def screwpinch(nx=68,
ny=16,
nz=128,
xcentre=1.5,
fname='screwpinch.fci.nc',
a=0.2,
npoints=421,
show_maps=False):
yperiod = 2 * np.pi
field = zb.field.Screwpinch(xcentre=xcentre,
yperiod=yperiod,
shear=0 * 2e-1)
ycoords = np.linspace(0.0, yperiod, ny, endpoint=False)
start_r = xcentre + a / 2.
start_z = 0.
print("Making curvilinear poloidal grid")
inner = zb.rzline.shaped_line(R0=xcentre,
a=a / 2.,
elong=0,
triang=0.0,
indent=0,
n=npoints)
outer = zb.rzline.shaped_line(R0=xcentre,
a=a,
elong=0,
triang=0.0,
indent=0,
n=npoints)
poloidal_grid = zb.poloidal_grid.grid_elliptic(inner, outer, nx, nz)
grid = zb.grid.Grid(poloidal_grid, ycoords, yperiod, yperiodic=True)
maps = zb.make_maps(grid, field)
zb.write_maps(grid, field, maps, str(fname), metric2d=False)
calc_curvilinear_curvature(fname, field, grid, maps)
if show_maps:
zb.plot.plot_forward_map(grid, maps, yslice=0)
# Generate a grid on each poloidal slice using the elliptic grid generator
nx = 20
ny = 20
pol_grids = [
zoidberg.poloidal_grid.grid_elliptic(inner_line, outer_line, nx, ny)
for inner_line in inner_lines
]
#############################################################################
# Create a grid, then calculate forward and backward maps
grid = zoidberg.grid.Grid(pol_grids, ycoords, yperiod, yperiodic=True)
maps = zoidberg.make_maps(grid, magnetic_field)
#############################################################################
# Write grid file
filename = "stellarator.fci.nc"
print("Writing to grid file '{0}'".format(filename))
zoidberg.write_maps(grid,
magnetic_field,
maps,
gridfile=filename,
new_names=False,
metric2d=True)
#############################################################################
outer_line = zoidberg.rzline.circle(R0=0.0, r=0.8)
#############################################################################
# Now have inner and outer boundaries for each poloidal grid
# Generate a grid on each poloidal slice using the elliptic grid generator
nx = 20
ny = 20
pol_grids = [ zoidberg.poloidal_grid.grid_elliptic(inner_line, outer_line, nx,ny) for inner_line in inner_lines ]
#############################################################################
# Create a grid, then calculate forward and backward maps
grid = zoidberg.grid.Grid( pol_grids, ycoords, yperiod, yperiodic=True)
maps = zoidberg.make_maps(grid, magnetic_field)
#############################################################################
# Write grid file
filename = "stellarator.fci.nc"
print("Writing to grid file '{0}'".format(filename))
zoidberg.write_maps(grid, magnetic_field, maps, gridfile=filename, new_names=False, metric2d=True)
#############################################################################
# Plot maps
zoidberg.plot.plot_forward_map(grid, maps)
def W7X(
nx=68,
ny=32,
nz=256,
fname='W7-X.fci.nc',
vmec_file='w7-x.wout.nc',
inner_VMEC=False,
inner_vacuum=False,
outer_VMEC=False,
outer_vacuum=False,
outer_vessel=False,
npoints=100,
a=2.5,
show_maps=False,
calc_curvature=True,
smooth_curvature=False,
plasma_field=False,
configuration=0,
vmec_url='http://svvmec1.ipp-hgw.mpg.de:8080/vmecrest/v1/w7x_ref_171/wout.nc'
):
yperiod = 2 * np.pi / 5.
ycoords = np.linspace(0.0, yperiod, ny, endpoint=False)
if outer_VMEC:
print("Aligning to outer VMEC flux surface...")
outer_lines = get_VMEC_surfaces(phi=ycoords,
s=1,
npoints=nz,
w7x_run=vmec_url)
elif outer_vessel:
print("Aligning to plasma vessel (EXPERIMENTAL) ...")
