Helical core formation and MHD stability in ITER-scale plasmas with fusion-born alpha particles

Abstract The effect of fusion-born alpha particles on the helical core (HC), a long-lived ideal saturation state of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> kink/quasi-interchange mode, is studied in the ITER-scale hybrid scenario where a core plasma has a low magnetic shear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>≳</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . The HC state is determined by 3D magnetohydrodynamic (MHD) force balance and all factors that contribute to it, such as plasma shaping, the safety factor profile, and the pressure profiles of all particle species. An incomplete but useful measure of the HC is the displacement of the magnetic axis, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>δ</mml:mi> <mml:mrow> <mml:mi>HC</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . Using MHD-particle-in-cell (PIC) simulations, we find that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>δ</mml:mi> <mml:mrow> <mml:mi>HC</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> is enhanced by increasing alpha particle pressure <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>α</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . Within the ITER operating alpha pressure <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>α</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo>≲</mml:mo> <mml:mn>1</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> , <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>α</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> can be approximately treated as part of the total MHD pressure. In this regime, there is no notable flattening of the pressure profile, indicating that the HC preserves the omnigenity of the plasma. If one increases <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>α</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> beyond 1%, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>δ</mml:mi> <mml:mrow> <mml:mi>HC</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> continues to increase with <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>α</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> until it reaches an upper limit at <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>α</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> for our reference case. At this limit, both the bulk and alpha pressure profiles are partially flattened, indicating a reduction in omnigenity. After HC formation, a resistive pressure-driven MHD mode can become unstable, which seems to be triggered by the local steepening of the bulk plasma pressure gradient within the compressed magnetic flux region of the HC. This secondary mode consists of a broad spectrum of short-wavelength Fourier components that grow at identical rates and are thus part of a single coherent entity. Our present simulation model is insufficient to adequately represent such a secondary mode; however, preliminary results suggest that it can facilitate magnetic chaos, which affects plasma confinement. We also discuss possible m