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Flux surfaces mxh #193

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Flux surfaces mxh #193

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53 changes: 30 additions & 23 deletions src/physics/fluxsurfaces.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -937,20 +937,13 @@ function flux_surfaces(eqt::equilibrium__time_slice{T}; upsample_factor::Int=1)
FLUXEXPANSION = Vector{T}[]
INT_FLUXEXPANSION_DL = zeros(T, length(eqt.profiles_1d.psi))
BPL = zeros(T, length(eqt.profiles_1d.psi))
mxh = MXH(0.0, 0.0, 0.0, 0.0, 0.0, zeros(2), zeros(2))
for k in length(eqt.profiles_1d.psi):-1:1
psi_level = eqt.profiles_1d.psi[k]

if k == 1 # on axis flux surface is a synthetic one
eqt.profiles_1d.elongation[1] = eqt.profiles_1d.elongation[2] - (eqt.profiles_1d.elongation[3] - eqt.profiles_1d.elongation[2])
eqt.profiles_1d.triangularity_upper[1] = 0.0
eqt.profiles_1d.triangularity_lower[1] = 0.0

a = (eqt.profiles_1d.r_outboard[2] - eqt.profiles_1d.r_inboard[2]) / 100.0
b = eqt.profiles_1d.elongation[1] * a

t = range(0, 2π, 17)
pr = cos.(t) .* a .+ RA
pz = sin.(t) .* b .+ ZA
mxh.ϵ *= 0.1
pr, pz = mxh()

# Extrema on array indices
(imaxr, iminr, imaxz, iminz, r_at_max_z, max_z, r_at_min_z, min_z, z_at_max_r, max_r, z_at_min_r, min_r) = fluxsurface_extrema(pr, pz)
Expand All @@ -959,10 +952,10 @@ function flux_surfaces(eqt::equilibrium__time_slice{T}; upsample_factor::Int=1)
# trace flux surface
tmp = flux_surface( r, z, PSI, RA, ZA, fw.r, fw.z, psi_level, :closed)
if isempty(tmp)
# p = heatmap(r, z, PSI'; colorbar=true, aspect_ratio=:equal)
# contour!(r, z, PSI'; color=:white, levels=100)
# contour!(r, z, PSI'; levels=[eqt.profiles_1d.psi[end]], color=:white, lw=2)
# display(p)
p = heatmap(r, z, PSI'; colorbar=true, aspect_ratio=:equal)
contour!(r, z, PSI'; color=:white, levels=100)
contour!(r, z, PSI'; levels=[eqt.profiles_1d.psi[end]], color=:white, lw=2)
display(p)
error("IMAS: Could not trace closed flux surface $k out of $(length(eqt.profiles_1d.psi)) at ψ = $(psi_level)")
end
(pr, pz) = tmp[1]
Expand Down Expand Up @@ -1013,15 +1006,19 @@ function flux_surfaces(eqt::equilibrium__time_slice{T}; upsample_factor::Int=1)
eqt.profiles_1d.r_outboard[k] = max_r
eqt.profiles_1d.r_inboard[k] = min_r

# miller geometric coefficients
_, _, κ, δu, δl, ζou, ζol, ζil, ζiu = miller_R_a_κ_δ_ζ(pr, pz, r_at_max_z, max_z, r_at_min_z, min_z, z_at_max_r, max_r, z_at_min_r, min_r)
# miller geometric coefficients (from MXH, for accuracy)
_, _, κ, δu, δl = miller_R_a_κ_δ(r_at_max_z, max_z, r_at_min_z, min_z, z_at_max_r, max_r, z_at_min_r, min_r)
MXH!(mxh, pr, pz; rmin = min_r, rmax = max_r, zmin = min_z, zmax = max_z)
κ = mxh.κ
δ = sin(mxh.s[1])
ζ = -mxh.s[2]
eqt.profiles_1d.elongation[k] = κ
eqt.profiles_1d.triangularity_upper[k] = δu
eqt.profiles_1d.triangularity_lower[k] = δl
eqt.profiles_1d.squareness_lower_outer[k] = ζol
eqt.profiles_1d.squareness_upper_outer[k] = ζou
eqt.profiles_1d.squareness_lower_inner[k] = ζil
eqt.profiles_1d.squareness_upper_inner[k] = ζiu
eqt.profiles_1d.squareness_lower_outer[k] = ζ
eqt.profiles_1d.squareness_upper_outer[k] = ζ
eqt.profiles_1d.squareness_lower_inner[k] = ζ
eqt.profiles_1d.squareness_upper_inner[k] = ζ

# poloidal magnetic field (with sign)
Br, Bz = Br_Bz(PSI_interpolant, pr, pz)
Expand Down Expand Up @@ -1497,17 +1494,27 @@ function x_points_inside_wall(x_points::IDSvector{T}, wall::IMAS.wall) where {T<
end

"""
miller_R_a_κ_δ_ζ(pr, pz, r_at_max_z, max_z, r_at_min_z, min_z, z_at_max_r, max_r, z_at_min_r, min_r)
miller_R_a_κ_δ(r_at_max_z, max_z, r_at_min_z, min_z, z_at_max_r, max_r, z_at_min_r, min_r)

Returns R0, a, κ, δu, δl, ζou, ζol, ζil, ζiu of a contour
Returns R0, a, κ, δu, δl given extrema
"""
function miller_R_a_κ_δ_ζ(pr::Vector{T}, pz::Vector{T}, r_at_max_z::T, max_z::T, r_at_min_z::T, min_z::T, z_at_max_r::T, max_r::T, z_at_min_r::T, min_r::T) where {T<:Real}
function miller_R_a_κ_δ(r_at_max_z::T, max_z::T, r_at_min_z::T, min_z::T, z_at_max_r::T, max_r::T, z_at_min_r::T, min_r::T) where {T<:Real}
R0 = 0.5 * (max_r + min_r)
a = 0.5 * (max_r - min_r)
b = 0.5 * (max_z - min_z)
κ = b / a
δu = (R0 - r_at_max_z) / a
δl = (R0 - r_at_min_z) / a
return R0, a, κ, δu, δl
end

"""
miller_R_a_κ_δ_ζ(pr, pz, r_at_max_z, max_z, r_at_min_z, min_z, z_at_max_r, max_r, z_at_min_r, min_r)

Returns R0, a, κ, δu, δl, ζou, ζol, ζil, ζiu of a contour
"""
function miller_R_a_κ_δ_ζ(pr::Vector{T}, pz::Vector{T}, r_at_max_z::T, max_z::T, r_at_min_z::T, min_z::T, z_at_max_r::T, max_r::T, z_at_min_r::T, min_r::T) where {T<:Real}
R0, a, κ, δu, δl = miller_R_a_κ_δ(r_at_max_z, max_z, r_at_min_z, min_z, z_at_max_r, max_r, z_at_min_r, min_r)
ζou, ζol, ζil, ζiu = luce_squareness(pr, pz, r_at_max_z, max_z, r_at_min_z, min_z, z_at_max_r, max_r, z_at_min_r, min_r)
return R0, a, κ, δu, δl, ζou, ζol, ζil, ζiu
end
Expand Down