outer_lines = get_W7X_vessel(phi=ycoords, nz=nz)
elif (outer_vacuum or inner_vacuum):
xmin = 4.05
xmax = 4.05 + 2.5
zmin = -1.35
zmax = -zmin
field = zb.field.W7X_vacuum(phimax=2 * np.pi / 5.,
x_range=[xmin, xmax],
z_range=[zmin, zmax],
include_plasma_field=plasma_field)
xcentre, zcentre = field.magnetic_axis(phi_axis=ycoords[0],
configuration=configuration)
start_r = xcentre + a / 2.
start_z = zcentre
if inner_vacuum:
print("Aligning to inner vacuum flux surface...")
inner_lines = get_lines(field,
start_r,
start_z,
ycoords,
yperiod=yperiod,
npoints=npoints)
if outer_vacuum:
print("Aligning to outer vacuum flux surface...")
outer_lines = get_lines(field,
start_r + a,
start_z,
ycoords,
yperiod=yperiod,
npoints=npoints)
xmin = np.min([min(outer_lines[i].R) for i in range(ny)])
xmax = np.max([max(outer_lines[i].R) for i in range(ny)])
zmin = np.min([min(outer_lines[i].Z) for i in range(ny)])
zmax = np.max([max(outer_lines[i].Z) for i in range(ny)])
if inner_VMEC:
print("Aligning to inner VMEC flux surface...")
inner_lines = get_VMEC_surfaces(phi=ycoords,
s=0.67,
npoints=nz,
w7x_run=vmec_url)
print("creating grid...")
poloidal_grid = [
zb.poloidal_grid.grid_elliptic(inner, outer, nx, nz, show=show_maps)
for inner, outer in zip(inner_lines, outer_lines)
]
# Create the 3D grid by putting together 2D poloidal grids
grid = zb.grid.Grid(poloidal_grid, ycoords, yperiod, yperiodic=True)
field = zb.field.W7X_vacuum(phimax=2 * np.pi / 5.,
x_range=[xmin, xmax],
z_range=[zmin, zmax],
include_plasma_field=plasma_field)
maps = zb.make_maps(grid, field)
zb.write_maps(grid, field, maps, str(fname), metric2d=False)
if calc_curvature:
print("calculating curvature...")
calc_curvilinear_curvature(fname, field, grid)
if (calc_curvature and smooth_curvature):
smooth_metric(fname,
write_to_file=True,
return_values=False,
smooth_metric=True)
if show_maps:
zb.plot.plot_forward_map(grid, maps, yslice=-1)
def rotating_ellipse(nx=68,
ny=16,
nz=128,
xcentre=5.5,
I_coil=0.01,
curvilinear=True,
rectangular=False,
fname='rotating-ellipse.fci.nc',
a=0.4,
curvilinear_inner_aligned=True,
curvilinear_outer_aligned=True,
npoints=421,
Btor=2.5,
show_maps=False,
calc_curvature=True,
smooth_curvature=False,
return_iota=True,
write_iota=False):
yperiod = 2 * np.pi / 5.
field = zb.field.RotatingEllipse(xcentre=xcentre,
I_coil=I_coil,
radius=2 * a,
yperiod=yperiod,
Btor=Btor)
# Define the y locations
ycoords = np.linspace(0.0, yperiod, ny, endpoint=False)
start_r = xcentre + a / 2.
start_z = 0.
if rectangular:
print("Making rectangular poloidal grid")
poloidal_grid = zb.poloidal_grid.RectangularPoloidalGrid(
nx, nz, 1.0, 1.0, Rcentre=xcentre)
elif curvilinear:
print("Making curvilinear poloidal grid")
inner = zb.rzline.shaped_line(R0=xcentre,
a=a / 2.,
elong=0,
triang=0.0,
indent=0,
n=npoints)
outer = zb.rzline.shaped_line(R0=xcentre,
a=a,
elong=0,
triang=0.0,
indent=0,
n=npoints)
if curvilinear_inner_aligned:
print("Aligning to inner flux surface...")
inner_lines = get_lines(field,
start_r,
start_z,
ycoords,
yperiod=yperiod,
npoints=npoints)
if curvilinear_outer_aligned:
print("Aligning to outer flux surface...")
