ISSN:
1572-9613
Keywords:
Plasma
;
kinetic theory
;
wave–particle interaction
;
mean-field limit
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract A system of N particles $$\xi ^N = x_1 ,\upsilon_1,...,x_N ,\upsilon _N )$$ interacting self-consistently with one wave Z = A exp(iφ) is considered. Given initial data (Z (N)(0), ξ N (0)), it evolves according to Hamiltonian dynamics to (Z (N)(t), ξ N (t)). In the limit N → ∞, this generates a Vlasov-like kinetic equation for the distribution function f(x, v, t), abbreviated as f(t), coupled to the envelope equation for Z: initial data (Z (∞)(0), f(0)) evolve to (Z (∞)(t), f(t)). The solution (Z, f) exists and is unique for any initial data with finite energy. Moreover, for any time T〉0, given a sequence of initial data with N particles distributed so that the particle distribution f N(0) → f(0) weakly and with Z (N)(0) → Z(0) as N → ∞, the states generated by the Hamiltonian dynamics at all times 0 ≤ t ≤ T are such that (Z (N)(t), f N(t)) converges weakly to (Z (∞)(t), f(t)).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/B:JOSS.0000026732.51044.87
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