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By neglecting gravity, but now including magnetism, a plasma at rest with constant density, ρ_{0}, and uniform magnetic field, B_{0}, undergoes a small perturbation (subscripts 1) resulting in a plasma flow such that
B = B_{0} + B_{1}
ρ = ρ_{0} + ρ_{1}
v = v_{1}
Differentiating Eqn. 23 with respect to time, and substituting linearised forms of Eqns. 11 (with a large ), 17 & 21 leads to a second generalised wave equation,

(48) 
Assuming a plane wave solution, as for Eqn. 39, leads to,

(49) 
Subsections
James McAteer
20040114