Analytical and numerical study of the transverse Kelvin–Helmholtz instability in tokamak edge plasmas

Abstract

Sheared flows perpendicular to the magnetic field can be driven by the Reynolds stress or ion pressure gradient effects and can potentially influence the stability and turbulent saturation level of edge plasma modes. On the other hand, such flows are subject to the transverse Kelvin-Helmholtz (KH) instability. Here, the linear theory of KH instabilities is first addressed with an analytic model in the asymptotic limit of long wavelengths compared with the flow scale length. The analytic model treats sheared E × B flows, ion diamagnetism (including gyro-viscous terms), density gradients and parallel currents in a slab geometry, enabling a unified summary that encompasses and extends previous results. In particular, while ion diamagnetism, density gradients and parallel currents each individually reduce KH growth rates, the combined effect of density and ion pressure gradients is more complicated and partially counteracting. Secondly, the important role of realistic toroidal geometry is explored numerically using an invariant scaling analysis together with the 2DX eigenvalue code to examine KH modes in both closed and open field line regions. For a typical spherical torus magnetic geometry, it is found that KH modes are more unstable at, and just outside of, the separatrix as a result of the distribution of magnetic shear. Finally implications for reduced edge turbulence modelling codes are discussed.

Investigation of turbulent transport regimes in the tokamak edge by using two-fluid simulations

“…Furthermore, when the shearing rate, ρ −1 * ∂ 2 rrφ , is comparable to γ i , ballooning turbulence is nonlinearly suppressed (Burrell 1997;Terry 2000). At the same time, the E × B shear provides the drive of the KH instability through the Reynolds stress (Myra et al 2016). Indeed, our simulations show that, for values of the heat source sufficiently high, when ρ −1 * ∂ 2 rrφ > γ i , the interchange instability is suppressed in the edge and the KH instability becomes the primary instability driving the turbulent transport (Rogers & Dorland 2005;Myra et al 2016).…”

“…The growth rate of the KH instability is proportional to the shear (Myra et al. 2016), , having assumed . The KH mode being a global one, the size of the turbulent eddies it generates is comparable to the pressure gradient length, .…”

“…At the same time, the E × B shear provides the drive of the KH instability through the Reynolds stress (Myra et al 2016). Indeed, our simulations show that, for values of the heat source sufficiently high, when ρ −1 * ∂ 2 rrφ > γ i , the interchange instability is suppressed in the edge and the KH instability becomes the primary instability driving the turbulent transport (Rogers & Dorland 2005;Myra et al 2016). Figure 8 displays a typical snapshot of the electron temperature for a simulation in the suppressed transport regime (s T0 = 0.6 and ν 0 = 0.9) and compares it to two simulations having the same parameters, but with the KH and ballooning drives removed.…”

“…An analytical estimate of the equilibrium pressure gradient length in the edge when turbulence is driven by the KH instability can be derived by following a procedure similar to the one detailed in § 4.1 and discussed for a linear device by Rogers & Ricci (2010). The growth rate of the KH instability is proportional to the E × B shear (Myra et al 2016),…”

A reduced model of neutral-plasma interactions in the edge and scrape-off-layer: Verification comparisons with kinetic Monte Carlo simulations

“…12. Earlier simulations also led us to suspect that the flow shearing rates were large enough to drive the Kelvin-Helmholtz (K-H) instability in the edge region [33] and so to threaten access to a sustained H-mode. Although neutrals may enable such access by reducing the K-H growth rate (~|v Ey |), the reduced velocity shear may likewise allow an otherwise suppressed interchange instability if the interchange growth rate exceeds the flow shearing rate.…”