Influence of local density and temperature gradients on internal modes in high temperature plasmas

The authors have considered internal m = n = 1 modes associated with the crash phase of sawtooth oscillations in plasmas in high temperature regimes. The mode equations in the open-quote reconnection layer close-quote about the q(rs) = 1 singular surface for the collisionless ions and the collisional electrons are reduced to a single integro-differential equation in both real and Fourier transform space. This equation, written in terms of the parallel current bar J(k), retains the full ion perpendicular dynamics to all orders in the ion Larmor radius. For a numerical solution, however, it is convenient to use the radial component of the electric field bar Er(k) as dependent variable, as the matching condition with the external, ideal-MHD solution is in this case very simple, bar Er(k → 0) ∼ const. (1 - λHksgnk) (here λH is the ideal-MHD stability parameter). The authors have solved the bar Er-equation numerically for a broad range of plasma parameters, focusing in particular on the influence upon the mode growth rate of the local density and temperature gradients associated with the electron drift-wave and ion diamagnetic frequencies. While the influence of the density gradient scale length Ln ≡ (-dlnn/dr)-1 |r=r8 is always stabilizing leading to a reduction of the mode growth rate as Ls/Ln is increased (peaking of the density profile and/or increasing of the magnetic shear length Ls), the influence of the temperature gradient scale length LTj ≡ (-dlnTj/dr)-1 |r=r8 is more complicated