def make_upper_double_null_largesep(settings=None):
"""UDN with larger separation between X-points.
With psinorm = 1.1 this should be single null
With psinorm = 1.2 it's double null"""
if settings is None:
settings = {}
nx = 65
ny = 65
r1d = np.linspace(1.2, 1.8, nx)
z1d = np.linspace(-0.5, 0.5, ny)
r2d, z2d = np.meshgrid(r1d, z1d, indexing="ij")
r0 = 1.5
z0 = 0.3
def psi_func(R, Z):
return (np.exp(-((R - r0)**2 + Z**2) / 0.3**2) +
np.exp(-((R - r0)**2 + (Z + 2 * z0 + 0.02)**2) / 0.3**2) +
np.exp(-((R - r0)**2 + (Z - 2 * z0)**2) / 0.3**2))
settings.update(nx_inter_sep=1)
return tokamak.TokamakEquilibrium(
r1d,
z1d,
psi_func(r2d, z2d),
psi_func(np.linspace(1.6, 2.0, nx), np.zeros(nx)), # psi1d
np.linspace(0.0, 1.0, nx), # fpol1d
make_regions=False,
settings=settings,
)
def make_upper_double_null(settings=None):
if settings is None:
settings = {}
nx = 65
ny = 65
r1d = np.linspace(1.2, 1.8, nx)
z1d = np.linspace(-0.5, 0.5, ny)
r2d, z2d = np.meshgrid(r1d, z1d, indexing="ij")
r0 = 1.5
z0 = 0.3
def psi_func(R, Z):
return (np.exp(-((R - r0)**2 + Z**2) / 0.3**2) +
np.exp(-((R - r0)**2 + (Z + 2 * z0 + 0.002)**2) / 0.3**2) +
np.exp(-((R - r0)**2 + (Z - 2 * z0)**2) / 0.3**2))
settings["nx_inter_sep"] = 1
return tokamak.TokamakEquilibrium(
r1d,
z1d,
psi_func(r2d, z2d),
psi_func(np.linspace(1.6, 2.0, nx), np.zeros(nx)), # psi1d
np.linspace(0.0, 1.0, nx), # fpol1d
make_regions=False,
settings=settings,
)
def make_upper_single_null(settings=None):
if settings is None:
settings = {}
nx = 65
ny = 65
r1d = np.linspace(1.2, 1.8, nx)
z1d = np.linspace(-0.5, 0.5, ny)
r2d, z2d = np.meshgrid(r1d, z1d, indexing="ij")
r0 = 1.5
z0 = -0.3
# This has two O-points, and one x-point at (r0, z0)
def psi_func(R, Z):
Z = -Z # Upside-down
return np.exp(-((R - r0)**2 + (Z - z0 - 0.3)**2) / 0.3**2) + np.exp(-(
(R - r0)**2 + (Z - z0 + 0.3)**2) / 0.3**2)
return tokamak.TokamakEquilibrium(
r1d,
z1d,
psi_func(r2d, z2d),
np.linspace(0.0, 1.0, nx), # psi1d
np.linspace(0.0, 1.0, nx), # fpol1d
make_regions=False,
settings=settings,
)
def test_wall_clockwise():
nx = 65
ny = 65
# Limits of the domain
Rmin = 1.1
Rmax = 2.32
Zmin = -1.314
Zmax = 0.93
# Wall going clockwise. This should be reversed by TokamakEquilibrium
wall = [(Rmin, Zmax), (Rmax, Zmax), (Rmax, Zmin), (Rmin, Zmin)]
eq = tokamak.TokamakEquilibrium(
np.linspace(Rmin, Rmax, nx),
np.linspace(Zmin, Zmax, ny),
np.zeros((nx, ny)), # psi2d
np.linspace(0.0, 1.0, nx), # psi1d
np.linspace(0.0, 1.0, nx), # fpol1d
wall=wall,
make_regions=False,
)
assert len(eq.wall) == 4
# Wall ordering reversed
assert eq.wall[0].R == Rmin
assert eq.wall[0].Z == Zmin
assert eq.wall[1].R == Rmax
assert eq.wall[1].Z == Zmin
def test_bounding():
nx = 65
ny = 65
# Limits of the domain
Rmin = 1.1
Rmax = 2.32
Zmin = -1.314
Zmax = 0.93
eq = tokamak.TokamakEquilibrium(
np.linspace(Rmin, Rmax, nx),
