Magnetization¶

integer :: magnetType
real,dimension(3) :: u_ea, u_oa1, u_oa2
real :: mu_r_ea, mu_r_oa
real :: Mrem
real,dimension(3) :: M
integer :: stateFunctionIndex

Magnet Type¶

1 = hard magnet
2 = soft magnet with state function
3 = soft magnet with constant permeability

The tile can have different magnetic properties. It can be a hard magnet, which has a constant magnetization during the simulation. Soft magnets can be defined either with a state function (hysteresis loop), which relates the magnetization of the tile to the currently H-field. The third option describes a softmagnet with a constant permeability \(\mu \equiv \mu_0 ( 1 + \chi_m)\) and therefore a linear relationship for the magnetization with the H-field: \(M = \chi_m H\)

Easy axis and other axes¶

The easy axis defines the direction of preferred magnetization in the magnetic tile. With the other axes a orthonormal set is formed. In the Matlab and python interfaces, the easy axis of the magnetization of is de fined according to the global three-dimensional global coordinate system with two angles: polar angle \(\theta\), and azimuth \(\phi\), where \(\theta \in [0, \pi]\) and \(\phi \in [0, 2 \pi]\) .

\[\begin{split}\begin{pmatrix} u\_ea_x \\ u\_ea_y \\ u\_ea_z \end{pmatrix} = \begin{pmatrix} sin(\theta) cos(\phi)\\ sin(\theta) sin(\phi) \\ cos(\theta) \end{pmatrix}\end{split}\]

\[\begin{split}\begin{pmatrix} u\_oa1_x \\ u\_oa1_y \\ u\_oa1_z \end{pmatrix} = \begin{pmatrix} sin(\theta) sin(\phi)\\ -sin(\theta) cos(\phi) \\ 0 \end{pmatrix}\end{split}\]

\[\begin{split}\begin{pmatrix} u\_oa2_x \\ u\_oa2_y \\ u\_oa2_z \end{pmatrix} = \begin{pmatrix} \frac{1}{2}sin(2\theta) cos(\phi)\\ \frac{1}{2}sin(2\theta) sin(\phi) \\ -\sin^{2}(\theta) \end{pmatrix}\end{split}\]

The permeability of the easy axis \(\mu_{r\_ea}\) and the permeability of the other axes \(\mu_{r\_oa}\) can be specified individually. .. note:: Its default value is 1.

Remanent Magnetization \(M_{rem}\)¶

The value of \(M_{rem}\) specifies magnetization, which is remanent in the direction of the easy axis of the magnetic tile. .. note:: Its unit is measured in \(A/m\) in MagTense.

Magnetization \(M\)¶

The magnetization of the tile in the global three-dimensional global coordinate system. Its quantity is calculated in MagTense and the effect on the other existing tiles in the model is done through iterations. For a hard (permanent) magnet with \(\mu_{r\_ea} = \mu_{r\_oa} = 1\), the magnetization of the considered tile \(M = M_{rem} * u\_ea\).

State function index¶

For a soft magnet, whose magnetization is dependent on the H-field in the form of a hysteresis loop, a ‘state function’_ has to be delivered to MagTense. The state function index determines, which function of the possibly multiple given state functions belongs to that specific tile.