Per Helander, Max Planck Institute for Plasma Physics, Greifswald, Germany

"Available energy in magnetically confined plasmas"

Abstract: In this talk, I address the question of how much of the thermal energy of a magnetically confined plasma is "available" to drive instabilities and turbulence.

For this purpose, I consider the energy budget of a collisionless plasma with electrostatic fluctuations and calculate the excess of thermal energy over the minimum accessible to it under various constraints that limit the possible forms of plasma motion. 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.

If the first or second adiabatic invariant of particle motion 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.

Density-gradient-driven turbulence in tokamaks and stellarators is thought to be driven by trapped-electron modes, whose frequency is lower than the electron bounce frequency. Both adiabatic invariants mentioned above are thus conserved for the electrons, and the amount of energy that the turbulence can extract from them is severely constrained. As a result, the available energy of the electrons under these constraints is correlated with the turbulence level. Indeed a comparison between the energy flux in gyrokinetic simulations and the available energy shows a close correlation over nearly three orders of magnitude. At least in this case, the available energy is thus a useful measure for predicting turbulence properties of magnetically confined plasmas.