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equilParams_class.py
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"""
Interface to read EFIT g-file equilibria.
Author: A. Wingen
First Implemented: Sep. 10. 2012
Please report bugs to: wingen@fusion.gat.com
Python 3 version
"""
_VERSION = 5.2
_LAST_UPDATE = 'Feb 03. 2025'
import os
import numpy as np
import scipy.integrate as integ
import scipy.interpolate as interp
import warnings
from . import geqdsk as gdsk # this is a relative import
from . import equilibrium as eq
try: from . import IMAS_EQ # this is a relative import
except: pass # if not found skip this import; then only geqdsk functionality available
class equilParams:
def __init__(self, filename, EQmode='geqdsk',
nw=0, nh=0, thetapnts=0, grid2G=True,
tree=None, server='atlas.gat.com', time=10.4,
psiMult=1.0, BtMult=1.0, IpMult=1.0):
"""
Open EQ file, read it, and provide dictionary self.g as well as 1D and 2D interpolation functions.
if EQmode == 'netcdf', uses a netCDF reader,
if EQmode == 'json', uses a json reader,
else uses GEQDSK reader
filename is name of EQ file (GEQDSK, JSON, HDF5, NETCDF)
EQmode is string that identifies file type
nw is grid radial dimension
nh is grid vertical dimension
thetapnts is number of points in poloidal angle
grid2G is
tree is string of tree if using MDS+
server is MDS+ server
time is timestep of this equilibrium
psiMult is multiplier for psi quantities (ie psiRZ, psiSep, psiAxis)
BtMult is multiplier for Bt quantities (Bt, Fpol)
IpMult is multipler for Ip
"""
#read GEQDSKs text file or IMAS formatted file (netCDF, HDF5, JSON)
GEQDSKflag = False
if ('.json' in filename[-5::]) or ('.JSON' in filename[-5::]): EQmode = 'json'
if EQmode == 'netcdf':
print("NetCDF EQmode")
imas_nc = IMAS_EQ.netCDF_IMAS()
self.data = imas_nc.readNetCDF(filename, time)
elif EQmode == 'json':
print("JSON EQmode")
imas_js = IMAS_EQ.JSON_IMAS(filename)
self.data = imas_js.getEQ(time)
if self.data is None: return
else:
#print("GEQDSK EQmode")
GEQDSKflag = True
self.readGfile(filename, tree, server, nw=0, nh=0, thetapnts=0, grid2G=True)
if GEQDSKflag == False:
self.shot = 1 #arbitrary for now
self.time = time *1e3 # time is in ms
for key, value in self.data.items():
setattr(self, key, value)
# ---- normalize variables per arguments ----
self.siAxis *= psiMult
self.siBry *= psiMult
self.bcentr *= BtMult
self.Ip *= IpMult
# ---- default Functions ----
self.PROFdict = self.profiles(BtMult)
self.RZdict = self.RZ_params()
self.PSIdict = self.getPsi(psiMult)
self.PHIdict = self.getTorPsi()
# ---- more Variables ----
self.dpsidZ, self.dpsidR = np.gradient(self.PSIdict['psi2D'], self.RZdict['dZ'],
self.RZdict['dR'])
self.B_R = self.dpsidZ / self.RZdict['Rs2D']
self.B_Z = -self.dpsidR / self.RZdict['Rs2D']
self.Bp_2D = np.sqrt(self.B_R**2 + self.B_Z**2)
self.theta = np.linspace(0.0, 2.*np.pi, self.thetapnts)
psiN2D = self.PSIdict['psiN_2D'].flatten()
idx = np.where(psiN2D <= 1)[0]
Fpol_sep = self.PROFdict['ffunc'](1.0) #self.bcentr * abs(self.R0)
Fpol2D = np.ones(psiN2D.shape) * Fpol_sep
