def force_balance(psixy, Rxy, Bpxy, Btxy, hthe, pxy):
MU = 4.e-7 * numpy.pi
a = old_div(DDX(psixy, Rxy), Rxy)
b = MU * DDX(psixy, pxy) - Bpxy * DDX(psixy, Bpxy * hthe) / hthe
return DDX(psixy, Btxy) + a * Btxy + old_div(b, Btxy)
def newton_Bt ( psixy, Rxy, Btxy, Bpxy, pxy, hthe, mesh):
#global psi, a, b
MU = 4.e-7*numpy.pi
s = numpy.shape(Rxy)
nx = s[0]
ny = s[1]
axy = old_div(DDX(psixy, Rxy), Rxy)
bxy = MU*DDX(psixy, pxy) - Bpxy*DDX(psixy, Bpxy*hthe)/hthe
Btxy2 = numpy.zeros((nx, ny))
for i in range (ny) :
psi = psixy[:,i]
a = axy[:,i]
b = bxy[:,i]
print("Solving f for y=", i)
sol=root(Bt_func, Btxy[:,i], args=(psi, a, b) )
Btxy2[:,i] = sol.x
# Average f over flux surfaces
fxy = surface_average(Btxy2*Rxy, mesh)
return old_div(fxy, Rxy)
def correct_hthe ( Rxy, psixy, Btxy, Bpxy, hthe, pressure, fixhthe=None):
# global xarr, fixpos, h0, a, b
s = numpy.shape(Rxy)
nx = s[0]
ny = s[1]
MU = 4.e-7*numpy.pi
if fixhthe==None : fixhthe = 0
if fixhthe < 0 : fixhthe = 0
if fixhthe > nx-1 : fixhthe = nx-1
fixpos = fixhthe
print("FIX = ", fixhthe)
axy =( Btxy*DDX(psixy, Btxy) + Bpxy*DDX(psixy, Bpxy)
+ Btxy**2*DDX(psixy, Rxy)/Rxy + MU*DDX(psixy, pressure))
bxy = Bpxy**2
nh = numpy.zeros((nx, ny))
nh[fixhthe,:] = hthe[fixhthe,:]
for i in range (ny) :
print("Correcting y index ", i)
xarr = psixy[:,i]
a = axy[:,i]
b = bxy[:,i]
h0 = hthe[fixhthe,i]
if fixhthe == 0 :
htmp = hthe[1::,i]
elif fixhthe >= nx-1 :
# fix last point
htmp = hthe[0:(nx-1),i]
fixhthe = nx-1
else:
# fix somewhere in the middle
htmp = numpy.append(hthe[0:(fixhthe),i], hthe[(fixhthe+1)::,i])
sol = root(new_hfunc, htmp , args=(xarr,a,b,h0,fixpos))
htmp=sol.x
if fixhthe == 0 :
nh[1::] = htmp
elif fixhthe >= nx-1 :
nh[0:(nx-1), i] = htmp
else:
nh[0:(fixhthe), i] = htmp[0:(fixhthe)]
nh[(fixhthe+1)::, i] = htmp[fixhthe::]
w = numpy.size(numpy.where(nh[:,i] < 0.0))
if w > 0 :
print("Error in hthe solver: Negative solution at y = ", i)
#sys.exit()
return nh
def solve_f(Rxy, psixy, pxy, Bpxy, hthe):
MU = 4.e-7 * numpy.pi
s = numpy.shape(Rxy)
nx = s[0]
ny = s[1]
a = old_div(-DDX(psixy, Rxy), Rxy)
b = -MU * DDX(psixy, pxy) - Bpxy * DDX(Bpxy * hthe) / hthe
def adjust_jpar(grid, smoothp=None, jpar=None, noplot=None):
#type = numpy.type(grid)
#if type == 'str' :
# #; Input is a string. Read in the data
# data = file_import(grid)
#elif type == 'bunch.Bunch' :
# #; A structure, hopefully containing the grid data
data = grid
#else:
# print "ERROR: Not sure what to do with this type of grid input"
# return
#; Find the inboard midplane. Use inboard since this is maximum B
#; Matching here rather than outboard produces more realistic results
#; (current doesn't reverse direction at edge)
mid_ind = -1
status = gen_surface(mesh=data) # Start generator
while True:
period, yi, xi, last = gen_surface(last=None, xi=None, period=None)
if period:
mid_ind = numpy.argmin(data.Rxy[xi, yi])
out_mid = numpy.argmax(data.Rxy[xi, yi])
break
if last == 1: break
if mid_ind < 0:
print("ERROR: No closed flux surfaces?")
return
#; Calculate 2*b0xk dot Grad P
kp = 2. * data.bxcvx * DDX(data.psixy, data.pressure)
#; Calculate B^2 Grad_par(Jpar0)
gj = data.Bxy**2 * grad_par(old_div(data.jpar0, data.Bxy), data)
#; Generate Jpar0 by integrating kp (Pfirsch-Schluter current)
#; Grad_par = (Bp / (B*hthe))*d/dy
gparj = -kp * data.hthe / (data.Bxy * data.Bpxy)
ps = data.Bxy * int_y(gparj, data, nosmooth='nosmooth') * data.dy
#; In core region add divergence-free parallel current to match input at
#; inboard midplane. Using inboard as if the outboard is matched then
#; unphysical overshoots in jpar can result on the inboard side
#
#; Need to make sure this bootstrap current is always in the same
#; direction
dj = data.jpar0[:, mid_ind] - ps[:, mid_ind]
ind = numpy.argmax(numpy.abs(dj))
s = numpy.sign(dj[ind])
w = numpy.where(dj * s < 0.0)[0] # find where contribution reverses
if w.size > 0: dj[w] = 0.0 # just zero in this region
jpar = ps
status = gen_surface(mesh=data) # Start generator
while True:
period, yi, xi, last = gen_surface(period=period, last=last, xi=xi)
if period == None:
# Due to multi-point differencing, dp/dx can be non-zero outside separatrix
ps[xi, yi] = 0.0
jpar[xi, yi] = 0.0
w = numpy.size(numpy.where(yi == mid_ind))
if (w != 0) and period != None:
# Crosses midplane
dj_b = old_div(dj[xi], data.Bxy[xi, mid_ind])
jpar[xi, yi] = jpar[xi, yi] + dj_b * data.Bxy[xi, yi]
if last == 1: break
# if noplot!=None :
# WINDOW, xsize=800, ysize=800
# !P.multi=[0,2,2,0,0]
# SURFACE, data.jpar0, tit="Input Jpar0", chars=2
# SURFACE, jpar, tit="New Jpar0", chars=2
# PLOT, data.jpar0[0,*], tit="jpar at x=0. Solid=input", yr=[MIN([data.jpar0[0,*],jpar[0,*]]), $
# MAX([data.jpar0[0,*],jpar[0,*]])]
# OPLOT, jpar[0,*], psym=1
#
# #;x = data.ixseps1-1
# #;PLOT, data.jpar0[x,*], tit="Jpar at x="+STR(x)+" Solid=input", $
# #; yr=[MIN([data.jpar0[x,*],jpar[x,*]]), $
# #; MAX([data.jpar0[x,*],jpar[x,*]])]
# #;OPLOT, jpar[x,*], psym=1
#
# y = out_mid
# PLOT, data.jpar0[*,y], tit="Jpar at y="+STR(y)+" Solid=input", $
# yr=[MIN([data.jpar0[*,y],jpar[*,y]]), $
# MAX([data.jpar0[*,y],jpar[*,y]])]
# OPLOT, jpar[*,y], psym=1
return jpar
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")