Stability of Adiabatic Processes and Evolution of Pickup Ion Dimensionality

Abstract In adiabatic processes, such as in many space plasmas, particles flow with no heat entering or exiting their system, while, more generally, the difference between polytropic and adiabatic indices provides a measure of any heating. In this paper, we investigate the thermodynamics of polytropic processes and the relationship between heating and the difference between polytropic and adiabatic indices, extended to account for variable kinetic degrees of freedom. Then, we examine the stability of fluctuating adiabatic process. We show that fluctuations of the adiabatic index cannot be effectively damped to restore equality between polytropic and adiabatic indices, unless the variability of degrees of freedom introduces another source of entropy and heating. We find that the convergence of the stability of the pickup ion (PUI) adiabatic index is very slow, and thus PUIs are rarely adiabatic; in contrast, solar wind protons at ∼1 au are nearly adiabatic. Moreover, we develop the relationship between heat transfer and variable dimensionality. We use this to characterize the evolution of the PUI distribution in the heliosphere. While the initial pickup and final thermalization phases are instantaneous and asymptotically reached, we characterize their duration by the time needed for the dimensionality to change by ∼0.1, and derive the time scales of the phases of PUI evolution: (i) pickup phase is the shorter, ∼1 hr; (ii) isotropization phase takes ∼1 day, (iii) cooling phase is much longer, ∼10 days; and (iv) thermalization phase, ∼1.5 yr. Finally, using observations from Voyager, we verify this model of the evolution of the PUI dimensionality.