Fpol2D[idx] = self.PROFdict['ffunc'](psiN2D[idx])
Fpol2D = Fpol2D.reshape(self.PSIdict['psiN_2D'].shape)
self.Bt_2D = Fpol2D / self.RZdict['Rs2D']
# ---- more Functions ----
self.psiFunc = interp.RectBivariateSpline(self.RZdict['Rs1D'], self.RZdict['Zs1D'],
self.PSIdict['psiN_2D'].T)
self.BpFunc = interp.RectBivariateSpline(self.RZdict['Rs1D'], self.RZdict['Zs1D'],
self.Bp_2D.T)
self.BtFunc = interp.RectBivariateSpline(self.RZdict['Rs1D'], self.RZdict['Zs1D'],
self.Bt_2D.T)
self.BRFunc = interp.RectBivariateSpline(self.RZdict['Rs1D'], self.RZdict['Zs1D'],
self.B_R.T)
self.BZFunc = interp.RectBivariateSpline(self.RZdict['Rs1D'], self.RZdict['Zs1D'],
self.B_Z.T)
shape = self.get_FluxShape(1.0) # {'kappa', 'tri_avg', 'triUP', 'triLO', 'aminor', 'aspect', 'radius'}
# ---- g dict ----
self.g = {'shot': self.shot, 'time': self.time, 'NR': self.nw, 'NZ': self.nh,
'Xdim': self.rdim, 'Zdim': self.zdim,
'R0': self.R0, 'R1': self.R1,
'Zmid': self.Zmid, 'RmAxis': self.rmaxis, 'ZmAxis': self.zmaxis,
'psiAxis': self.siAxis, 'psiSep': self.siBry, 'Bt0': self.bcentr,
'Ip': self.Ip, 'Fpol': self.PROFdict['fpol'],
'Pres': self.PROFdict['pres'], 'FFprime': self.PROFdict['ffprime'],
'Pprime': self.PROFdict['pprime'], 'qpsi': self.PROFdict['q_prof'],
'q': self.PROFdict['q_prof'], 'psiRZ': self.PSIdict['psi2D'],
'R': self.RZdict['Rs1D'], 'Z': self.RZdict['Zs1D'], 'dR': self.RZdict['dR'],
'dZ': self.RZdict['dZ'], 'psiRZn': self.PSIdict['psiN_2D'],
'Nlcfs': len(self.lcfs), 'Nwall': len(self.wall),
'lcfs': self.lcfs, 'wall':self.wall,
'psi': self.PSIdict['psi1D'], 'psiN': self.PSIdict['psiN1D'],'Rsminor': self.Rsminor,
'kappa': shape['kappa'], 'triUP': shape['triUP'][0], 'triLO': shape['triLO'][0],
'aminor': shape['aminor'], 'aspect': shape['aspect']}
self.Swall, self.Swall_max = self.length_along_wall()
self.isHelicity = self.helicity()
self.g['helicity'] = self.isHelicity
self.FluxSurfList = None
return
# --------------------------------------------------------------------------------
def readGfile(self, gfileNam, tree=None, server='atlas.gat.com',
nw=0, nh=0, thetapnts=0, grid2G=True):
"""
reads a geqdsk file into self.data
"""
# ---- get path, shot number and time from file name ----
# returns location of last '/' in gfileNam or -1 if not found
idx = gfileNam[::-1].find('/')
if(idx == -1):
gpath = '.'
gfile = gfileNam
else:
idx *= -1
gpath = gfileNam[0:idx - 1] # path without a final '/'
gfile = gfileNam[idx::]
if '_' in gfile:
gfileA,gfileB = gfile.split('_')
if '.' in gfileA:
idx = gfileA.find('.')
shot, time = gfileA[1:idx], gfileA[idx + 1::]
else:
shot, time = gfileA[1::], gfileB
fmtstr = '0' + str(len(shot)) + 'd'
elif '.' in gfile:
idx = gfile.find('.')
shot, time = gfile[1:idx], gfile[idx + 1::]
fmtstr = '0' + str(len(shot)) + 'd'
else:
shot, time, fmtstr = 0, 0, '06d'
try: shot = int(shot)
except: shot, fmtstr = 0, '06d'
try: time = float(time)
except: time = 0
self.shot = shot
self.time = time
if (not os.path.isfile(gfileNam)) and (tree is None):
raise NameError('g-file not found -> Abort!')
