Test2d27, an example of an electrode defined by users equations.

A parabolic reflector.

This illustrates the option (added July 2012) for electrodes to be defined by user-supplied equations.

See also test3d33.

2 parabolas are defined, z = r^2 and z = r^2 - 0.01.

They have the applied voltages 0 and -2 respectively, and so form a parabolic mirror for electrons of energy 1eV.

The first parabola is defined by the equations

r = u

z = u^2.

The first variable 'u' is subdivided uniformly into 200 segments between the limits 0 and 1.

The second parabola is similarly defined using the variables u and b, where b = 0.01.

(In fact there is no need to use the fixed variable c here, since it could be incorporated into the defining equations.)

Electrons start from a plate at z = 1, with the energy 1eV. A second plate has been added to anchor the potential more accurately.

The theoretical point of focus for the first parabola is at z = 0.25. The electrons are reflected midway between the the parabolas and so the expected focal point is at z = 0.245. In fact in this example the crossing points are spread by 0.004 around this position.

See notes on the 'users equations' option.