Linear instablity at large wavelength (low ky) in electrostatic two species simulations

[David Dickinson]

In a simple periodic system with one ion and one electron species a linear instability can be found in the absence of gradients (tprim=fprim=0.0) and this is not suppressed by finite bakdif (unlike the case described in issue #108).

The instability can be avoided by:

1. Selecting a homogeneous source (i.e. turning off the contribution from phi)
2. By artificially removing the drifts (driftknob = 0.0).
3. Removing the variation in B along the field line (eps = 0). Simply zeroing the trapped integration weights does not remove the instability (unlike reported in issue #108).

Points 1 and 2 help identify -i wdrift * phigavg as the problematic source term.

The growth rate is only partially reduced by increasing ntheta

At higher shear the issue remains but stability is found when setting trapped_particles = F. The issue also goes away when switching from periodic to zero boundary conditions provided fexpr < 0.5. One shared feature of these two options is that they influence the use of the homogeneous solution (either in ensuring the bounce condition or the periodicity).

[David Dickinson]

It’s not very sensitive to the mass ratio, but does get a bit better for equal masses

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[David Dickinson]

Increasing shear from zero doesn’t drastically change things until one also switches from periodic to zero boundaries:

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[David Dickinson]

Increasing ntheta helps to reduce the growth rate, however, even by ntheta = 256 the baseline case is unstable at low (0.05) and high (0.75) bakdif values tested.

In addition, introducing Lorentz collisions with vnewk ~ 0.1 can also suppress the instability (at least at bakdif=0.05).

[David Dickinson]

When looking at the final potential one can note clear oscillations near to the boundary. However, increasing nperiod from 1 to 2 does not remove the oscillations around theta = +/- pi. This appears to indicate that it is not a consequence of the boundary (directly) but rather due to some other property near this location.

Increasing ntheta seems to confine these oscillations to a smaller region in theta, although the total structure changes slightly

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[David Dickinson]

The oscillation on the inboard side appears to be related to setting nmax = 15 in addition to what is in the template input file. Increasing this to 33 (to match ntheta) appears to be sufficient to avoid these oscillations but does not avoid the instability.

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