def process_grid(rz_grid,
mesh,
output=None,
poorquality=None,
gui=None,
parent=None,
reverse_bt=None,
curv=None,
smoothpressure=None,
smoothhthe=None,
smoothcurv=None,
settings=None):
if settings == None:
# Create an empty structure
settings = Bunch(dummy=0)
# Check settings
settings.calcp = -1
settings.calcbt = -1
settings.calchthe = -1
settings.calcjpar = -1
# ;CATCH, err
# ;IF err NE 0 THEN BEGIN
# ; PRINT, "PROCESS_GRID failed"
#; PRINT, " Error message: "+!ERROR_STATE.MSG
# ; CATCH, /cancel
# ; RETURN
# ;ENDIF
MU = 4.e-7 * numpy.pi
poorquality = 0
if output == None: output = "bout.grd.nc"
# Size of the mesh
nx = numpy.int(numpy.sum(mesh.nrad))
ny = numpy.int(numpy.sum(mesh.npol))
# Find the midplane
ymid = 0
status = gen_surface(mesh=mesh) # Start generator
while True:
period, yi, xi, last = gen_surface(period=None, last=None, xi=None)
if period:
rm = numpy.max(mesh.Rxy[xi, yi])
ymidindx = numpy.argmax(mesh.Rxy[xi, yi])
ymid = yi[ymidindx]
break
if last == 1: break
Rxy = numpy.asarray(mesh.Rxy)
Zxy = numpy.asarray(mesh.Zxy)
psixy = mesh.psixy * mesh.fnorm + mesh.faxis # Non-normalised psi
pressure = numpy.zeros((nx, ny))
# Use splines to interpolate pressure profile
status = gen_surface(mesh=mesh) # Start generator
while True:
# Get the next domain
period, yi, xi, last = gen_surface(period=period, last=last, xi=xi)
if period:
# Pressure only given on core surfaces
# pressure[xi,yi] = SPLINE(rz_grid.npsigrid, rz_grid.pres, mesh.psixy[xi,yi[0]], /double)
sol = interpolate.UnivariateSpline(rz_grid.npsigrid,
rz_grid.pres,
s=1)
pressure[xi, yi] = sol(mesh.psixy[xi, yi[0]])
else:
pressure[xi, yi] = rz_grid.pres[numpy.size(rz_grid.pres) - 1]
if last == 1: break
# Add a minimum amount
if numpy.min(pressure) < 1.0e-2 * numpy.max(pressure):
print("****Minimum pressure is very small:", numpy.min(pressure))
print("****Setting minimum pressure to 1% of maximum")
pressure = pressure + 1e-2 * numpy.max(pressure)
if smoothpressure != None:
p0 = pressure[:, ymid] # Keep initial pressure for comparison
while True:
#!P.multi=[0,0,2,0,0]
fig = figure()
plot(p0,
xtitle="X index",
ytitle="pressure at y=" + numpy.strip(numpy.str(ymid), 2) +
" dashed=original",
color=1,
lines=1)
plot(pressure[:, ymid], color=1)
plot(deriv(p0),
xtitle="X index",
ytitle="DERIV(pressure)",
color=1,
lines=1)
plot(deriv(pressure[:, ymid]), color=1)
sm = query_yes_no(
"Smooth pressure profile?") #, gui=gui, dialog_parent=parent)
if sm:
# Smooth the pressure profile
p2 = pressure
for i in range(6):
status = gen_surface(mesh=mesh) # Start generator
while True:
# Get the next domain
period, yi, xi, last = gen_surface(period=period,
last=last,
xi=xi)
if (xi > 0) and (xi < (nx - 1)):
for j in range(numpy.size(yi)):
p2[xi,
yi[j]] = (0.5 * pressure[xi, yi[j]] + 0.25 *
(pressure[xi - 1, yi[j]] +
pressure[xi + 1, yi[j]]))
# Make sure it's still constant on flux surfaces
p2[xi, yi] = numpy.mean(p2[xi, yi])
if last != None: break
pressure = p2
if sm == 0: break
if numpy.min(pressure) < 0.0:
print("")
print("============= WARNING ==============")
print("Poor quality equilibrium: Pressure is negative")
print("")
poorquality = 1
dpdpsi = DDX(psixy, pressure)
#;IF MAX(dpdpsi)*mesh.fnorm GT 0.0 THEN BEGIN
#; PRINT, ""
#; PRINT, "============= WARNING =============="
#; PRINT, "Poor quality equilibrium: Pressure is increasing radially"
#; PRINT, ""
#; poorquality = 1
#;ENDIF
# Grid spacing
dx = numpy.zeros((nx, ny))
for y in range(ny):
dx[0:(nx - 1), y] = psixy[1::, y] - psixy[0:(nx - 1), y]
dx[nx - 1, y] = dx[nx - 2, y]
# Sign
bpsign = 1.
xcoord = psixy
if numpy.min(dx) < 0.:
bpsign = -1.
dx = -dx # dx always positive
xcoord = -xcoord
dtheta = 2. * numpy.pi / numpy.float(ny)
dy = numpy.zeros((nx, ny)) + dtheta
# B field components
# Following signs mean that psi increasing outwards from
# core to edge results in Bp clockwise in the poloidal plane
# i.e. in the positive Grad Theta direction.
Brxy = old_div(mesh.dpsidZ, Rxy)
Bzxy = old_div(-mesh.dpsidR, Rxy)
Bpxy = numpy.sqrt(Brxy**2 + Bzxy**2)
# Determine direction (dot B with grad y vector)
dot = (Brxy[0, ymid] * (Rxy[0, ymid + 1] - Rxy[0, ymid - 1]) +
Bzxy[0, ymid] * (Zxy[0, ymid + 1] - Zxy[0, ymid - 1]))
if dot < 0.:
print(
"**** Poloidal field is in opposite direction to Grad Theta -> Bp negative"
)
Bpxy = -Bpxy
if bpsign > 0: sys.exit() # Should be negative
bpsign = -1.0
else:
if bpsign < 0: sys.exit() # Should be positive
bpsign = 1.
