def DDY( var, mesh):
f = copy.deepcopy(var)
dtheta = 2.*numpy.pi / numpy.float(numpy.sum(mesh.npol))
status = gen_surface(mesh=mesh) # Start generator
while True:
period, yi, xi, last = gen_surface(last=None, xi=None, period=None)
if period :
f[xi,yi] = numpy.real(fft_deriv(var[xi,yi]))
else:
f[xi,yi] = numpy.gradient(var[xi,yi])
if last : break
return old_div(f, dtheta)
def DDY(var, mesh):
f = copy.deepcopy(var)
dtheta = 2. * numpy.pi / numpy.float(numpy.sum(mesh.npol))
status = gen_surface(mesh=mesh) # Start generator
while True:
period, yi, xi, last = gen_surface(last=None, xi=None, period=None)
if period:
f[xi, yi] = numpy.real(fft_deriv(var[xi, yi]))
else:
f[xi, yi] = numpy.gradient(var[xi, yi])
if last: break
return old_div(f, dtheta)
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 = old_div(dr, dl)
dz = old_div(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=old_div(dr[j],hthexy[x,y]), z=old_div(dz[j],hthexy[x,y]), phi=0.0 )
grad_Phi=Bunch( r=0.0,z=0.0,phi=old_div(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=old_div(BRxy[x,y],bstrength[x,y]),
z=old_div(BZxy[x,y],bstrength[x,y]),
phi=old_div(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, old_div(BRxy,bstrength), x, y, yp, ym)
grad_Bz_unit = pdiff_rz(Rxy, Zxy, old_div(BZxy,bstrength), x, y, yp, ym)
grad_Bphi_unit = pdiff_rz(Rxy, Zxy, old_div(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 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 = old_div(dr, dl)
dz = old_div(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=old_div(dr[j], hthexy[x, y]),
z=old_div(dz[j], hthexy[x, y]),
phi=0.0)
grad_Phi = Bunch(r=0.0, z=0.0, phi=old_div(
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=old_div(BRxy[x, y], bstrength[x, y]),
z=old_div(BZxy[x, y], bstrength[x, y]),
phi=old_div(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, old_div(BRxy, bstrength), x, y,
yp, ym)
grad_Bz_unit = pdiff_rz(Rxy, Zxy, old_div(BZxy, bstrength), x, y,
yp, ym)
grad_Bphi_unit = pdiff_rz(Rxy, Zxy, old_div(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
