Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems
- Space Science Center, Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, New Hampshire 03824 (United States)
Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most fundamental concepts in plasma physics. While the former describes the surprising damping of linear plasma waves in a collisionless plasma, the latter describes exact undamped nonlinear solutions of the Vlasov equation. There does exist a relationship between the two: Landau damping can be described as the phase mixing of undamped eigenmodes, the so-called Case-Van Kampen modes, which can be viewed as BGK modes in the linear limit. While these concepts have been around for a long time, unexpected new results are still being discovered. For Landau damping, we show that the textbook picture of phase mixing is altered profoundly in the presence of collision. In particular, the continuous spectrum of Case-Van Kampen modes is eliminated and replaced by a discrete spectrum, even in the limit of zero collision. Furthermore, we show that these discrete eigenmodes form a complete set of solutions. Landau-damped solutions are then recovered as true eigenmodes (which they are not in the collisionless theory). For BGK modes, our interest is motivated by recent discoveries of electrostatic solitary waves in magnetospheric plasmas. While one-dimensional BGK theory is quite mature, there appear to be no exact three-dimensional solutions in the literature (except for the limiting case when the magnetic field is sufficiently strong so that one can apply the guiding-center approximation). We show, in fact, that two- and three-dimensional solutions that depend only on energy do not exist. However, if solutions depend on both energy and angular momentum, we can construct exact three-dimensional solutions for the unmagnetized case, and two-dimensional solutions for the case with a finite magnetic field. The latter are shown to be exact, fully electromagnetic solutions of the steady-state Vlasov-Poisson-Ampere system.
- OSTI ID:
- 20783121
- Journal Information:
- Physics of Plasmas, Vol. 13, Issue 5; Other Information: DOI: 10.1063/1.2186187; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ANGULAR MOMENTUM
BERNSTEIN MODE
BOLTZMANN-VLASOV EQUATION
COLLISIONLESS PLASMA
ELECTRON COLLISIONS
GUIDING-CENTER APPROXIMATION
ION COLLISIONS
LANDAU DAMPING
MAGNETIC FIELDS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PLASMA WAVES
RADIATION TRANSPORT
SOLITONS
STEADY-STATE CONDITIONS
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS