T. Sato

Y. Todo

National Institute for Fusion Science (NIFS-Repository)

§2. Linear and Nonlinear Simulation Study on Toroidal Alfven Eigenmode Todo, Y., Sato, T. In fusion reactors, successful confinement of alpha particles is required for self-sustained operation. The alpha particles born from 0-T reactions can destabilize the macroscopic modes such as the toroidal Alfven eigenmode (T AE mode) and the fishbone mode. Nonlinear behaviors of such hybrid kinetic-MHO modes and alpha particles are one of the major physics uncertainties for fusion reactors. Linear and nonlinear particle-MHO simulation codes [1, 2] are developed to analyze hybrid kinetic-MHO modes. The background plasma is described by an MHO fluid model, and the MHO equations are solved by a finite difference method. The particle simulation technique is used for the alpha particle component. The contribution of the alpha particle current is extracted from the total current in the MHO momentum equation to take into account the effects of alpha particles on the background plasma in a self -consistent way. In the linear particle-MHO simulation code [2], the particle weight is a function of the toroidal angle. This new technique reduces required particle number. The initial alpha particle distribution is the slowing -down distribution which is isotropic in the velocity space with the maximum energy of 3.5 MeV. The magnetic field strength at the magnetic axis is 5T, the number density of the background plasma is 1Q2<Jn-\ the minor radius is 0.9m, and the aspect ratio is 3. Resonance condition between energetic alpha particles and T AE mode is investigated with this code. Resonance condition for each particle can be expected as 1=( W0-nwcp)/wb (1) where W 0 , wcp, and wb are the ·eigenfrequency of T AE mode, toroidal precession rate, and bounce frequency, respectively. In Eq. (1) n is the toroidal mode number (=2 in this report) and 1 is an arbitrary integer. From simulation results 1 is plotted for resonant alpha particles in Figure 1. Figure 1 shows that the values of 1 are actually close to integers. It is interesting to note that trapped particles also resonate with T AE mode. With the same initial condition nonlinear simulations are carried out. Alpha particles are lost being induced by TAB mode. For ~a=3%, the fraction of lost particles is 1.2%. Initial distribution of lost alpha particles is shown in Figure 2. They distribute around the passing/trapped boundary. 252 Counter-passing particles are lost when they cross the passing/trapped boundary. Trapped particles are also lost if they are close to the passing/trapped boundary. As investigated in the linear simulation trapped particles also resonate with T AE mode. 6 4 ClQ) 0 c:sxm:u:IP 2 1:1 c 0 e 0 -2 Clm) -4 -3 -2 -1 0 2 3 w'P Fig. 1. Values of l which is defined by Eq. (1) are close to integers for resonant particles. Circles and squares denote passing particles and trapped particles, respectively. The horizontal axis is the toroidal precession rate. 1.2 w 0.8 :t 0.6 0.4 0.2 0 ~~~~~~~~~~~~ 0 0.2 0.4 0.6 0.8 ria Fig. 2. Initial distribution of lost alpha particles in r-p.l t plane. Triangles denote counter-passing particles which cross the passing/trapped boundary. Squares and circles represent the other passing particles and trapped particles, respectively. References 1) Y. Todo, T. Sato, and The Complexity Simulation Group, IAEA Fusion Energy Conference CN-64/02-3 (1996). 2) Y. Todo and T. Sato, submitted to J. Comput. Phys. 

Linear and Nonlinear Simulation Study on Toroidal Alfven Eigenmode

Abstract

Similar works

Full text

Available Versions

National Institute for Fusion Science (NIFS-Repository)