Finite-image periodic2 configuration

This page is the canonical periodic2 setup for studying regolith charging and photoelectron surface redistribution with a boundary reservoir + closed PE. The solar-wind VDF is defined at z-high, only photoelectrons are closed, and potential is read relative to the z-high plane mean. This baseline does not enable a matching-plane outer-sheath closure.

Distinguish the two configurations first

Configuration	Solar-wind inflow	Photoelectrons	Potential reference	Use
Boundary reservoir + closed PE	uncorrected VDF at z-high	z-high reflection + neutral_return	z-high plane mean	baseline on this page; surface redistribution and batch sensitivity
Scalar barrier	infinity_barrier	common potential_barrier	phi_infty	comparison using one scalar barrier

Do not stack these alternatives in one run. In particular, do not add infinity_barrier or potential_barrier to the closed-PE baseline.

Recommended integrated configuration

The complete runnable example is examples/periodic2_closed_photoelectron.toml.

[sim]
field_solver = "fmm"
field_periodic_image_layers = 1
field_periodic_far_correction = "none"

[domain]
box_origin = [0.0, 0.0, 0.0]
box_size = [1.0e-4, 1.0e-4, 1.0e-3]
periodic_axes = ["x", "y"]

[field_boundary]
mode = "periodic2"

[particle_boundary]
z_low = "open"
z_high = "open"
ordinary_open_model = "escape"

[reservoir]
inflow_model = "source_vdf"
face_potential_grid_n = 5

[domain] owns the cell and periodic topology; [field_boundary] owns field closure. The current periodic2 mode accepts only periodic_axes=["x", "y"] with a nonperiodic z axis. Periodicity is common to all species and cannot be overridden by a species or [particle_boundary]. The former [external_boundary] table has been removed. Configure external-reservoir conditions in [reservoir], per-species inflow faces in [particles.species.boundary_inflow], and outward particle actions on nonperiodic faces in [particle_boundary].

Use boundary_inflow="reservoir" on z-high for solar-wind electrons and ions. Density, temperature, and drift describe a local boundary VDF on z-high; surface potential does not filter accessibility or map speed.

Only the photoelectron species gets the closed surface-charge closure:

[[particles.species]]
species_key = "photoelectron"
source_mode = "photo_raycast"
deposit_opposite_charge_on_emit = true
surface_charge_closure = "neutral_return"

[particles.species.boundary]
z_high = "reflect"

The species-level z_high="reflect" reverses only normal velocity at nonperiodic z-high. Solar-wind species retain "inherit" and follow particle_boundary.z_high="open" with ordinary_open_model="escape".

This baseline preserves the in-plane position of the boundary event. For a sensitivity comparison that uniformly redistributes return positions over the x-y plane, replace it with z_high="redistributed_reflect". The velocity action is unchanged; only position is resampled. This is an alternative return-destination model for closed PE, not a self-consistent sheath. See Photoelectron emission and lifecycle for context and simultaneous-event rules.

What one batch does

1. Build a finite-image field snapshot from batch-start surface charge.
2. Inject solar wind from the z-high local VDF and photoelectrons from ray hits.
3. Track all particles in the frozen snapshot, reflecting only photoelectrons at z-high.
4. Close unresolved photoelectrons from the resolved return distribution and commit all charge deltas.
5. Optionally write element potential and z-high mean from the same post-commit charge.

The field is not refreshed inside a batch. batch_duration is therefore both physical duration and explicit charge-update width. Closed PE removes divergence from net photoelectron current; it does not remove solar-wind batch-width dependence. ¹

Quantity closed by neutral_return

For a negative photoelectron species, define signed macro charge within one batch:

$$S=\sum_{\mathrm{emitted}}qw<0,\qquad R=\sum_{\mathrm{resolved\ absorption}}qw<0.$$

neutral_return multiplies deposits at measured return destinations by

$$s_{\mathrm{return}}=\frac{S}{R}.$$

The source reaction charge is $-S$, hence

$$(-S)+s_{\mathrm{return}}R=0.$$

This species does not change total surface charge; it only builds a distribution from emission sources to resolved return destinations. Solar-wind net charge remains unconstrained.

