Nonlinear Alfvén instability simulation and EP transport for ITER reversed shear (steady-state) and monotonic q-profile regimes^*

Abstract The nonlinear evolution and dynamics of energetic particle (EP) driven instabilities in both steady-state (reversed shear q-profile) and monotonic q-profile regimes of ITER are examined using the global gyro-Landau closure model FAR3d. Both neutral beam and alpha components are included, leading to synergistic effects between the two populations. In order to maintain computational feasibility, the present nonlinear simulation includes all toroidal mode numbers ranging from n = 0 to 15. It cannot be excluded that n ’s above this range could introduce larger linear growth rates; however, as indicated from the results, the n = 0 to 15 range is sufficient to provide a strong linear drive and significant nonlinear transport effects. While the toroidal mode numbers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>6</mml:mn> <mml:mo>,</mml:mo> <mml:mn>13</mml:mn> </mml:mrow> </mml:math> dominate the linear instability growth phase, nonlinear energy transfers in the saturated phase reverse this trend, leading to the dominance of lower n ’s in the saturated phase of the simulation. Zonal flow structure generation and EP density flattening are further consequences of the nonlinear phase. The density profile flattening is caused by collectively driven EP radial transport fluxes, which have non-local characteristics. Instantaneous alpha particle transport fluxes are significant ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">Γ</mml:mi> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>20</mml:mn> </mml:mrow> </mml:msup> <mml:mtext> </mml:mtext> <mml:mrow> <mml:msup> <mml:mi mathvariant="normal">m</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mstyle scriptlevel="0"/> <mml:msup> <mml:mi mathvariant="normal">s</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> ) for the reversed shear regime and lower ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">Γ</mml:mi> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>1.1</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>20</mml:mn> </mml:mrow> </mml:msup> <mml:mtext> </mml:mtext> <mml:mrow> <mml:msup> <mml:mi mathvariant="normal">m</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mstyle scriptlevel="0"/> <mml:msup> <mml:mi mathvariant="normal">s</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> ) for the monotonic q-profile case.