Magnetohydrodynamics has treated the plasma as a fluid with all particles moving at the same speed, the bulk speed. The thermal motion is ignored. Space plasmas often are hot plasmas with the thermal speed by far exceeding the flow speed. Thus thermal motion has to be taken into account and the plasma has to be described by a distribution function which considers the positions and velocities of the individual particles. The Boltzmann equation gives the equation of motion for this phase space density.
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