xmpl3d76, 76th 'example' data file for CPO3D

Simple achromatic quadrupole lens.


Simple achromatic quadrupole lens, including options for 'related voltages' and 'focus optimisation'.


The geometry and the magnetic quadrupole sources are very simple. These would need to be greatly improved for a realistic simulation.


The electrostatic quadrupole lens has a diameter 5mm, a length 4.8mm and plates that subtend 86 degrees.


The magnetic quadrupole lens is superimposed on the electrostatic lens. It consists of 4 simple solenoids oriented with the gaps in the electrostatic lens.


The voltage V is initially +0.2 on the x electrodes and -0.2 on the y electrodes. The 'related voltages' option is used to link the x and y voltages (which is useful for the focus optimisation option, see below). The scaling factor f for the magnetic field is initially 3.


For achromatic action the optical strength of the magnetic lens should be twice that of the electrostatic lens and should be of the opposite sign. Here is the action of the combined lens under different excitations:


V f action

0.2 0 focusses in yz plane at z approx 40, large chromatic aberration.

0 1.5 focusses in yz plane at z approx 40, large chromatic aberration.

-0.2 3 focusses in yz plane at z approx 40, small chromatic aberration.


There is defocussing in the xz plane. Clearly more than one lens of this type would have to be used to design a system in which there is achromatic focussing in both planes.


5 rays are used with energies from 0.9 to 1.1eV. The 'focus optimisation' option is used to optimise V and f. After 30 iterations the values become V = 0.2046, f = 2.981.