def pdiff_xy ( nr, nz, r, z, f ):
# Get field components
dfdR = numpy.zeros((nr, nz))
dfdZ = numpy.zeros((nr, nz))
for i in range (nz) :
dfdR[:,i] = deriv(r, f[:,i])
for i in range (nr) :
dfdZ[i,:] = deriv(z, f[i,:])
return Bunch(r=dfdR, z=dfdZ, phi=0.0)
def pdiff ( nr, nz, r, z, f):
print "Calculating DCT..."
dctf= dct2dslow( f )
print "Finished DCT"
drdi = deriv(r)
dzdi = deriv(z)
# Get field components
dfdR = numpy.zeros((nr, nz))
dfdZ = numpy.zeros((nr, nz))
for i in range (nr) :
for j in range (nz) :
g = local_gradient(dctf, i, j, status=None)
status=g.status
dfdr=g.dfdr[0][0]
dfdz=g.dfdz[0][0]
# dfd* are derivatives wrt the indices. Need to divide by dr/di etc
dfdR[i,j] = dfdr/drdi[i]
dfdZ[i,j] = dfdz/dzdi[j]
return Bunch(r=dfdR, z=dfdZ, phi=0.0)
def new_hfunc ( h, psi, a, b, h0, fixpos ):
# global psi, fixpos, h0, a, b
if fixpos == 0 :
h2 = numpy.append(h0, h)
elif fixpos == numpy.size(psi)-1 :
h2 = numpy.append(h, h0)
else:
h2 = numpy.append(numpy.append(h[0:(fixpos)], h0), h[fixpos::])
f = a*h2 + b*deriv( h2, psi)
if fixpos == 0 :
f = f[1::]
elif fixpos == numpy.size(psi)-1 :
f = f[0:(numpy.size(f)-1)]
else:
f = numpy.append(f[0:(fixpos)], f[(fixpos+1)::])
return f
def curvature( nx, ny, Rxy, Zxy, BRxy, BZxy, BPHIxy, PSIxy, THETAxy, hthexy,
CURLB=None, JXB=None, CURVEC=None, BXCURVEC=None, BXCV=None,
DEBUG=None, mesh=None):
#;
#; Calculate the magnetic field curvature and other related quantities
#;--------------------------------------------------------------------
print 'Calculating curvature-related quantities...'
#;;-vector quantities are stored as 2D arrays of structures {r,phi,z}
vec=Bunch( r=0.,phi=0.,z=0.)
curlb=numpy.tile(vec,(nx,ny))
jxb=numpy.tile(vec,(nx,ny))
curvec=numpy.tile(vec,(nx,ny))
bxcurvec=numpy.tile(vec,(nx,ny))
bxcv=Bunch()
bxcv.psi=numpy.zeros((nx,ny))
bxcv.theta=numpy.zeros((nx,ny))
bxcv.phi=numpy.zeros((nx,ny))
status = gen_surface(mesh=mesh) # Start generator
while True:
period, yi, xi, last = gen_surface(period=None, last=None, xi=None)
nys = numpy.size(yi)
x=xi
# Get vector along the surface
if period ==1 :
dr = fft_deriv(Rxy[x,yi])
dz = fft_deriv(Zxy[x,yi])
else:
dr = deriv(Rxy[x,yi])
dz = deriv(Zxy[x,yi])
dl = numpy.sqrt(dr**2 + dz**2)
dr = dr / dl
dz = dz / dl
for j in range (nys) :
y = yi[j]
if period :
yp = yi[ (j+1) % nys ]
ym = yi[ (j-1+nys) % nys ]
else:
yp = yi[ numpy.min([j+1 , nys-1]) ]
ym = yi[ numpy.max([j-1 , 0]) ]
grad_Br = pdiff_rz(Rxy, Zxy, BRxy, x, y, yp, ym)
grad_Bz = pdiff_rz(Rxy, Zxy, BZxy, x, y, yp, ym)
grad_Bphi = pdiff_rz(Rxy, Zxy, BPHIxy, x, y, yp, ym)
grad_Psi = pdiff_rz(Rxy, Zxy, PSIxy, x, y, yp, ym)
#grad_Theta = pdiff_rz(Rxy, Zxy, THETAxy, x, y, yp, ym)
grad_Theta = Bunch( r=dr[j]/hthexy[x,y], z=dz[j]/hthexy[x,y], phi=0.0 )
grad_Phi=Bunch( r=0.0,z=0.0,phi=1./Rxy[x,y] ) #-gradient of the toroidal angle
