Discussion Forum

Edit: I said "no" to this initially, but it appears that Comsol actually has introduced interactions of the particles back on to the applied field (see https://www.comsol.com/particle-tracing-module). So, there does appear to be considerable similarity here. That essay also says "if the number density of charged species is less than around 10^13 /m^3, the effect of the particles on the fields can be neglected. This allows you to compute the fields independently from the particle trajectories. The fields are then used to compute the electric, magnetic, and collisional forces on the particles." Fair enough. But what if the density is higher? A PIC code can address that regime and solve for the particle motions and fields self-consistently. Can the particle tracing module address that or not? The rest of the essay implies that it can, at least in principle, but at the same time it appears to be suggesting (at least, as I interpret it) that it will become computationally cumbersome to do this (after all, PIC codes are notoriously computationally intensive, and Comsol was not originally designed to operate efficiently as a PIC code). I look forward to seeing any comments about your question from Comsol personnel!

Edit: I said "no" to this initially, but it appears that Comsol actually has introduced interactions of the particles back on to the applied field (see https://www.comsol.com/particle-tracing-module). So, there does appear to be considerable similarity here. That essay also says "if the number density of charged species is less than around 10^13 /m^3, the effect of the particles on the fields can be neglected. This allows you to compute the fields independently from the particle trajectories. The fields are then used to compute the electric, magnetic, and collisional forces on the particles." Fair enough. But what if the density is higher? A PIC code can address that regime and solve for the particle motions and fields self-consistently. Can the particle tracing module address that or not? The rest of the essay implies that it can, at least in principle, but at the same time it appears to be suggesting (at least, as I interpret it) that it will become computationally cumbersome to do this (after all, PIC codes are notoriously computationally intensive, and Comsol was not originally designed to operate efficiently as a PIC code). I look forward to seeing any comments about your question from Comsol personnel!

Thank you very much for your reply. What is exactly meant with "solve the fields self consistently", I come across this term quite often in literature. Does this mean that the force on the particle is partially created by the field of that same particle?

At any time t, the motion (positions and velocity) of the charges will generally be changing in response to the fields. So at time t+dt, the fields will generally be different, because the charges moved, and their motion (and presence) contributed to both the electric and magnetic fields present. If you ignore that perturbation, then your solution is not self-consistent. For example, you might compute the fields in a particle accelerator in the absence of particles being accelerated. Then, when you introduce the charges, if there are only a few, you might assume they will move in accordance with your previously computed fields, and that would be a valid assumption. But if you introduce too many charges, the fields will be altered. If you don't take that into account, and/or if you don't update it at every time step, then you won't accurately compute the motion of the charges or the values of the fields. PIC codes generally seek self-consistent solutions. But "particle tracing" doesn't necessarily do that. Consider a magnetron with a constant externally imposed magnetic field. Start with no current or applied voltage. Now, turn on the DC-bias field and allow particles to be emitted from the cathode. Without a self-consistent solution, the particles would simply orbit around and ultimately terminate on the walls. Now, solve it self-consistently, and you'll get bunching of particles with rotating spokes of space charge, and (most importantly) generation of microwaves.

At any time t, the motion (positions and velocity) of the charges will generally be changing in response to the fields. So at time t+dt, the fields will generally be different, because the charges moved, and their motion (and presence) contributed to both the electric and magnetic fields present. If you ignore that perturbation, then your solution is not self-consistent. For example, you might compute the fields in a particle accelerator in the absence of particles being accelerated. Then, when you introduce the charges, if there are only a few, you might assume they will move in accordance with your previously computed fields, and that would be a valid assumption. But if you introduce too many charges, the fields will be altered. If you don't take that into account, and/or if you don't update it at every time step, then you won't accurately compute the motion of the charges or the values of the fields. PIC codes generally seek self-consistent solutions. But "particle tracing" doesn't necessarily do that. Consider a magnetron with a constant externally imposed magnetic field. Start with no current or applied voltage. Now, turn on the DC-bias field and allow particles to be emitted from the cathode. Without a self-consistent solution, the particles would simply orbit around and ultimately terminate on the walls. Now, solve it self-consistently, and you'll get bunching of particles with rotating spokes of space charge, and (most importantly) generation of microwaves.

That does clarify it, thank you. Thus, self consistent simulations also take into account the collective effect of space charge which generates a self field that partially nullifies the external field. Is that a correct way to put it?

I do know of particle tracing codes that use matrix formalism that just use externally defined fields and use matrix multiplication to calculate the trajectories without taking into account the particle self fields.