
Problem Type:
Planeparallel electrostatic problem
Geometry:
Cylindrical deflector analyzer (CDA) is a part of a cylindrical capacitor with angular sector of 127°17'. CDA has two slits made for the particles to enter and exit the CDA field.
In this example the beam of electrons enters the CDA perpendicular to the cylinder's radius with initial kinetic energy E_{0} = 1500 eV and angle dispersion of 6°
Given:
Radius of external cylinder R_{2} = 0.1 m
Radius of internal cylinder R_{1} = 0.07 m
CDA voltage U = 1000 V
Initial kinetic energy of electrons E_{0} = 1500 eV
Relative permittivity of air ε = 1;
Problem:
Define the beam focus point.
Solution:
At the beginning we solve the electrostatic problem calculating the CDA field. After that we open the Point Source Emitter dialog using the Particle Trajectory command (View menu). Using the Emitter dialog page we position the point particle emitter at the center of the CDA's entrance slit (x = 0.076 m, y = 0.037 m) and specify the range for the starting angles between 62 and 68 degrees. Using the Particle dialog page we choose the desired particle type  electron  from the list, and define the value of initial kinetic energy E_{0} = 1500 eV. To obtain the result, we click Apply and view the particle trajectories on screen.
Results:
The beam focus point: (0.081, 0.027).
The focusing angle (approx.): 127° + 8.5° = 135.5°.
Theory says that with some value of CDA voltage depending on the energy of electrons, the beam will be focused at the exit slit. In ideal case the voltage for our example would be U = 1070 V. The focusing angle and the CDA voltage in our example are slightly different because of the CDA fringing effects.
See the Elec3.pbm problem in the Examples folder.