Study Of Transport In Phase Space In The Interactions Of Charged Particles With Electrostatic Waves

Nuclear fusion energy is an ideal energy for human development in the furture.Tokamak is the most promising experimental device for magnetic confinement fusion.In order to realize the self-sustained burning of the plasma,the confinement and heating becomes the key point at present. The auxiliary current drive is necessary for the confinement and heating. The wave-particle interaction is a key physical mechanism of plasma heating and current driving in the tokamak, and also an important subject of plasma physics. This paper investigates the effects of the phases of the electrostatic waves on chaotic diffusion in the velocity space, the interaction of plasma with two lower hybrid waves, and the interaction of plasma with multiple hybrid waves.The chaotic diffusion in velocity space has been studied. Firstly, the model of multi-step standard mapping is introduced. Then, the effects of the wave phases on the threshold of large scale chaos and the chaotic diffusion are studied by numerically solving the motion equation of charged particles. The diffusion coefficient in velocity space is obtained by analytically calculating the correlation functions. The analytical results are compared with the numerical ones and good agreements are achived. It is found that the diffusion in velocity space strongly depends on the wave phase spectrum.For the periodic spectrum with two different phases, a small relative phase makes the diffusion deviate from the quasi-linear one even for an arbitrarily large overlap parameter. The quasi-linear approximation is valid when the overlap parameter is large for the spectrum in which the wave phases of any group of three neighboring waves are different. The quasi-linear threshold can be much larger than the zero phased standard mapping.The effects of perturbed orbits on the interactions of electrons with two lower hybrid waves simutaneously, one of which is resonant with electrons at a low phase velocity (vpl=3.8Vthe, where vpl is the wave phase velocity and Vthe is the electron thermal speed) while the other is off-resonant at a high phase velocity (vp2=5.5Vthe),have been studied by using the particle simulation code based on the gyro-kinetic electron and fully-kinetic ion (GeFi) model [Lin et al., Plasma Phys. Control. Fusion 47, 657 (2005)]. When the amplitude of the off-resonant wave is sufficiently small so that the resonances of these two waves do not overlap, the variation of the resonant wave amplitude is similar to that predicted by O’Neil theory [O’Neil, Plasma of Fluid 8,12 (1965)]. With the amplitude increasing, the two resonances overlap and large scale chaos emerges. As a result, the damping of the resonant wave can be enhanced, which is due to that the trapped electron orbits are significantly perturbed by the off-resonant wave. The diffusion process gives rise to the enhanced damping. When the overlap is sufficiently large, the damping of the off-resonant wave and the oscillatory behavior of the wave amplitude are observed. In addition, the resonant plateau in the distribution function can be broadened due to the change of the chaotic region boundaries as the electron perturbed orbits are taken into account.The interactions of electrons with multiple lower hybrid waves have been studied by using the particle simulation code based on GeFi model. The evolution of the wave spectrum, as well as the distribution of the electrons in phase space, is investigated. The growths of the waves with lower and intermittent mode numbers are found. The growths are due to the electron with higher velocities transfering kinetic energy to these waves through chaotic transport in phase space. The growth of the waves with intermittent phase velocities bridges the gap between non-overlapping resonances. For the single peak spectrum, particle trapping effects of the peak wave is found and the resonant plateau in the velocity distribution function is formed. For the double-peak spectrum, when the resonances of the two peak waves slightly overlap, two resonant plateaus with two different levels in the velocity distribution function are formed due to the wave damping and non-overlapping of the resonances. When the resonances of the two peak waves strongly overlap, even though the resonant waves damp to lower levels, two resonant plateaus merge into one longer plateau in the velocity distribution function due to the growths the waves with intermittent mode numbers.