Section 2.5 of the User's Guide for CPO2D and CPO3D

(or proceed to section 2.6)


Units of length, time, etc.


The program assumes that in the input data the lengths are in millimetres, times are in milliseconds, potentials are in Volts, energies are in eV, magnetic fields are in Teslas, charges are in units of the charge of the electron and masses are in units of the atomic mass. The velocities calculated by the program are therefore in units of mm/ms (which is m/s), electric fields are in units of V/mm, etc.


In a purely electrostatic system the equations of motion are such that the shapes of the rays are independent of the unit of length. They are also independent of the charge to mass ratio of the particles (provided that all the particles are initially accelerated through the same potential difference). The numbers entered in the data file for lengths can therefore represent any unit of length (for example micrometre, cm) that is convenient for the user.


But if

 (1) flight time are wanted, or

 (2) a field-emission cathode is used, or

 (3) a magnetic field has been added.

then the lengths that are entered should normally be in millimetres.



Sometimes however it might be more convenient to scale the lengths. For example the actual dimensions might be microns but the dimensions of the system might be entered as though they are millimetres (that is, scaled up by a factor f of 1000). Then the output distances will also be scaled up by the same factor, while the velocities will be unaltered and the times will be scaled up by f. If a magnetic field is present it should be scaled by 1/f to give the correct results in the scaled unit of length.


(proceed to next section)