xmpl3d93, 93rd 'example' data file for CPO3DS
Hexapole aberration corrector.
Based on the data files used for the publication Computer simulations of hexapole aberration correctors, by L.A. Baranova, F.H. Read and D. Cubric, Physics Procedia 1 (2008) 185-191.
The present example file uses lower accuracy, fewer trajectories and fewer iterations than the data files used for the publication, for a quick demonstration.
Also, those data files were run with the 'scattering' version of CPO3D, in which the scattering option was used to simulate a 'perfect' thin round objective lens to focus the beam at the required image position.
The present example file does not need the scattering version of CPO3D. Instead the final beam is made as parallel as possible by using the 'automatic focusing' option to minimize the angles between the trajectories and the axial direction.
In more detail:
The HRRH configuration is used, where H and R represent round lenses and hexapole components respectively (see the paper cited above).
The hexapole voltages are kept constant here, although in the original study they were of course optimized.
In the present example the voltage of the round lenses is optimized using the 'automatic focusing' option. Only this voltage is varied.
Only 5 trajectories are traced, with only a modest inaccuracy (for a fast simulation). These trajectories are in the xz, yz and diagonal planes.
Instead of using a simulated final 'perfect' round objective lens to form a point image we set the parameters of the 'automatic focusing' option to produce a beam that is as parallel as possible. This is done by specifying an 'angular constraint' which looks at the angles between the directions of the trajectories and the axial direction. The program is asked to multiply these angles by 1.E10 to convert them to equivalent radial deviations at the test plane, which are then added to the actual radial deviations to give artificially enhanced values. The 'automatic focusing' option then varies the round lens voltage to try to minimise the enhanced root-mean-square radial deviations. In this way the angles are minimized and the beam is made as parallel as possible.
In fact in this example only 8 focusing iterations are used and the optimum round lens voltage is found to be 2.9425, which is similar to the value given in the publication.
Please note:
(1) To include the hexapole voltages in the optimization process it is necessary to use the 'related voltages' option.
(2) For a more accurate study it is necessary to use higher accuracy -that is, more segments, shorter step lengths, smaller inaccuracies for trajectory integrations and field evaluations.
(3) The option to 'force hexagonal symmetry' cannot be used because the relevant symmetry for the hexapole units is +-+-+-, while would destroy the axial symmetry of the round lenses.