Linear instablity at large wavelength (low ky) in electrostatic two species simulations
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:
- Selecting a homogeneous source (i.e. turning off the contribution from phi)
- By artificially removing the drifts (driftknob = 0.0).
- 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).
Comments (7)
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reporter -
reporter Increasing shear from zero doesn’t drastically change things until one also switches from periodic to zero boundaries:
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reporter 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).
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reporter - edited description
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reporter 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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reporter - edited description
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reporter 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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It’s not very sensitive to the mass ratio, but does get a bit better for equal masses