vecR=Bunch( r=Rxy[x,y],z=Zxy[x,y] )
vecB=Bunch( r=BRxy[x,y],z=BZxy[x,y],phi=BPHIxy[x,y] )
curlb[x,y]=curlcyl(vecR, vecB, grad_Br, grad_Bphi, grad_Bz)
jxb[x,y]=xprod(curlb[x,y], vecB)
#-magnitude of B at 5 locations in cell
bstrength = numpy.sqrt(BRxy**2 + BZxy**2 + BPHIxy**2)
#-unit B vector at cell center
vecB_unit=Bunch( r=BRxy[x,y]/bstrength[x,y],
z=BZxy[x,y]/bstrength[x,y],
phi=BPHIxy[x,y]/bstrength[x,y] )
#-components of gradient of unit B vector at 5 locations in cell
grad_Br_unit = pdiff_rz(Rxy, Zxy, BRxy/bstrength, x, y, yp, ym)
grad_Bz_unit = pdiff_rz(Rxy, Zxy, BZxy/bstrength, x, y, yp, ym)
grad_Bphi_unit = pdiff_rz(Rxy, Zxy, BPHIxy/bstrength, x, y, yp, ym)
#-curl of unit B vector at cell center
curlb_unit=curlcyl(vecR, vecB_unit, grad_Br_unit, grad_Bphi_unit, grad_Bz_unit)
#-curvature vector at cell center
curvec[x,y]=xprod(vecB_unit,curlb_unit,minus='MINUS')
#-unit b cross curvature vector at cell center
bxcurvec[x,y]=xprod(vecB_unit,curvec[x,y])
#-calculate bxcurvec dotted with grad_psi, grad_theta, and grad_phi
bxcv.psi[x,y]=dotprod(bxcurvec[x,y],grad_Psi)
bxcv.theta[x,y]=numpy.real(dotprod(bxcurvec[x,y],grad_Theta))
bxcv.phi[x,y]=dotprod(bxcurvec[x,y],grad_Phi)
if last==1 : break
# if DEBUG : sys.exit()
print '...done'
return bxcv
def follow_gradient( interp_data, R, Z, ri0, zi0, ftarget, ri, zi, status=0,
boundary=None, fbndry=None, ibndry=None ):
global rd_com, idata, lastgoodf, lastgoodpos, Rpos, Zpos, ood, tol, Ri, Zi, dR, dZ
tol = 0.1
Rpos = R
Zpos = Z
Ri=numpy.arange(Rpos.size).astype(float)
Zi=numpy.arange(Zpos.size).astype(float)
dR=deriv(Rpos)
dZ=deriv(Zpos)
ibndry = -1
idata = interp_data
if boundary != None :
bndry = boundary
ri0c = ri0
zi0c = zi0
else:
bndry = 0
ood = 0
if ftarget==None : print ftarget
# Get starting f
out=local_gradient( interp_data, ri0, zi0, status=status, f=0., dfdr=None, dfdz=None)
status=out.status
f0=out.f
if status == 1 :
ri = ri0
zi = zi0
status = 1
return Bunch(status=status, ri=ri, zi=zi)
fmax = ftarget # Target (with maybe boundary in the way)
# CATCH, theError
# try :
# Call LSODE to follow gradient
rzold = [ri0, zi0]
rcount = 0
# while True:
#@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
# toggle this for lsode
solver = lsode(radial_differential, f0, rzold)
rznew=solver.integrate(ftarget)
nsteps = solver.steps
#@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
# toggle this for odeint
# get the value out of a list
# x0 = chain.from_iterable(f0)
# x0 = list(x0)[0]
#
# # print x0, ftarget
# solode=odeint(radial_differential,rzold,[x0,ftarget],full_output=True)
#
# rznew=solode[0][1,:]
# nsteps=solode[1]['nst'][0]
#@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
lstat=0
# print 'nsteps=',nsteps
#print rzold, rznew
#
#sys.exit()
