be about 2.5 earth radii, instead of less than or equal to 1 earth radius, as indicated by observations. Furthermore, it is shown qualitatively that a considerable velocity shear must be present in the tail current sheet if the plasma sheet is indeed much thicker than the neutral sheet.
Kan, J. R.↗
Diamagnetic boundary layers - A kinetic theory
A kinetic theory is presented for boundary layers associated with MHD tangential 'discontinuities' in a collisionless magnetized plasma, such as those observed in the solar wind. The theory consists of finding self-consistent solutions of Vlasov's equation and Maxwell's equation for stationary one-dimensional boundary layers separating two Maxwellian plasma states. Layers in which the current is carried by electrons are found to have a thickness of the order of a few electron gyroradii, but the drift speed of the current-carrying electrons is found to exceed the Alfven speed, and accordingly such layers are not stable. Several types of layers in which the current is carried by protons are discussed; in particular, cases are considered in which the magnetic-field intensity, direction, or both, changed across the layer. In every case, the thickness was of the order of a few proton gyroradii, and the field changed smoothly, although the characteristics depended somewhat on the boundary conditions. The drift speed was always less than the Alfven speed, consistent with stability of such structures. These results are consistent with observations of boundary layers in the solar wind near 1 AU.
Lemaire, J.↗
Structure of current sheets in magnetic holes at 1 AU
Current density profiles in several types of interplanetary magnetic holes were calculated assuming that the currents flow in planar sheets and that the magnetic field varies only in the direction normal to the sheet. The planarity was verified in four holes which were observed by two suitably spaced spacecraft. The structure of the current sheets ranges from very simple in some holes to very complex in others. The observed structures are found to be qualitatively consistent with models based on self-consistent solutions of Vlasov's equation and Maxwell's equations. Examples of complex, irregular magnetic holes are also presented, and they are shown to contain multiple, current sheets in which currents flow parallel to one another.
Fitzenreiter, R. J.↗
Interplanetary magnetic holes: Theory
Magnetic holes in the interplanetary medium are explained as stationary, non-propagating, equilibrium structures in which there are field-aligned enhancements of the plasma density and/or temperature. Magnetic anti-holes are considered to be associated with depressions in the plasma pressure. In this model, the observed changes in the magnetic field intensity and direction are due to diamagnetic currents that are carried by ions which drift in a sheath as the result of gradients in the magnetic field and in the plasma pressure within the sheath. The thickness of the sheaths considered is approximately a few ion Larmor radii. An electric field is normal to the magnetic field in the sheath. Solutions of Vlasov's equation and Maxwell's equations are presented which account for several types of magnetic holes, including null-sheets, that were observed.
Burlaga, L. F.↗
Interplanetary magnetic holes - Theory
Magnetic holes in the interplanetary medium are explained as stationary nonpropagating equilibrium structures in which there are field-aligned enhancements of the plasma density and/or temperature. Magnetic antiholes are considered to be associated with depressions in the plasma pressure. In this model the observed changes in the magnetic field intensity and direction are due to diamagnetic currents that are carried by ions which drift in a sheath as the result of gradients in the magnetic field and in the plasma pressure within the sheath. The thickness of the sheaths that we consider is approximately a few ion Larmor radii. An electric field is normal to the magnetic field in the sheath. Solutions of Vlasov's equation and Maxwell's equations are presented which account for several types of magnetic holes, including 'null sheets,' that have been observed.
Burlaga, L. F.↗
A unified kinetic model of the tangential magnetopause structure
In the self-consistent model of the tangential magnetopause, formulated in the present paper on the basis of the Vlasov-Maxwell equations, the plasmas on both sides are magnetized and the magnetic field is everywhere parallel to the magnetopause (i.e., the normal field component is zero) and rotates through an arbitrary angle across the magnetopause. It is shown that the thickness of the magnetopause is greater than the gyroradius of the plasma ions. The presence of a trapped particle population within the magnetopause is shown to be required to allow the magnetic field to rotate more than a certain critical angle (-90 degrees). The model proposed can reproduce the observed features of the tangential magnetopause structure by specifying boundary conditions on both sides of the magnetopause.
Lee, L. C.↗
Double layers on auroral field lines
Time-stationary solutions to the Vlasov-Poisson equation for ion holes and double layers were examined along with particle simulations which pertain to recent observations of small amplitude (e phi)/t sub e approx. 1 electric field structures on auroral field lines. Both the time-stationary analysis and the simulations suggest that double layers evolve from holes in ion phase space when their amplitude reaches (e phi)/t sub e approx. 1. Multiple small amplitude double layers which are seen in long simulation systems and are seen to propagate past spacecraft may account for the acceleration of plasma sheet electrons to produce the discrete aurora.
Hudson, M. K.↗
Collisionless electrostatic interchange instabilities
The linear Vlasov dispersion equation for electrostatic plasma instabilities driven by gravity and weak density gradients perpendicular to a uniform magnetic field is derived and solved numerically. Two interchange instabilities emerge: the well-known fluid mode at long wavelengths and a kinetic model at wavelengths short compared with the ion gyroradius. The properties of both instabilities are studied, as well as the effects of gravity on the universal and lower-hybrid density drift instabilities. The results show that the kinetic interchange generally has a larger growth rate than the fluid interchange instability, indicating that, whenever the latter is present in a collisionless plasma, the former may also be found.
Gray, S. P.↗
Solitary waves and double layers on auroral field lines
Time stationary solutions to the Vlasov-Poisson equations for ion holes and double layers are examined along with particle simulations that pertain to recent observations of small amplitude electric field structures on auroral field lines. Both the time stationary analysis and the simulations suggest that the observed double layers evolve from holes in ion phase space. Multiple small amplitude double layers, as seen in long simulation systems, are observed to propagate past the spacecraft and may account for the acceleration of plasma sheet electrons to produce inverted-V precipitation.
Hudson, M. K.↗
Nonlinear upper hybrid drift waves for a longitudinal electric field perpendicular to a uniform magnetic field in the Vlasov-Maxwell approximation
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.
Abraham-Shrauner, B.↗
Theory of beat-resonant coupling of electrostatic modes
A general expression is derived for the beat-resonant coupling electrostatic modes in a Vlasov plasma. The result for the coupling of two modes has a simple structure: the appropriate momentum gradient of the equilibrium particle distribution is weighted by a positive coupling coefficient and averaged over the resonance surface in momentum space. The contributions of all the resonance surfaces are then summed. This basic structure had been previously exhibited only for specific homogeneous plasma models. The present theory, which unifies and greatly simplifies these individual treatments, is based on a variational formulation of the Vlasov-Poisson equations. Using Lie transforms, the variational principle is reexpressed in oscillation-center variables, and then the nonlinear wave dynamics are obtained from the independent variations of the wave phase and the wave amplitude. The power of the method is then applied to a strongly magnetized, strongly inhomogeneous, non-neutral plasma model.
Crawford, John David↗