Source code for pyrfu.pyrf.calc_dng
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# 3rd party imports
import numpy as np
import xarray as xr
# Local imports
from .ts_scalar import ts_scalar
__author__ = "Louis Richard"
__email__ = "louisr@irfu.se"
__copyright__ = "Copyright 2020-2023"
__license__ = "MIT"
__version__ = "2.4.2"
__status__ = "Prototype"
[docs]def calc_dng(p_xyz):
r"""Computes agyrotropy coefficient as in [15]_
.. math::
D_{ng} = \frac{\sqrt{8 (P_{12}^2 + P_{13}^2 + P_{23}^2)}}
{P_\parallel + 2 P_\perp}
Parameters
----------
p_xyz : xarray.DataArray
Time series of the pressure tensor
Returns
-------
d_ng : xarray.DataArray
Time series of the agyrotropy coefficient of the specie.
References
----------
.. [15] Aunai, N., M. Hesse, and M. Kuznetsova (2013), Electron
nongyrotropy in the context of collisionless magnetic
reconnection, Phys. Plasmas, 20(6), 092903,
doi: https://doi.org/10.1063/1.4820953.
Examples
--------
>>> from pyrfu import mms, pyrf
Time interval
>>> tint = ["2019-09-14T07:54:00.000","2019-09-14T08:11:00.000"]
Spacecraft index
>>> ic = 1
Load magnetic field and electron pressure tensor
>>> b_xyz = mms.get_data("b_gse_fgm_srvy_l2", tint, 1)
>>> p_xyz_e = mms.get_data("pe_gse_fpi_fast_l2", tint, 1)
Rotate electron pressure tensor to field aligned coordinates
>>> p_fac_e_pp = mms.rotate_tensor(p_xyz_e, "fac", b_xyz, "pp")
Compute agyrotropy coefficient
>>> d_ng_e = pyrf.calc_dng(p_fac_e_pp)
"""
# Check input type
assert isinstance(p_xyz, xr.DataArray), "p_xyz must be a xarray.DataArray"
# Check import shape
message = "p_xyz must be a time series of a tensor"
assert p_xyz.data.ndim == 3 and p_xyz.shape[1] == 3 and p_xyz.shape[2] == 3, message
# Parallel and perpendicular components
p_para = p_xyz.data[:, 0, 0]
p_perp = (p_xyz.data[:, 1, 1] + p_xyz.data[:, 2, 2]) / 2
# Off-diagonal terms
p_12, p_13, p_23 = [p_xyz.data[:, 0, 1], p_xyz.data[:, 0, 2], p_xyz.data[:, 1, 2]]
d_ng = np.sqrt(8 * (p_12**2 + p_13**2 + p_23**2))
d_ng /= p_para + 2 * p_perp
d_ng = ts_scalar(p_xyz.time.data, d_ng)
return d_ng