Landau resonance between charged particles and plasma waves

Possible interactions between plasma waves and charged particles are considered, where the particles move with slow to relativistic speeds relative to a thermalised plasma. The electromagnetic perturbation is formulated as an elliptically polarised wave, and the collisionless plasma is described by a Maxwellian distribution in phase space, which is realised in cylindrical coordinates. The linearised Vlasov equation is solved to obtain the perturbed distribution function in the rest frame of the observer. The perturbed currents supported by the ionized medium are then calculated, so that an expression can be written for the total amount of energy available for transfer through the Landau mechanism. In the literature, Landau resonances are described analytically by explicitly using the dielectric tensor, which invoke rather complicated calculations [1,2]. In a previous work [3], it was shown that the calculations can be simplified by employing an identity derived in [4]. It thus transpires that there are only certain discrete channels allowed for the transfer of energy through the Landau mechanism. The total energy available for transfer can be written as [3] W = −p