In this work, we detail the derivation of a plasma kinetic theory leading to the components of the dielectric tensor for a magnetized dusty plasma with variable charge on the dust particles, considering that the dust component of the plasma contains spherical dust particles with different sizes, which are charged both by inelastic collisions of electrons and ions and by photoionization.

We present general expressions for the components of the dielectric tensor of magnetized dusty plasmas, valid for arbitrary direction of propagation and for situations in which populations of dust particles of different sizes are present in the plasma. These expressions are derived using a kinetic approach which takes into account the variation of the charge of the dust particles due to inelastic collisions with electrons and ions, and features the components of the dielectric tensor in terms of a finite and an infinite series, containing all effects of harmonics and Larmor radius, and is valid for the whole range of frequencies above the plasma frequency of the dust particles, which are assumed to be motionless. The integrals in velocity space which appear in the dielectric tensor are solved assuming that the electron and ion populations are described by anisotropic non-thermal distributions characterized by parameters κ and κ ⊥ , featuring the Maxwellian as a limiting case. These integrals can be written in terms of generalized dispersion functions, which can be expressed in terms of hypergeometric functions. The formulation therefore becomes specially suitable for numerical analysis.

Simulation of neoclassical transport with the continuum gyrokinetic code COGENT Phys. Plasmas 20, 012513 (2013) Nonlinear dynamics of beta-induced Alfvén eigenmode in tokamak Phys. Plasmas 20, 012510 (2013) Gyrokinetic simulation of global and local Alfvén eigenmodes driven by energetic particles in a DIII-D discharge Phys. Plasmas 20, 012508 (2013) Investigation of an ion-ion hybrid Alfvén wave resonator Phys. Plasmas 20, 012111 (2013) We utilize a kinetic description to study the dispersion relation of Alfv en waves propagating parallelly to the ambient magnetic field in a dusty plasma, taking into account the fluctuation of the charge of the dust particles, which is due to inelastic collisions with electrons and ions. We consider a plasma in which the velocity distribution functions of the plasma particles are modelled as anisotropic kappa distributions, study the dispersion relation for several combinations of the parameters j k and j ? , and emphasize the effect of the anisotropy of the distributions on the mode coupling which occurs in a dusty plasma, between waves in the branch of circularly polarized waves and waves in the whistler branch. V C 2012 American Institute of Physics.[http://dx

Starting from the exact microscopic equations for an unmagnetized dusty plasma, where the dust charge is regarded as a new degree of freedom of the system, we present a self-consistent set of equations that is suitable for weak turbulence analyses, where we have considered that the dust is electrically charged by absorption of plasma particles through inelastic collisions. In the quasilinear limit of the wave-particle interaction, we find a modified equation for the spectral energy density of the plasma electric field, and two other equations of the spectral energy densities associated with the fluctuation of the dust distribution due to plasma particle absorption, and with the fluctuation of the dust charging current. Different dispersion relations are found respectively for each type of oscillation. The corresponding kinetic equations for the waves are given, as well as the temporal evolution equations of the dust and plasma particles.

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