Are magnetospheric suprathermal particle distributions ( κ functions) inconsistent with maximum entropy considerations?

Abstract

The Maxwellian distribution is the most popular plasma distribution and has become the default assumption when the detailed distribution function is unknown. The reason is in part because, given a fixed average energy, the distribution that maximizes the specific entropy is the Maxwellian. However, magnetospheres are dynamic systems and space plasma particle distributions gain and lose energy, for example by fueling and damping wave activity, so that the average energy is not fixed as these distributions evolve. Thus, it is not surprising, and in fact is expected, that the distributions most commonly observed in magnetospheric charged particle populations are not Maxwellians. We argue that taking the average order of magnitude of the energy, rather than the average energy, of the distribution as constant is a more appropriate constraint for dynamic space plasma distributions. We show that the distribution that maximizes entropy subject to this constraint is exactly the κ function.