Excitation Mechanism of Low-$n$ Edge Harmonic Oscillations in Edge Localized Mode-Free, High Performance, Tokamak Plasmas

The excitation mechanism for low-$n$ edge harmonic oscillations in quiescent $H$-mode regimes is identified analytically. We show that the combined effect of diamagnetic and poloidal magnetohydrodynamic flows, with the constraint of a Doppler-like effect of the ion flow, leads to the stabilization of short wavelength modes, allowing low-$n$ perturbation to grow. The analysis, performed in tokamak toroidal geometry, includes the effects of large edge pressure gradients, associated with the local flattening of the safety factor and diamagnetic flows, sheared parallel and $\mathit{E}\times \mathit{B}$ rotation, and a vacuum region between plasma and the ideal metallic wall. The separatrix also is modeled analytically.

Figure 1

Example of a model safety factor profile employed in our analysis. Note the $(m+1)/n$ resonance at the plasma boundary mimicking the separatrix.

Figure 2

Real (a) and imaginary (b) parts of $\gamma$ evaluated from Eq. (8) with $q\approx 5$, $ϵ=1/3$, $r_1/a=0.95$, ${\mathrm{\Omega }}_1/{\omega }_A=5\times {10}^{-2}$, ${\omega }_I/{\omega }_A=3\times {10}^{-3}$, ${\beta }_1=0.3\%$, and $\delta q=0.1$.