magpack.vectorop.vorticity#
- vorticity(vector_field)#
Calculates the magnetic vorticity vector field for the given vector field.
- Parameters:
- vector_fieldnp.ndarray
Three-dimensional vector field shaped (3, nx, ny, nz) for which the vorticity will be calculated.
- Returns:
- np.ndarray
Three-dimensional vorticity vector field shaped (3, nx, ny, nz).
Notes
The magnetic vorticity, \(\mathbf{\Omega}\), of the magnetization vector field, \(\mathbf{m}\), is given by [1], [2]:
\[\Omega_i = \frac{1}{8\pi}\epsilon_{abc}\epsilon_{ijk}m_{i}\partial_{b}m_{j}\partial_{c}m_{k}\]Warning
This calculation is slow and can be improved by writing out the expression explicitly.
References