Initializing the self field while using PSATD in a PWFA simulation

[michaelquin]

I’m running a PWFA simulation in RZ geometry.

Numerical dispersion is an issue here so I’m using the PSATD solver with the following boundary conditions:

boundary.field_hi = none damped
boundary.field_lo = none damped

The initial simulations ran more or less as expected, but there are some odd perturbations for the fields (E, rho) inside the driver beam and elsewhere. So, I’d like to repeat this with the self field properly initialized.

My first attempt was to add the following lines to the input file:

warpx.poisson_solver = fft
warpx.use_2d_slices_fft_solver = 1
beam.initialize_self_fields = 1

which throws up the following error:

ERROR : The FFT Poisson solver only works in 3D

This error is a bit confusing:

The documentation suggests that FFT Poisson is implemented for RZ (see warpx.use_2d_slices_fft_solver = 1). It also says that I should be using PML boundaries for the fields – but as far as I’m aware that hasn’t been implemented for PSATD yet.

Also, I’m working under the impression that warpx.poisson_solver = multigrid is just for electrostatic mode, but do correct me if I’m wrong. It seems to require PEC boundary conditions for the fields, which seems to conflict with my need to use PSATD, and isn't really suitable for this simulation anyway.

[RemiLehe]

Thanks for your question and for your interest in WarpX.

Here are a few answers:

• Regarding using the FFT Poisson solver: this solver is indeed incompatible with cylindrical / RZ geometry (which I assume is what you meant by "quasi-3D") and only works in Cartesian geometry (use_2d_slices_fft_solver still only works in Cartesian geometry). As a side note, PML have been implemented with PSATD in WarpX, but only to aborb waves at the outer radial boundary: Implement PML for the outer RZ boundary with PSATD #2211

• As far as I know, multigrid would be the only option for you. It is electrostatic **in the beam rest frame (when using e.g. beam.initialize_self_fields = 1), so it would be fine in your case from the physics point of view. However, it is true that finding boundary conditions that work both for the initial Poisson solver and the PSATD solver may not be possible. In the future, we are planning to have an interface to specify different boundary conditions for the initial Poisson solver and the subsequent Maxwell solver.

In the meantime, you could change your local version of WarpX, to make the Poisson solver less strict about the type of boundary conditions that it accepts (so that it would run without error, when you use the "none" boundary condition): see this for an example of how to modify the code: https://github.com/BLAST-WarpX/warpx/pull/2514/files

[michaelquin]

Thanks for the advice, Remi.

Just to clarify, I’m using RZ geometry.

It turns out my original problem was easy to solve; the radius of the box was too small.

Apparently the density of the driver near r_max was too high, which created strange fields inside the box. Changing r_max=2σ to r_max=3σ solved the problem, where σ is the transverse standard deviation of the driver, of peak density 10^19 particles/cm^3.

About the self-field initialization:

I did modify PoissonBoundaryHandler.cpp to use Dirichlet boundary conditions at r_max, z_min and z_max with the Poisson solver.

Here I hit an error “RZ electrostatic only implemented for a single mode” in RelativisticExplicitES.cpp. Is there a work around for this?

WarpX did run with one azimuthal mode – and at first glance the initial field of the driver was as expected.

Although, the purpose of these simulations is to study photon acceleration of a laser pulse situated in the wake. I think two azimuthal modes is the bare minimum I need.