Revisiting thermodynamics properties of electrons in nearly collisionless expanding plasmas

Low collisional magnetically expanding laboratory plasmas (e.g. from Helicon sources) exhibit interesting ions and electrons dynamics properties which can share dominant similarities with space plasmas. The formation of potential structures, sometimes in the form of double layers yield ion acceleration with the measurements of ion beam and ion conics. Electrons behave nonlocally since the nearly collisionless plasma is very far from Local Thermodynamic Equilibrium (LTE is isothermal with a polytropic index of 1). Through the study of electrons moving along a potential path in a laboratory helicon double layer experiment, a conservation relation between the electron enthalpy and plasma potential is found by applying traditional thermodynamic concepts and applying Druyvesten theory to spatial measurements of Electron Energy Probability Functions (EEPFs). The effective electron temperature and density show a polytropic correlation with an index of Ge = 1.17 ± 0.02 along the divergent magnetic field, implying a nearly isothermal plasma (Ge = 1) with heat being brought into the system. However, the evolution of electrons along the divergent magnetic field is essentially an adiabatic process, which should have a Ge = 5/3. To complement this finding, correlation between the effective electron temperature and effective density can be approximated by the polytropic relation for which three typical cases of bi-Maxwellian EEPFs with convex, linear, and concave shapes are subsequently treated. Multiple polytropic indexes can be achieved during an adiabatic process depending on the specific shape of non-local EEPFs. The classic adiabatic index of 5/3 for non-LTE systems is only one element in the set of polytropic indexes for non-LTE adiabatic systems governed by non-local particles. These results suggest that although the electrons in the solar wind have a polytropic index of less than 5/3, their actual transport might be adiabatic. The study of momentum flux imparted from such expanding plasma (for electric propulsion application) using a thrust balance and plasma plume mapping provides direct information on plasma momentum transfer from electron pressure into directed ion momentum and on electron diamagnetic effect on axial force. The convective momentum of ions, which can be assumed as a cold species, is determined by the effective electron pressure and the effective electron enthalpy is shown to be the source for ion acceleration. For proton acceleration (solar wind) additional effects related to proton pressure and solar gravity need to be considered. More recently a specially constructed experiment has shown the near perfect adiabatic expansion of an ideal electron gas resulting in a polytropic index greater than 1.4, approaching the adiabatic value of 5/3, when removing electric fields from the system, while the polytropic index close to unity is observed when the electrons are trapped by the electric fields. In this controlled experiment, the system cannot be in thermodynamic equilibrium, yet thermodynamic concepts can be used, with caution, in explaining the results.