Coherent and Incoherent Radiation from a Plasma

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Abstract
The Vlasov equations have been derived previously by Harris by starting from the Liouville equation and treating both plasma particles and electromagnetic field statistically. A byproduct of this derivation was an equation for fλ(qλ,pλ), the probability density in the phase space of one of the radiation field oscillators. These functions are now used to define an entropy for the electromagnetic field. If the phases and amplitudes of all electromagnetic waves are precisely defined (coherent radiation), the field entropy is negatively infinite. Any incoherence increases the entropy. A direct consequence of the fλ equation is that the field entropy is a constant of the motion. This is analogous to Newcomb's proof that the particle entropy is constant. It follows that incoherent radiation cannot be calculated from the Vlasov equations.

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