I am using the FDTD method for the simulation of electron-cyclotron beam propagation in cold, anisotropic, time-independent plasma. My setup has the specialty that the "scatterer", i.e. the plasma, extends up to the boundary condition layer, because it is not desirable to surround the plasma region with vacuum in order not to have reflections (we wish to model through-propagation from the plasma layer). Known textbooks (Kunz-Luebbers, Taflove, Kalluri) do not include this case, these are mostly focused in cases where the scatterer is embedded in vacuum (like e.g an aircraft). I am interested in finding out what is the most proper choice for a boundary layer (what kind of PML actually, since Mur's conditions cannot be applied due to the associated vacuum cells) and for a field-handler method (total field, scattered field or total-field-scattered-field?), but also any other comment of bibliographic reference will be of much help.
I do suggest Berenger’s PML Absorbing Boundary for such problem, that its specifications should be optimized to the medium of the problem space attached to the PML, This has been used on modelling ground penetrating radar when the ground attached to the PML.
you might want to look into uniaxial anisotropic perfectly matched layer (UPML) in view of the inhomogeneous truncated nature of your problem
I am not exactly familiar with such problems as you are facing, but if you cannot terminate your plasma just before the PML (so you need to extend to infinity an already lossy(?) medium) then I would lookin to a convolution-PML like described in : Microwave and Optical Technology letters, vol. 27, p 334 (2000) by Roden and Gedney. I have used it successfully to terminate dispersive metal/dielectric layers (that support surface plasmons) without reflections. It was not so obvious (at least to me) at first how to get appropriate maximum sigma/kappa values (how to write an algorithm to do that automatically based on the material inside the PML), but after some experimenting it worked.
Thank you all for your help! After discussions, we decided to follow the CPML technique.
Tomasz, my presentation of the problem is a little short, and I did not provide some details for your understanding... I have to clarify that the plasmas we study are collisionless in the parameter regime of interest, and the only mechanism of wave damping is cyclotron resonance absorption (some people refer to this as "electromagnetic Landau damping"). So, in most calculations, the plasma is not significantly lossy.
However, I am still worried about the second part of my question...
My implementation at the moment is based on the scattered field formalism, do you think this might create any inaccuracies for the case of a large scatterer? Is it possible that the total field formalism is more appropriate?
Unfortunately I have not used the scattered field formalism before but rather the other two that you mentioned, i.e. total field and TF/SF. I have used large scatterers with their size on the order of up to 5-8 wavelengths and did not have any problems aside from memory issues once in a while. The SF and TF/SF approaches are somewhat related and from what I remember Taflove (but probably other books as well) discuss these issues and can provide the answers in a clearer way, however, I do recall that under certain conditions (regions with low values of the total field) the TF/SF method has a wider dynamic range.
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