Initial value problem for plasma oscillations
The solution of the initial value problem for the linearised one-dimensional electron Vlasov-Poisson equations in a field-free homogeneous equilibrium is examined for small and large ratios k of Debye length and wavelength, assuming initial perturbing distribution functions varying on the same velocity scale as the equilibrium. Previously known approximations of the initial evolution are extended to longer times, and to arbitrary stable or unstable equilibria. In the quasifluid regime (small k), the electric field, within an additive error O(k(2)), and independently of the initial data, performs an oscillation near the plasma frequency that corresponds to an eigenmode, if it is unstable or marginal, but to an approximate eigenmode arising from the continuous spectrum otherwise. If other unstable or marginal modes are present, these influence only the time-asymptotic behaviour because their amplitudes are initially O(k(2)). In the ballistic regime (large k), there are no instabilities and the perturbing density, now within an error O(k-2), is the Fourier transform of the initial perturbing distribution function, thus following an arbitrary decay law that is independent of the equilibrium. The errors are shown to be time-independent, implying that either approximation is relevant, at least until the perturbing density has essentially damped out. Hence the dominating damping mechanism (in the stable case) is Landau damping if k is much smaller than 1, but ballistic particle mixing if k is much greater than 1.
Bibliographic Reference: Article: Physics of Fluids B, Vol. 3 (1991) No. 5, pp. 1158-1166
Record Number: 199111095 / Last updated on: 1994-12-02
Original language: en
Available languages: en