Xmpl2d55, 55th 'example' data file for CPO2D

Magnetic bottle.

See also xmpl3d20.

Electrons are confined between 2 circular loops of current, at z = =/- 20. 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 temp55a.dat)

An electron of energy 1eV is started at the midway point. The maximum step time is set at 1E-7ms.

It can be seen that the ray is reflected for the first time at z = 15.6, where the magnitude of the magnetic field is 5.93mT (as determined by using the 'contour' option).

During ray tracing the picture on the screen shows r*cos(phi) versus z, but on completion this becomes r versus z, which is usually the more meaningful information. But here the r*cos(phi) versus z plot should be restored using the 'view' drop-down menu.

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 (ie 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 and from the fact that the ray eventually escapes 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:

non meridional set of single rays

0 0 0.5 1 0 1 0 r,z,vr,vz,vphi,energy,current

0.5 0 0.5 1 0 1 0 r,z,vr,vz,vphi,energy,current

0.5 0 0.5 1 0.5 1 0 r,z,vr,vz,vphi,energy,current

0.5 0 0 1 0.5 1 0 r,z,vr,vz,vphi,energy,current

0.5 0 0.5 1 0 1 0 r,z,vr,vz,vphi,energy,current

last of this set of rays

At the same time it would be advisable to decrease the cut-off time, to 3E-4, 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.