np.linspace(Zmin, Zmax, ny),
np.zeros((nx, ny)), # psi2d
np.linspace(0.0, 1.0, nx), # psi1d
np.linspace(0.0, 1.0, nx), # fpol1d
make_regions=False,
)
assert np.isclose(eq.Rmin, Rmin)
assert np.isclose(eq.Rmax, Rmax)
assert np.isclose(eq.Zmin, Zmin)
assert np.isclose(eq.Zmax, Zmax)
def test_xpoint(psi_interpolation_method):
settings = {"psi_interpolation_method": psi_interpolation_method}
nx = 65
ny = 65
r1d = np.linspace(1.0, 2.0, nx)
z1d = np.linspace(-1.0, 1.0, ny)
r2d, z2d = np.meshgrid(r1d, z1d, indexing="ij")
r0 = 1.5
z0 = -0.3
# This has two O-points, and one x-point at (r0, z0)
def psi_func(R, Z):
return np.exp(-((R - r0)**2 + (Z - z0 - 0.3)**2) / 0.3**2) + np.exp(-(
(R - r0)**2 + (Z - z0 + 0.3)**2) / 0.3**2)
eq = tokamak.TokamakEquilibrium(
r1d,
z1d,
psi_func(r2d, z2d),
np.linspace(0.0, 1.0, nx), # psi1d
np.linspace(0.0, 1.0, nx), # fpol1d
make_regions=False,
settings=settings, # psi1d, fpol
)
assert len(eq.x_points) == 1
assert len(eq.psi_sep) == 1
assert np.isclose(eq.x_points[0].R, r0, atol=1.0 / nx)
assert np.isclose(eq.x_points[0].Z, z0, atol=1.0 / ny)
assert np.isclose(eq.psi_sep[0], psi_func(r0, z0), rtol=1.0 / nx)
def test_tokamak_interpolations(psi_interpolation_method):
"""Test interpolations and derivatives"""
settings = {"psi_interpolation_method": psi_interpolation_method}
# Define 2D (R,Z) grid
r1d = np.linspace(1.0, 2.0, 129)
z1d = np.linspace(-1.0, 1.0, 129)
r2d, z2d = np.meshgrid(r1d, z1d, indexing="ij")
# A poloidal flux function
r0 = 1.5
z0 = 0.0
def psi_func(R, Z):
return np.exp(-((R - r0)**2 + (Z - z0)**2) / 0.3**2)
def dpsi_dr(R, Z):
"Derivative of psi in R"
return -(2 / 0.3**2) * (R - r0) * psi_func(R, Z)
def dpsi_dz(R, Z):
"Derivative of psi in Z"
return -(2 / 0.3**2) * (Z - z0) * psi_func(R, Z)
psi2d = psi_func(r2d, z2d)
def fpol_func(psi):
"Define a simple profile for poloidal current function f = R * Bt"
return 1.0 - 0.1 * psi**2
def fpolprime_func(psi):
"Derivative of fpol"
return -0.2 * psi
psi1d = np.linspace(0, 1, 65)
fpol1d = fpol_func(psi1d)
eq = tokamak.TokamakEquilibrium(r1d,
z1d,
psi2d,
psi1d,
fpol1d,
make_regions=False,
settings=settings)
# Check interpolation of psi, f and f' at some locations
for r, z in [(1.2, 0.1), (1.6, -0.4), (1.8, 0.9)]:
psi = psi_func(r, z)
# Poloidal flux
assert np.isclose(eq.psi(r, z), psi, atol=1e-5)
# Poloidal current function
assert np.isclose(eq.fpol(psi), fpol_func(psi))
assert np.isclose(eq.fpolprime(psi), fpolprime_func(psi))
# Poloidal magnetic field
assert np.isclose(eq.Bp_R(r, z), dpsi_dz(r, z) / r, atol=1e-3)
assert np.isclose(eq.Bp_Z(r, z), -dpsi_dr(r, z) / r, atol=3e-3)
# vector Grad(psi)/|Grad(psi)|**2
assert np.isclose(
eq.f_R(r, z),
dpsi_dr(r, z) / (dpsi_dr(r, z)**2 + dpsi_dz(r, z)**2),
rtol=1e-3,
)
assert np.isclose(
eq.f_Z(r, z),
dpsi_dz(r, z) / (dpsi_dr(r, z)**2 + dpsi_dz(r, z)**2),
rtol=1e-3,
)
