Generalize PIC deposition to arbitrary B-spline order

[mochell]

Goal

Replace the hard-coded linear (CIC, order 1) particle→grid weighting with a B-spline order P = 1, 2, 3, … selectable at model setup, to reduce grid-imprint anisotropy (cardinal-axis spikes) and grid-scale noise seen in the dx30_dy10 ring test.

Why this is safe (conservation)

The 2D deposit is purely additive (grid[...,:] += wx*wy*charge), and B-spline weights of any order satisfy partition of unity (Σw=1), so total energy/momentum are conserved exactly independent of P.

Plan

• Edit src/ParticleInCell.jl: add order-dispatched bspline_stencil, update get_absolute_i_and_w, compute_weights_and_index_mininal, construct_loop (3 functions)
• Edit src/Operators/mapping_2D.jl: thread order through both ParticleToNode! methods
• Add spline_order::Int = 1 config field (location TBD: model config vs grid struct)
• wni struct and push_to_grid! need no changes

Gotchas

• Higher order needs wider halo (order 2 → ±1, order 3 → −1..+2); non-periodic boundaries need extra ghost layers
• Cost scales as (P+1)² per particle (4/9/16 for P=1/2/3)
• Convert Int→Val at a function barrier (outside hot loop) to avoid dynamic dispatch
• Even orders center on round(z), odd on floor(z) — ensure normalized grid units

Validation checklist

• test/unit/test_pic_2d_propagation_energy_conservation.jl passes for P=1,2,3
• P=1 output bit-identical to current (regression guard)
• Re-run dx30_dy10 ring for P=1,2,3 — cardinal spikes should weaken, ring isotropize
• Check non-periodic boundary case for edge energy leakage
• Benchmark wall-time vs P (~(P+1)² scaling)

Reference files

• src/ParticleInCell.jl
• src/Operators/mapping_2D.jl
• src/Operators/core_2D.jl
• src/custom_structures.jl
• test/unit/test_pic_2d_propagation_energy_conservation.jl

Follow-up (separate)

The ring's energy growth (188→376) is not a deposition issue — investigate GetVariablesAtVertex log/ratio reconstruction as a Jensen-bias source, and consider an isotropic binomial filter on deposited fields at remesh as a complementary mitigation.