Estimating phase space.

The last option associated with test planes is the option to estimate the range of phase space occupied by a beam -available only in CPO3D.

The option is only valid for a beam that has its axis in the z (or -z) direction. Two requirements are (1) that the 1st test plane (that is, the beam section) must be perpendicular to the z axis, and (2) that there are 9 or more trajectories (because with only 8 they could all be related through 3 reflections).

The x and y directions are treated separately and independently. The following remarks are in terms of x, but also apply to y.

The beam section is at z = z_section, say, and here the coordinates x and velocities vx are known for all the rays. The profile of the beam is tested to find the beam waist, by using a series of values z_test of z that extend in the direction of the waist, and beyond it.

At each z_test the rays at the beam section are extrapolated linearly from z_section to z_test to give the coordinate x_test at z_test. The mean value x_mean is calculated, and then the rms (root-mean-square) deviation from this mean. The value of z_test is adjusted until the minimum rms value of x is obtained -this value of z_test is effectively the position of a type of 'line of least confusion' or beam waist for the x direction. The value of z obtained in this way for the beam waist does not depend on z_section, provided that the region is field-free. The corresponding rms value of x is in some circumstances an approximate measure of the range of the x coordinate part of phase space.

Finally the rms deviation of the transverse velocity is calculated. The required volume of phase space in the transverse direction is of course the product of the ranges of x, y, vx and vy (but remember that the program outputs the rms values, not the ranges).

The ranges of coordinates and velocities are intended as a guide to the volume of phase space occupied by the beam, and are not to be taken too literally. In particular the way that they are calculated takes no account of the fact that most phase space diagrams have a non-circular (or non-oval) shape.

For users who are editing or constructing an 'input data file' without the use of the data-builder -that is, pre-processor:

But Manual editing is certainly not recommended -it is a relic from the time when the databuilder was not available All users are strongly encouraged to use the databuilder, which always gives the correct formats and which has many options for which the formats are not described or easily deduced.

Put the letter 'p' in the 8th space of the line that gives the number of test planes.