**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;