pyrfu.pyrf.c_4_j#

pyrfu.pyrf.c_4_j(r_list: Sequence[DataArray], b_list: Sequence[DataArray]) → tuple[xarray.core.dataarray.DataArray, xarray.core.dataarray.DataArray, xarray.core.dataarray.DataArray, xarray.core.dataarray.DataArray, xarray.core.dataarray.DataArray, xarray.core.dataarray.DataArray][source]#

Calculate the current density using the four spacecraft technique.

Computes the current density \(J\) using the four spacecraft technique [1], the divergence of the magnetic field \(\nabla \cdot B\), magnetic field at the center of mass of the tetrahedron, \(J \times B\) force, part of the divergence of stress associated with curvature \(\nabla.T_{shear}\) and gradient of the magnetic pressure \(\nabla P_b\). Where :

\[ \begin{align}\begin{aligned}J = \frac{\nabla \times B}{\mu_0}\\J \times B = \nabla.T_{shear} - \nabla P_b\\\nabla.T_{shear} = \frac{(B.\nabla) B}{\mu_0}\\\nabla P_b = \nabla \frac{B^2}{2\mu_0}\end{aligned}\end{align} \]

The divergence of the magnetic field is current density units as it shows the error on the estimation of the current density [2] .

Parameters:

  • r_list (list of DataArray) – Time series of the spacecraft position [km].

  • b_list (list of DataArray) – Time series of the magnetic field [nT].

Returns:

  • j (DataArray) – Time series of the current density [A.m^{-2}].

  • div_b (DataArray) – Time series of the divergence of the magnetic field [A.m^{-2}].

  • b_avg (DataArray) – Time series of the magnetic field at the center of mass of the tetrahedron, sampled at 1st SC time steps [nT].

  • jxb (DataArray) – Time series of the \(J \times B\) force [T A m^{-2}] = [N m^{-3}].

  • div_t_shear (DataArray) – Time series of the part of the divergence of stress associated with curvature [T A m^{-2}].

  • div_pb (DataArray) – Time series of the gradient of the magnetic pressure [T A m^{-2}].

See also

pyrfu.pyrf.c_4_k

Calculates reciprocal vectors in barycentric coordinates.

pyrfu.pyrf.c_4_grad

Calculate gradient of physical field using 4 spacecraft technique.

References

[1]

Dunlop, M. W., A. Balogh, K.-H. Glassmeier, and P. Robert (2002a), Four-point Cluster application of magnetic field analysis tools: The Curl- ometer, J. Geophys. Res., 107(A11), 1384, doi : https://doi.org/10.1029/2001JA005088.

[2]

Robert, P., et al. (1998), Accuracy of current determination, in Analysis Methods for Multi-Spacecraft Data, edited by G. Paschmann and P. W. Daly, pp. 395–418, Int. Space Sci. Inst., Bern. url : http://www.issibern.ch/forads/sr-001-16.pdf

Examples

>>> import numpy as np
>>> from pyrfu import mms, pyrf

Time interval

>>> tint = ["2019-09-14T07:54:00.000", "2019-09-14T08:11:00.000"]

Spacecraft indices

>>> mms_list = np.arange(1,5)

Load magnetic field and spacecraft position

>>> b_mms = [mms.get_data("b_gse_fgm_srvy_l2", tint, i) for i in mms_list]
>>> r_mms = [mms.get_data("r_gse_mec_srvy_l2", tint, i) for i in mms_list]

Compute current density, divergence of b, etc. using curlometer technique

>>> j_xyz, _, b_xyz, _, _, _ = pyrf.c_4_j(r_mms, b_mms)