Xmpl2d51, 51st 'example' data file for CPO2D

A non-meridional beam.

This test file simulates a non-meridional beam in a 2D magnetic field.

The geometry, magnetic field and beam energy are as in test2d28.dat.

Because a magnetic field is present the beam option automatically switches to non-meridional motion (and note that non-meridional motion can also be selected voluntarily when there are no magnetic fields). The 'random' beam option is also required for non-meridional motion. Another restriction is that the window and pupil that define the beam must both be centred on the axis, because in systems with 2D cylindrical symmetry, off-axis windows and pupils cannot be defined.

The pupil has been chosen to give rays that are emitted over a 45 degree half angle. 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. The r*cos(phi) versus z plot can be restored using the 'view' drop-down menu (see below). It can be seen that rays emitted at the largest angles to the perpendicular have the shortest pitch lengths.

It also appears that there is a low density of rays near the axis. However, if a large number of rays are run and the zoom function is used to look at the initial positions then it can be verified that the number in a range r1 to r2 is proportional to (r2**2 - r1**2) -that is, the density of rays is constant.

As explained in the notes on non-meridional motion, there is a choice of viewing the final ray plots either as r versus z or as r*cos(phi) versus z. This choice appears in the ‘View’ drop-down menu. Here phi is the angle around the axis, so therefore r*cos(phi) is essentially the projection of the motion on the fixed xz plane. The value of phi always starts as 0, but r*cos(phi) can of course become negative. On the other hand the plot of r versus z shows the maximum distance r from the axis (and r is of course always >= 0).

It is also staed there that axially symmetric systems a ‘ray’ seen in the plots actually represent a cut through an axially symmetric sheet. The plot of r versus z is therefore the more realistic one, and is the only one allowed for space-charge plots.