# Get toroidal field from poloidal current function fpol
Btxy = numpy.zeros((nx, ny))
fprime = numpy.zeros((nx, ny))
fp = deriv(rz_grid.npsigrid * (rz_grid.sibdry - rz_grid.simagx),
rz_grid.fpol)
status = gen_surface(mesh=mesh) # Start generator
while True:
# Get the next domain
period, yi, xi, last = gen_surface(period=period, last=period, xi=xi)
if period:
# In the core
#fpol = numpy.interp(rz_grid.fpol, rz_grid.npsigrid, mesh.psixy[xi,yi], /spline)
sol = interpolate.UnivariateSpline(rz_grid.npsigrid,
rz_grid.fpol,
s=1)
# fpol = SPLINE(rz_grid.npsigrid, rz_grid.fpol, mesh.psixy[xi,yi[0]], 'double')
fpol = sol(mesh.psixy[xi, yi[0]])
sol = interpolate.UnivariateSpline(rz_grid.npsigrid, fp, s=1)
# fprime[xi,yi] = SPLINE(rz_grid.npsigrid, fp, mesh.psixy[xi,yi[0]], 'double')
fprime[xi, yi] = sol(mesh.psixy[xi, yi[0]])
else:
# Outside core. Could be PF or SOL
fpol = rz_grid.fpol[numpy.size(rz_grid.fpol) - 1]
fprime[xi, yi] = 0.
Btxy[xi, yi] = old_div(fpol, Rxy[xi, yi])
if last == 1: break
# Total B field
Bxy = numpy.sqrt(Btxy**2 + Bpxy**2)
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
# Go through the domains to get a starting estimate
# of hthe
hthe = numpy.zeros((nx, ny))
# Pick a midplane index
status = gen_surface(mesh=mesh) # Start generator
while True:
# Get the next domain
period, yi, xi, last = gen_surface(period=period, last=last, xi=xi)
if period:
# In the core
rmax = numpy.argmax(Rxy[xi, yi])
ymidplane = yi[rmax]
break
if last == 1: break
status = gen_surface(mesh=mesh) # Start generator
while True:
# Get the next domain
period, yi, xi, last = gen_surface(period=period, last=last, xi=xi)
n = numpy.size(yi)
# Get distance along this line
if period:
# Periodic, so can use FFT
#drdi = REAL_PART(fft_deriv(Rxy[xi, yi]))
#dzdi = REAL_PART(fft_deriv(Zxy[xi, yi]))
line = numpy.append(Rxy[xi, yi[n - 1::]], Rxy[xi, yi])
line = numpy.append(line, Rxy[xi, yi[0:1]])
drdi = deriv(line)[1:n + 1]
line = numpy.append(Zxy[xi, yi[n - 1::]], Zxy[xi, yi])
line = numpy.append(line, Zxy[xi, yi[0:1]])
dzdi = deriv(line)[1:n + 1]
else:
# Non-periodic
drdi = numpy.gradient(Rxy[xi, yi])
dzdi = numpy.gradient(Zxy[xi, yi])
dldi = numpy.sqrt(drdi**2 + dzdi**2)
if 0:
# Need to smooth to get sensible results
if period:
n = numpy.size(dldi)
line = numpy.append(dldi[(n - 2)::], dldi) # once
line = numpy.append(line, dldi[0:2])
dldi = SMOOTH(line, 5)[4:(n + 4)]
line = numpy.append(dldi[(n - 2)::], dldi) #twice
line = numpy.append(line, dldi[0:2])
dldi = SMOOTH(line, 5)[4:(n + 4)]
line = numpy.append(dldi[(n - 2)::], dldi) # three
line = numpy.append(line, dldi[0:2])
dldi = SMOOTH(line, 5)[4:(n + 4)]
else:
line = dldi
dldi = SMOOTH(line, 5)[2:n + 2]
line = dldi
dldi = SMOOTH(line, 5)[2:n + 2]
line = dldi
dldi = SMOOTH(dldi, 5)[2:n + 2]
hthe[xi, yi] = old_div(dldi, dtheta) # First estimate of hthe
# Get outboard midplane
if period and xi == 0:
m = numpy.argmax(Rxy[0, yi])
ymidplane = yi[m]
if last == 1: break
print("Midplane index ", ymidplane)
fb0 = force_balance(psixy, Rxy, Bpxy, Btxy, hthe, pressure)
print("Force imbalance: ", numpy.mean(numpy.abs(fb0)),
numpy.max(numpy.abs(fb0)))
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
# Correct pressure using hthe
print("Calculating pressure profile from force balance")
try:
# Calculate force balance
dpdx = old_div((-Bpxy * DDX(xcoord, Bpxy * hthe) -
Btxy * hthe * DDX(xcoord, Btxy) -
(Btxy * Btxy * hthe / Rxy) * DDX(xcoord, Rxy)),
(MU * hthe))
# Surface average
dpdx2 = surface_average(dpdx, mesh)
pres = numpy.zeros((nx, ny))
# Integrate to get pressure
for i in range(ny):
pres[:, i] = int_func(psixy[:, i], dpdx2[:, i])
pres[:, i] = pres[:, i] - pres[nx - 1, i]
status = gen_surface(mesh=mesh) # Start generator
while True:
# Get the next domain
period, yi, xi, last = gen_surface(period=None, last=None, xi=None)
ma = numpy.max(pres[xi, yi])
for i in range(numpy.size(yi)):
pres[:, yi[i]] = pres[:, yi[i]] - pres[xi, yi[i]] + ma
if last == 1: break
pres = pres - numpy.min(pres)