The statistical assumption is that unresolved particles have the same return-destination distribution as particles resolved in the same batch. When s_return differs substantially from one, the closure assumption rather than resolved orbits controls the local distribution. This fixed contract closes only a small long-lived population. BEACH stops without correction when the unresolved fraction exceeds 5%. The limit is not configurable; converge below it by revisiting max_step, dt, and box height.

neutral_return does not mathematically remove every $k_\parallel=0$ structure. It makes the surface-charge monopole increment zero, but transfer between surfaces at different heights can retain a plane-averaged vertical dipole.

The batch is rejected when:

• emission is nonzero but resolved return charge is zero;
• a photoelectron actually escapes or is soft_discarded;
• a nonfinite value or charge-sign mismatch occurs.

Only particles still alive at max_step are statistically closed. The raw unresolved charge, correction, scale, and unresolved fraction remain separate in charge_ledger.csv.

Read potential relative to the z-high plane

With [domain], output.write_files=true, output.write_potential_history=true, and output.history_stride>0, top_reference_history.csv is written at the same batches as potential_history.csv.

$$\bar\phi_{\mathrm{top}} =\frac{1}{N^2}\sum_{a,b}\phi(x_a,y_b,z_{\mathrm{high}}^-),\qquad \phi_{\mathrm{rel}}(\mathbf r)=\phi(\mathbf r)-\bar\phi_{\mathrm{top}}.$$

$N$ is reservoir.face_potential_grid_n, and the samples are cell centered across the full periodic top face. Join the two histories on batch and subtract potential_mean_V from element potential_V at that same batch.

[output]
history_stride = 1000
write_mesh_potential = true
write_potential_history = true

The plane mean is neither infinity potential nor plasma potential, and it does not feed back into solar-wind injection. It removes a constant gauge but not dependence on box height, zero mode, or finite-image truncation. A large potential_std_V or min/max span weakens the interpretation of z-high as one reservoir plane.

With either write_mesh_potential=true or write_potential_history=true, summary.txt also records top statistics for the final state. Use those values to reference final mesh_potential.csv. If the final batch is not on the history stride, do not reuse a top value from another batch.

Meaning of finite images

field_periodic_image_layers=N adds source cells through shell $N$ around the primary cell.

$N$	Cells included
0	primary only, $1\times1$
1	one surrounding shell, $3\times3$
2	two surrounding shells, $5\times5$

With field_periodic_far_correction="none", BEACH does not replace cells beyond that shell with an Ewald or cached operator. Top-relative potential does not turn this into an infinite-periodic solution. Increase image layers until target quantities stop changing. Use field_periodic_far_correction="cached_kneq0" when the infinite-periodic nonzero mode is required, and follow the convergence procedure in periodic2 electrostatics.

Acceptance order

1. Check that abs(neutral_return_weight_scale-1) and neutral_return_unresolved_fraction are small.
2. When reducing dt, maintain or increase max_step*dt; also increase rays_per_batch to converge the return distribution.
3. Vary batch_duration by at least $T,T/2,T/4$ and compare charge, relative potential, and force histories.
4. Move z-high and increase reservoir.face_potential_grid_n to check top mean and variation.
5. Increase image shells through $N,N+1,N+2$.
6. Check solar-wind macro-particle count and random-seed uncertainty. With redistributed_reflect, also vary particle count and seed for the additional return-position sampling.

Full reflection is an artificial top mirror, not a self-consistent sheath or quasineutral solution. The result describes surface redistribution with zero net photoelectron current under the specified boundary solar-wind flux.

Scalar-barrier comparison

For a scalar-barrier comparison, remove the closed-PE settings and combine reservoir.inflow_model="infinity_barrier", reservoir.phi_infty, and particle_boundary.ordinary_open_model="potential_barrier". This comparison filters an upstream VDF with a face-average scalar and classifies reflection or escape from energy at each open crossing. See boundary inflow and particle escape and return for configuration, equations, and constraints.