Thermal equilibria and thermodynamics of trapped plasmas with a single sign of charge

Abstract

Plasmas consisting exclusively of particles with a single sign of charge (e.g., pure electron plasmas and pure ion plasmas) can be confined by static electric and magnetic fields (e.g., in a Penning trap) and also be in a state of global thermal equilibrium. This important property distinguishes these totally un-neutralized plasmas from neutral and quasineutral plasmas. This paper reviews the conditions for and structure of the thermal equilibrium states and then develops a thermodynamic theory of the trapped plasmas. Thermodynamics provides hundreds of general relations (Maxwell relations) between partial derivatives of thermodynamic variables with respect to one another. Thermodynamic inequalities place general and useful bounds on various quantities. General and relatively simple expressions are provided for fluctuations of the thermodynamic variables. In practice, trapped plasmas are often made to evolve through a sequence of thermal equilibrium states through the slow addition (or subtraction) of energy and angular momentum (say, by laser cooling and torque beams). A thermodynamic approach to this late time transport describes the evolution through coupled ordinary differential equations for the thermodynamic variables, which is a huge reduction in complexity compared to the partial differential equations typically required to describe plasma transport. These evolution equations provide a theoretical basis for the dynamical control of the plasmas.