solarwindpy.instabilities.verscharen2016

Instability thresholds from Verscharen et al. (2016).

The empirical fits of [] are implemented to evaluate when a plasma becomes unstable in the (beta, R) plane.

References

[1]

Verscharen, D., Chandran, B. D. G., Klein, K. G., & Quataert, E. Collisionless Isotropization of the Solar-Wind Protons By Compressive Fluctuations and Plasma Instabilities, Astrophys. J., 831, 128 (2016).

Functions

beta_ani_inst(beta[, a, b, c])

Return the anisotropy threshold for a given beta.

Classes

StabilityCondition(growth_rate, beta, anisotropy)

Evaluate plasma stability using the Verscharen et al. fits.

StabilityContours(beta)

Precompute and plot instability contours.
beta_ani_inst(beta, a=None, b=None, c=None)[source]

Return the anisotropy threshold for a given beta.

Implements Eq. (5) of []:

\[R_p = 1 + \frac{a}{(\beta_{\parallel,p} - c)^b}\]

where $p$ is defined assuming only a single proton population is fit.

Parameters:

  • beta (array-like) – Parallel proton beta.

  • a (float) – Fit parameters from Verscharen et al. (2016).

  • b (float) – Fit parameters from Verscharen et al. (2016).

  • c (float) – Fit parameters from Verscharen et al. (2016).

Returns:

Threshold anisotropy values.

Return type:

numpy.ndarray

Examples

>>> beta = np.logspace(-2, 2, 5)
>>> beta_ani_inst(beta, a=0.367, b=-0.408, c=0.011)
array([       nan, 1.1367783..., 1.36534751..., 1.93857946..., 3.40240693...])
class StabilityCondition(growth_rate, beta, anisotropy)[source]

Bases: object

Evaluate plasma stability using the Verscharen et al. fits.

Parameters:

  • growth_rate (int) – Index of the growth-rate table to use (-2, -3 or -4).

  • beta (pandas.Series) – Parallel proton beta.

  • anisotropy (pandas.Series) – Temperature anisotropy.

instability_thresholds

Threshold anisotropies for each instability.

Type:

pandas.DataFrame

is_unstable

Boolean mask indicating unstable modes.

Type:

pandas.DataFrame

stability_bin

Integer label describing the dominant instability.

Type:

pandas.Series

__init__(growth_rate, beta, anisotropy)[source]

Initialize the object.

Parameters:

  • growth_rate (int) – Growth rate index (-2, -3 or -4).

  • beta (pandas.Series) – Arrays of parallel beta and temperature anisotropy.

  • anisotropy (pandas.Series) – Arrays of parallel beta and temperature anisotropy.

property fill

Used to build data containers and check all entries are visited.

property instability_parameters

The Pandas DataFrame of instability parameters.

property data

DataFrame with beta and anisotropy measurements.

property beta

The beta values of the object.

property anisotropy

The anisotropy values of the object.

property stability_map

The map of ints to strings identifying the instabilities.

property stability_map_inverse

The inverse of stability_map.

property instability_thresholds

The value of the anisotropy for which the plasma goes unstable.

property instability_tests

The tests used for each instability threshold.

The keys are "AIC", "MM", "FMW", and "OFI" for Alfven/Ion-Cyclotron, Mirror Mode, Fast Magnetosonic / Whistler, and Oblique Firehose. The values are NumPy ufuncs.

property is_unstable

Boolean DataFrame indicating instability to a given instability.

property stability_bin

The integer corresponding to the (in)stability condition.

property cmap

A linearly segmented colormap for the (in)stability condition.

property norm

The normalization instance used for plotting the stability bin.

property cbar_kwargs

Keyword arguments for drawing a colorbar.

set_instability_parameters(growth_rate)[source]

Take the instability parameters corresponding to growth_rate.

Parameters:

growth_rate (int) – Growth-rate index (-2, -3 or -4).

set_beta_ani(beta, anisotropy)[source]

Set the beta and anisotropy values.

calculate_stability_criteria()[source]

Run the full instability calculation.

This method calls _calc_instability_thresholds(), _calc_is_unstable(), and _calc_stability_bin() in that order. Use this method over calling the private methods individually.

class StabilityContours(beta)[source]

Bases: object

Precompute and plot instability contours.

Parameters:

beta (numpy.ndarray) – Parallel proton beta values used for the contours.

__init__(beta)[source]
property beta

Proton core parallel beta.

set_beta(new)[source]
property contours
plot_contours(ax, fix_scale=True, plot_gamma=None, tk_kind=None, **kwargs)[source]

Add the instability contours to the plot.

Parameters:

  • ax (mpl.axis)

  • fix_scale (bool) – If True, make x- and y-axes log scaled.

  • plot_gamma (None, -2, -3, -4) – If not None, the instability parameter to plot.

  • tk_kind (None, str, list-like of str) – Contours to plot. Valid options are “MM”, “AIC”, “FMW”, “OFI”, and any combination thereof.