# Some sort of smoothing here?
fb0 = force_balance(psixy, Rxy, Bpxy, Btxy, hthe, pres)
print("Force imbalance: ", numpy.mean(numpy.abs(fb0)),
numpy.max(numpy.abs(fb0)))
#!P.MULTI=[0,0,2,0,0]
fig = figure(figsize=(7, 11))
subplots_adjust(left=.07,
bottom=.07,
right=0.95,
top=0.95,
wspace=.3,
hspace=.25)
SURFACE(pressure, fig, xtitle="X", ytitle="Y", var='Pa', sub=[2, 1, 1])
title("Input pressure")
SURFACE(pres, fig, xtitle="X", ytitle="Y", var='Pa', sub=[2, 1, 2])
title("New pressure")
# arrange the plot on the screen
# mngr = get_current_fig_manager()
# geom = mngr.window.geometry()
# x,y,dx,dy = geom.getRect()
# mngr.window.setGeometry(0, 0, dx, dy)
#
show(block=False)
calcp = settings.calcp
if calcp == -1:
calcp = query_yes_no(
"Keep new pressure?") #, gui=gui, dialog_parent=parent)
else:
time.sleep(2)
if calcp == 1:
pressure = pres
dpdpsi = dpdx2
except Exception:
print("WARNING: Pressure profile calculation failed: "
) #, !ERROR_STATE.MSG
pass
#CATCH, /cancel
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
# Correct f = RBt using force balance
calcbt = settings.calcbt
if calcbt == -1:
calcbt = query_yes_no("Correct f=RBt using force balance?"
) #, gui=gui, dialog_parent=parent)
if calcbt == 1:
new_Btxy = newton_Bt(psixy, Rxy, Btxy, Bpxy, pres, hthe, mesh)
fb0 = force_balance(psixy, Rxy, Bpxy, new_Btxy, hthe, pressure)
print("force imbalance: ", numpy.mean(numpy.abs(fb0)),
numpy.max(numpy.abs(fb0)))
fig = figure(figsize=(7, 11))
subplots_adjust(left=.07,
bottom=.07,
right=0.95,
top=0.95,
wspace=.3,
hspace=.25)
subplot(211)
SURFACE(Btxy, fig, xtitle="X", ytitle="Y", var='T', sub=[2, 1, 1])
title("Input Bt")
subplot(212)
SURFACE(new_Btxy, fig, xtitle="X", ytitle="Y", var='T', sub=[2, 1, 2])
title("New Bt")
# arrange the plot on the screen
#mngr = get_current_fig_manager()
#geom = mngr.window.geometry()
#x,y,dx,dy = geom.getRect()
#mngr.window.setGeometry(600, 0, dx, dy)
show(block=False)
calcbt = settings.calcbt
if calcbt == -1:
calcbt = query_yes_no(
"Keep new Bt?") #, gui=gui, dialog_parent=parent)
if calcbt == 1:
Btxy = new_Btxy
Bxy = numpy.sqrt(Btxy**2 + Bpxy**2)
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
# CALCULATE HTHE
# Modify hthe to fit force balance using initial guess
# Does not depend on signs
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
calchthe = settings.calchthe
if calchthe == -1:
calchthe = query_yes_no("Adjust hthe using force balance?"
) #, gui=gui, dialog_parent=parent)
if calchthe == 1:
# This doesn't behave well close to the x-points
fixhthe = numpy.int(old_div(nx, 2))
nh = correct_hthe(Rxy,
psixy,
Btxy,
Bpxy,
hthe,
pressure,
fixhthe=fixhthe)
fb0 = force_balance(psixy, Rxy, Bpxy, Btxy, nh, pressure)
print("Force imbalance: ", numpy.mean(numpy.abs(fb0)),
numpy.max(numpy.abs(fb0)))
print("numpy.maximum difference in hthe: ",
numpy.max(numpy.abs(hthe - nh)))
print("numpy.maximum percentage difference: ",
100. * numpy.max(numpy.abs(old_div((hthe - nh), hthe))))
#!P.multi=[0,0,1,0,0]
fig = figure(figsize=(7, 4))
title("Poloidal arc length at midplane. line is initial estimate")
plot(hthe[:, 0], '-')
plot(nh[:, 0], 'r-+')
# arrange the plot on the screen
#mngr = get_current_fig_manager()
#geom = mngr.window.geometry()
#x,y,dx,dy = geom.getRect()
#mngr.window.setGeometry(0, 1150, dx, dy)
show(block=False)
if query_yes_no(
"Keep new hthe?") == 1: #, gui=gui, dialog_parent=parent) :
hthe = nh
if smoothhthe != None:
# Smooth hthe to prevent large jumps in X or Y. This
# should be done by creating a better mesh in the first place
# Need to smooth in Y and X otherwise smoothing in X
# produces discontinuities in Y
hold = hthe
if 1:
# Nonlinear smoothing. Tries to smooth only regions with large
# changes in gradient
hthe = 0. # smooth_nl(hthe, mesh)
else:
# Just use smooth in both directions
for i in range(ny):
hthe[:, i] = SMOOTH(SMOOTH(hthe[:, i], 10), 10)
status = gen_surface(mesh=mesh) # Start generator
while True:
