Showing papers by "Boris Breizman published in 1997"

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 that 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, characterized by explosive behavior, where the saturation level is independent of the closeness to threshold. In the hard regime, rapid oscillations typically arise that lead to large frequency shifts in a fully developed nonlinear stage. 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.

Nonlinear theory of kinetic instabilities near threshold

Abstract: A new nonlinear equation has been derived and solved for the evolution of an unstable collective mode in a kinetic system close to the threshold of linear instability The resonant particle response produces the dominant nonlinearity, which can be calculated iteratively in the near-threshold regime as long as the mode doe snot trap resonant particles With sources and classical relaxation processes included, the theory describes both soft nonlinear regimes, where the mode saturation level is proportional to an increment above threshold, and explosive nonlinear regimes, where the mode grows to a level that is independent of the closeness to threshold The explosive solutions exhibit mode frequency shifting For modes that exist in the absence of energetic particles, the frequency shift is both upward and downward For modes that require energetic particles for their existence, there is a preferred direction of the frequency shift The frequency shift continues even after the mode traps resonant particles

TFTR DT experiments

Abstract: The Tokamak Fusion Test Reactor (TFTR) is a large tokamak which has performed experiments with 50:50 deuterium - tritium fuelled plasmas. Since 1993, TFTR has produced about 1090 D - T plasmas using about 100 grams of tritium and producing about 1.6 GJ of D - T fusion energy. These plasmas have significant populations of 3.5 MeV alphas (the charged D - T fusion product). TFTR research has focused on alpha particle confinement, alpha driven modes, and alpha heating studies. Maximum D - T fusion power production has aided these studies, requiring simultaneously operation at high input heating power and large energy confinement time (to produce the highest temperature and density), while maintaining low impurity content. The principal limitation to the TFTR fusion power production was the disruptive stability limit. Secondary limitations were the confinement time, and limiter power handling capability.

Evolution of toroidal Alfven eigenmode instability in Tokamak Fusion Test Reactor

Abstract: The nonlinear behavior of the toroidal Alfven eigenmode (TAE) driven unstable by energetic ions in the Tokamak Fusion Test Reactor (TFTR) [Phys. Plasmas 1, 1560 (1994)] is studied. The evolution of instabilities can take on several scenarios: a single mode or several modes can be driven unstable at the same time, the spectrum can be steady or pulsating, and there can be negligible or anomalous loss associated with the instability. This paper presents a comparison between experimental results and recently developed nonlinear theory. Many features observed in experiment are compatible with the consequences of the nonlinear theory. Examples include the structure of the saturated pulse that emerges from the onset of instability of a single mode, and the decrease, but persistence, of TAE signals when the applied rf power is reduced or shut off.

Nonlinear dynamics of microwave instability in accelerators

Abstract: We develop a nonlinear theory of the weak single bunch instability in electron and positron circular accelerators and damping rings. A nonlinear equation is derived that governs the evolution of the amplitude of unstable oscillations with account of quantum diffusion effects due to the synchrotron radiation. Numerical solutions to this equation show a large variety of nonlinear regimes depending on the growth rate of the instability and the diffusion coefficient. Comparison with the observation in the Stanford Linear Collider Damping Ring at the Stanford Linear Accelerator Center shows qualitative agreement with the patterns observed in the experiment. {copyright} {ital 1997} {ital The American Physical Society}

Spontaneous hole-clump pair creation in weakly unstable plasmas

Abstract: A numerical simulation of a kinetic instability near threshold shows how a hole and clump spontaneously appear in the particle distribution function. The hole and clump support a pair of Bernstein, Greene, Kruskal (BGK) nonlinear waves that last much longer than the inverse linear damping rate while they are upshifting and downshifting in frequency. The frequency shifting allows a balance between the power nonlinearly extracted from the resonant particles and the power dissipated into the background plasma. These waves eventually decay due to phase space gradient smoothing caused by collisionality.

Self-focused particle beam drivers for plasma wakefield accelerators

Abstract: Strong radial forces are experienced by the particle beam that drives the wakefield in plasma-based accelerators. These forces may destroy the beam although, under proper arrangements, they can also keep it in radial equilibrium which allows the beam to maintain the wakefield over a large distance and to provide high energy gain for the accelerated particles. This paper demonstrates the existence of acceptable equilibria for the prebunched beams and addresses the issue of optimum bunch spacing, with implications for forthcoming experiments.