def slab(nx, ny, nz,
filename="fci.grid.nc",
Lx=0.1, Ly=10., Lz = 1.,
Bt=1.0, Bp = 0.1, Bpprime = 1.0):
"""
nx - Number of radial points
ny - Number of toroidal points (NOTE: Different to BOUT++ standard)
nz - Number of poloidal points
Lx - Radial domain size [m]
Ly - Toroidal domain size [m]
Lz - Poloidal domain size [m]
Bt - Toroidal magnetic field [T]
Bp - Poloidal magnetic field [T]
Bpprime - Gradient of Bp [T/m] Bp(x) = Bp + Bpprime * x
"""
MXG = 2
# Make sure input types are sane
nx = int(nx)
ny = int(ny)
nz = int(nz)
Lx = float(Lx)
Ly = float(Ly)
Lz = float(Lz)
delta_x = old_div(Lx,(nx-2.*MXG))
delta_pol = old_div(Lz,(nz))
delta_tor = old_div(Ly,(ny))
# Coord arrays
x = Lx * (np.arange(nx) - MXG + 0.5)/(nx - 2.*MXG) # 0 and 1 half-way between cells
y = np.linspace(0,Ly,ny)
z = np.linspace(0,Lz,nz,endpoint=False)
############################################################
# Effective major radius
R = old_div(Ly, (2.*pi))
# Set poloidal magnetic field
Bpx = Bp + (x-old_div(Lx,2)) * Bpprime
Bpxy = np.transpose(np.resize(Bpx, (nz, ny, nx)), (2,1,0))
Bxy = np.sqrt(Bpxy**2 + Bt**2)
class Mappoint(object):
def __init__(self, xt, zt):
self.xt = xt
self.zt = zt
self.xt_prime = old_div(xt,delta_x) + MXG - 0.5
self.zt_prime = old_div(zt,delta_pol)
def unroll_map_coeff(map_list, coeff):
coeff_array = np.transpose(np.resize(np.array([getattr(f, coeff) for f in map_list]).reshape( (nx,nz) ), (ny, nx, nz) ), (1, 0, 2) )
return coeff_array
def b_field(vector, y):
x0 = old_div(Lx,2.) # Centre of box, where bz = 0.
x, z = vector;
bx = 0.
bz = Bp + (x-x0) * Bpprime
return [bx, bz]
def field_line_tracer(direction, map_list):
result = np.zeros( (nx, nz, 2) )
for i in np.arange(0,nx):
for k in np.arange(0,nz):
result[i,k,:] = odeint(b_field, [x[i], z[k]], [0, delta_tor*direction])[1,:]
result[i,k,1] = np.mod(result[i,k,1], Lz)
map_list.append(Mappoint(result[i,k,0],result[i,k,1]))
return result
forward_map = []
forward_coords = field_line_tracer(+1, forward_map)
backward_map = []
backward_coords = field_line_tracer(-1, backward_map)
X,Y = np.meshgrid(x,y,indexing='ij')
x0 = 0.5
g_22 = old_div(((Bp + (X-x0) * Lx * Bpprime)**2 + Bt**2), Bt**2)
with bdata.DataFile(filename, write=True, create=True) as f:
f.write('nx', nx)
f.write('ny', ny)
f.write('nz', nz)
f.write("dx", delta_x)
f.write("dy", delta_tor)
f.write("g_22", g_22)
f.write("Bxy", transform3D(Bxy))
# Note: If "nz" is put into the file, then 3D variables
# should not be transformed since they will be read directly into
# BOUT++ arrays without Fourier transforming
xt_prime = unroll_map_coeff(forward_map, 'xt_prime')
#f.write('forward_xt_prime', transform3D(xt_prime))
f.write('forward_xt_prime', xt_prime)
zt_prime = unroll_map_coeff(forward_map, 'zt_prime')
#f.write('forward_zt_prime', transform3D(zt_prime))
f.write('forward_zt_prime', zt_prime)
xt_prime = unroll_map_coeff(backward_map, 'xt_prime')
#f.write('backward_xt_prime', transform3D(xt_prime))
f.write('backward_xt_prime', xt_prime)
zt_prime = unroll_map_coeff(backward_map, 'zt_prime')
#f.write('backward_zt_prime', transform3D(zt_prime))
f.write('backward_zt_prime', zt_prime)
