Impurity effects on kinetic ballooning instability in high <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> regions of tokamak plasmas

Abstract The impurity effects on kinetic ballooning modes (KBMs) in high <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> regions of tokamak plasmas are numerically investigated, using a full gyrokinetic description for main and impurity ions. The findings indicate that the critical plasma pressure ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>β</mml:mi> <mml:mrow> <mml:mtext>c</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> for KBM is significantly lower (higher) than the first (second) stable threshold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>β</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>MHD</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> predicted by MHD theory. The KBM exhibits stronger extended instabilities for low <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> , while the instability region of KBM becomes significantly narrow for high <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> , resulting in a more concentrated instability window (localized in narrow medium- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> region). In addition, the contributions from electromagnetic effect and Shafranov shift are identified in detail, i.e. the electromagnetic destabilizing effect is suppressed by the Shafranov shift, and strong stabilizing effect of Shafranov shift for high <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>β</mml:mi> <mml:mrow> <mml:mtext>e</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> on KBM is pronounced. The impurity ions with negative gradient ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>e</mml:mtext> </mml:mrow> <mml:mi>z</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> have stabilizing (destabilizing) effects on KBMs for high (low) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> . Such distinct behaviors are demonstrated to be associated with the used parameters close to the second and first unstable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> region, i.e. the instability reduces and enhances with the increase of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> , respectively. Significantly, the presence of impurities, regardless of the peaking directions of their density profiles, serves to stabilize KBMs and reduce the window of extended instability for high <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> region, which is in significant contrast with the results for low <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> region. Furthermore, high concentration, steep negative gradient ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>ez</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , and high mass numbers of impurity ions as well as large temperature gradient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>η</mml:mi> <mml:mrow> <mml:mtext>i</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>η</mml:mi> <mml:mrow> <mml:mtext>e</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow>