Test planes

Associated notes are:

Stopping rays at selected test planes.

Second plane needed for a cathode.

Information on the rays can be given ( in the information box on the screen and the output data file) for up to 25 'test planes' that are crossed by the rays.

A 'test plane' is a plane at which all the information about those rays that cross the plane is retained. That is, if a ray crosses a test plane all the ray parameters at the crossing point will be stored and put in the output data file and at end of the ray tracing. The output parameters are:

CPO2D: r, z, vr, vz, kinetic energy, potential and time.

For some print levels the angles to the z axis and the extrapolated values of z (that is, the z at which the ray would cross the axis) are given instead if the test plane has the form z = constant.

CPO3D: x, y, z, vx, vy, vz, kinetic energy, potential and time.

Up to 25 'test planes' can be defined.

In CPO2D the 'planes' are defined by the 3 numbers a, b and c, giving

a*r + b*z = c for cylindrical symmetry,

a*x + b*z = c for planar symmetry.

For example, a = 0 gives b*z = c, which is z = c/b, which is a plane at constant z, for both cylindrical and axial symmetry. For cylindrical symmetry, the 'plane' defined by non-zero values of both a and b is in fact a conical surface. When b is zero it becomes the cylindrical surface r = c/a. When b and c are both zero (but a is non-zero), the 'plane' becomes the axis of the system -a frequently used condition.

In CPO3D the test planes are defined by the formula

a*x + b*y + c*z = d

which gives a unique flat surface for constant values of a, b, c and d. For example for a = 1, b = 0, c = 0, d = 5, the plane is x = 5.

The ray parameters that are stored are evaluated at the crossing point. They are given in the information box on the screen and are also put in the ray output file.

When a cathode is in use at least two test planes must be defined. The first is used to test the cathode (see note on cathodes) while the second is a normal test plane, situated for example at a focal plane.

(Technical note on accuracy of test plane information:

The values of the parameters at the crossing point are evaluated by a 5-point interpolation using the 2 end points of the ray step that crossed the plane and those of the following step and the 2 previous steps (if these exist), giving a 5 point interpolation. The interpolation routine can give inaccurate answers (see note on ray tracing details) for a test plane that is at or near the end of a ray, but this problem can be avoided by extending the length of the ray. An interpolation is used to find the time at which the value of d in the above formula is zero, and then further interpolations are used to find the values of the parameters at this time -this avoids problems with double-valued parameters, but it does mean that the above formula for the plane will not be satisfied exactly.)

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.

Enter the number of test planes in the first 3 spaces. Then enter one line for each plane, giving the values of a, b, c and d.