Y. Shiozaki

Y. Todo

National Institute for Fusion Science (NIFS-Repository)

§23. Computer Simulation of Fishbone Oscillation Shiozaki, Y. (Grad. Univ. Advenced Studies), Todo, Y. Fishbone instability was first observed during near-perpendicular neutral beam injection in the PDX toka-mak [lJ. The instability takes place in recurrent bursts, accompanied by frequency decrease during each burst. Two types of fishbone modes, precessional fishbones [2J and thermal ion diamagnetic drift fishbones [3], were the-oretically prediced. Little is known about self-consistent nonlinear evolution of the precessional fishbones. Per-turbative approach is not valid for the precessional fish-bones, since the mode frequency emerges from the shear Alfven continuous spectrum and depends intrinsically on the energetic ion distribution. We carried out particle-Magnetohydrodynamic (MHD) hybrid simulations [4J with parameters similar to the PDX experiments. In this model plasma is divided into two parts, bulk plasma and energetic ions. The bulk plasma is described by the nonlinear full MHD equa-tions. Electromagnetic field is given by the MHD de-scription. This approximation is reasonable under the condition that the energetic ion density is much less than the bulk plasma density. The drift-kinetic. descrirtion is employed for the energetic iollS. In order to reduce nu-merical noise, the 8f particle simulation method is ap-plied to the energetic ions. The effect of the energetic ions on the MHD fluid is taken into account in the MHD momentum equation through the energetic ion perpen-dicular current. It must be noted that we start simula-tion from correct MHD equilibrium. In the PDX exper-iment NBI injection wa,."3 nearly perpendiicular. There-fore, the Grad-Shafranov equation_should be extended. We solve an extended Grad-Shafranov equation found in Ref. [5J. The following simulation parameters are employed. The major and minor radii are R=1.43m, a=0.44m, respec-tively. The magnetic field at the magnetic axis is 1.5T. The bulk ions and the beam ions are hydrogen and deu-teriulIl, respectiyely. NBI injection energy is 50keV. Ini-tial energetic ion distribution in the velocity space is as-sumed to be a slowing down distribution. The number of particle used is 5.2 x 105 . The number of grid point is 101 x 48 x 101 for cylindrical coordinates (R, q" Z) Figure 1 shows growth rate of min = 1/1 harmonic for various energetic ion beta values. In case of nearly perpendicular NBI injection, it is found that kink mode is not so stabilized as that of isotropic NBI injection. We have investigated energy evolution. For low energetic ion beta values onJy the magnetic energy is decreasing, and MHO fluid kinetic energy, MHD thermal energy are in-creasing. While for relatively high energetic ion beta values only the energetic ion energy is decreasing, and all of the MHD energy are increasing. This clearly indi-cates that instability driving source is different between low energetic ion beta values and high energetic ion beta values. We call the latter fishbone instability. Amplitude evolution of min = 1/1 harmonic of the radial velocity Vr is shown in Fig. 2. Solid lille and dashed line show the ca."3e of central energetic beta value = 2.0% and 3.0%, respectively. The saturation level of the radial velocity is almost constant ( ~ 5.0 x 10-3 ) in each case. In other words, saturation level dose not depend on energetic ion beta value. 0.02 1 nearlY perpe~~!cular • I' isotropiC 0 0.015 • • ~ 0.01 • >- 0 0.005 0 0 0 0 0.5 1.5 2 2.5 3 ~ener9rtic(OlO) Fig. 1 Growth rate of min = 1/1 harmonic for various i3h values. 0.01 0.001 0.0001 • le·005 ~ > le·006 le·007 belah-2.O% --beta.,=3.0% .......... . le·ooa le·009 0 100 200 300 400 500 600 700 WAt Fig. 2 Amplitude evolution of min = 1/1 harmonic of radial velocity Vr . Reference [lJ K. Mcguire, R. Goldston, M. Bell et aZ., Phys. R.ev. Lett. 50, 891 (1983). [2J L. Chen, R.. B. White, and M. N. Rosenbluth, Phys. Rev. Lett. 52, 1122 (1984). [3J B. Coppi and F. Porcelli, Phys. Rev. Lett. 57, 2272 (1986). [4J Y. Todo and T. Sato, Phys. Plasmas 5, 1321 (1998). [5J E. V. Belova, N. N. Gorelenkov, and C. Z. Cheng, Phys. Plasmas 10, 3240.(2003). 347 

Computer Simulation of Fishbone Oscillation

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