Theoretical Study Of Beta-induced Alfven Eigenmodes Excited By Energetic Particles In Tokamak Plasmas

Nuclear-Fusion, which may potentially provide clean and inexhaustible energy supply in the future, is one of the most important ways for finally solving mankind’s demand for energy without polluting the environment. Tokamak, as a kind of magnetic confinement fusion equipment, is believed to be one of the most promising candidates to achieve this goal.Since the mid-20th century, scientists have pursued magnetic confinement fusion en-ergy research and have made a great progress in this field. Among various problems of the tokamak physics, the confinement of the thermal and energetic particles is intensively related to the success of the fusion. Proper understanding of shear Alfven wave interac-tion with energetic particles produced by auxiliary heating or nuclear fusion reactions in tokamaks is necessary for achieving better confinement of the latter, since resonant wave-particle interactions can destabilize Alfven modes, which, conversely, can cause significant fast-ion redistribution or loss, and as a result substantial damage to the containment ves-sel. Among these Alfven eigenmodes, the beta-induced Alfven eigenmodes (BAEs), which possess frequencies located below the shear Alfven continuous spectrum in a frequency gap caused by the finite thermal plasma compressibility, are particularly important since they can resonate with both thermal ions (at short wavelengths) and energetic particles (at long wavelengths).In this thesis, we study the characteristics of BAEs in the presence of energetic parti-cles (EPs) in large aspect-ratio, finite-β tokamaks with shifted circular flux surfaces. The main results are as follows:First, in the theoretical framework of the generalized fishbone-like dispersion relation (GFLDR), the linear properties of BAEs and energetic particle continuum modes (EPMs) excited by anisotropic slowing-down energetic ions are investigated analytically and nu-merically. The resonant contribution of energetic ions to the potential energy perturbation as well as fluid-like term describing the background plasma and adiabatic contribution of energetic ions are derived. For the high-mode numbers, numerical results show the smooth transition between the EP continuous spectrum and BAE in the gap. EPMs and/or BAEs are destabilized by energetic ions, with real frequencies and growth rates strongly depen-dent on the energetic particle density and resonant frequency. For EPM the frequency as well as the corresponding growth rate increase with τ, energetic particle velocity νE and density nE;however, compared with the situation of the real frequency change, the growth rates are strongly dependent on the above parameters. Besides, EPM cannot exist below the threshold excitation condition which is determined by continuum damping. For BAE, the τmode is marginally stable in absence of EPs, and the mode can be excited when a small drive from the EPs to compensate Landau damping. Besides, the frequency is determined by t and the parameters of EPs, the growth rate increase with νE and nE. All numerical results above can be explained by the GFLDR.Secondly, in the framework of the WKB-ballooning mode representation, a global dis-persion relation for high-mode-number beta-induced Alfven eigenmodes (BAEs) in large aspect-ratio finite-β tokamaks is obtained and the two-dimensional structure of the BAE excited by a radial energetic ion beam is investigated. Analytical and numerical analyses demonstrate that, when the non-perturbative EP wave-particle resonant effect is considered, the BAE is radially localized into the EP-pressure-gradient potential well and it is most un-stable in the lowest bound state; the BAE exhibits the twisting radial mode structure relative to the ideal MHD limit with the up-down symmetric characteristic. That is because the anti-Hermitian contributions due to wave-energetic particle resonance can twist the radial mode structure away from ν*= 0 with ν* being the location of the mode maximum amplitude, resulting in the loss of up-down symmetry in the global mode structure. The present results offer the theoretic explanation of the existing experiment and numerical simulations about the asymmetric mode structure in the poloidal plane.