Vlasov-2D Configuration Reference

The vlasov-2d solver evolves the 2D2V Vlasov–Maxwell system

∂f/∂t + v·∇_x f + (q/m)(E + v × B)·∇_v f = C[f]
∂Ex/∂t =  c² ∂Bz/∂y − Jx
∂Ey/∂t = −c² ∂Bz/∂x − Jy
∂Bz/∂t = ∂Ex/∂y − ∂Ey/∂x

with f(x, y, vx, vy) on a periodic 2D box. Time stepping is Strang-split:

½ x-streaming (spectral) → ½ y-streaming (spectral)
Velocity push: ½ E_x → ½ E_y → full Bz-rotation (2D SL) → ½ E_y → ½ E_x
½ y-streaming → ½ x-streaming
Spectral Maxwell update with currents (Jx_self + Jx_driver, Jy_self + Jy_driver)
Collisions (Dougherty FP, Krook) and optional Hou–Li filter

Top-level keys

Key	Required	Description
`solver`	yes	Must be `vlasov-2d`.
`units`	yes	Plasma normalization.
`density`	yes	Density-component definitions.
`grid`	yes	Spatial and temporal grid.
`terms`	no	Time-integration & physics toggles.
`drivers`	no	External EM current drivers.
`save`	yes	Output / diagnostic save points.
`mlflow`	yes	Experiment name and run name.

`units`

units:
  laser_wavelength: 351nm    # optional
  normalizing_temperature: 2000eV
  normalizing_density: 1.5e21/cc

Sets n0, T0, v0 = √(T0/m_e), λ_D, ωp0. Lengths in the config are in Debye lengths, times in 1/ωp0, velocities in v0, fields normalized to m_e v0 ωp0 / e.

`grid`

grid:
  dt: 0.1
  nx: 32
  ny: 16
  nvx: 64
  nvy: 64
  tmin: 0.0
  tmax: 60.0
  vmax: 6.0
  xmin: 0.0
  xmax: 20.94
  ymin: -10.0
  ymax: 10.0
  parallel: false
  distribution-sharding:
    enabled: false
    mesh_axes: ["x"]
    mesh_shape: [1]
    partition: ["x", null, null, null]

dt will be capped to 0.5 * min(dx, dy) / c_norm whenever any EM driver is enabled (Maxwell CFL).

distribution-sharding enables distributed initialization of the global f(x, y, vx, vy) arrays. When enabled, the solver uses JAX make_array_from_callback to materialize each device’s shard directly instead of allocating the full distribution on the host first. The partition tuple is ordered as [x, y, vx, vy] and each entry must either be null or a name from mesh_axes.

For example, a two-dimensional spatial mesh over all visible devices can be configured as:

grid:
  distribution-sharding:
    enabled: true
    mesh_axes: ["x", "y"]
    mesh_shape: [4, 2]
    partition: ["x", "y", null, null]

If mesh_shape is omitted, all visible JAX devices are placed on the first mesh axis. Sharded initialization currently requires deterministic density profiles: set noise_type: none or noise_val: 0.0. The sharding helper also exposes a reshard primitive for future distributed FFT pushers to make a transform axis local before an exponential step.

`density`

Like the 1D solver, each species-<name> key under density describes one additive component that contributes a density profile and a bi-supergaussian in (vx, vy):

density:
  quasineutrality: true
  species-background:
    noise_type: gaussian       # uniform | gaussian | none
    noise_val: 0.0
    noise_seed: 420
    v0x: 0.0                   # drift in vx
    v0y: 0.0                   # drift in vy
    T0: 1.0                    # temperature
    m: 2.0                     # supergaussian order; 2 = Maxwellian
    basis: sine                # uniform | sine
    baseline: 1.0
    amplitude: 1.0e-3          # for `basis: sine`
    wavenumber-x: 0.3
    wavenumber-y: 0.0
    # Optional spatial masks (multiplied in):
    space-x: {center: 10.0, rise: 1.0, width: 1e6, baseline: 0.0, bump_height: 1.0}
    space-y: {center: 0.0,  rise: 1.0, width: 1e6, baseline: 0.0, bump_height: 1.0}

For multi-species runs add a terms.species list of explicit SpeciesConfig entries (name, charge, mass, vmax, nvx, nvy, density_components).