outer_lines = get_lines(field,
xcentre + a,
start_z,
ycoords,
yperiod=yperiod,
npoints=npoints)
print("creating grid...")
if curvilinear_inner_aligned:
if curvilinear_outer_aligned:
poloidal_grid = [
zb.poloidal_grid.grid_elliptic(inner,
outer,
nx,
nz,
show=show_maps)
for inner, outer in zip(inner_lines, outer_lines)
]
else:
poloidal_grid = [
zb.poloidal_grid.grid_elliptic(inner,
outer,
nx,
nz,
show=show_maps)
for inner in inner_lines
]
else:
poloidal_grid = zb.poloidal_grid.grid_elliptic(
inner, outer, nx, nz)
# Create the 3D grid by putting together 2D poloidal grids
grid = zb.grid.Grid(poloidal_grid, ycoords, yperiod, yperiodic=True)
maps = zb.make_maps(grid, field)
zb.write_maps(grid, field, maps, str(fname), metric2d=False)
if (curvilinear and calc_curvature):
print("calculating curvature...")
calc_curvilinear_curvature(fname, field, grid, maps)
if (calc_curvature and smooth_curvature):
smooth_metric(fname,
write_to_file=True,
return_values=False,
smooth_metric=True)
if (return_iota or write_iota):
rindices = np.linspace(start_r, xcentre + a, nx)
zindices = np.zeros((nx))
iota_bar = calc_iota(field, start_r, start_z)
if (write_iota):
f = DataFile(str(fname), write=True)
f.write('iota_bar', iota_bar)
f.close()
else:
print("Iota_bar = ", iota_bar)
nx = 5
ny = 6
nz = 7
# Create magnetic field
magnetic_field = zoidberg.field.StraightStellarator(radius = 1.0)
# Create a rectangular grid in (x,y,z)
rectangle = zoidberg.grid.rectangular_grid(nx,ny,nz,
Lx = 1.0, Lz = 1.0, Ly = 10.0,
yperiodic = True)
# Here both the field and and grid are centred at (x,z) = (0,0)
# and the rectangular grid here fits entirely within the coils
maps = zoidberg.make_maps(rectangle, magnetic_field)
# Pick a poloidal slice and the next slice
yslice = 0
pol, ycoord = rectangle.getPoloidalGrid(yslice)
pol_next, ycoord_next = rectangle.getPoloidalGrid(yslice+1)
# Plot the grid points at this poloidal slice
plt.plot(pol.R, pol.Z, 'x')
# Get the coordinates which the forward map corresponds to
R_next, Z_next = pol_next.getCoordinate( maps['forward_xt_prime'][:,yslice,:], maps['forward_zt_prime'][:,yslice,:] )
plt.plot(R_next, Z_next, 'o')
plt.show()
#!/usr/bin/env python
import numpy as np
import zoidberg
field = zoidberg.field.GEQDSK("g014220.00200") # Read magnetic field
grid = zoidberg.grid.rectangular_grid(100, 10, 100,
1.5-0.1, # Range in R (max - min)
2*np.pi, # Toroidal angle
3., # Range in Z
xcentre=(1.5+0.1)/2, # Middle of grid in R
yperiodic=True) # Periodic in toroidal angle
# Create the forward and backward maps
maps = zoidberg.make_maps(grid, field)
# Save to file
zoidberg.write_maps(grid, field, maps, gridfile="tokamak.fci.nc")
#############################################################################
# Plot maps
zoidberg.plot.plot_forward_map(grid, maps)
def W7X(nx=68,
ny=16,
nz=256,
fname='W7-X.fci.nc',
VMEC=True,
vmec_file='w7-x.wout.nc',
inner_VMEC=True,
inner_vacuum=False,
outer_VMEC=True,
outer_vacuum=False,
outer_vessel=False,
npoints=100,
a=0.5,
show_maps=False,
calc_curvature=True,
smooth_curvature=False,
configuration=0):
field = zb.field.W7X(phimax=2 * np.pi / 5.)
yperiod = 2 * np.pi / 5.