# Get the next domain
period, yi, xi, last = gen_surface(period=None, last=None, xi=None)
n = numpy.size(yi)
if period:
hthe[xi, yi] = (SMOOTH([
hthe[xi, yi[(n - 4):(n - 1)]], hthe[xi, yi], hthe[xi,
yi[0:3]]
], 4))[4:(n + 3)]
else:
hthe[xi, yi] = SMOOTH(hthe[xi, yi], 4)
if last == 1: break
# Calculate field-line pitch
pitch = hthe * Btxy / (Bpxy * Rxy)
# derivative with psi
dqdpsi = DDX(psixy, pitch)
qinty, qloop = int_y(pitch,
mesh,
loop=0,
nosmooth='nosmooth',
simple='simple')
qinty = qinty * dtheta
qloop = qloop * dtheta
sinty = int_y(dqdpsi, mesh, nosmooth='nosmooth', simple='simple') * dtheta
# NOTE: This is only valid in the core
pol_angle = numpy.zeros((nx, ny))
for i in range(nx):
pol_angle[i, :] = 2.0 * numpy.pi * qinty[i, :] / qloop[i]
#;;;;;;;;;;;;;;;;;;; THETA_ZERO ;;;;;;;;;;;;;;;;;;;;;;
# re-set zshift to be zero at the outboard midplane
print("MIDPLANE INDEX = ", ymidplane)
status = gen_surface(mesh=mesh) # Start generator
while True:
# Get the next domain
period, yi, xi, last = gen_surface(period=None, last=None, xi=None)
w = numpy.size(numpy.where(yi == ymidplane))
if w > 0:
# Crosses the midplane
qinty[xi, yi] = qinty[xi, yi] - qinty[xi, ymidplane]
sinty[xi, yi] = sinty[xi, yi] - sinty[xi, ymidplane]
else:
# Doesn't include a point at the midplane
qinty[xi, yi] = qinty[xi, yi] - qinty[xi, yi[0]]
sinty[xi, yi] = sinty[xi, yi] - sinty[xi, yi[0]]
if last == 1: break
print("")
print("==== Calculating curvature ====")
#;;;;;;;;;;;;;;;;;;; CURVATURE ;;;;;;;;;;;;;;;;;;;;;;;
# Calculating b x kappa
if curv == None:
print("*** Calculating curvature in toroidal coordinates")
thetaxy = numpy.zeros((nx, ny))
status = gen_surface(mesh=mesh) # Start generator
while True:
# Get the next domain
period, yi, xi, last = gen_surface(period=None, last=None, xi=None)
thetaxy[xi,
yi] = numpy.arange(numpy.size(yi)).astype(float) * dtheta
if last == 1: break
bxcv = curvature(nx,
ny,
Rxy,
Zxy,
Brxy,
Bzxy,
Btxy,
psixy,
thetaxy,
hthe,
mesh=mesh)
bxcvx = bpsign * bxcv.psi
bxcvy = bxcv.theta
bxcvz = bpsign * (bxcv.phi - sinty * bxcv.psi - pitch * bxcv.theta)
# x borders
bxcvx[0, :] = bxcvx[1, :]
bxcvx[nx - 1, :] = bxcvx[nx - 2, :]
bxcvy[0, :] = bxcvy[1, :]
bxcvy[nx - 1, :] = bxcvy[nx - 2, :]
bxcvz[0, :] = bxcvz[1, :]
bxcvz[nx - 1, :] = bxcvz[nx - 2, :]
elif curv == 1:
# Calculate on R-Z mesh and then interpolate onto grid
# ( cylindrical coordinates)
print("*** Calculating curvature in cylindrical coordinates")
bxcv = rz_curvature(rz_grid)
# DCT methods cause spurious oscillations
# Linear interpolation seems to be more robust
bxcv_psi = numpy.interp(bxcv.psi, mesh.Rixy, mesh.Zixy)
bxcv_theta = old_div(numpy.interp(bxcv.theta, mesh.Rixy, mesh.Zixy),
hthe)
bxcv_phi = numpy.interp(bxcv.phi, mesh.Rixy, mesh.Zixy)
# If Bp is reversed, then Grad x = - Grad psi
bxcvx = bpsign * bxcv_psi
bxcvy = bxcv_theta
bxcvz = bpsign * (bxcv_phi - sinty * bxcv_psi - pitch * bxcv_theta)
elif curv == 2:
# Curvature from Curl(b/B)
bxcvx = bpsign * (Bpxy * Btxy * Rxy * DDY(old_div(1., Bxy), mesh) /
hthe)
bxcvy = -bpsign * Bxy * Bpxy * DDX(xcoord,
Btxy * Rxy / Bxy ^ 2) / (2. * hthe)
bxcvz = Bpxy ^ 3 * DDX(xcoord, old_div(
hthe, Bpxy)) / (2. * hthe * Bxy) - Btxy * Rxy * DDX(
xcoord, old_div(Btxy, Rxy)) / (2. * Bxy) - sinty * bxcvx
else:
# calculate in flux coordinates.
print("*** Calculating curvature in flux coordinates")
dpb = numpy.zeros((nx, ny)) # quantity used for y and z components
for i in range(ny):
dpb[:, i] = MU * dpdpsi / Bxy[:, i]
dpb = dpb + DDX(xcoord, Bxy)
bxcvx = bpsign * (Bpxy * Btxy * Rxy * DDY(old_div(1., Bxy), mesh) /
hthe)
bxcvy = bpsign * (Bpxy * Btxy * Rxy * dpb / (hthe * Bxy ^ 2))
bxcvz = -dpb - sinty * bxcvx
if smoothcurv:
# Smooth curvature to prevent large jumps
# Nonlinear smoothing. Tries to smooth only regions with large
# changes in gradient
bz = bxcvz + sinty * bxcvx
print("Smoothing bxcvx...")
bxcvx = 0. #smooth_nl(bxcvx, mesh)
print("Smoothing bxcvy...")
bxcvy = 0. #smooth_nl(bxcvy, mesh)
print("Smoothing bxcvz...")
