pg_utils.numerics.utils.eigenfreq_Malkus_3d
- pg_utils.numerics.utils.eigenfreq_Malkus_3d(m: Union[int, ndarray], n: Union[int, ndarray], Le: float, mode: str = 'all', timescale: str = 'spin')[source]
Analytic eigenfrequency for 3D eigemodes with Malkus bg field
- Parameters:
- Returns:
eigenfrequency array(s)
Note
When using spin rate for characteristic time scale, i.e. \(\tau=\Omega^{-1}\)
\[\omega = \frac{\omega_0}{2} \left(1 \pm \sqrt{\mathrm{Le}^2 \frac{4m(m - \omega_0)}{\omega_0^2}}\right)\]When using Alfven time scale, i.e. \(\tau=\frac{\sqrt{\rho\mu_0}L}{B}\)
\[\omega = \frac{\omega_0}{2\mathrm{Le}} \left(1 \pm \sqrt{\mathrm{Le}^2 \frac{4m(m - \omega_0)}{\omega_0^2}}\right)\]where \(\omega_0\) is the inertial mode eigenfrequency in 3-D, see
eigenfreq_inertial3d
for details. The plus sign gives the fast mode, and the minus sign gives the slow mode.