# External magnetic fields

SLaSi supporst the next list of in-build field types:

• constant,
• linear $H = h_1q + h_2$,
• harmonic $H = h \cos (\omega q + \phi)$,

where q means space or time coordinate.

Each the field can be defined repeatedly with different parameters for the axes X, Y or Z. For fields a smoothing hat function $A \exp(-t^2/T^2)$ can be defined for avoiding of beats. The common syntax follows:

field<Axis> = select <fieldParams1> <fieldSpec> <fieldParams2> <hatTime>

Here <Axis> defines the axis for field, X, Y or Z. For example, fieldX, fieldY or fieldZ. <fieldParams1> means the spatial and temporal coordinates in which field is applied. <fieldSpec> can be const, lin or harm and <fieldParams> list depends on it. <hatTime> defines $T$ from the hat function (can be 0 for absence of smoothing).

<fieldParams1> are defined as set of commands select with coordinate specification and > or < symbol with number. They can repeat for defining an interval. For example

fieldX = select t > 0.0 select y < 10 ...

defines the field along X axis which starts from the beginning of the simulations and acts from the first to ninth nodes along Y axis.

For the <fieldSpec> equals const <fieldParams2> is only one number: field strength. For example:

fieldX = select t > 10.0 const 0.3 30

Such command generates magnetic field along X axis with strength 0.3 units with smoothing during 30 time units after time equal 10 units.

For the <fieldSpec> equals lin <fieldParams2> is a construction like h1 q h2, which means $H = h_1q + h_2$ where q takes values x, y, z or t and h1 and h2 are numbers. For example:

fieldX = select t > 0.0 lin 0.1 t 0.0 0.0

Such command generates magnetic field along X axis which linearly increase in time with speed 0.1.

For the <fieldSpec> equals harm <fieldParams2> is a construction like h omega q phi, which means $H = h \cos (\omega q + \phi)$ where q takes values x, y, z or t, h is a field strength and phi is a phase. For example:

fieldX = select t > 0.0 harm 0.1 -6.2 t 1.57 0.0

Such command generates alternating sinusoidal magnetic field along X with frequency equal 1.

You can specify till 100 different fields along each axis.