The present version of CAIN accepts a constant external field only.
The covariant form of the equation of motion
where 
is the proper time and 
the electromagnetic
field tensor, can be solved exactly when the field is constant.
The eigenvalues of the matrix
is given by 
and
, where
with
Then, the solution is
where the upper (lower) sign applies to 
(
)
and 
with 
being the antisymmetric tensor of
rank 4.
The classical spin motion of electrons is given by the Thomas-BMT
equation
where a is the coefficient of
anomalous magnetic moment and
Figure 1: Field dependence of the anomalous magnetic
moment of electron
When the field is very strong, a is different from the well-known
value 
but is a function of the field strength
characterized the parameter 
.
The functional form of 
is shown in Fig.1.
Simple polynomial approximations are used in CAIN.