Review and correct handling of is_closed_toroidal parameter in vacuum code

[jhalpern30]

Summary

Address issues and inconsistencies related to the is_closed_toroidal parameter in the vacuum code, as discussed in PR #126 ("Cleaning up kernel function").

Background

The recent refactoring of the kernel! function in the vacuum code (PR #126) highlighted questions and potential problems with the use and propagation of the is_closed_toroidal parameter. Ensuring this parameter is handled properly is essential for correct vacuum region modeling, especially as the code evolves.

Key Issues from PR #126 Discussion

1. Hard-coded value in kernel! function: Currently is_closed_toroidal = true is hard-coded in VacuumInternals. jl: 246, preventing the use of open toroidal walls even though the parameter exists in the WallGeometry struct.

2. Parameter not passed to kernel!: The WallGeometry struct has an is_closed_toroidal field (default true), but this value is never passed to the kernel! function where it's needed for residue calculations.

3. Residue calculation depends on wall type: The residue calculation uses different formulas for closed vs. open toroidal walls (Chance 1997 eq. 89 vs. eq. 90), but currently only the closed case is implemented.

4. Unclear support status: The discussion in PR Cleaning up kernel function #126 revealed uncertainty about whether open walls should be supported, with @logan-nc noting that "we only support closed toroidal walls" but the flag was left in to indicate where changes would be needed.

Relevant Code Locations

1. Hard-coded value in kernel! (VacuumInternals. jl: 244-257)

# Set residue based on logic similar to Table I of Chance 1997 + existing δⱼᵢ in eq. 69
# Would need to pass in wall geometry to generalize this to open walls
is_closed_toroidal = true

View code

2. Residue calculation using the parameter (VacuumInternals.jl:258-270)

if is_closed_toroidal
    residue = (j1 == 2.0) ? 0.0 : (j2 == 1 ? 2.0 : -2.0) # Chance eq. 89
else
    # TODO:  this line can be gotten rid of if we are never doing open walls
    residue = (j1 == j2) ? 2.0 : 0.0 # Chance eq. 90
end

View code

3. WallGeometry struct definition (VacuumStructs. jl:76-96)

@kwdef struct WallGeometry
    nowall::Bool = true
    is_closed_toroidal::Bool = true
    x::Vector{Float64} = Float64[]
    z::Vector{Float64} = Float64[]
    dx_dtheta::Vector{Float64} = Float64[]
    dz_dtheta::Vector{Float64} = Float64[]
end

View code

4. Usage in Vacuum.jl (line 267)

(abs(n) <= 1e-5 && !wall.nowall && wall.is_closed_toroidal) && begin
    @warn "Adding $cn0 to diagonal of grdgre to regularize n=0 mode; this may affect accuracy of results."
    ... 
end

View code

5. Equal arc length check (VacuumStructs. jl:336-353)

if wall_settings.equal_arc_wall && (wall_settings.shape != "nowall")
    @info "Re-distributing wall points to equal arc length spacing"
    if ! is_closed_toroidal
        @error "Wall is not closed toroidally; equal arc length distribution assumes periodicity and cannot be safely used."
    end
    ... 
end

View code

Proposed Solutions

Based on the PR #126 discussion, choose one of:

Option A: Remove support for open walls entirely

• Remove is_closed_toroidal field from WallGeometry struct
• Remove the else branch in the residue calculation
• Add clear documentation stating only closed toroidal walls are supported
• Update docstrings for kernel! and wall initialization functions

Option B: Properly implement open wall support

• Pass wall. is_closed_toroidal to kernel! function
• Remove hard-coded is_closed_toroidal = true line
• Verify residue calculations for open walls (Chance 1997 eq. 90)
• Add tests for open wall cases
• Handle zero-crossing detection properly for open walls

Tasks

• Decide on Option A or B based on current and future use cases
• If Option A: Remove is_closed_toroidal parameter and simplify code
• If Option B: Pass parameter correctly and verify all calculations
• Update documentation (docstrings and web docs) to clearly state wall support
• Add or update tests covering the chosen approach
• Remove TODO comment once resolved

References

• PR Cleaning up kernel function #126 discussion: Cleaning up kernel function #126
• Relevant comments: #126 (comment), #126 (comment)
• Chance 1997 equations: eq. 89 (closed walls), eq. 90 (open walls)
• More search results for is_closed_toroidal