https://github.com/ProjectTorreyPines/MXHEquilibrium.jl
Equilibrium.jl with MXH (Miller Extended Harmonics) support
https://github.com/ProjectTorreyPines/MXHEquilibrium.jl
Last synced: 8 days ago
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Equilibrium.jl with MXH (Miller Extended Harmonics) support
- Host: GitHub
- URL: https://github.com/ProjectTorreyPines/MXHEquilibrium.jl
- Owner: ProjectTorreyPines
- License: apache-2.0
- Created: 2022-11-22T04:18:48.000Z (over 2 years ago)
- Default Branch: master
- Last Pushed: 2025-05-21T19:48:25.000Z (about 1 month ago)
- Last Synced: 2025-06-16T02:46:13.626Z (11 days ago)
- Language: Julia
- Homepage: https://projecttorreypines.github.io/MXHEquilibrium.jl/dev
- Size: 804 KB
- Stars: 0
- Watchers: 10
- Forks: 1
- Open Issues: 8
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
- awesome-ml-in-plasma-physics - MXHEquilibrium.jl - MHD equilibrium solver in Julia (Tools / Simulation and Modeling Frameworks)
- awesome-ml-in-plasma-physics - MXHEquilibrium.jl - MHD equilibrium solver in Julia (Tools / Simulation and Modeling Frameworks)
README
# MXHEquilibrium.jl
MXHEquilibrium.jl is a fork of Equilibrium.jl and provides functionality for Miller Extended Harmonic fitting.
## AbstractEquilibrium API
```julia
using MXHEquilibrium
typeof(S) <: AbstractEquilibrium
psi = S(r, z) # Poloidal flux at r,z
gradpsi = psi_gradient(S, r, z)
B = Bfield(S, r, z)
Bp = poloidal_Bfield(S, r, z)
J = Jfield(S, r, z)
Jp = poloidal_Jfield(S, r, z)
F = poloidal_current(S, psi)
Fprime = poloidal_current_gradient(S, psi)
p = pressure(S, psi)
pprime = pressure_gradient(S, psi)
V = electric_potential(S, psi)
gradV = electric_potential_gradient(S, psi)
q = safety_factor(S, psi)
maxis = magnetic_axis(S)
btip = B0Ip_sign(S)
rlims, zlims = limits(S)
psi_lims = psi_limits(S)
cc = cocos(S) # Return COCOS structure
fs = flux_surface(S, psi) # returns a boundary object
```
## Solov'ev Equilibrium
Solov'ev Equilibrium are analytic solutions to the Grad-Shafranov equation where the p' and FF' are constant.
The resulting Grad-Shafranov equation takes the form `Δ⋆ψ = α + (1-α)x²` where `α` is some constant.
The boundary conditions are found using a plasma shape parameterization.
```julia
# ITER parameters
δ = 0.33 # Triangularity
ϵ = 0.32 # Inverse aspect ratio a/R0
κ = 1.7 # Elongation
B0 = 5.3 # Magnitude of Toroidal field at R0 [T]
R0 = 6.2 # Major Radius [m]
Z0 = 0.0 # Elevation
qstar = 1.57 # Kink safety factor
alpha = -0.155 # constant
S = solovev(B0, MillerShape(R0, Z0, ϵ, κ, δ), alpha, qstar, B0_dir=1, Ip_dir=1)
SolovevEquilibrium
B0 = 2.0 [T]
S = MillerShape{Float64}(6.2, 0.0, 0.32, 1.7, 0.33)
α = -0.155
q⋆ = 1.57
βp = 1.1837605469381924
βt = 0.049177281028224634
σ = 1
diverted = false
symmetric = true
```
## EFIT Equilibrium
EFIT geqdsk files are a commonly used file format.
Here we provide routines for converting the GEQDSK files into an Equilibrium object.
```julia
using EFIT
g = readg("g000001.01000")
M = efit(g, clockwise_phi=false) # direction of phi needed to determine COCOS ID
wall = Wall(g)
in_vessel(wall, r, z)
# or
# M, wall = read_geqdsk("g000001.01000",clockwise_phi=false)
```
## COCOS: Tokamak Coordinate Conventions
We provide routines for working determining, transforming, and checking COCOS's.
