M. Yagi

National Institute for Fusion Science (NIFS-Repository)

§19. Nonlinear Simulation of Neoclassical Tearing Mode Yagi, M. (RIAM, Kyushu Univ.) Nonlinear simulation with a single helicity mJn~21l is performed using the reduced neoclassical MHD equations[ I]. The formula in the banana regime is used for the neoclassical viscosity. In addition, the numerical viscosity (or the classical viscosity) with the order of 10-5 is introduced for the numerical stability. It is found that the combined effect between the neoclassical viscosity, whose effective collision frequency corresponds to the one in collisional regime in reality (we calculate the value of neoclassical viscosity using the nonnalized resistivity with '1 ~ 10-5 ) and the numerical viscosity makes the fictitious modes in the high toroidal mode number regime for weak shear parameter. Figure I shows the dependence of the toroidal mode number on the growth rate of tearing mode. Here we use the model q profile as q(r) ~ q, (I + (r / r,n' + q, (I) with q,~(q,-qo)/(2b-I), q,~qo-q" q,~2, a~3, b~l, r,~0.6. Cases with qo~1.0,1.l,1.2 are plotted. The corresponding shear parameters are s ~ 1.50,1.35,1.20. 210" qo ~1_2.s=1.20 010° -2 10" y -4 10" _610-2 -8 10" !:-,---~,.......~~,,:;,;,~';!;:-~;c;-.......,~~. o 5 10 15 20 25 30 35 n Fig.1 Linear growth rate versus toroidal mode number n. This situation never happen for the realistic parameter with '1~ 10-'. In this case, thc growth rate is negative for all toroidal mode numbers (even for the lowest mode with (m,n)~(2,1) as is discussed in detail[I]). However, our simulation might be interpreted as the idealized case with micro-turbulence in the high k regime_ Figure 2 shows the time evolution of the electromagnetic energy in cases with various Fourier modes_ qo;:: 1.2 is used for these simulations. The nonlinear acceleration is observed in the linearly growing phase. On the other hand, the saturation amplitude of the electromagnetic energy is not changed so drastically, which implies the high n modes (in other words, micro-turbulence) weakly affect on the island saturation. 10-1 ". ;>. e> ". " c W ... 10-7 :; C ,,' Cl .. E 10-11 2 U " 10·\3 iii 10·" 10·" 0 1000 2000 3000 4<100 sooo· Fig.2 Time evolution of electromagnetic energy. Figure 3 shows the time evolution of power spectrum of electromagnetic energy in the case with 64 Fourier modes. The inverse cascade is observed in the spectral space and (2, I) magnetic island is formed. This result is clearly different from the case of classical tearing mode. 10.3 '2 -. 10-5 W '0 E 10-7 2 U 10~ " -VI ~ 10-11 ~ T"2000 Tc4000 0.. 10-13 1"1000 10.15 L-.~_~_~_~_~_~_~......J o 8 16 24 32 40 48 56 64 n Fig_3 Power spectrum_of electromagnetic energy. As the future work, we will introduce neoclassical ballooning mode in the system and perform the nonlinear simulation for '1~ 10-8 which will give the threshold value ofNTM excitation as the function of turbulence amplitude. Reference 1) Furuya, A., Yagi, M. and Itoh, S.-I., J. Phys. Soc. Jpn., 72 (2003) 313. 343 

Nonlinear Simulation of Neoclassical Tearing Mode

Abstract

Similar works

Full text

Available Versions

National Institute for Fusion Science (NIFS-Repository)