bz = 0. #smooth_nl(bz, mesh)
bxcvz = bz - sinty * bxcvx
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
# CALCULATE PARALLEL CURRENT
#
# Three ways to calculate Jpar0:
# 1. From fprime and pprime
# 2. From Curl(B) in field-aligned coords
# 3. From the curvature
#
# Provides a way to check if Btor should be reversed
#
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
print("")
print("==== Calculating parallel current ====")
jpar0 = -Bxy * fprime / MU - Rxy * Btxy * dpdpsi / Bxy
# Set to zero in PF and SOL
status = gen_surface(mesh=mesh) # Start generator
while True:
# Get the next domain
period, yi, xi, last = gen_surface(period=None, last=None, xi=None)
if period == None: jpar0[xi, yi] = 0.0
if last == 1: break
# Curl(B) expression for Jpar0 (very noisy usually)
j0 = (bpsign * ((Bpxy * Btxy * Rxy / (Bxy * hthe)) *
(DDX(xcoord, Bxy**2 * hthe / Bpxy) - bpsign * Btxy * Rxy *
DDX(xcoord, Btxy * hthe /
(Rxy * Bpxy))) - Bxy * DDX(xcoord, Btxy * Rxy)) / MU)
# Create a temporary mesh structure to send to adjust_jpar
tmp_mesh = Bunch(mesh,
bxcvx=bxcvx,
bxcvy=bxcvy,
bxcvz=bxcvz,
Bpxy=Bpxy,
Btxy=Btxy,
Bxy=Bxy,
dx=dx,
dy=dy,
hthe=hthe,
jpar0=jpar0,
pressure=pressure)
tmp_mesh.psixy = psixy
jpar = adjust_jpar(tmp_mesh, noplot='noplot')
#!P.multi=[0,2,2,0,0]
fig = figure(figsize=(15, 11))
subplots_adjust(left=.07,
bottom=.07,
right=0.95,
top=0.95,
wspace=.3,
hspace=.25)
subplot(221)
SURFACE(jpar0, fig, xtitle="X", ytitle="Y", var='A', sub=[2, 2, 1])
title("Jpar from F' and P'")
subplot(222)
SURFACE(jpar, fig, xtitle="X", ytitle="Y", var='A', sub=[2, 2, 2])
title("Jpar from curvature")
subplot(223)
plot(jpar0[0, :], '-', jpar[0, :], '+')
ylim([
numpy.min([jpar0[0, :], jpar[0, :]]),
numpy.max([jpar0[0, :], jpar[0, :]])
])
title("jpar at x=0. Solid from f' and p'")
subplot(224)
plot(jpar0[:, ymidplane], '-', jpar[:, ymidplane], '+')
ylim([
numpy.min([jpar0[:, ymidplane], jpar[:, ymidplane]]),
numpy.max([jpar0[:, ymidplane], jpar[:, ymidplane]])
])
title("Jpar at y=" + numpy.str(ymidplane) + " Solid from f' and p'")
# arrange the plot on the screen
#mngr = get_current_fig_manager()
#geom = mngr.window.geometry()
#x,y,dx,dy = geom.getRect()
#mngr.window.setGeometry(1350, 0, dx, dy)
show(block=False)
# !P.multi=0
calcjpar = settings.calcjpar
if calcjpar == -1:
calcjpar = query_yes_no(
"Use Jpar from curvature?") #, gui=gui, dialog_parent=parent)
if calcjpar == True:
jpar0 = jpar
if 0:
# Try smoothing jpar0 in psi, preserving zero points and maxima
jps = jpar0
for y in range(ny):
j = jpar0[:, y]
js = j
ma = numpy.max(numpy.abs(j))
ip = numpy.argmax(numpy.abs(j))
if (ma < 1.e-4) or (ip == 0):
jps[:, y] = j
level = 1.
#i0 = MAX(WHERE(ABS(j[0:ip]) LT level))
i1 = numpy.min(numpy.where(numpy.abs(j[ip::]) < level))
#IF i0 LE 0 THEN i0 = 1
i0 = 1
if i1 == -1:
i1 = nx - 2
else:
i1 = i1 + ip
if (ip <= i0) or (ip >= i1):
# Now preserve starting and end points, and peak value
div = numpy.int(old_div(
(i1 - i0),
10)) + 1 # reduce number of points by this factor
inds = [i0] # first point
for i in [i0 + div, ip - div, div]:
inds = [inds, i]
inds = [inds, ip] # Put in the peak point
# Calculate spline interpolation of inner part
js[0:ip] = spline_mono(inds,
j[inds],
numpy.arange(ip + 1),
yp0=(j[i0] - j[i0 - 1]),
ypn_1=0.0)
inds = [ip] # peak point
for i in [ip + div, i1 - div, div]:
inds = [inds, i]
inds = [inds, i1] # Last point
js[ip:i1] = spline_mono(inds,
j[inds],
ip + numpy.arange(i1 - ip + 1),
yp0=0.0,
ypn_1=(j[i1 + 1] - j[i1]))
jps[:, y] = js
#;;;;;;;;;;;;;;;;;;; TOPOLOGY ;;;;;;;;;;;;;;;;;;;;;;;
# Calculate indices for backwards-compatibility
nr = numpy.size(mesh.nrad)
np = numpy.size(mesh.npol)
if (nr == 2) and (np == 3):
print("Single null equilibrium")
ixseps1 = mesh.nrad[0]
ixseps2 = nx
jyseps1_1 = mesh.npol[0] - 1
jyseps1_2 = mesh.npol[0] + numpy.int(old_div(mesh.npol[1], 2))
ny_inner = jyseps1_2
jyseps2_1 = jyseps1_2
jyseps2_2 = ny - mesh.npol[2] - 1
elif (nr == 3) and (np == 6):
print("Double null equilibrium")
ixseps1 = mesh.nrad[0]
ixseps2 = ixseps1 + mesh.nrad[1]
jyseps1_1 = mesh.npol[0] - 1
jyseps2_1 = jyseps1_1 + mesh.npol[1]
ny_inner = jyseps2_1 + mesh.npol[2] + 1
jyseps1_2 = ny_inner + mesh.npol[3] - 1
jyseps2_2 = jyseps1_2 + mesh.npol[4]
elif (nr == 1) and (np == 1):
print("Single domain")
ixseps1 = nx
ixseps2 = nx
jyseps1_1 = -1
jyseps1_2 = numpy.int(old_div(ny, 2))
jyseps2_1 = numpy.int(old_div(ny, 2))
ny_inner = numpy.int(old_div(ny, 2))
jyseps2_2 = ny - 1
else:
print("***************************************")
print("* WARNING: Equilibrium not recognised *")
print("* *")
print("* Check mesh carefully! *")
print("* *")
print("* Contact Ben Dudson *")
print("* [email protected] *")
print("***************************************")
ixseps1 = -1
ixseps2 = -1
jyseps1_1 = -1
jyseps1_2 = numpy.int(old_div(ny, 2))
jyseps2_1 = numpy.int(old_div(ny, 2))
ny_inner = numpy.int(old_div(ny, 2))
jyseps2_2 = ny - 1
print("Generating plasma profiles:")
print(" 1. Flat temperature profile")
print(" 2. Flat density profile")
print(" 3. Te proportional to density")
while True:
opt = input("Profile option:")
if eval(opt) >= 1 and eval(opt) <= 3: break
if eval(opt) == 1:
# flat temperature profile
print("Setting flat temperature profile")
while True:
Te_x = eval(input("Temperature (eV):"))
# get density
Ni = old_div(pressure, (2. * Te_x * 1.602e-19 * 1.0e20))
print("numpy.maximum density (10^20 m^-3):", numpy.max(Ni))
done = query_yes_no("Is this ok?")
