Perturbations in a plasma
  The perturbations of a homogeneous non-relativistic two-component plasma are studied in the Coulomb gauge. Starting from the solution found [2] of the equations of electromagnetic self consistency in a plasma [1], we add small perturbations to all quantities involved, and we enter the perturbed quantities in the equations, keeping only the first order terms in the perturbations. Because the unperturbed quantities are solutions of the equations, they cancel each other, and we are left with a set of 12 linear equations for the 12 perturbations (unknown quantities). Then we solve this set of linearized equations, in the approximation of small ratio of the masses of electrons over those of ions, and under the assumption that the plasma remains homogeneous. 
Evangelos Chaliasos