```julia
julia> cocos(3)
COCOS = 3
e_Bp = 0
σ_Bp = -1
σ_RΦZ = (R,Φ,Z): 1
σ_ρθΦ = (ρ,Φ,θ): -1
Φ from top: CCW
θ from front: CCW
ψ_ref: Decreasing assuming +Ip, +B0
sign(q) = -1 assuming +Ip, +B0
sign(p') = 1 assuming +Ip, +B0
julia> transform_cocos(3,1)
Dict{Any, Any} with 14 entries:
"Z" => 1.0
"Q" => -1
"P" => 1.0
"B" => 1.0
"F_FPRIME" => -1.0
"ψ" => -1.0
"TOR" => 1.0
"Φ" => 1.0
"PSI" => -1.0
"I" => 1.0
"J" => 1.0
"R" => 1.0
"F" => 1.0
"PPRIME" => -1.0
```
## Boundaries
MXHEquilibrium.jl also provides routines for working with boundries such as walls or flux surfaces. Internally boundaries are stored as a list of points forming a polygon.
```julia
fs = flux_surface(S, psi)
in_plasma(fs, r, z) # or in_vessel(fs, r, z), in_boundary(fs, r, z)
cicumference(fs)
area(fs) # Area enclosed by the boundary
volume(fs) # assuming toroidal symmetry. F can be a vector with the same length as fs or a function of (r,z)
average(fs, F) # Average F over the boundary
area_average(fs, F) # average F over the area
volume_average(fs, F) # average F over the volume
```
## Parameterized Plasma Shapes
MXHEquilibrium.jl provides the commonly used plasma shape parameterizations.
```julia
help?> MillerShape # alias = MShape
MillerShape Structure
Defines the Miller Plasma Shape Parameterization
Fields:
R0 - Major Radius [m]
Z0 - Elevation [m]
ϵ - Inverse Aspect Ratio a/R0 where a = minor radius
κ - Elongation
δ - Triangularity
help?> TurnbullMillerShape # alias = TMShape
TurnbullMillerShape Structure
Defines the Turnbull-Miller Plasma Shape Parameterization
> Turnbull, A. D., et al. "Improved magnetohydrodynamic stability through optimization of higher order moments in cross-section shape of tokamaks." Physics of Plasmas 6.4 (1999): 1113-1116.
Fields:
R0 - Major Radius [m]
Z0 - Elevation [m]
ϵ - Inverse Aspect Ratio a/R0 where a = minor radius
κ - Elongation
δ - Triangularity
ζ - Squareness
help?> AsymmetricMillerShape # alias = AMShape
AsymmetricMillerShape Structure
Defines the Asymmetric Miller Plasma Shape Parameterization
Fields:
R0 - Major Radius [m]
Z0 - Elevation [m]
ϵ - Inverse Aspect Ratio a/R0 where a = minor radius
κ - Elongation
δl - Lower Triangularity
δu - Upper Triangularity
help?> MillerExtendedHarmonicShape # alias = MXHShape
MillerExtendedHarmonicShape Structure
Defines the Miller Extended Harmonic Plasma Shape Parameterization
> Arbon, Ryan, Jeff Candy, and Emily A. Belli. "Rapidly-convergent flux-surface shape parameterization." Plasma Physics and Controlled Fusion 63.1 (2020): 012001.
Fields:
R0 - Major Radius [m]
Z0 - Elevation [m]
ϵ - Inverse Aspect Ratio a/R0 where a = minor radius
κ - Elongation
c0 - Tilt
c - Cosine coefficients i.e. [ovality,...]
s - Sine coefficients i.e. [asin(triangularity), squareness,...]
```
## Flux Surface Fitting
MXHEquilibrium.jl provides routines for fitting flux surfaces to a PlasmaShape
```julia
julia> g = readg(@__DIR__*"/test/g150219.03200");
julia> M = efit(g,clockwise_phi=false);
julia> bdry = boundary(M);
julia> MXH = fit(bdry,MXHShape(10)) # use 10 fourier components
MillerExtendedHarmonicShape{10, Float64}
R0 = 1.6667475890195798 [m]
Z0 = -0.14918543837718545 [m]
ϵ = 0.3278211449811159
κ = 1.8166930389369045
δ = 0.4745349500498265
ζ = 0.0640865222160445
ξ = -0.12517240241115193
τ = -0.0847654065659985
julia> bdry = boundary(MXH; N=100)
julia> fMXH = fit(bdry,MXHShape(10))
MillerExtendedHarmonicShape{10, Float64}
R0 = 1.6667278385191975 [m]
Z0 = -0.14918543837718545 [m]
ϵ = 0.3277787473904293
κ = 1.8167208515952422
δ = 0.4745418627448689
ζ = 0.06313553088494958
ξ = -0.11595260388302828
τ = -0.08051086241624195
```
## Online documentation
For more details, see the [online documentation](https://projecttorreypines.github.io/MXHEquilibrium.jl/dev).
