Update PIC algorithm docu

[fabidie]

A more detailed description of the PIC algorithm. Let me know whether it is more comprehensive now and if you want to add any information.

[steindev]

Just a few comments, mainly misspelled markup.
You can also check the preview yourself at (https://picongpu--5251.org.readthedocs.build/en/5251/models/AOFDTD.html#model-aofdtd)

[chillenzer]

Haven't read through it yet, I'll have a closer look when the rendering issues are fixed. But as a general direction, we might want to add pictures like the two attached. Both are from the PIConGPU part of the alpaka workshop in October.

Simple idealistic PIC cycle:

Actual implementation (probably less pertinent here):

[steindev]

@chillenzer the second (larger) picture is great and fits nicely at the end of @fabidie's new text. We, i.e. you, would just need to update the "current update" step. It should display the continuity equation in differential form and not the current formula. In detail, $\vec v$ and $f$ are known at different times in the simulation (they are displaced by half a time step), and thus the currently printed equation for the computation of $J$ is inconsistent and leads to violation of charge conservation.

[finnolec]

It reads well and I especially like the "blob" for macroparticles.

[finnolec]

If the picture from @chillenzer is added we might also want to include documentation for the moving window somewhere in the documentation, but this doesn't belong into the PIC algorithm.

[BrianMarre]

and close Issue #5056

[steindev]

Only one missing colon (for correct rendering)...Otherwise I'm good.

[chillenzer]

If nobody insists, I promised @steindev to merge this once everything renders correctly.

As discussed with @steindev

[chillenzer]

Renders fine and @steindev said it's good content-wise.