xmpl3d20, 20th 'example' data file for CPO3D

Magnetic bottle.

See also xmpl2d55.

Electrons are confined between two circular loops of current.

Cylinders at zero voltage are used to indicate the positions of the loops.

The magnetic field has the strength 1.3488mT at the midway position, and 7.6474mT at the centre of each loop (see the data in the output file temp20a.dat).

An electron of energy 1eV is started at the midway point and can be seen to be reflected when it approaches the loops. The first point of reflection is at z = 15.70, where the magnitude of the magnetic field is 5.993mT (as determined by using the 'contour' option). Labelling the starting point as 'i' and the point of reflection as 'f', the relationship

pt_i/P_i = sqrt(B_i/B_f)

should hold if the motion is adiabatic, where pt_i is the initial transverse momentum and P_i is the initial total momentum. In fact pt_i/P_i = 0.447, sqrt(B_i/B_f) = 0.474, so there is a small divergence from adiabaticity (that is, the magnetic field changes significantly over the distance of one loop of the near-helical motion), The divergence from adiabaticity is also clear from the fact that the values of z at which the rays are reflected is not the same for all reflections. After a sufficiently long time the ray will escape from the bottle.

For a quantitative treatment of adiabacity, see the paper Magnetic field paralleliser for 2? electron spectrometer and electron image magnifier, by P Kruit and F H Read, J.Phys.E (Sci.Instrum.) 16, 313-24 (1983).

To see the behaviour of electrons that have a range of initial starting directions, use a ray specification such as:

set of single rays:*********************************

0. 0. 0. 0. 2.0 1.0 1.0 0

0. 0. 0. 0. 1.5 1.0 1.0 0.

0. 0. 0. 0. 1.0 1.0 1.0 0.

0. 0. 0. 0. 0.75 1.0 1.0 0.

0. 0. 0. 0. 0.5 1.0 1.0 0.

0. 0. 0. 0. 0.25 1.0 1.0 0.

last of this set of rays****************************

At the same time it would be advisable to decrease the cut-off time:

3.E-4ms, say.

A final comment:

In principle the 'nearly helical' option might be used to reduce the computing time. This option is described in Help. But in this example the magnetic field is not approximately uniform except at the mid-point and so the option does not help.