#
# # if nsteps > 100 : lstat = -1
# if lstat == -1 :
# print " -> Excessive work "+str(f0)+" to "+str(ftarget)+" Trying to continue..."
# lstat = 2 # continue
# rcount = rcount + 1
# if rcount > 3 :
# print " -> Too many repeats. Giving Up."
#
# ri = lastgoodpos[0]
# zi = lastgoodpos[1]
# fmax = lastgoodf
#
# return Bunch(status=status,ri=ri,zi=zi)
#
# # Get f at this new location
# out=local_gradient( interp_data, rznew[0], rznew[1], status=status, f=f0, dfdr=None, dfdz=None)
# status=out.status
# f0=out.f
#
# if status == 1 :
# ri = ri0
# zi = zi0
# status = 1
# return Bunch(status=status, rinext=ri, zinext=zi)
#
# rzold = rznew
#
#
# else :
# print "I break"
# break
#
# print 'am I here?'
#
# if status==0:
# print 'I break from try?'
# break
#
# if lstat < 0 :
# print "Error in LSODE routine when following psi gradient."
# print "LSODE status: ", lstat
# #STOP
#
#
# except Exception as theError:
# print theError
ri = rznew[0]
zi = rznew[1]
# else:
# # An error occurred in LSODE.
# # lastgoodf contains the last known good f value
# #PRINT, "CAUGHT ERROR "+!ERROR_STATE.MSG
# #CATCH, /cancel
# ri = lastgoodpos[0]
# zi = lastgoodpos[1]
# fmax = lastgoodf
# if ood :
# # Gone Out Of Domain
# status = 2
# fbndry = lastgoodf
# #PRINT, "Out of domain at f = ", fbndry
# # Repeat to verify that this does work
# rzold = [ri0, zi0]
# try :
# fbndry = lastgoodf - 0.1*(ftarget - f0)
# if theError != 0 :
# print " Error again at ", fbndry
#
#
# solver=lsode(radial_differential, f0, rzold)
# rznew=solver.integrate(fbndry - f0)
# except Exception as theError:
# print theError
#
# return Bunch(status=status, rinext=ri, zinext=zi)
#
# # Otherwise just crossed a boundary
#
# #CATCH, /cancel
#if boundary != None:
## Check if the line crossed a boundary
##PRINT, "Checking boundary ", boundary[*,1:2], [ri0, ri], [zi0, zi]
# cpos, ncross, inds2 = line_crossings([ri0, ri], [zi0, zi], 0,
# boundary[0,:], boundary[1,:], 1, ncross=0, inds2=0)
# if (ncross % 2) == 1 : # Odd number of boundary crossings
# if numpy.sqrt( (ri - cpos[0,0])**2 + (zi - cpos[1,0])**2 ) > 0.1 :
# #PRINT, "FINDING BOUNDARY", SQRT( (ri - cpos[0,0])^2 + (zi - cpos[1,0])^2 )
# # Use divide-and-conquer to find crossing point
#
# tol = 1e-4 # Make the boundary crossing stricter
#
# ibndry = inds2[0] # Index in boundary where hit
#
# fcur = f0 # Current known good position
# rzold = [ri0,zi0]
# rzcur = rzold
# while True:
# fbndry = (fcur + fmax) / 2
# # Try to go half-way to fmax
# #CATCH, theError
# if theError != 0 :
# # Crossed boundary. Change fmax
# #CATCH, /cancel
# fmax = fbndry
# ibndry = inds2[0] # refined boundary index
# else:
# solver=lsode(radial_differential, f0, rzold)
# rznew=solver.integrate(fbndry - f0)
#
# # Didn't cross. Make this the new current location
# fcur = fbndry
# rzcur = rznew
#
# #CATCH, /cancel
#
# if numpy.abs(fmax - fcur) < 0.01*numpy.abs(ftarget - f0):
# break
# ri = rzcur[0]
# zi = rzcur[1]
# fbndry = fcur
#
# #PRINT, "Hit boundary", ri, zi, " f =", fbndry
# status = 2
# return Bunch(status=status, rinext=ri, zinext=zi, fbndry=fbndry, ibndry=ibndry)
#print "follow_gradient"
#print ri, zi
return Bunch(status = 0, rinext=ri, zinext=zi, fbndry=fbndry, ibndry=ibndry)
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 = mesh.dpsidZ / Rxy
Bzxy = -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.fpol, rz_grid.npsigrid*(rz_grid.sibdry - rz_grid.simagx))
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] = 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] = 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 = ( -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(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((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 = 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(1. / Bxy, mesh) / hthe)
bxcvy = -bpsign*Bxy*Bpxy * DDX(xcoord, Btxy*Rxy/Bxy^2) / (2.*hthe)
bxcvz = Bpxy^3 * DDX(xcoord, hthe/Bpxy) / (2.*hthe*Bxy) - Btxy*Rxy*DDX(xcoord, 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(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((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(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(ny/2)
jyseps2_1 = numpy.int(ny/2)
ny_inner = numpy.int(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(ny/2)
jyseps2_1 = numpy.int(ny/2)
ny_inner = numpy.int(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 = raw_input("Profile option:")
if eval(opt) >= 1 and eval(opt) <= 3 : break
if opt == 1 :
# flat temperature profile
print "Setting flat temperature profile"
while True:
Te_x = eval(raw_input("Temperature (eV):"))
# get density
Ni = 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 opt == 2 :
print "Setting flat density profile"
while True:
Ni_x = eval(raw_input("Density [10^20 m^-3]:"))
# get temperature
Te = 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(raw_input("Maximum temperature [eV]:"))
Ni_x = 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 Bt_func ( Bt , psi, a, b):
#global psi, a, b
return deriv( Bt, psi ) + a*Bt + b / Bt
