**Problem Type:**

Plane-parallel 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.