Plasma Science: From Fundamental Research to Technological Applications (1995)
Chapter: Gyrokinetics
Coherent Structures and Self-Organization
The theoretical discovery of solitons, long-lived coherent solutions to certain nonlinear fluid equations, arose out of plasma physics research in the 1950s. In recent years, a more general class of nonlinear structures, including both solitons and less permanent, but still robust objects (solitary waves), has been found to play a significant role in plasma evolution. Thus, large-scale turbulence is often dominated by vortical structures, analogous to fluid vortices, but depending on the interaction of the plasma with electromagnetic fields. At smaller scales, such phase-space structures as clumps or holes can critically affect plasma dissipation. The past 10 years have seen significant progress in classifying, explaining, and assessing the importance of such phenomena. Their importance in laboratory plasma confinement, nonneutral plasmas, magnetosphere evolution, and solar physics is now firmly established, although much of the difficult nonlinear physics remains to be understood.
Strong Plasma Turbulence
The past decade has contributed to a greater, although still incomplete, understanding of plasma turbulence. Strong turbulence theory has been applied to many microinstabilities (drift waves and ion temperature gradient, trapped-particle, microtearing, and magnetic modes in tokamak plasmas). Resonance broadening has been addressed, and the direct interaction approximation (DIA), although still heuristic and difficult to implement numerically, has been extended to provide a general form that can be used for simpler transport models. Some understanding has been developed of turbulent cascades in plasmas, of nonlinear transport mechanisms, and of the coupling of heat and particle transport. Numerical studies of solar convection have greatly improved our understanding of turbulence in stars.
Gyrokinetics
During the past decade there has been a refinement of gyrokinetics, the approximate theory of the motion of charged particles in strong magnetic fields, with applications to stability theory and magnetohydrodynamics. Of particular note is the successful application of this description to the numerical simulation of a class of slow instabilities, the ion temperature gradient mode, resulting in mode spectra in excellent agreement with tokamak experiments. Also, a hybrid magnetohydrodynamic-gyrokinetic code has successfully simulated both fishbone and toroidal Alfvén eigenmodes, although greater computing power is needed to definitively study the latter.
