Publication date: May 2013
Abstract:
The problem of formulating a kinetic treatment for quasi-stationary
collisionless plasmas in axisymmetric systems subject to the possibly
independent presence of local strong velocity-shear and supersonic
rotation velocities is posed. The theory is developed in the framework
of the Vlasov-Maxwell description for multi-species non-relativistic
plasmas. Applications to astrophysical accretion discs arising around
compact objects and to plasmas in laboratory devices are considered.
Explicit solutions for the equilibrium kinetic distribution function
(KDF) are constructed based on the identification of the relevant
particle adiabatic invariants. These are shown to be expressed in terms
of generalized non-isotropic Gaussian distributions. A suitable
perturbative theory is then developed which allows for the treatment of
non-uniform strong velocity-shear/supersonic plasmas. This yields a
series representation for the equilibrium KDF in which the leading-order
term depends on both a finite set of fluid fields as well as on the
gradients of an appropriate rotational frequency. Constitutive equations
for the fluid number density, flow velocity, and pressure tensor are
explicitly calculated. As a notable outcome, the discovery of a new
mechanism for generating temperature and pressure anisotropies is
pointed out, which represents a characteristic feature of plasmas
considered here. This is shown to arise as a consequence of the
canonical momentum conservation and to contribute to the occurrence of
temperature anisotropy in combination with the adiabatic conservation of
the particle magnetic moment. The physical relevance of the result and
the implications of the kinetic solution for the self-generation of
quasi-stationary electrostatic and magnetic fields through a kinetic
dynamo are discussed.
Authors:
Cremaschini, Claudio; Stuchlík, Zdeněk; Tessarotto, Massimo;