Growth rate and mode frequency plotted as a function of β for . ITG is stabilized with increasing β, and MT requires a critical β for instability. A transition of the dominant mode from ITG to MT occurs at . Also shown is the growth rate for a case where , where MT is stabilized, to show more complete suppression of the ITG.
A comparison of GENE (red ) and GYRO (green ) results for in the RFP. Other parameters are given in the text. The two codes show good agreement. The moderate difference in real frequency at high may be related to issues of numerical convergence.
Growth rate and frequency as a function of wavenumber for two different values of β. ITG is seen to be dominant at , microtearing at . In this convention, a negative (positive) real frequency indicates a mode in the ion (electron) diamagnetic direction. Collisions are turned off for these simulations.
β stabilization of ITG for the parameters . A parabolic fit has been used to project out to a critical β for stabilization of .
Eigenmode structure for the MT mode in electrostatic potential and magnetic potential with both real (green dashed curve) and imaginary (red solid curve) components. The fields are plotted against the magnetic-field-following ballooning angle . This mode displays tearing parity, which is recognized as even parity in and odd parity in .
Growth rate plotted against temperature gradient for in the case of MT (red squares) and ITG (green circles). Both instabilities have a threshold around , for their respective driving gradients.
Growth rate plotted against the temperature ratio for . Shown are MT (a) and ITG (b). The qualitative dependence is consistent with expectations of modes with either ion or electron gradient drives.
MT growth rate and frequency plotted against the collisional frequency ν for . There appear to be two distinct regimes: a region of constant growth rate and constant real frequency at low ν and a separate region at ν with a peak in growth rate and a real frequency that scales linearly with ν.
MT wavenumber spectrum at (a) and collisionality scan (b) for different values of r / a. The corresponding values of q 0 and shear are: r 0/a = 0.4: (red solid curve); r 0/a = 0.5: , (green dashed curve); r 0/a = 0.6: (blue dotted curve). There is stabilization of MT with increasing radius r 0/a, especially prevalent at low ν. Increased radius coincides with increased shear, which may play a role in stabilization.
The role of magnetic drift in the MT instability. The parameter α is a factor regulating the strength of the electron magnetic drift (including both curvature and drifts) in the code. Shown are (a) and (b), as well as (red solid curve) and . This behavior is similar to that seen in Ref. 28 . The points at low α represent a separate mode that has not been studied in detail.
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