Estimating the charge in a 2D simulation.

[caeruleus01]

Hello everyone.

I encountered the following issue. In doing 2D simulations for LWFA, I have to measure the charge of the electron injected bunch. We developed a code in Python that extracts data from SDF and we obtained values for this charge of the order -1e-8C, obtained by multiplying the electron's charge with the sum of weights in that area (excluding also background).

Still, I think this is quite large. My question is, is this a charge per distance quantity C/m actually? Should I further multiply by a third dimension and obtain a charge of the order 1e-13C or 10e-13C? Is there some gauge for such a third dimension?

Thank you.

[DanRRRR]

In 2D third dimension is infinite or set to some value (1m in case of EPOCH). So it is not trivial to tell exactly what are the parameters of what in real life was 3D. You can only estimate that. Another solution is to do 2D simulation in r-z coordinates. Some PIC codes can do that.

[caeruleus01]

So, for example, if i multiply this value (e times the sum of weights) with a third dimension equal to the vertical one, would this be correct? it would mean multiplication by some tens of microns and may be closer to pC values. And still i'm not sure if the weight in 2d in m^-1 or adimensional. Anyway, thank you.

[TomGoffrey]

As I think you've worked out, this large value is due to the assumption that the grid size in the 3rd dimension, dz, is equal to 1.

To convert to a more physical estimate, you should apply a scaling to the 2D value. One option would be to scale by the ratio of the true laser energy you wish to simulate to the 2D laser energy, which will also be abnormally large due to the dz=1.0 assumption.

Another option would be to use the focal spot size, as suggested in #728.

[caeruleus01]

From what i understand, i have to basically establish a gauge for this. And probably there is no standard quantity here except for the third dimension 1m. I would probably multiply by the transversal dimension of the box, which is symmetric, and would be a quantity of order of microns. Still, it feels a bit arbitrary and there should be a more accurate method... Also, thanks for answear.

[TomGoffrey]

There's certainly no definitive answer, no. The only real answer is to do the simulations in 3D, which is often prohibitively expensive. A possible intermediate option would be to carry out some low resolution 2D and 3D simulations, and see if you can infer any scaling and/or test my previous suggestions. Of course, you have no guarantee that the scaling will hold for high resolution.