Space-charge is the charge in space due to charged particles in space. Often is is neglible relative to charges on electrode surfaces and often it is ignored for simulation purposes. However, at higher beam currents is can become important.

Normally, SIMION assumes that space-charge is negligible, as it often is. That is, all charges are assumed to be on the electrode surfaces (not in space) as defined by the electrode voltages, and SIMION solves the potentials in space using the Laplace Equation (a form of the Poisson Equation with space-charge density set to zero), and from that it calculates electric field in space. The charge from the particle trajectories themselves is assumed sufficiently small (sufficiently small current). In practice, any space-charge in the particle trajectories would affect the fields, which in turn circularly affect the particle trajectories, etc. ad infinitum. Really quantitative methods of space-charge calculation, such as done by CPO for static fields, solve the fields and trajectories together via an iterative method until convergence.

SIMION 7.0/8.0 do have support a couple “charge-repulsion” methods. When enabled, this accounts for Coulomb’s Law-like “particle-particle” forces (with ion-cloud correction) to simulate repulsion between all the particles or beam lines. It does not, however, account for forces between the particles and the surface charges on the electrode surfaces, which requires the Poisson Equation, and moreover since the particle charges and electrode surfaces charges mutually interact, it requires an iterative method of solving where the potentials/fields in space and the particle trajectories are recalculated alternately until convergence. These “charge repulsion” methods are generally used to “estimate the onset of space-charge.” See p. 2-6 of the SIMION 8.0 manual (2-5 of the SIMION 7.0 manual) and p. 8-17 (“The Charge Repulsion Controls”). Details of the calculation methods are in the “Compuational Methods” appendix to the SIMION manual as well as in this SIMION user group post (SIMION Discussion: coulombic repulsion). There is a further discussion of SIMION’s charge-repulsion methods in the 2005 Appelhans and Dahl paper. Some of the SIMION examples using this, or at least suggesting its use in their README files, include the “einzel”, “drag”, and “trap” examples. Moreover the “repulsion” examples in SIMION 8.0.4 contain a much more thorough discussion (README file) and analysis (with SIMION examples) of the use and reliability of these repulsion methods.

SIMION 8.1 (in development) does have a true Poisson solver that is currently available to 8.0 users for preview in early access mode (See Poisson Equation ). Iterative methods can be implemented in user code, but only a few examples are currently developed.

One advantage of repulsion methods is that, although it is an approximation, it can handle (even efficiently) pulsed means and time-dependent fields. CPO space-charge methods are much more suitable for continuous beams in static fields, such as accurate calculation of space-charge effects near the cathode surface (e.g. pierce gun with Child’s Law current limiting effect) or in beam repulsion, where the space-charge is steady-state (allowing convergence).

See Also

• Space Charge in Mass Spectrometry (K.L. Busch, Spectroscopy, June 2004)