The adiabatic transport of superthermal distributions modelled by Kappa Functions

The Boltzmann entropy of a superthermal distribution modelled by a kappa function is calculated. It is shown that, for adiabatic transport, the quantity (Tcore3/2/n)ξ(κ) remains constant where Tcore is the core Maxwellian temperature, n is the density, and ξ(κ) is a function of the high energy spectral index, κ. For large values of kappa commonly found in space plasmas (κ > 4), the quantity T3/2/n where T = {κ/(κ ‐ 3/2)} Tcore is approximately constant for adiabatic transport.