def test_readwrite():
"""Test reading/writing to a file round-trip"""
tokamak = freegs.machine.MAST_sym()
eq = freegs.Equilibrium(
tokamak=tokamak,
Rmin=0.1,
Rmax=2.0,
Zmin=-1.0,
Zmax=1.0,
nx=17,
ny=17,
boundary=freegs.boundary.freeBoundaryHagenow,
)
profiles = freegs.jtor.ConstrainPaxisIp(1e4, 1e6, 2.0)
# Note here the X-point locations and isoflux locations are not the same.
# The result will be an unbalanced double null configuration, where the
# X-points are on different flux surfaces.
xpoints = [(1.1, -0.6), (1.1, 0.8)]
isoflux = [(1.1, -0.6, 1.1, 0.6)]
constrain = freegs.control.constrain(xpoints=xpoints, isoflux=isoflux)
freegs.solve(eq, profiles, constrain, maxits=25, atol=1e-3, rtol=1e-1)
memory_file = io.BytesIO()
with freegs.OutputFile(memory_file, "w") as f:
f.write_equilibrium(eq)
with freegs.OutputFile(memory_file, "r") as f:
read_eq = f.read_equilibrium()
assert tokamak == read_eq.tokamak
assert allclose(eq.psi(), read_eq.psi())
# Specify locations of the X-points
# to use to constrain coil currents
xpoints = [(1.1, -0.6), # (R,Z) locations of X-points
(1.1, 0.6)]
isoflux = [(1.1,-0.6, 1.1,0.6), # (R1,Z1, R2,Z2) pair of locations
(1.7, 0.0, 0.84, 0.0)]
constrain = freegs.control.constrain(xpoints=xpoints, isoflux=isoflux, gamma = 1e-17)
#########################################
# Nonlinear solve
freegs.solve(eq, # The equilibrium to adjust
profiles, # The toroidal current profile function
constrain) # Constraint function to set coil currents
# Currents in the coils
tokamak.printCurrents()
# Forces on the coils
eq.printForces()
############################
# Optimise
# Minimise the maximum force on the coils, while avoiding intersection of the LCFS and walls
# by modifying the radius of the P2U and P2L coils.
import freegs
from freegs import geqdsk
from freegs.equilibrium import refine
from freegs.plotting import plotEquilibrium
# Reading MAST equilibrium, up-down symmetric coils
tokamak = freegs.machine.MAST()
#with open("g014220.00200") as f:
with open("mast.geqdsk") as f:
eq = geqdsk.read(f, tokamak, show=True)
# Increase resolution by a factor of 2
eq2 = refine(eq)
# Re-solve, keeping the same control points and profiles
freegs.solve(eq2, eq._profiles, eq.control, rtol=1e-6)
# Save to G-EQDSK
with open("mast-highres.geqdsk", "w") as f:
geqdsk.write(eq2, f)
plotEquilibrium(eq2)
1e3, # Plasma pressure on axis [Pascals]
2e5, # Plasma current [Amps]
2.0) # Vacuum f=R*Bt
xpoints = [
(1.1, -0.6), # (R,Z) locations of X-points
(1.1, 0.8)
]
isoflux = [(1.1, -0.6, 1.1, 0.6)] # (R1,Z1, R2,Z2) pair of locations
constrain = freegs.control.constrain(xpoints=xpoints, isoflux=isoflux)
freegs.solve(
eq, # The equilibrium to adjust
profiles, # The toroidal current profile function
constrain,
rtol=rtol)
############################################
# Now have initial solution
resolutions = [eq.R.shape[0]]
psivals = [eq.psiRZ(*location)]
brvals = [eq.Br(*location)]
volumevals = [eq.plasmaVolume()]
coilcurrents = [eq.tokamak["P1L"].current]
# List of l2 and l∞ norms
l2vals = []
linfvals = []
# Plasma equilibrium (Grad-Shafranov) solver
import freegs
# Boundary conditions
import freegs.boundary as boundary
profiles = freegs.jtor.ConstrainPaxisIp(
1e4, # Plasma pressure on axis [Pascals]
1e6, # Plasma current [Amps]
1.0) # fvac = R*Bt
eq = freegs.Equilibrium(Rmin=0.1,
Rmax=2.0,
Zmin=-1.0,
Zmax=1.0,
nx=65,
ny=65,
boundary=boundary.fixedBoundary)
# Nonlinear solver for Grad-Shafranov equation
freegs.solve(
eq, # The equilibrium to adjust
profiles) # The toroidal current profile function
print("Done!")
# Plot equilibrium
from freegs.plotting import plotEquilibrium
plotEquilibrium(eq)
# ,(0.7,-1.1, 1.5,-1.9) # Lower X-point, lower outer leg
# ,(0.7,1.1, 1.5, 1.9) # Upper X-point, upper outer leg
]
constrain = freegs.control.constrain(xpoints=xpoints,
gamma=1e-12,
isoflux=isoflux)
constrain(eq)
#########################################
# Nonlinear solve
freegs.solve(
eq, # The equilibrium to adjust
profiles, # The plasma profiles
constrain, # Plasma control constraints
show=True) # Shows results at each nonlinear iteration
# eq now contains the solution
print("Done!")
print("Plasma current: %e Amps" % (eq.plasmaCurrent()))
print("Pressure on axis: %e Pascals" % (eq.pressure(0.0)))
print("Plasma poloidal beta: %e" % (eq.poloidalBeta()))
print("Plasma volume: %e m^3" % (eq.plasmaVolume()))
eq.tokamak.printCurrents()
##############################################
boundaries = [("A", 0.1, 2.0, -1.0, 1.0), ("B", 0.5, 1.75, -0.8, 1.1)]
for n in resolutions:
for bndry_name, Rmin, Rmax, Zmin, Zmax in boundaries:
# Re-create objects so no state is retained between runs
tokamak = freegs.machine.TestTokamak()
eq = freegs.Equilibrium(
tokamak=tokamak,
Rmin=Rmin,
Rmax=Rmax, # Radial domain
Zmin=Zmin,
Zmax=Zmax, # Height range
nx=n,
ny=n) # Number of grid points
freegs.solve(
eq, # The equilibrium to adjust
profiles, # The toroidal current profile function
constrain, # Constraint function to set coil currents
rtol=1e-6,
show=False)
# Save solution for later analysis
with open("test-02-" + bndry_name + "-" + str(n) + ".pkl", "wb") as f:
pickle.dump(n, f)
pickle.dump((bndry_name, Rmin, Rmax, Zmin, Zmax), f)
pickle.dump(eq, f)
