Xmpl2d21, 21st 'example' data file for CPO2D

Parallel wire deflector, planar symmetry.

The following data were obtained when the memory and speed of PC's was much more limited than at present, so the available number of segments was small and the requested inaccuracies were fairly high to give a quick demonstration.

Two infinitely long, parallel, round wires are used to deflect a beam.

Here 'planar' symmetry is used, so that the system extends an infinite distance in the +/- y directions. The electrodes are specified as arcs of circles that subtend 90 degrees. After reflection in the x=0 and z=0 planes these become full circles. With the planar symmetry they becomes cylinders of infinite length.

For wires of radius r and separation 2s (where r = 0.0125 and s = 0.5 in the present example), and with potentials +/-V applied to the wires, the potential at a general point (x,z) outside the wires is:

(0.5*V/ln((s+t)/r))*ln(((x+t)**2+z**2)/((x-t)**2+z**2))

where

t = sqrt(s**2-r**2).

On the z axis the potential is zero and the transverse electric field is

(2*V*t/ln((s+t)/r))/(t**2+z**2).

Values calculated by the program conform to these expressions, within the stated inaccuracy.

A beam of 7 rays that initially converge to the point (0,12) is set up.

After deflection the rays converge to the point (0.9906,11.15). The deflection voltage of 0.1274 is chosen to give a deflection of approximately 2s. The spread in the x direction is approximately 0.0018.

Comparison of 3 deflectors:

 Type V x z dx xmpl2d21 Wire .1274 .9906 11.15 .0018 xmpl2d22 Edge .0374 .9991 11.72 .00030 xmpl2d23 Plate .0274 .9992 11.48 .00028

See 3D deflectors for a comprehensive comparison of deflectors.