For an unbounded homogeneous electron gas, characterized by the following velocity distribution function, where a 0 is

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For an unbounded homogeneous electron gas, characterized by the following velocity distribution function,

where a0 is a constant, show that the dispersion relation for the right circularly polarized wave, propagating along the magnetostatic field B0 = B0ẑ, is given by

From this result show that the cyclotron damping coefficient is given approximately by

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