# Available energy and ground states of collisionless plasmas

## TL;DR

This paper analyzes the energy limits and stability of collisionless plasmas, introducing the concept of available energy and ground states, and examines conditions under which plasmas are stable or unstable.

## Contribution

It defines the available energy as a nonlinear measure of plasma stability and characterizes ground states in collisionless plasmas with respect to fluctuations and invariants.

## Key findings

- Available energy is proportional to mean square fluctuations.
- Certain stellarator plasmas are in ground states and thus stable.
- Magnetically confined plasmas often are not in ground states, affecting stability.

## Abstract

The energy budget of a collisionless plasma subject to electrostatic fluctuations is considered, and the excess of thermal energy over the minimum accessible to it under various constraints that limit the possible forms of plasma motion is calculated. This excess measures how much thermal energy is "available" for conversion into plasma instabilities, and therefore constitutes a nonlinear measure of plasma stability. A distribution function with zero available energy defines a "ground state" in the sense that its energy cannot decrease by any linear or nonlinear plasma motion. In a Vlasov plasma with small density and temperature fluctuations, the available energy is proportional to the mean square of these quantities, and exceeds the corresponding energy in ideal or resistive magnetohydrodynamics. If the first or second adiabatic invariant is conserved, ground states generally have inhomogeneous density and temperature. Magnetically confined plasmas are usually not in any ground state, but certain types of stellarator plasmas are so with respect to fluctuations that conserve both these adiabatic invariants, making the plasma linearly and nonlinearly stable to such fluctuations. Similar stability properties can also be enjoyed by plasmas confined by a dipole magnetic field.