Showing papers by "Boris Breizman published in 1996"

Nonlinear dynamics of a driven mode near marginal stability.

Abstract: The nonlinear dynamics of a linearly unstable mode in a driven kinetic system is investigated to determine scaling of the saturated fields near the instability threshold. To leading order, this problem reduces to solving an integral equation with a temporally nonlocal cubic term. This equation can exhibit a self-similar solution that blows up in a finite time. When the blow-up occurs, higher nonlinearities become important and the mode saturates due to plateau formation arising from particle trapping in the wave. Otherwise, the simplified equation gives a regular solution that leads to a different saturation scaling reflecting the closeness to the instability threshold.

Nonlinear response of driven systems in weak turbulence theory

Abstract: A method is presented for predicting the saturation levels and particle transport in weakly unstable systems with a discrete number of modes. Conditions are established for either steady‐state or pulsating responses when several modes are excited for cases where there is and there is not resonance overlap. The conditions for saturation and the associated transport are discussed. Depending on parameters, the saturation level can be low, with only a small fraction of the available free energy released to waves and with no global transport, or the saturation level can be quite high, with almost complete conversion of free energy to wave energy coupled with rapid transport.

Critical nonlinear phenomena for kinetic instabilities near threshold

Abstract: A universal integral equation has been derived and solved for the nonlinear evolution of collective modes driven by kinetic wave particle resonances just above the threshold for instability. The dominant nonlinearity stems from the dynamics of resonant particles which can be treated perturbatively near the marginal state of the system. With a resonant particle source and classical relaxation processes included, the new equation allows the determination of conditions for a soft nonlinear regime, where the saturation level is proportional to the increment above threshold, or a hard nonlinear regime, where the saturation level is independent of the closeness to threshold. It has been found, both analytically and numerically, that in the hard regime the system exhibits explosive behavior and rapid oscillations of the mode amplitude. When the kinetic response is a requirement for the existence of the mode, this explosive behavior is accompanied by frequency chirping. The universality of the approach suggests that the theory applies to many types of resonant particle driven instabilities, and several specific cases, viz. energetic particle driven Alfven wave excitation, the fishbone oscillation, and a collective mode in particle accelerators, are discussed.

Multiplicity of low-shear toroidal Alfven eigenmodes

Abstract: An enlarged spectrum of ideal toroidal Alfven eigenmodes is demonstrated to exist within a toroidicity-induced Alfven gap when the inverse aspect ratio is comparable to or larger than the value of the magnetic shear. This limit is appropriate for the low-shear region in most tokamaks, especially those with low aspect ratio. The new modes may be destabilized by fusion-product alpha particles more easily than the standard toroidal Alfven eigenmodes.