ycoords = np.linspace(0.0, yperiod, ny, endpoint=False)
xcentre, zcentre = field.magnetic_axis(phi_axis=ycoords[0],
configuration=configuration)
start_r = xcentre + a / 2.
start_z = zcentre
print("Making curvilinear poloidal grid")
inner = zb.rzline.shaped_line(R0=xcentre,
a=a / 2.,
elong=0,
triang=0.0,
indent=0,
n=npoints)
outer = zb.rzline.shaped_line(R0=xcentre,
a=a,
elong=0,
triang=0.0,
indent=0,
n=npoints)
if inner_vacuum:
print("Aligning to inner vacuum flux surface...")
inner_lines = get_lines(field,
start_r,
start_z,
ycoords,
yperiod=yperiod,
npoints=npoints)
elif inner_VMEC:
print("Aligning to inner VMEC flux surface...")
inner_lines = get_VMEC_surfaces(phi=ycoords, s=0.5, npoints=nz)
if outer_vacuum:
print("Aligning to outer vacuum flux surface...")
outer_lines = get_lines(field,
start_r + a,
start_z,
ycoords,
yperiod=yperiod,
npoints=npoints)
elif outer_VMEC:
print("Aligning to outer VMEC flux surface...")
outer_lines = get_VMEC_surfaces(phi=ycoords, s=1, npoints=nz)
elif outer_vessel:
print("Aligning to plasma vessel (EXPERIMENTAL) ...")
outer_lines = get_W7X_vessel(phi=ycoords, nz=nz)
print("creating grid...")
poloidal_grid = [
zb.poloidal_grid.grid_elliptic(inner, outer, nx, nz, show=show_maps)
for inner, outer in zip(inner_lines, outer_lines)
]
# Create the 3D grid by putting together 2D poloidal grids
grid = zb.grid.Grid(poloidal_grid, ycoords, yperiod, yperiodic=True)
maps = zb.make_maps(grid, field)
zb.write_maps(grid, field, maps, str(fname), metric2d=False)
if calc_curvature:
print("calculating curvature...")
calc_curvilinear_curvature(fname, field, grid)
if (calc_curvature and smooth_curvature):
smooth_metric(fname,
write_to_file=True,
return_values=False,
smooth_metric=True)
nx = 5
ny = 6
nz = 7
# Create magnetic field
magnetic_field = zoidberg.field.StraightStellarator(radius = 1.0)
# Create a rectangular grid in (x,y,z)
rectangle = zoidberg.grid.rectangular_grid(nx,ny,nz,
Lx = 1.0, Lz = 1.0, Ly = 10.0,
yperiodic = True)
# Here both the field and and grid are centred at (x,z) = (0,0)
# and the rectangular grid here fits entirely within the coils
maps = zoidberg.make_maps(rectangle, magnetic_field)
# Pick a poloidal slice and the next slice
yslice = 0
pol, ycoord = rectangle.getPoloidalGrid(yslice)
pol_next, ycoord_next = rectangle.getPoloidalGrid(yslice+1)
# Plot the grid points at this poloidal slice
plt.plot(pol.R, pol.Z, 'x')
# Get the coordinates which the forward map corresponds to
R_next, Z_next = pol_next.getCoordinate( maps['forward_xt_prime'][:,yslice,:], maps['forward_zt_prime'][:,yslice,:] )
plt.plot(R_next, Z_next, 'o')
plt.show()
#!/usr/bin/env python
import numpy as np
import zoidberg
field = zoidberg.field.GEQDSK("g014220.00200") # Read magnetic field
grid = zoidberg.grid.rectangular_grid(
100,
10,
100,
1.5 - 0.1, # Range in R (max - min)
2 * np.pi, # Toroidal angle
3., # Range in Z
xcentre=(1.5 + 0.1) / 2, # Middle of grid in R
yperiodic=True) # Periodic in toroidal angle
# Create the forward and backward maps
maps = zoidberg.make_maps(grid, field)
# Save to file
zoidberg.write_maps(grid, field, maps, gridfile="tokamak.fci.nc")
#############################################################################
# Plot maps
zoidberg.plot.plot_forward_map(grid, maps)