-- Advanced electrostatics for space-charge, cathodes, and high accuracy

CPO - Charged Particle Optics Software

Figure: hemispherical deflection analyzer example in CPO

Summary: CPO is a software application that calculates electrostatic/magnetic fields and the trajectories of charged particles through those fields, a bit like SIMION. However, CPO differs fundamentally in its powerful and highly accurate methods of calculation (Boundary Element Method--BEM), and it offers well-tested space-charge, cathode emission, dielectric, and other advanced features.


  • Extremely accurate BEM methods proven with over 200 benchmark and other tests. See examples and publications.
  • Help system that is exceptionally clear, comprehensive and supported with examples
  • Developed continuously since 1974 by one of the leading research group in electrostatic systems (University of Manchester, UK).
  • Vast range of capabilities and options, with advanced underlying algorithms, all at a competitive price for a high-end package.


surface mesh of a nanocone
as a field emission source Electrostatic field solving is done to high accuracy using the Boundary Element Method (BEM) rather than traditional FEM or FDM methods. The BEM has unique advantages and is well-suited to space-charge, cathode problems and nano-structures in the presence of large electrodes. Adaptive surface meshes get smaller where accuracy is critical. The BEM even easily simulates fine meshes and non-enclosed systems. Low-frequency oscillations, such as in a quadrupole, may also be simulated.

image of space-charge repulsion of an isolated beam that initially converges to a point Particle trajectories of charged particles are calculated (Bulirsch-Stoer), accurately accounting for space-charge and relativistic effects. Space-charge is handled with iterative convergence tube and mesh methods--accuracy of 1% against theoretical results have been obtained.

image of spherical emitting cathode Cathode emissions limited by space charge are simulated, including thermionic, field and extended Schottky emissions. Supports Child's Law/Langmuir, Fowler-Nordheim and Richardson-Dushman relationships, plus user-defined properties. CPO specially handles space-charge effects at the critical cathode region.

image of secondary emissions in a photomultiplier Secondary emissions can be generated when a particle hits an electrode. The current multiplication factor and energy/angular distributions of the secondaries are chosen by the user.

image of scattering of particles by a background gas Particle scattering and losses due to grid, background gas or secondary emissions are given in the examples included in the scattering version of CPO. Particle-particle scattering inside the beam is possible with the stochastic version. User-defined routines can be written in C++.

magnetic countour lines on a solenoid coilcolor magnetic field map on a solenoid coil Magnetic elements of various types such as solenoids, wire loops and user-defined fields are available. Various contour and field plots can be displayed.

image of einzel lens Aberration coefficients and lens properties may be calculated directly. An iterative automatic focusing option can find optimum electrode voltages.

Dielectrics calculations now available as a special module! (NEW - Nov 2006)

(full list of features)

Try out CPO (FREE):

Request a free demo, and we will send you a fully working version of the CD and manual to try for ~30 days. Many examples are included and fully documented.

CPO is available from

Scientific Instrument Services, Inc.,
Authorized CPO Distributor.
See Prices and Sales.

Why CPO? What makes CPO unique from SIMION? CPO is a high-end package providing accurate calculations of space charge and space-charge limited cathode emissions, highly accurate field calculations via the Boundary Element Method (BEM), a vast number of examples, and various added benefits such as direct calculation of abberation coefficients, dielectrics, magnetic fields from wire currents, and built-in autofocusing routines. Prices start at a few thousand US $ depending on version.

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