Pulsed beams.

Examples of space-charge repulsion of a pulsed beam are given in xmpl2d54, test3d31 and xmpl3d86.

This option can be difficult to use, so please look at the advice given here and in the above files.

The option is accessed at the bottom of the page /databuilder/setting up rays/sources of rays/

The option is useful only for space-charge simulations (including stochastic scattering simulations) and is accessed in /databuilder/sources of rays/sources of rays/.

The option applies to most types of beam. The pulse duration is the same for all rays.

A ray that has a current I ma and a duration t_pulse ms represents a charge q = current*time = I*t_pulse*1.E-6 coulomb. In practical simulations q would usually be much larger than the charge of a single electron or ion.

During ray tracing a ray advances in a series of steps; the user controls the physical length or time of these steps. In the space-charge tube method, which has to be used with this option, there is one tube per step and the space-charges are deposited in the tubes. Each ray therefore has a continuous series of tubes, all of which are charged. The initial and final time of each tube are recorded.

When the program wants to calculate the space-charge force on a particle in a ray it looks at all the space-charge tubes in all the other rays (but excludes the tubes of the particle ray itself, see below). The program knows the present time t of the particle at its present position and it also knows the initial and final times, t1 and t2 say, of all the tubes. The program uses the present time t of the particle to define a time interval Ti = t - t_pulse/2, Tf = t + t_pulse/2. The relevant tubes are then those that have t1 and/or t2 inside this time interval. If t1 and t2 are both within the interval then the space-charge of the whole tube is used to give a contribution to the field that acts on the particle. On the other hand if either t1 or t2 is outside the interval then only the appropriate fraction of charge is used. (Some refinements are needed at the starting times of rays.)

With this procedure, the space-charge force on a particle is due only to those space-charge tubes that exist at the same time.

It is advisable to make the maximum step time (dtmax) smaller or equal to the pulse duration t_pulse. If dtmax is made longer then the calculations can become less accurate (see test3d31). In practice, a small dtmax implies a large number of ray steps and so the maximum value of the total number of steps that the program allows might be exceeded.

A pulsed beam simulation with space-charge will involve space-charge iterations. The surface charges are influenced by the space charges and so in principle the surface charges should be recalculated at a series of times, as the pulse moves through the system, but this would greatly increase the computing time. Since the only space-charges that exist at the end of a run are the final ones the option to disable the recalulation of surface charges should usually be used. This should not be a serious omission when the pulse time is short and the total charge carried in the beam is much smaller than the surface charges, since then the surface charges are not much affected.

As mentioned above, when the program calculates the space-charge force on a particle in a ray it looks at all the space-charge tubes except the tubes of the particle ray itself, created in the previous iteration. This is logical of course, but a practical reason is that in pulsed beam simulations the space-charges in the tubes tend to be large and so the fields very near to them also tend to be large, which would sometimes give unwanted large deflections. We refer to this as ‘self-field exclusion’.