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The energy budget of a collisionless plasma subject to electrostaticfluctuations is considered, and the excess of thermal energy over the minimumaccessible to it under various constraints that limit the possible forms ofplasma motion is calculated. This excess measures how much thermal energy is"available" for conversion into plasma instabilities, and therefore constitutesa nonlinear measure of plasma stability. A distribution function with zeroavailable energy defines a "ground state" in the sense that its energy cannotdecrease by any linear or nonlinear plasma motion. In a Vlasov plasma withsmall density and temperature fluctuations, the available energy isproportional to the mean square of these quantities, and exceeds thecorresponding energy in ideal or resistive magnetohydrodynamics. If the firstor second adiabatic invariant is conserved, ground states generally haveinhomogeneous density and temperature. Magnetically confined plasmas areusually not in any ground state, but certain types of stellarator plasmas areso with respect to fluctuations that conserve both these adiabatic invariants,making the plasma linearly and nonlinearly stable to such fluctuations. Similarstability properties can also be enjoyed by plasmas confined by a dipolemagnetic field.

Available energy and ground states of collisionless plasmas