Kinetic-ballooning-mode turbulence in low-average-magnetic-shear equilibria

Abstract

Kinetic-ballooning-mode (KBM) turbulence is studied via gyrokinetic flux-tube simulations in three magnetic equilibria that exhibit small average magnetic shear: the Helically Symmetric eXperiment (HSX), the helical-axis Heliotron-J and a circular tokamak geometry. For HSX, the onset of KBM being the dominant instability at low wavenumber occurs at a critical value of normalized plasma pressure $\beta ^{\rm KBM}_{\rm crit}$ that is an order of magnitude smaller than the magnetohydrodynamic (MHD) ballooning limit $\beta ^{\rm MHD}_{\rm crit}$ when a strong ion temperature gradient (ITG) is present. However, $\beta ^{\rm KBM}_{\rm crit}$ increases and approaches the MHD ballooning limit as the ITG tends to zero. For these configurations, $\beta ^{\rm KBM}_{\rm crit}$ also increases as the magnitude of the average magnetic shear increases, regardless of the sign of the normalized magnetic shear. Simulations of Heliotron-J and a circular axisymmetric geometry display behaviour similar to HSX with respect to $\beta ^{\rm KBM}_{\rm crit}$ . Despite large KBM growth rates at long wavelengths in HSX, saturation of KBM turbulence with $\beta > \beta _{\rm crit}^{\rm KBM}$ is achievable in HSX and results in lower heat transport relative to the electrostatic limit by a factor of roughly five. Nonlinear simulations also show that KBM transport dominates the dynamics when KBMs are destabilized linearly, even if KBM growth rates are subdominant to ITG growth rates.

Influence of magnetic configuration properties on kinetic ballooning modes in W7-X

“…The flux tube extends one poloidal turn around the torus, which is enough for the instabilities we study in the present work (see figure 1). Note that this is not always the case (McKinney et al 2021;Faber et al 2018), especially close to marginality, where eigenfunctions are more extended along the field line. For each calculation with a rather small β we check that the obtained results are unaffected by the number of poloidal turns.…”

“…Note that this is not always the case (McKinney et al. 2021; Faber et al. 2018), especially close to marginality, where eigenfunctions are more extended along the field line.…”

“…For example, in the work of McKinney et al. (2021), it was demonstrated that KBM transport becomes significant, potentially reaching a level of particle and heat fluxes comparable to those found in the electrostatic case, even for smaller than the critical for ideal ballooning mode destabilization. In some circumstances, the nonlinear transport due to KBMs is the dominant one, even if KBM growth rates (around ) are smaller than that of the ion temperature gradient (ITG)-driven instability (at larger ).…”

“…2013, 2015, 2019), and for the Helically Symmetric eXperiment (McKinney et al. 2019, 2021). Linear studies of KBMs in the optimized stellarator Wendelstein 7-X (W7-X) can be found in Aleynikova et al.…”

“…The physics of kinetic ballooning modes (KBMs) (Antonsen & Lane 1980;Tang, Connor & Hastie 1980), while being an extensively studied topic in tokamaks (Connor, Hastie & Taylor 1978;Antonsen & Lane 1980;Tang et al 1980;Kotschenreuther 1986;Pueschel, Kammerer & Jenko 2008;Groebner et al 2010Groebner et al , 2013Snyder et al 2011;Diallo et al 2014), still remains relatively unexplored in stellarator geometry. Kinetic ballooning modes have been studied in helical devices, both linearly and nonlinearly (Ishizawa et al 2013(Ishizawa et al , 2015(Ishizawa et al , 2019, and for the Helically Symmetric eXperiment (McKinney et al 2019(McKinney et al , 2021. Linear studies of KBMs in the optimized stellarator Wendelstein 7-X (W7-X) can be found in Aleynikova et al (2018).…”