if __name__ == "__main__":
forward_map = []
forward_coords = field_line_tracer(+1, forward_map)
backward_map = []
backward_coords = field_line_tracer(-1, backward_map)
X,Y = np.meshgrid(x,y,indexing='ij')
x0 = 0.5
g_22 = np.sqrt(((Bp + (X-x0) * Lx * Bpprime)**2 + 1))
with bdata.DataFile('fci.grid.nc', write=True, create=True) as f:
f.write('nx', nx)
f.write('ny', ny)
f.write('nz', nz)
f.write("dx", delta_x)
f.write("dy", delta_tor)
f.write("g_22", g_22)
f.write("Bxy", transform3D(Bxy))
xt_prime = unroll_map_coeff(forward_map, 'xt_prime')
f.write('forward_xt_prime', transform3D(xt_prime))
zt_prime = unroll_map_coeff(forward_map, 'zt_prime')
f.write('forward_zt_prime', transform3D(zt_prime))
xt_prime = unroll_map_coeff(backward_map, 'xt_prime')
f.write('backward_xt_prime', transform3D(xt_prime))
zt_prime = unroll_map_coeff(backward_map, 'zt_prime')
f.write('backward_zt_prime', transform3D(zt_prime))
import boututils.datafile as bdata
from boutdata.input import transform3D
# Parameters
nx = 10
ny = 20
nz = 8
shape = [nx, ny, nz]
xt_prime = zeros(shape)
zt_prime = zeros(shape)
for x in range(nx):
# No interpolation in x
xt_prime[x,:,:] = x
# Each y slice scans between neighbouring z points
for z in range(nz):
zt_prime[x,:,z] = z + concatenate([linspace(-1, 1, ny-1), [0]])
with bdata.DataFile('simple_test.nc', write=True, create=True) as f:
f.write('nx',nx)
f.write('ny',ny)
for direction_name in ['forward', 'backward']:
f.write(direction_name + '_xt_prime', transform3D(xt_prime))
f.write(direction_name + '_zt_prime', transform3D(zt_prime))
def slab(nx,
ny,
nz,
filename="fci.grid.nc",
Lx=0.1,
Ly=10.,
Lz=1.,
Bt=1.0,
Bp=0.1,
Bpprime=1.0):
"""
nx - Number of radial points
ny - Number of toroidal points (NOTE: Different to BOUT++ standard)
nz - Number of poloidal points
Lx - Radial domain size [m]
Ly - Toroidal domain size [m]
Lz - Poloidal domain size [m]
Bt - Toroidal magnetic field [T]
Bp - Poloidal magnetic field [T]
Bpprime - Gradient of Bp [T/m] Bp(x) = Bp + Bpprime * x
"""
MXG = 2
# Make sure input types are sane
nx = int(nx)
ny = int(ny)
nz = int(nz)
Lx = float(Lx)
Ly = float(Ly)
Lz = float(Lz)
delta_x = old_div(Lx, (nx - 2. * MXG))
delta_pol = old_div(Lz, (nz))
delta_tor = old_div(Ly, (ny))
# Coord arrays
x = Lx * (np.arange(nx) - MXG + 0.5) / (nx - 2. * MXG
) # 0 and 1 half-way between cells
y = np.linspace(0, Ly, ny)
z = np.linspace(0, Lz, nz, endpoint=False)
############################################################
# Effective major radius
R = old_div(Ly, (2. * pi))
# Set poloidal magnetic field
Bpx = Bp + (x - old_div(Lx, 2)) * Bpprime
Bpxy = np.transpose(np.resize(Bpx, (nz, ny, nx)), (2, 1, 0))
Bxy = np.sqrt(Bpxy**2 + Bt**2)
class Mappoint(object):
def __init__(self, xt, zt):
self.xt = xt
self.zt = zt
self.xt_prime = old_div(xt, delta_x) + MXG - 0.5
self.zt_prime = old_div(zt, delta_pol)
def unroll_map_coeff(map_list, coeff):
coeff_array = np.transpose(
np.resize(
np.array([getattr(f, coeff) for f in map_list]).reshape(
(nx, nz)), (ny, nx, nz)), (1, 0, 2))
return coeff_array
def b_field(vector, y):
x0 = old_div(Lx, 2.) # Centre of box, where bz = 0.
x, z = vector
bx = 0.
