Kinetic description of quasi-stationary axisymmetric collisionless accretion disk plasmas with arbitrary magnetic field configurations

Abstract

A kinetic treatment is developed for collisionless magnetized plasmas occurring in hightemperature, low-density astrophysical accretion disks, such as are thought to be present in some radiatively-inefficient accretion flows onto black holes. Quasi-stationary configurations are investigated, within the framework of a Vlasov-Maxwell description. The plasma is taken to be axisymmetric and subject to the action of slowly time-varying gravitational and electromagnetic fields. The magnetic field is assumed to be characterized by a family of locally nested but open magnetic surfaces. The slow collisionless dynamics of these plasmas is investigated, yielding a reduced gyrokinetic Vlasov equation for the kinetic distribution function. For doing this, an asymptotic quasi-stationary solution is first determined, represented by a generalized bi-Maxwellian distribution expressed in terms of the relevant adiabatic invariants. The existence of the solution is shown to depend on having suitable kinetic constraints and conditions leading to particle trapping phenomena. With this solution one can treat temperature anisotropy, toroidal and poloidal flow velocities and finite Larmor-radius effects. An asymptotic expansion for the distribution function permits analytic evaluation of all of the relevant fluid fields. Basic theoretical features of the solution and their astrophysical implications are discussed. As an application, the possibility of describing the dynamics of slowly time-varying accretion flows and the self-generation of magnetic field by means of a "kinetic dynamo effect" is discussed. Both effects are shown to be related to intrinsically-kinetic physical mechanisms.

Absolute Stability of Axisymmetric Perturbations in Strongly Magnetized Collisionless Axisymmetric Accretion Disk Plasmas

“…As pointed out in Ref. [13], ignoring slow-time dependencies, this is of the generic form f eq * s = f eq * s (X * s , (ψ * s , Φ * s )). Here X * s are the invariants X * s ≡ E s , ψ * s , p ′ ϕs , m ′ s , while the brackets (ψ * s , Φ * s ) denote implicit dependencies for which the perturbative expansions (1) and (2) are performed.…”

“…These are identified with ε M,s , ε s and σ s , to be referred to as Larmor-radius, canonical momentum and eq is the characteristic scale-length of the equilibrium fluid fields, v is the single-particle velocity and v ϕ ≡ v · R∇ϕ. Systems satisfying the asymptotic ordering 0 ≤ σ s , ε s , ε, ε M,s ≪ 1 are referred to as strongly-magnetized and gravitationally-bound plasmas [12,13], with the parameters σ s , ε s and ε M,s to be considered as independent while ε ≡ max {ε s , s = 1, n}. In the following, we shall assume that the poloidal flux is of the form ψ ≡ 1 ε ψ(x), with ψ(x) ∼ O(ε 0 ), while the equilibrium electric field satisfies the constraint…”

“…We restrict attention to the treatment of non-relativistic, strongly-magnetized and gravitationally-bound (see definition below) collisionless AD plasmas around compact objects for which the theory developed in Refs. [12,13] applies. The plasmas can be considered quasi-neutral and characterized by a mean-field interaction.…”

“…Apart from possible gyrokinetic and finite Larmor-radius effects (which are typically not included for MRI and TMI), this concerns consistent treatment of the kinetic constraints which must be imposed on the fluid fields (see related discussion in Refs. [12,13]). This concerns, in particular, the correct determination of the constitutive equations for the relevant fluid fields.…”

“…[12][13][14], where a perturbative kinetic theory for collisionless plasmas has been developed and the existence of asymptotic kinetic equilibria has been demonstrated for axisymmetric magnetized plasmas. In AD plasmas, in particular, they are characterized by the presence of stationary azimuthal and poloidal species-dependent flows and can support stationary kinetic dynamo effects, responsible for the self-generation of azimuthal and poloidal magnetic fields [15], together with stationary accretion flows.…”