pyrfu.models.ion_anisotropy_thresh#

pyrfu.models.ion_anisotropy_thresh(beta, instability_type, growth_rate='10^-2')[source]#

Compute the threshold using the empirical model defined in [1] and the fit parameters of [2].

\[R_i = T_{i\perp} / T_{i\parallel} = 1 + a / (\beta_{i\parallel} -\beta_0)^b\]

This is a wrapper of pyrfu.pyrf.anisotropy_thresholds().

Parameters:

  • beta (float or numpy.ndarray or xarray.DataArray) – Time series or array of parallel ion plasma beta. It is not modified.

  • instability_type ({"proton-cyclotron", "mirror", "parallel-firehose",) – “oblique-firehose”} Instability.

  • growth_rate ({"10^-2", "10^-3", "10^-4"}, Optional) – Maximum growth rate of the instability in units of the proton cyclotron frequency. Default is “10^-2”.

Returns:

r_i_thresh – Time series or array of threshold temperature anisotropy at the given beta, of the same type as beta. NaN where the fit is undefined (\(\beta_{i\parallel} \leq \beta_0\)).

Return type:

float or numpy.ndarray or xarray.DataArray

Raises:

ValueError – If growth_rate or instability_type is not recognized.

References

[1]

Hellinger, P., P. Travnicek, J. C. Kasper, and A. J. Lazarus (2006), Solar wind proton temperature anisotropy: Linear theory and WIND/SWE observations, Geophys. Res. Lett., 33, L09101, doi:10.1029/2006GL025925.

[2]

Verscharen, D., B. D. G. Chandran, K. G. Klein, and E. Quataert (2016), Collisionless isotropization of the solar-wind protons by compressive fluctuations and plasma instabilities, Astrophys. J., 831, 128, doi:10.3847/0004-637X/831/2/128.