bz = Bp + (x - x0) * Bpprime
return [bx, bz]
def field_line_tracer(direction, map_list):
result = np.zeros((nx, nz, 2))
for i in np.arange(0, nx):
for k in np.arange(0, nz):
result[i, k, :] = odeint(b_field, [x[i], z[k]],
[0, delta_tor * direction])[1, :]
result[i, k, 1] = np.mod(result[i, k, 1], Lz)
map_list.append(Mappoint(result[i, k, 0], result[i, k, 1]))
return result
forward_map = []
forward_coords = field_line_tracer(+1, forward_map)
backward_map = []
backward_coords = field_line_tracer(-1, backward_map)
X, Y = np.meshgrid(x, y, indexing='ij')
x0 = 0.5
g_22 = old_div(((Bp + (X - x0) * Lx * Bpprime)**2 + Bt**2), Bt**2)
with bdata.DataFile(filename, write=True, create=True) as f:
f.write('nx', nx)
f.write('ny', ny)
f.write('nz', nz)
f.write("dx", delta_x)
f.write("dy", delta_tor)
f.write("g_22", g_22)
f.write("Bxy", transform3D(Bxy))
# Note: If "nz" is put into the file, then 3D variables
# should not be transformed since they will be read directly into
# BOUT++ arrays without Fourier transforming
xt_prime = unroll_map_coeff(forward_map, 'xt_prime')
#f.write('forward_xt_prime', transform3D(xt_prime))
f.write('forward_xt_prime', xt_prime)
zt_prime = unroll_map_coeff(forward_map, 'zt_prime')
#f.write('forward_zt_prime', transform3D(zt_prime))
f.write('forward_zt_prime', zt_prime)
xt_prime = unroll_map_coeff(backward_map, 'xt_prime')
#f.write('backward_xt_prime', transform3D(xt_prime))
f.write('backward_xt_prime', xt_prime)
zt_prime = unroll_map_coeff(backward_map, 'zt_prime')
#f.write('backward_zt_prime', transform3D(zt_prime))
f.write('backward_zt_prime', zt_prime)
def write_maps(grid,
magnetic_field,
maps,
gridfile='fci.grid.nc',
legacy=False):
"""Write FCI maps to BOUT++ grid file
Inputs
------
grid - Grid generated by Zoidberg
magnetic_field - Zoidberg magnetic field object
maps - Dictionary of FCI maps
gridfile - Output filename
legacy - If true, write FCI maps using FFTs
"""
nx, ny, nz = (grid.nx, grid.ny, grid.nz)
xarray, yarray, zarray = (grid.xarray, grid.yarray, grid.zarray)
g_22 = np.zeros((nx, ny)) + 1. / grid.Rmaj**2
totalbx = np.zeros((nx, ny, nz))
totalbz = np.zeros((nx, ny, nz))
Bxy = np.zeros((nx, ny, nz))
for i in np.arange(0, nx):
for j in np.arange(0, ny):
for k in np.arange(0, nz):
Bxy[i, j, k] = np.sqrt((
magnetic_field.Bxfunc(xarray[i], zarray[k], yarray[j])**2 +
magnetic_field.Bzfunc(xarray[i], zarray[k], yarray[j])**2))
totalbx[i, j,
k] = magnetic_field.Bxfunc(xarray[i], zarray[k],
yarray[j])
totalbz[i, j,
k] = magnetic_field.Bzfunc(xarray[i], zarray[k],
yarray[j])
with bdata.DataFile(gridfile, write=True, create=True) as f:
ixseps = nx + 1
f.write('nx', grid.nx)
f.write('ny', grid.ny)
if not legacy:
# Legacy files don't need nz
f.write('nz', grid.nz)
f.write("dx", grid.delta_x)
f.write("dy", grid.delta_y)
f.write("ixseps1", ixseps)
f.write("ixseps2", ixseps)
f.write("g_22", g_22)
f.write("Bxy", Bxy[:, :, 0])
f.write("bx", totalbx)
f.write("bz", totalbz)
# Legacy grid files need to FFT 3D arrays
if legacy:
from boutdata.input import transform3D
f.write('forward_xt_prime', transform3D(maps['forward_xt_prime']))
f.write('forward_zt_prime', transform3D(maps['forward_zt_prime']))
f.write('backward_xt_prime',
transform3D(maps['backward_xt_prime']))
f.write('backward_zt_prime',
transform3D(maps['backward_zt_prime']))
else:
f.write('forward_xt_prime', maps['forward_xt_prime'])
f.write('forward_zt_prime', maps['forward_zt_prime'])
f.write('backward_xt_prime', maps['backward_xt_prime'])
f.write('backward_zt_prime', maps['backward_zt_prime'])
