Linear instabilities in the hot-ion regime in a high-field spherical tokamak

Abstract The present operating high-field compact spherical tokamak ST40 is an important step toward an ST-based fusion reactor (Gryaznevich and Asunta 2017 Fusion Eng. Des. 123 177; McNamara 2023 Nucl. Fusion 63 054002). Temperature and density profiles and their uncertainties in recent hot ion ST40 plasmas with central ion temperatures exceeding 8.6 keV, have been inferred using an integrated analysis of several diagnostics including line-of-sight integration and volume average measurements, as well as limited profile information from a charge-exchange-recombination spectrometer. A linear gyrokinetic stability analysis has been carried out to identify the most unstable micro-instabilities in these hot ion plasmas. In one of these plasmas, it is found that linear growth rates of both ion- and electron-scale ( <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>s</mml:mi> </mml:msub> <mml:mo>⩾</mml:mo> <mml:mn>0.2</mml:mn> </mml:mrow> </mml:math> where k θ is the poloidal wavenumber and ρ s is the ion gyro-radius with sound speed) modes decrease from the edge toward the core of the plasma (i.e. from ρ = 0.8 to 0.3 where ρ is the square root of the normalized magnetic flux), while the change of linear growth rates at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>θ</mml:mi> </mml:msub> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mn>0.2</mml:mn> </mml:math> is non-monotonic. In particular, at ρ = 0.3 no unstable mode was found at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>θ</mml:mi> </mml:msub> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mn>5</mml:mn> </mml:math> , and about an order of magnitude reduction in the maximum linear growth rate in the ion-scale wavenumber range of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.2</mml:mn> <mml:mo>⩽</mml:mo> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>θ</mml:mi> </mml:msub> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mn>1</mml:mn> </mml:math> is seen at ρ = 0.3 compared with the ρ = 0.8 location. It is found through parametric scans that while the ion temperature gradient (ITG) mode/trapped electron mode (TEM) and kinetic ballooning mode (KBM)/kinetic shear Alfvén (KSA) mode are more important in the plasma core, ubiquitous mode (UM) is found to be the important ion-scale instability at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ρ</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>0.6</mml:mn> </mml:math> . At ρ = 0.8, two instabilities are found at the electron scale, with one being the typical electrostatic electron temperature gradient (ETG) mode at ρ e scale and beyond and the other being an unidentified low-real-frequency instability (at the intermediate scale between electron and ion gyroradii) which can propagate in the ion direction and is driven by ETG. The existence of UM at the ion scale and the low-real-frequency instability and ETG mode at the electron scale at ρ = 0.8 is supported by an extensive linear gyrokinetic stability analysis of another ST40 hot ion plasma in a wider parametric range, taking into account the uncertainties in the experimental profiles.