Global gyrokinetic particle simulation of kinetic ballooning modes with energetic ions

Abstract Interactions between energetic ions (EIs) and kinetic ballooning modes (KBMs) are inevitable in fusion reactors characterized by high- β plasmas with a large population of alpha particles ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>h</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:msub> <mml:mi>β</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mo>,</mml:mo> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>β</mml:mi> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo>,</mml:mo> <mml:mi>e</mml:mi> <mml:mo>,</mml:mo> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>μ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo>,</mml:mo> <mml:mi>e</mml:mi> <mml:mo>,</mml:mo> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mn>0</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> ). In this work, the effects of EIs on KBM stability are investigated using first-principles gyrokinetic simulations, which demonstrate the roles of magnetohydrodynamic (MHD) ballooning-interchange drive, wave–particle resonance and orbital effects in several parameter regimes of practical interest. In particular, it is found that EI–KBM interactions are mostly determined by three dimensionless parameters: the EI–thermal electron temperature ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>h</mml:mi> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:math> , the KBM perpendicular wave vector normalized by EI orbit width <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>θ</mml:mi> </mml:msub> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:mrow> </mml:math> and the EI pressure ratio β h , which are associated with resonance condition, finite orbit width (FOW) screening and EI drive strength for Alfvénic modes. For typical orderings of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>h</mml:mi> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> <mml:mo>≫</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>h</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:msub> <mml:mi>β</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mo>,</mml:mo> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>θ</mml:mi> </mml:msub> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:mrow> </mml:math> becomes crucial for relevant physical processes. (i) In the short-wavelength regime of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>θ</mml:mi> </mml:msub> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>d</mml:mi> </mml:msub> <mml:mo>≫</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , the response of EIs to KBM electromagnetic fluctuations is greatly reduced due to strong FOW screening, which leads to a weakly stabilizing effect on KBMs via thermal ion dilution, despite the large β h . (ii) In the long-wavelength regime of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">