A section of the eigenmode of the DBM18 equilibrium overlaid with the finite element mesh. The magenta line represents the foot of the pedestal.
Growth rates are calculated using two different time-step methods for the three equilibria described in Sec. III A, at various mesh resolutions. Here is the average inverse element length scale of the mesh, and is the approximate poloidal wavenumber of the mode, where is the safety factor at the center of the pedestal, is the surface-averaged minor radius at the center of the pedestal, and is the toroidal mode number ( here). Each curve shows the fractional difference from the growth rate calculated with the most highly resolved mesh in the curve.
The eigenfunction of the normal velocity for the MEUDAS1 equilibrium near the active x-point. Left: step-function plasma density and resistivity [Eqs. (10) and (11)]; right: nonuniform, continuous plasma density and Spitzer resistivity [Eqs. (14) and (15)].
The surface-averaged ballooning parameter and normalized parallel current density of the three equilibria studied here, as a function of the normalized poloidal flux . The geometry of each equilibrium can be seen in Fig. 7.
The fractional difference in the growth rate of the eigenmode from the case where and as or is varied.
The normalized growth rate vs toroidal mode number in the ideal limit, for the CBM18, DBM18, and MEUDAS1 equilibria. Results using the isothermal equation of state have also been plotted for the CBM18 case, and are bracketed by the compressionless and adiabatic results.
The eigenfunction of the normal velocity for the three benchmark equilibria, as calculated by . The thick curve marks the boundary of the computational domain (which is treated as a perfectly conducting wall). The thin curve represents the foot of the pedestal, which (in these cases) is the position of the vacuum-plasma interface. In the MEUDAS1 equilibrium, the foot of the pedestal coincides with the separatrix.
The eigenfunction of the normal velocity for the MEUDAS1 equilibrium. Only regions having are highlighted. The outermost surface plotted is .
The growth rate of the eigenmode of the MEUDAS1 case with the conducting wall in the standard position and expanded outward by 8% , vs the resistivity in the outer region . At , the distance of the wall from the separatrix is roughly double that at along the upper-half of the outboard edge.
The growth rate of the eigenmode vs the plasma-vacuum interface offset . Growth rates are normalized to the growth rate at zero offset; the offsets are normalized to distance from the foot of the pedestal to the center of the pedestal in the relevant equilibrium. A negative offset indicates an inward shift of the plasma-vacuum interface.
The resistivity at in the MEUDAS1 equilibrium for three cases: ; Spitzer resistivity with in the outer region; and Spitzer resistivity with in the outer region. The foot of the pedestal is at roughly here.
Growth rates are plotted vs toroidal mode number using and (ideal); and a nonuniform profile (nonuniform ); and and a nonuniform profile (nonuniform , ) for each equilibrium.
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