`terms`

terms:
  edfdv: exponential    # exponential | sl   (sl = 2D cubic interpolation)
  vdfdx: exponential    # exponential (only option)
  fokker_planck:
    is_on: false
    type: dougherty
    time:    {center: 0.0, rise: 1.0, width: 1e6, baseline: 0.0, bump_height: 1.0}
    space-x: {center: 0.0, rise: 1.0, width: 1e6, baseline: 0.0, bump_height: 1.0}
    space-y: {center: 0.0, rise: 1.0, width: 1e6, baseline: 0.0, bump_height: 1.0}
  krook:
    is_on: false
    time:    {...}      # same shape as fokker_planck
    space-x: {...}
    space-y: {...}
  hou_li_filter:
    is_on: false
    alpha: 36.0
    order: 36
    dimensions: ["x", "y", "vx", "vy"]

The Dougherty FP relaxes f toward a local Maxwellian centred at the local mean velocity, separable in vx then vy (Lie split). Conserves density, momentum, and energy along each axis exactly.
The Krook operator drags f toward n(x,y) · M(vx) · M(vy) with unit thermal speed.
The Hou–Li filter is separable; pick any subset of {x, y, vx, vy}.

`drivers`

External EM current sources. Each driver adds J = −w² · a0 · env(x, y, t) · sin(kx·x + ky·y − w·t) to either Jx or Jy:

drivers:
  ex: {}
  ey:
    "0":
      params: {a0: 1.0e-5, k0x: 0.0, k0y: 0.5, w0: 1.5, dw0: 0.0}
      envelope:
        time:    {center: 5.0, rise: 1.0, width: 30.0, baseline: 0.0, bump_height: 1.0}
        space-x: {center: 10.0, rise: 1.0, width: 1e6, baseline: 0.0, bump_height: 1.0}
        space-y: {center: 0.0,  rise: 1.0, width: 1e6, baseline: 0.0, bump_height: 1.0}
      polarization: y      # "x" or "y"

The driver source enters Maxwell as an additional current at time t + dt/2.

`save`

save:
  fields:
    t: {nt: 32}              # only {t} is supported for fields right now
  electron:
    snapshots:
      t:  {nt: 5}
      x:  {xmin: 0.0,  xmax: 20.94, nx: 16}
      y:  {ymin: -10.0, ymax: 10.0, ny: 8}
      vx: {vxmin: -6.0, vxmax: 6.0, nvx: 32}
      vy: {vymin: -6.0, vymax: 6.0, nvy: 32}

fields writes species moments (n, ux, uy, Txx, Tyy, T) plus shared fields (Ex, Ey, Bz, Jx_driver, Jy_driver).
Distribution saves under a species name accept either {t} (full resolution) or {t, x, y, vx, vy} (linear interpolation onto a coarser output grid). 4D output files are large; the coarse grid keeps things sane.

`mlflow`

mlflow:
  experiment: vlasov-2d-tests
  run: my-run-name

Example: 2D Landau damping

solver: vlasov-2d
units: {normalizing_temperature: 2000eV, normalizing_density: 1.5e21/cc}
density:
  quasineutrality: true
  species-background:
    v0x: 0.0
    v0y: 0.0
    T0: 1.0
    m: 2.0
    basis: sine
    baseline: 1.0
    amplitude: 1.0e-3
    wavenumber-x: 0.3
    wavenumber-y: 0.0
grid:
  dt: 0.1
  nx: 32
  ny: 16
  nvx: 64
  nvy: 64
  tmax: 60.0
  vmax: 6.0
  xmin: 0.0
  xmax: 20.94
  ymin: -10.0
  ymax: 10.0
terms: {edfdv: exponential, vdfdx: exponential}
drivers: {ex: {}, ey: {}}
save:
  fields: {t: {nt: 32}}
  electron:
    snapshots:
      t: {nt: 5}
mlflow: {experiment: vlasov-2d-tests, run: landau-damping}

A full template ships in configs/vlasov-2d/base.yaml.

Vlasov-2D Configuration Reference

Top-level keys

units

grid

density

terms

drivers

save

mlflow