if done == 1: break
Te = numpy.zeros((nx, ny)) + Te_x
Ti = Te
Ni_x = numpy.max(Ni)
Ti_x = Te_x
elif eval(opt) == 2:
print("Setting flat density profile")
while True:
Ni_x = eval(input("Density [10^20 m^-3]:"))
# get temperature
Te = old_div(pressure, (2. * Ni_x * 1.602e-19 * 1.0e20))
print("numpy.maximum temperature (eV):", numpy.max(Te))
if query_yes_no("Is this ok?") == 1: break
Ti = Te
Ni = numpy.zeros((nx, ny)) + Ni_x
Te_x = numpy.max(Te)
Ti_x = Te_x
else:
print("Setting te proportional to density")
while True:
Te_x = eval(input("Maximum temperature [eV]:"))
Ni_x = old_div(numpy.max(pressure),
(2. * Te_x * 1.602e-19 * 1.0e20))
print("Maximum density [10^20 m^-3]:", Ni_x)
Te = Te_x * pressure / numpy.max(pressure)
Ni = Ni_x * pressure / numpy.max(pressure)
if query_yes_no("Is this ok?") == 1: break
Ti = Te
Ti_x = Te_x
rmag = numpy.max(numpy.abs(Rxy))
print("Setting rmag = ", rmag)
bmag = numpy.max(numpy.abs(Bxy))
print("Setting bmag = ", bmag)
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
# save to file
# open a new netCDF file for writing.
handle = file_open(output)
print("Writing grid to file " + output)
# Size of the grid
s = file_write(handle, "nx", nx)
s = file_write(handle, "ny", ny)
# Topology for original scheme
s = file_write(handle, "ixseps1", ixseps1)
s = file_write(handle, "ixseps2", ixseps2)
s = file_write(handle, "jyseps1_1", jyseps1_1)
s = file_write(handle, "jyseps1_2", jyseps1_2)
s = file_write(handle, "jyseps2_1", jyseps2_1)
s = file_write(handle, "jyseps2_2", jyseps2_2)
s = file_write(handle, "ny_inner", ny_inner)
# Grid spacing
s = file_write(handle, "dx", dx)
s = file_write(handle, "dy", dy)
s = file_write(handle, "ShiftAngle", qloop)
s = file_write(handle, "zShift", qinty)
s = file_write(handle, "pol_angle", pol_angle)
s = file_write(handle, "ShiftTorsion", dqdpsi)
s = file_write(handle, "Rxy", Rxy)
s = file_write(handle, "Zxy", Zxy)
s = file_write(handle, "Bpxy", Bpxy)
s = file_write(handle, "Btxy", Btxy)
s = file_write(handle, "Bxy", Bxy)
s = file_write(handle, "hthe", hthe)
s = file_write(handle, "sinty", sinty)
s = file_write(handle, "psixy", psixy)
# Topology for general configurations
s = file_write(handle, "yup_xsplit", mesh.yup_xsplit)
s = file_write(handle, "ydown_xsplit", mesh.ydown_xsplit)
s = file_write(handle, "yup_xin", mesh.yup_xin)
s = file_write(handle, "yup_xout", mesh.yup_xout)
s = file_write(handle, "ydown_xin", mesh.ydown_xin)
s = file_write(handle, "ydown_xout", mesh.ydown_xout)
s = file_write(handle, "nrad", mesh.nrad)
s = file_write(handle, "npol", mesh.npol)
# plasma profiles
s = file_write(handle, "pressure", pressure)
s = file_write(handle, "Jpar0", jpar0)
s = file_write(handle, "Ni0", Ni)
s = file_write(handle, "Te0", Te)
s = file_write(handle, "Ti0", Ti)
s = file_write(handle, "Ni_x", Ni_x)
s = file_write(handle, "Te_x", Te_x)
s = file_write(handle, "Ti_x", Ti_x)
s = file_write(handle, "bmag", bmag)
s = file_write(handle, "rmag", rmag)
# Curvature
s = file_write(handle, "bxcvx", bxcvx)
s = file_write(handle, "bxcvy", bxcvy)
s = file_write(handle, "bxcvz", bxcvz)
# Psi range
s = file_write(handle, "psi_axis", mesh.faxis)
psi_bndry = mesh.faxis + mesh.fnorm
s = file_write(handle, "psi_bndry", psi_bndry)
file_close, handle
print("DONE")
def create_grid( F, R, Z, in_settings, critical,
boundary=None,
iter=None,
fpsi=None, fast=None):#, # f(psi) = R*Bt current function
#nrad_flexible,
#single_rad_grid,
#xpt_mindist, xpt_mul, strictbndry,debug):
# if size(nrad_flexible) == 0 :
# nrad_flexible = 0
if iter==None:
iter = 0
if iter > 3:
print("ERROR: Too many iterations")
return #, {error:1}
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
# Check the settings
# If a setting is missing, set a default value
# inspect.getargspec(create_grid)
# if N_PARAMS() LT 3 THEN BEGIN
# PRINT, "ERROR: Need at least a 2D array of psi values, R and Z arrays"
# RETURN, {error:1}
#ENDIF ELSE IF N_PARAMS() LT 4 THEN BEGIN
