Nonlinear Evolution of Plasma Modes Driven by Fast Particles in Tokamaks

Abstract: In fusion plasmas, high-energy ions arising from plasma heating as well as being generated in fusion reactions may lead to the occurrence of wave micro-instabilities. The basic reason for these instabilities is the deviation of the high-energy ions distribution function from the thermodynamic equilibrium. The presence of thermonuclear instabilities may in turn cause anomalous losses of plasma energy and high-energy particles and consequently may have direct impact on the operation scenarios and ignition conditions. Investigations of the initial phase of these instabilities are connected with an identification of the stability threshold with respect to wave excitation by fast ions as well as with the study of nonlinear dynamics of the wave - fast ion system above the stability threshold. The theory describing the nonlinear dynamics of a driven mode near the marginal stability threshold has been developed by H. Berk and B. Breizmann et al. in the 90’s and was also verefied to some extend in tokamak experiments. This theory is limited to the case of only a single plasma mode with a fixed wave number. However, in practice many plasma modes with different wave numbers may be excited in a tokamak plasma. In the present thesis, the single mode theory is extended to the case of two different, linearly unstable plasma modes driven by fast ions at the linear stability threshold. Futhermore, based on analogy to mechanical nonlinear systems, the model equations are reduced to a set of differential equations of the nonlinear oscillator type. Numerical analysis of the two mode model reveals interesting features of the mode amplitude behavior, depending on the effect of classical relaxation processes represented by the Krook, diffusive, and dynamical friction collision operators.