H. Wang

Y. Todo

Wang,  H.

Todo,  Y.

NIFS-Repository (National Institute for Fusion Science)

Alfve´n eigenmodes are important issues in the cur-rent fusion science and technology. An important ques-tion for fusion burning plasmas is whether the ener-getic particle transport changes or not when the tran-sition between reversed shear Alfve´n eigenmodes (RSAEmodes) and toroidal Alfve´n eigenmodes (TAE modes)takes place. In order to answer this question, we haveinvestigated the interaction of energetic particles withRSAE modes or TAE modes using the MEGA code1),a hybrid simulation code for magnetohydrodynamics(MHD) and energetic particles. We focus on the dif-ference in energetic particle transport between RSAEmodes and TAE modes. When the energetic particledistribution is isotropic in velocity space, we have foundthat the energetic particles both co- and counter-goingare transported by the TAE modes, whereas only theco-going particles are transported by the RSAE modes.The growth rate takes the minimum value just beforethe transition from RSAE mode to TAE mode. Thereason for these results are examined by complementarysimulations using purely co- or counter-going energeticparticles.We focus on n = 4 Alfve´n eigenmodes, which are ex-act solutions of the equations of a quarter of the tokamakdomain with the toroidal angle taken from 0 ≤ φ ≤ π2 .Then, the simulation region is Rc−a ≤ Rc ≤ Rc+a,0 ≤φ ≤ π2 and −a ≤ z ≤ a, where Rc is the major ra-dius. The outermost magnetic surface is circular withaspect ratio Rc/a = 3.0. The number of marker parti-cles is 5.24×105, but a larger particle number is also usedto investigate the numerical convergence. The numberof grid points is 100×16×100 for the cylindrical coordi-nates (R, φ, z). The viscosity and diﬀusivity are set to beν = νn = 10−6vARc and the resistivity η = 10−6μ0vARcin the simulation, where vA is the Alfve´n speed. Dif-ferent energetic particle slowing-down distribution func-tions, i) slowing-down distribution which is isotropic invelocity space, ii) slowing-down distribution with onlyco-passing particles, and iii) slowing-down distributionwith only counter-passing particles, are applied to studythe diﬀerences between RSAE modes and TAE modes.When the energetic particle distribution is isotropicin velocity space, the transition from low-frequencyRSAE mode to TAE mode was demonstrated as the min-imum safety-factor value decreases from 1.975 to 1.825.The frequency rises up from a level above the geodesicacoustic mode frequency to the TAE frequency. Thisqualitatively reproduces the frequency up-shift observedin the tokamak experiments. In addition, it was foundthat the energetic particles both co- and counter-going tothe plasma current are transported by the TAE mode,whereas only the co-going particles are transported bythe low-frequency RSAE mode, as shown in Fig. 1.In order to acquire the better understanding of therole of the co- and counter-going particles, the addi-tional runs were performed with only co- or only counter-passing particles. It was found that when only the co-passing particles are retained, the low-frequency RSAEmodes are destabilized. On the other hand, the high-frequency RSAE modes are destabilized when only thecounter-passing particles are retained. In the purely co-passing and the purely counter-passing particle cases, noTAE mode was destabilized for the low qmin values. Thisis diﬀerent from the isotropic velocity distribution casewhere the TAE modes are destabilized for the low qminvalues, although the energetic particle beta values forthe co-passing and the counter-passing particle cases arechosen so that the growth rate for qmin = 1.95 is closeto that for the isotropic velocity distribution case. Thisdiﬀerence arises from the fact that for the isotropic veloc-ity distribution, both the co-going and the counter-goingparticles interact with and destabilize the TAE modeswhile only the co-going particles interact with the low-frequency RSAE modes.-1×10-3-8×10-4-4×10-4 0×100 4×10-4 0  0.25  0.5  0.75  1δn   [(B2 /μ 0)/mhvA2 ]r/a(a)(b)cocounter-3×10-4-2×10-4-1×10-4 0×100 1×10-4 0  0.25  0.5  0.75  1δn   [(B2 /μ 0)/mhvA2 ]r/acocounterFig. 1: Comparison of energetic particle density proﬁleperturbations between (a) RSAE mode for qmin = 1.95and (b) TAE mode for qmin = 1.875. Co-going parti-cles to the plasma current are transported by the RSAEmode; whereas both the co- and counter-going particlesare transported by the TAE mode.1) Y. Todo: Phys. Plasmas 13 (2006) 082503.349§10. Interaction between Energetic Particles and Alfvén Eigenmodes in Reversed Shear PlasmasWang, H. (Grad. Univ. Advanced Studies), Todo, Y.

Interaction between Energetic Particles and Alfv?n Eigenmodes in Reversed Shear Plasmas

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Interaction between Energetic Particles and Alfv?n Eigenmodes in Reversed Shear Plasmas

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