This paper discusses the first nonlinear numerical simulation results of fishbone excitation by a magnetically trapped supra-thermal electron population with pressure profile peaked on axis due to, e.g. electron cyclotron resonance heating. The precession resonance underlying the linear instability is clearly identified. Meanwhile, mode saturation is shown to occur because of the secular resona...

A stochastic model of a continuous nondemolition observation of a free quantum Brownian motion is presented. The nonlinear stochastic wave equation describing the posterior dynamics of the observed quantum system is solved in a Gaussian case for a free particle of mass m > 0. It is shown that the dispersion of the wave packet does not increase to infinity like for the free unobserved particle b...

Within the framework of the thermal wave model, an investigation is made of the longitudinal dynamics of high energy charged particle beams. The model includes the self-consistent interaction between the beam and its surroundings in terms of a nonlinear coupling impedance, and when resistive as well as reactive parts are included, the evolution equation becomes a generalised nonlinear Schröding...

From numerical simulation and analytical modeling it is shown that fast ions can resonate with plasma waves at fractional values of the particle drift-orbit transit frequency when the plasma wave amplitude is sufficiently large. The fractional resonances, which are caused by a nonlinear interaction between the particle orbit and the wave, give rise to an increased density of resonances in phase...

A nonlinear oscillation of frequency and amplitude is found by massively parallel gyrokinetic simulations of Alfvén eigenmodes excited by energetic particles in toroidal plasmas. The fast and repetitive frequency chirping is induced by the evolution of coherent structures in the phase space. The dynamics of the coherent structures is controlled by the competition between the phase-space island ...

Presented is a numerical model for solving the nonlinear dynamics of Alfvén eigenmodes and energetic ions self-consistently. The model is an extension of a previous bump-on-tail model [1, 2], taking into account particle orbits and wave fields in realistic toroidal geometries. The model can be used in conjunction with an orbit averaged Monte Carlo code that handles heating and current drive (si...

We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show that a nonlinear Møller wave operator describing the scattering of a soliton and a wave can be defined. We also consider the dynamics of a soliton in a slowly varying background potential W(εx). We prove that the soliton decomposes into a soliton plus a scattering wave (radi...

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 pr...

An overview is presented of the theory for the nonlinear behavior of instabilities driven by the resonant wave particle interaction. The approach should be applicable to a wide variety of kinetic systems in magnetic fusion devices and accelerators. Here we emphasize application to Alfv en wave driven instability, and the principles of the theory are used to interpret experimental data.