Abstract
The concept of the available energy of a collisionless plasma is discussed in the context of magnetic confinement. The available energy quantifies how much of the plasma energy can be converted into fluctuations (including nonlinear ones) and is thus a measure of plasma stability, which can be used to derive linear and nonlinear stability criteria without solving an eigenvalue problem. In a magnetically confined plasma, the available energy is determined by the density and temperature profiles as well as the magnetic geometry. It also depends on what constraints limit the possible forms of plasma motion, such as the conservation of adiabatic invariants and the requirement that the transport be ambipolar. A general method based on Lagrange multipliers is devised to incorporate such constraints in the calculation of the available energy, and several particular cases are discussed for which it can be calculated explicitly. In particular, it is shown that it is impossible to confine a plasma in a Maxwellian ground state relative to perturbations with frequencies exceeding the ion bounce frequency.
Highlights
In a previous publication (Helander 2017), hereafter referred to as I, a quantity called the ‘available energy’ was proposed as a measure of nonlinear plasma stability
We demonstrate that the amount of available energy from temperature variations within the plasma in general depends on the density profile even if the latter is held fixed
The available energy of a plasma – the amount of thermal energy that can be converted into linear and nonlinear fluctuations – depends on what constraints limit the possible forms of plasma motion
Summary
In a previous publication (Helander 2017), hereafter referred to as I, a quantity called the ‘available energy’ was proposed as a measure of nonlinear plasma stability. It is analogous to a quantity called the ‘available potential energy’ in meteorology, which is defined as the difference between the potential energy of the atmosphere and the minimum attainable by any adiabatic redistribution of mass (Lorenz 1955). This analogy is made mathematically explicit in the appendix A.
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