Vacuum Examples

This page demonstrates the usage of the Vacuum module for magnetostatic calculations.

Basic Vacuum Field Calculation

Setting up DCON Parameters

The vacuum module requires initialization with DCON (Displacement CONtinuum) parameters:

using JPEC

# Define DCON parameters
mthin = Int32(4)     # Number of theta points
lmin = Int32(1)      # Minimum poloidal mode number
lmax = Int32(4)      # Maximum poloidal mode number
nnin = Int32(2)      # Toroidal mode number
qa1in = 1.23         # Safety factor parameter

# Create geometry arrays
n_modes = lmax - lmin + 1
xin = rand(Float64, n_modes)      # Radial coordinates
zin = rand(Float64, n_modes)      # Vertical coordinates  
deltain = rand(Float64, n_modes)  # Displacement data

# Initialize DCON interface
JPEC.VacuumMod.set_dcon_params(mthin, lmin, lmax, nnin, qa1in, xin, zin, deltain)

Vacuum Matrix Calculation

# Set up vacuum calculation parameters
mpert = 5              # Number of perturbation modes
mtheta = 256           # Number of theta points for plasma
mthvac = 256           # Number of theta points for vacuum

# Initialize result matrix
wv = zeros(ComplexF64, mpert, mpert)

# Calculation flags
complex_flag = true     # Use complex arithmetic
kernelsignin = -1.0    # Kernel sign 
wall_flag = false      # Include wall effects
farwal_flag = true     # Far wall approximation

# Geometry and source data
grrio = rand(Float64, 2*(mthvac+5), mpert*2)  # Geometry data
xzptso = rand(Float64, mthvac+5, 4)           # Source points

# Perform vacuum matrix calculation
JPEC.VacuumMod.mscvac(
    wv, mpert, mtheta, mthvac,
    complex_flag, kernelsignin,
    wall_flag, farwal_flag,
    grrio, xzptso
)

println("Vacuum matrix calculation completed")
println("Result matrix dimensions: ", size(wv))

Analyzing Results

using Plots

# Plot magnitude of vacuum matrix elements
heatmap(abs.(wv), 
        title="Vacuum Matrix |W| Elements",
        xlabel="Mode j", 
        ylabel="Mode i",
        color=:plasma)

# Plot phase information
heatmap(angle.(wv), 
        title="Vacuum Matrix Phase",
        xlabel="Mode j",
        ylabel="Mode i", 
        color=:phase)

Advanced Usage

Including Wall Effects

# Enable wall calculations
wall_flag = true
farwal_flag = false  # Do not use far wall approximation

# Additional wall parameters might be needed
# (specific implementation depends on geometry)

JPEC.VacuumMod.mscvac(
    wv, mpert, mtheta, mthvac,
    complex_flag, kernelsignin,
    wall_flag, farwal_flag,
    grrio, xzptso
)

Multi-mode Analysis

# Analyze eigenvalues of vacuum matrix
using LinearAlgebra

eigenvals = eigvals(wv)
eigenvecs = eigvecs(wv)

# Plot eigenvalue spectrum
scatter(real.(eigenvals), imag.(eigenvals),
        title="Vacuum Matrix Eigenvalues",
        xlabel="Real part",
        ylabel="Imaginary part",
        legend=false)

# Identify most unstable mode
max_growth_idx = argmax(imag.(eigenvals))
println("Most unstable eigenvalue: ", eigenvals[max_growth_idx])

Coupling with Equilibrium Data

# This example shows how vacuum calculations integrate with equilibrium

# 1. Set up equilibrium (using spline example from equilibrium page)
# ... equilibrium setup code ...

# 2. Extract boundary data for vacuum calculation
# boundary_data = extract_boundary(psi_spline, flux_surface)

# 3. Convert to DCON format
# xin, zin, deltain = process_boundary_data(boundary_data)

# 4. Perform vacuum calculation
# JPEC.VacuumMod.set_dcon_params(mthin, lmin, lmax, nnin, qa1in, xin, zin, deltain)
# ... vacuum calculation ...

# 5. Analyze stability
# stability_analysis(wv, eigenvals)

Troubleshooting

Common Issues

1. Initialization Error: Ensure set_dcon_params is called before mscvac
2. Memory Issues: Large mtheta/mthvac values require significant memory
3. Convergence: Check that geometry arrays are properly normalized
4. Complex Arithmetic: Ensure complex_flag=true for stability analysis

Performance Optimization

# For large problems, consider:
# - Reducing mtheta/mthvac if possible
# - Using real arithmetic (complex_flag=false) when appropriate  
# - Parallelization (if available in Fortran backend)

# Monitor memory usage
using Pkg
Pkg.add("BenchmarkTools")
using BenchmarkTools

@time JPEC.VacuumMod.mscvac(wv, mpert, mtheta, mthvac, 
                           complex_flag, kernelsignin,
                           wall_flag, farwal_flag,
                           grrio, xzptso)