# ; Settings omitted. Set defaults
# print "Settings not given -> using default values"
# settings = {psi_inner:0.9,
# psi_outer:1.1,
# nrad:36,
# npol:64,
# rad_peaking:0.0,
# pol_peaking:0.0,
# parweight:0.0}
# ENDIF ELSE BEGIN
# print "Checking settings"
settings = in_settings # So the input isn't changed
# str_check_present, settings, 'psi_inner', 0.9
# str_check_present, settings, 'psi_outer', 1.1
# str_check_present, settings, 'nrad', 36
# str_check_present, settings, 'npol', 64
# str_check_present, settings, 'rad_peaking', 0.0
# str_check_present, settings, 'pol_peaking', 0.0
# str_check_present, settings, 'parweight', 0.0
#ENDELSE
s = numpy.ndim(F)
s1 = numpy.shape(F)
if s != 2:
print("ERROR: First argument must be 2D array of psi values")
return #, {error:1}
nx = s1[0]
ny = s1[1]
s = numpy.ndim(R)
s1 = numpy.size(R)
if s != 1 or s1 != nx :
print("ERROR: Second argument must be 1D array of major radii")
return # {error:1}
s = numpy.ndim(Z)
s1 = numpy.size(Z)
if s != 1 or s1 != ny:
print("ERROR: Second argument must be 1D array of heights")
return # {error:1}
# Get an even number of points for efficient FFTs
if nx % 2 == 1:
# odd number of points in R. Cut out last point
R = R[0:(nx-1)]
F = F[0:(nx-1), :]
nx = nx - 1
if ny % 2 == 1:
# Same for Z
Z = Z[0:(ny-1)]
F = F[:,0:(ny-1)]
ny = ny - 1
if boundary != None:
s = numpy.ndim(boundary)
s1= numpy.shape(boundary)
if s != 2 or s1[0] != 2:
print("WARNING: boundary must be a 2D array: [2, n]. Ignoring")
boundary = 0
else:
# Calculate indices
bndryi = numpy.zeros((2,1188))
bndryi[0,:] = numpy.interp(bndryi[0,:], R, numpy.arange(0.,nx))
bndryi[1,:] = numpy.interp(bndryi[1,:], Z, numpy.arange(0.,ny))
if bndryi == None :
bndryi = numpy.zeros((2,4))
bndryi[0,:] = [1, nx-1, nx-1, 1]
bndryi[1,:] = [1, 1, ny-1, ny-1]
#;;;;;;;;;;;;;; Psi interpolation data ;;;;;;;;;;;;;;
interp_data = Bunch(nx=nx, ny=ny,
method=0,
f= F) # Always include function
if fast == 'fast':
print("Using Fast settings")
interp_data.method = 2
#;;;;;;;;;;;;;;; First plot ;;;;;;;;;;;;;;;;
nlev = 100
minf = numpy.min(F)
maxf = numpy.max(F)
levels = numpy.arange(numpy.float(nlev))*(maxf-minf)/numpy.float(nlev-1) + minf
Rr=numpy.tile(R,ny).reshape(ny,nx).T
Zz=numpy.tile(Z,nx).reshape(nx,ny)
contour( Rr, Zz, F, levels=levels)
# arrange the plot on the screen
#mngr = get_current_fig_manager()
#geom = mngr.window.geometry()
#x,y,dx,dy = geom.getRect()
#mngr.window.setGeometry(100, 100, dx, dy)
# if boundary != None :
# plot(boundary[0,:],boundary[1,:],'r-')
show(block=False)
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
n_opoint = critical.n_opoint
n_xpoint = critical.n_xpoint
primary_opt = critical.primary_opt
inner_sep = critical.inner_sep
opt_ri = critical.opt_ri
opt_zi = critical.opt_zi
opt_f = critical.opt_f
xpt_ri = numpy.array(critical.xpt_ri).flatten()
xpt_zi = numpy.array(critical.xpt_zi).flatten()
xpt_f = numpy.array(critical.xpt_f).flatten()
# Overplot the separatrices, O-points
#oplot_critical, F, R, Z, critical
# Psi normalisation factors
faxis = opt_f[primary_opt]
fnorm = xpt_f[inner_sep] - opt_f[primary_opt]
# From normalised psi, get range of f
f_inner = faxis + numpy.min(settings.psi_inner)*fnorm
f_outer = faxis + numpy.max(settings.psi_outer)*fnorm
# Check the number of x-points
if critical.n_xpoint == 0 :
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
# Grid entirely in the core
print("Generating grid entirely in the core")
nrad = numpy.sum(settings.nrad) # Add up all points
npol = numpy.sum(settings.npol)
rad_peaking = settings.rad_peaking[0] # Just the first region
pol_peaking = settings.pol_peaking[0]
# work out where to put the surfaces in the core
fvals = radial_grid(nrad, f_inner, f_outer, 1, 1, [xpt_f[inner_sep]], rad_peaking)
fvals = fvals.flatten()
# Create a starting surface
sind = numpy.int(old_div(nrad, 2))
start_f = fvals[sind]
# contour_lines( F, numpy.arange(nx).astype(float), numpy.arange(ny).astype(float), levels=[start_f])
cs=contour( Rr, Zz, F, levels=[start_f])
p = cs.collections[0].get_paths()
#
# You might get more than one contours for the same start_f. We need to keep the closed one
vn=numpy.zeros(numpy.size(p))
v = p[0].vertices
