Linear and nonlinear particle-magnetohydrodynamic simulations of the toroidal Alfvén eigenmode

Abstract

Linear and nonlinear particle-magnetohydrodynamic ͑MHD͒ simulation codes are developed to study interactions between energetic ions and MHD modes. Energetic alpha particles with the slowing-down distribution are considered and the behavior of nϭ2 toroidal Alfvén eigenmodes ͑TAE modes͒ is investigated with the parameters pertinent to the present large tokamaks. The linear simulation reveals the resonance condition between alpha particles and TAE mode. In the nonlinear simulation, two nϭ2 TAE modes are destabilized and alpha particle losses induced thereby are observed. Counterpassing particles are lost when they cross the passing-trapped boundary. They are the major part of lost particles, but trapped particles are also lost appreciably.

Central flattening of the fast-ion profile in reversed-shear DIII-D discharges

“…Appel et al [50] found appreciable diffusion of super-Alfvénic alphas when the TAE or kinetic TAE amplitude was 4×10 −3 . In simulations of a global TAE, Todo and Sato [51] found appreciable alpha particle transport for mode amplitudes similar to Sigmar et al In the simulations of Candy et al [52], a single dominant TAE grew to a very large amplitude of B r /B 0 > 10 −2 . In simulations of beamion transport, Carolipio et al computed losses of a few percent for global TAEs at an amplitude of B r /B 0 = 4 × 10 −3 .…”

Nonlocal energetic particle mode in a JT-60U plasma

“…8 We reported that there is an unstable mode near the plasma center and frequency sweeping close to that of the fast FS mode takes place. 9 The ratio of the linear damping rate ␥ d to the linear growth rate ␥ L in the simulation is consistent with hole-clump pair creation which takes place when ␥ d / ␥ L is greater than 0.4.…”

“…(2) is just a scalar pressure gradient in the same form as the bulk pressure gradient. 8 Then, the equilibrium can be obtained from the GradShafranov equation neglecting the energetic-ion orbit width. However, if the energetic-ion pressure is anisotropic in the velocity space and/or the energetic-ion orbit width is not negligibly small, the Grad-Shafranov equation should be extended.…”

“…The E ϫ B drift v E disappears in j h due to quasineutrality. 8 It is important to start simulation from MHD equilibrium consistent with energetic-ion distribution. When the energetic-ion pressure is isotropic in the velocity space, the energetic-ion contribution in Eq.…”

“…The hybrid simulation model for MHD and energetic particles 23,24,8 is employed in the MEGA code. Plasma is divided into bulk plasma and energetic ions.…”