# ---- read from MDS+, if keyword tree is given ----
if not (tree is None):
# time needs not be exact, so time could change
time = self._read_mds(shot, time, tree=tree, gpath=gpath, Server=server)
# adjust filename to match time
gfileNam = gpath + '/g' + format(shot, fmtstr) + '.' + format(time, '05d')
# ---- open & read g-file ----
self.data = gdsk.Geqdsk()
self.data.openFile(gfileNam)
# ---- Variables ----
if grid2G:
self.nw = self.data.get('nw')
self.nh = self.data.get('nh')
self.thetapnts = 2 * self.nh
else:
self.nw = nw
self.nh = nh
self.thetapnts = thetapnts
self.bcentr = self.data.get('bcentr')
self.rmaxis = self.data.get('rmaxis')
self.zmaxis = self.data.get('zmaxis')
self.Rmin = self.data.get('rleft')
self.Rmax = self.Rmin + self.data.get('rdim')
self.Rbdry = self.data.get('rbbbs').max()
self.Rsminor = np.linspace(self.rmaxis, self.Rbdry, self.nw)
self.Zmin = self.data.get('zmid') - self.data.get('zdim')/2.0
self.Zmax = self.data.get('zmid') + self.data.get('zdim')/2.0
self.Zlowest = self.data.get('zbbbs').min()
self.siAxis = self.data.get('simag')
self.siBry = self.data.get('sibry')
self.lcfs = np.vstack((self.data.get('rbbbs'), self.data.get('zbbbs'))).T
self.wall = np.vstack((self.data.get('rlim'), self.data.get('zlim'))).T
self.rdim = self.data.get('rdim')
self.zdim = self.data.get('zdim')
self.R0 = abs(self.data.get('rcentr'))
self.R1 = self.data.get('rleft')
self.Zmid = self.data.get('zmid')
self.Ip = self.data.get('current')
return
# --------------------------------------------------------------------------------
def writeGEQDSK(self, file, shot = None):
"""
writes a new gfile. user must supply
file: name of new gfile
uses self.g: dictionary containing all GEQDSK parameters
Note that this writes some data as 0 (ie rhovn, kvtor, etc.)
"""
KVTOR = 0
RVTOR = 1.7
NMASS = 0
RHOVN = np.zeros(self.g['NR'])
if shot is None: shot = self.g['shot']
print('Writing to path: ' + file)
with open(file, 'w') as f:
f.write("{:<51}".format(' EFIT xx/xx/xxxx #' + str(shot) + ' ' + str(self.g['time']) + 'ms')) # this needs to be exactly 51 chars
f.write('3 ' + str(self.g['NR']) + ' ' + str(self.g['NZ']) + '\n')
f.write('% .9E% .9E% .9E% .9E% .9E\n'%(self.g['Xdim'], self.g['Zdim'], self.g['R0'], self.g['R1'], self.g['Zmid']))
f.write('% .9E% .9E% .9E% .9E% .9E\n'%(self.g['RmAxis'], self.g['ZmAxis'], self.g['psiAxis'], self.g['psiSep'], self.g['Bt0']))
f.write('% .9E% .9E% .9E% .9E% .9E\n'%(self.g['Ip'], 0, 0, 0, 0))
f.write('% .9E% .9E% .9E% .9E% .9E\n'%(0,0,0,0,0))
self._write_array(self.g['Fpol'], f)
self._write_array(self.g['Pres'], f)
self._write_array(self.g['FFprime'], f)
self._write_array(self.g['Pprime'], f)
self._write_array(self.g['psiRZ'].flatten(), f)
self._write_array(self.g['qpsi'], f)
f.write(str(self.g['Nlcfs']).rjust(5) + str(self.g['Nwall']).rjust(5) + '\n') # these need to be 5 char long numbers with leading spaces
self._write_array(self.g['lcfs'].flatten(), f)
self._write_array(self.g['wall'].flatten(), f)
f.write(str(KVTOR) + ' ' + format(RVTOR, ' .9E') + ' ' + str(NMASS) + '\n')
