Vlasov equation and collisionless hydrodynamics adapted to curved spacetime

Abstract

The modification of the Vlasov equation, in its standard form describing a charged particle distribution in the six-dimensional phase space, is derived explicitly within a formal Hamiltonian approach for arbitrarily curved spacetime. The equation accounts simultaneously for the Lorentz force and the effects of general relativity, with the latter appearing as the gravity force and an additional force due to the extrinsic curvature of spatial hypersurfaces. For an arbitrary spatial metric, the equations of collisionless hydrodynamics are also obtained in the usual three-vector form.

Axiomatic geometrical optics, Abraham-Minkowski controversy, and photon properties derived classically

“…For introduction to the tensor notation and index manipulation rules in particular, see Refs. [71,110,111].…”

Axiomatic Geometrical Optics, Abraham-Minkowski Controversy, and Photon Properties Derived Classically

“…For introduction to the tensor notation and index manipulation rules in particular, see Refs. [69,108,109].…”

Current drive in recombining plasma

“…In a recombining plasma, not only does a Langmuir wave change its phase velocity, but there is also plasmon destruction, i.e., nonresonant collisionless damping of the wave [22]. The plasmon destruction results in heating of the bulk electron distribution.…”

“…[22], recombination results in the conservation of the invariant U w /ω, so δU w ∼ U w (δω/ω). Since ω ≈ ω p ∝ n 1/2 , one finds δU w ∼ −(ν R /2)U w δt.…”

“…Time variation in neither the application of rf power nor changes in the current or poloidal magnetic field alters the underlying wave dynamics or the particle collisionality. In contrast, the cooling, heating, and densification associated with, for example, expanding, compressing, and recombining plasmas, can change the wave amplitude due to plasmon conservation [11,12] or plasmon destruction [22], change the wave phase velocity, and substantially alter the particle collisionality.…”