vn[0]=numpy.shape(v)[0]
xx=[v[:,0]]
yy=[v[:,1]]
if numpy.shape(vn)[0] > 1:
for i in range(1,numpy.shape(vn)[0]):
v = p[i].vertices
vn[i]=numpy.shape(v)[0]
xx.append(v[:,0])
yy.append(v[:,1])
#xx = [xx,v[:,0]]
#yy = [yy,v[:,1]]
print("PRIMARY: ", primary_opt, opt_ri[primary_opt], opt_zi[primary_opt])
if numpy.shape(vn)[0] > 1 :
# Find the surface closest to the o-point
opt_r = numpy.interp(opt_ri[primary_opt], numpy.arange(len(R)), R)
opt_z = numpy.interp(opt_zi[primary_opt], numpy.arange(len(Z)), Z)
ind = closest_line(xx, yy, opt_r, opt_z)
x=xx[ind]
y=yy[ind]
print("Contour: ", ind)
else:
ind = 0
x=xx[0]
y=yy[0]
# plot the start_f line
zc = cs.collections[0]
setp(zc, linewidth=4)
clabel(cs, [start_f], # label the level
inline=1,
fmt='%9.6f',
fontsize=14)
draw()
show(block=False)
#
ans=query_yes_no('Press enter to create grid')
if ans != 1 :
show()
sys.exit()
start_ri, start_zi=transform_xy(x,y,R,Z)
## Make sure that the line goes clockwise
#
m = numpy.argmax(numpy.interp(start_zi,numpy.arange(Z.size).astype(float), Z))
if (numpy.gradient(numpy.interp(start_ri, numpy.arange(R.size).astype(float), R)))[m] < 0.0:
# R should be increasing at the top. Need to reverse
start_ri = start_ri[::-1]
start_zi = start_zi[::-1]
print('points reversed')
## Last point should be the same as the first
#
# Smooth and refine the starting location
np = numpy.size(start_ri)
s = 3
ar=numpy.append(numpy.append(start_ri[(np-s-1):(np-1)], start_ri), start_ri[1:s+1])
start_ri = SMOOTH(ar, window_len=s)[s+1:(np+s+1)]
az=numpy.append(numpy.append(start_zi[(np-s-1):(np-1)], start_zi), start_zi[1:s+1])
start_zi = SMOOTH(az, window_len=s)[s+1:(np+s+1)]
for i in range (np) :
ri1=0.
zi1=0.
out=follow_gradient( interp_data, R, Z, start_ri[i], start_zi[i], start_f, ri1, zi1 )
status=out.status
ri1=out.rinext
zi1=out.zinext
start_ri[i] = ri1
start_zi[i] = zi1
a = grid_region(interp_data, R, Z,
start_ri, start_zi,
fvals,
sind,
npol,
boundary=boundary,
fpsi=fpsi,
parweight=settings.parweight,
oplot='oplot')
plot( numpy.append(a.rxy[0,:], a.rxy[0,0]), numpy.append(a.zxy[0,:], a.zxy[0,0]), 'r')
for i in range (1, nrad) :
plot( numpy.append(a.rxy[i,:], a.rxy[i,0]), numpy.append(a.zxy[i,:], a.zxy[i,0]), 'r')
for i in range (0, npol-1) :
plot( a.rxy[:,i], a.zxy[:,i], 'r')
draw()
# Get other useful variables
psixy = numpy.zeros((nrad, npol))
for i in range (0, npol) :
psixy[:,i] = old_div((fvals - faxis),fnorm) # to get normalised psi
# Calculate magnetic field components
dpsidR = numpy.zeros((nrad, npol))
dpsidZ = numpy.zeros((nrad, npol))
interp_data.method = 2
for i in range (nrad) :
for j in range (npol) :
out = local_gradient( interp_data, a.rixy[i,j], a.zixy[i,j], status=0, dfdr=0., dfdz=0.)
status=out.status
dfdr=out.dfdr[0][0]
dfdz=out.dfdz[0][0]
# dfd* are derivatives wrt the indices. Need to multiply by dr/di etc
dpsidR[i,j] = old_div(dfdr,numpy.interp(a.rixy[i,j], numpy.arange(R.size).astype(float),numpy.gradient(R)))
dpsidZ[i,j] = old_div(dfdz,numpy.interp(a.zixy[i,j], numpy.arange(Z.size).astype(float),numpy.gradient(Z)))
# Set topology to connect in the core
yup_xsplit = [nrad]
ydown_xsplit = [nrad]
yup_xin = [0]
yup_xout = [-1]
ydown_xin = [0]
ydown_xout = [-1]
#;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
# Create result structure
result = Bunch(error=0, # Signal success
psi_inner=settings.psi_inner, psi_outer=settings.psi_outer, # Unchanged psi range
nrad=nrad, npol=npol, #Number of points in radial and poloidal direction
Rixy=a.rixy, Zixy=a.zixy, # Indices into R and Z of each point
Rxy=a.rxy, Zxy=a.zxy, # Location of each grid point
psixy=psixy, # Normalised psi for each point
dpsidR=dpsidR, dpsidZ=dpsidZ, # Psi derivatives (for Bpol)
faxis=faxis, fnorm=fnorm, # Psi normalisation factors
settings=settings, # Settings used to create grid
critical=critical, # Critical points
yup_xsplit=yup_xsplit, # X index where domain splits (number of points in xin)
ydown_xsplit=ydown_xsplit,
yup_xin=yup_xin, yup_xout=yup_xout, # Domain index to connect to
ydown_xin=ydown_xin, ydown_xout=ydown_xout)
return result