Working reports.
These reports show the mathematics that was used in the development of the CPO programs and in the many tests that are included in the ‘benchmark’ and ‘example’ data files. They were written by Prof Frank Read purely for his own use. They are mostly hand-written and so are not necessarily legible to others. Nor are they necessarily intelligible. They contain many corrections, deletions, re‑workings and unexplained abbreviations, and are not guarenteed to be correct. They are therefore not suitable for publication.
Publicly-available information is of course given in CPO Help and in the footnotes of the benchmark and example data files and also in published papers (in particular the following papers in the list given in Help: 8, 18, 45, 46, 48, 52, 54, 58 and 60).
377. Magnetic field of a current loop.
405. Φ(r,z) from Φ(z) using surface charges.
407. chromatic aberration.
428. 3D boundary charge method (including exact expressions for potentials of triangles and rectangles, quadrature and other approximations, magnetic field of a loop, geodesic of a cone, near-fields, magnetic vector potentials).
439. Space charge near cathode, for CPO3DS.
440. Thermal distribution at cathode.
441. Miscellaneous calculation for CPO3D (making total charge zero, QMS, flight times through cathode region),
442. Cathode space-charge effects with non-zero temperature.
445. Evaluation of potentials and fields for axial symmetry (including multipole and other approximations, near_fields).
446. Evaluation of potentials and fields for planar symmetry.
447. Potentials and fields due to space-charge cells.
449. Differentiate convolution with a Gaussian.
450. Pierce gun.
451. Field emission.
452. Relativistic lens properties, and trajectories test.
453. Integrating Picht’s equation.
458. Mesh interpolation errors of potentials and fields.
459. Virtual space-charge segments for cathodes.
460. Tests for crossing a segment.
461. Improvement of matrix inversion.
469 Potentials and fields of trajectory space-charge tubes.
471. Potential distributions of planar wires and edges.
475. A further inscribing correction.
477. 3D toroidal electrode.
478. Integrating relativistic equations of motion, including 2D non-meridional.
480. Areas of overlapping circles, and averaging space-charge density.
481. Maxwell distribution.
482. Random Rutherford scattering.
485. Ura energy distribution.
491. Centre of circle, for reading dxf files.
494. Space-charge spreading in ion beams.
496. Subdividing thin triangle into 3 and 4 parts.
497. Dielectrics, and Neumann boundary conditions.
498. Trajectory in presence of mirror image force.
499. Importing charges.
500. magnetic cpo3d.
501. Better segmentation of a sphere.
502. Improvements to dielectric calculations.
503. Further dielectric improvements, for magnetic version.
504. Simulation of scattering at a grid.
505. Nearly helical motion.
506. Off-centre sphere, new type of electrode.
507. Creation of a ‘linear charges’ option.