Kelvin–Helmholtz instabilities in tokamak edge plasmas

Abstract

The parallel Kelvin–Helmholtz instability is investigated as a possible explanation for poloidal asymmetries of density fluctuations which reverse with the plasma current direction. It is shown that these modes are localized around the position where the radial gradient of parallel velocity is maximum. Two mechanisms lead to unstable Kelvin–Helmholtz modes; the acceleration of ions in a presheath and the anomalous Stringer spin-up due to asymmetries of the particle flux. Up–down asymmetries are explained by combining these two effects. Depending on the limiter configuration, the Stringer effect amplifies or weakens the flow due to presheath acceleration. This type of asymmetry reverses with the plasma current direction.

Multiple-Instabilities in Magnetized Plasmas with Density Gradient and Velocity Shears

“…This instability is called the D'Angelo mode [15,16], which has been observed in basic plasma experiments [17]. Turbulence simulation and theory suggest the importance of the D'Angelo mode at scrape off layers and spherical tokamaks [18,19]. The coexistence of the D'Angelo mode and drift wave has been observed [17].…”

How turbulence fronts induce plasma spin-up

“…When the magnetic drift is toward the x point of the magnetic separatrix, namely, for a favorable configuration, SOL flows are in the codirection and the edge toroidal flow shear is positive [5,36]. In this case, the positive toroidal flow at the edge breaks the parallel symmetry [32] to yield fluctuation momentum in the codirection P k ∝ k /k θ ∝ v φ | a > 0. This fluctuation momentum can be scattered into the core via the spreading process, and can result in a coincrement in the core flow.…”

“…In order for the wave momentum to have a finite value, symmetry breaking in the parallel direction is required [4]. In toroidal plasmas, symmetry can be broken by several mechanisms, such as the intensity gradient, up-down asymmetry [31], the radial electric field, toroidal flow shear [32], etc. Note that toroidal flow shear is important in the edge plasmas, since scrape-off-layer (SOL) flows with a Mach number of order unity are likely to cause a strong radial variation [5].…”

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

“…Magnetized plasmas generally have anisotropic flows across (v ⊥ ) and along (v ) the magnetic field, and these flows can have both perpendicular (∇ ⊥ ) and parallel (∇ ) gradients. The resulting instabilities broadly separate into classes depending on whether the free energy source is from the parallel velocity shear ∇ ⊥ v (D'Angelo 1965; Catto, Rosenbluth & Liu 1973;Garbet et al 1999;Wang et al 2015), the parallel shear of the perpendicular flows ∇ v ⊥ (Lee, Catto & Aamodt 1982;Tsidulko, Berk & Cohen 1994) or the perpendicular 'transverse' shear of the perpendicular flows b · ∇ ⊥ × v ⊥ (Perkins & Jassby 1971;Miura & Pritchett 1982;Horton, Tajima & Kamimura 1987;Pritchett 1987;Vranješ & Tanaka 2002;Rogers & Dorland 2005;Popovich et al 2010;Xi et al 2012;Fisher et al 2015). In the present paper we will be concerned only with the latter, and by KH we will mean the transverse KH instability.…”