self._write_array(RHOVN, f)
print('Wrote new gfile')
# --------------------------------------------------------------------------------
def readNetCDF(self, filename, nc_time):
"""
reads an IMAS formatted equilibrium netcdf
"""
imas_nc = IMAS_EQ.netCDF()
self.data = imas_nc.readNetCDF(filename, nc_time)
return
# --------------------------------------------------------------------------------
# Interpolation function handles for all 1-D fields in the g-file
def profiles(self, BtMult):
# ---- Profiles ----
fpol = self.data.get('fpol')
ffunc = interp.UnivariateSpline(np.linspace(0., 1., np.size(fpol)), fpol, s=0)
fprime = self.data.get('ffprime')/fpol
fpfunc = interp.UnivariateSpline(np.linspace(0., 1., np.size(fprime)), fprime, s=0)
ffprime = self.data.get('ffprime')
ffpfunc = interp.UnivariateSpline(np.linspace(0., 1., np.size(ffprime)), ffprime, s=0)
pprime = self.data.get('pprime')
ppfunc = interp.UnivariateSpline(np.linspace(0., 1., np.size(pprime)), pprime, s=0)
pres = self.data.get('pres')
pfunc = interp.UnivariateSpline(np.linspace(0., 1., np.size(pres)), pres, s=0)
q_prof = self.data.get('qpsi')
qfunc = interp.UnivariateSpline(np.linspace(0., 1., np.size(q_prof)), q_prof, s=0)
return {'fpol': fpol, 'ffunc': ffunc, 'fprime': fprime, 'fpfunc': fpfunc,
'ffprime': ffprime, 'ffpfunc': ffpfunc, 'pprime': pprime, 'ppfunc': ppfunc,
'pres': pres, 'pfunc': pfunc, 'q_prof': q_prof, 'qfunc': qfunc}
# --------------------------------------------------------------------------------
# 1-D and 2-D (R,Z) grid
def RZ_params(self):
dR = (self.Rmax - self.Rmin)/(self.nw - 1)
Rs1D = np.linspace(self.Rmin, self.Rmax, self.nw)
dZ = (self.Zmax - self.Zmin)/(self.nh - 1)
Zs1D = np.linspace(self.Zmin, self.Zmax, self.nh)
Rs2D, Zs2D = np.meshgrid(Rs1D, Zs1D)
return {'Rs1D': Rs1D, 'dR': dR, 'Zs1D': Zs1D, 'dZ': dZ, 'Rs2D': Rs2D, 'Zs2D': Zs2D}
# --------------------------------------------------------------------------------
# 1-D and 2-D poloidal flux, normalized and regular
# compared to the integral definition of psipol
# (psipol = 2pi integral_Raxis^Rsurf(Bpol * R * dR))
# regular is shifted by self.siAxis and missing the factor 2*pi !!!
# so: psipol = psi1D = 2pi * (self.siBry-self.siAxis) * psiN1D
def getPsi(self, psiMult):
psiN1D = np.linspace(0.0, 1.0, self.nw)
psi1D = 2 * np.pi * (self.siBry - self.siAxis) * psiN1D
psi2D = self.data.get('psirz') * psiMult
psiN_2D = (psi2D - self.siAxis) / (self.siBry - self.siAxis)
# psiN_2D[np.where(psiN_2D > 1.2)] = 1.2
return {'psi2D': psi2D, 'psiN_2D': psiN_2D, 'psi1D': psi1D, 'psiN1D': psiN1D}
# --------------------------------------------------------------------------------
# 1-D normalized toroidal flux
# dpsitor/dpsipol = q -> psitor = integral(q(psipol) * dpsipol)
# dummy input variable for backward compatability <-> this input is unused!!!
def getTorPsi(self, dummy=None):
dpsi = (self.siBry - self.siAxis)/(self.nw - 1) * 2*np.pi
#try except to accomodate multiple versions of scipy (after 1.6 cumtrapz -> cumulative_trapezoid)
try:
hold = integ.cumtrapz(self.PROFdict['q_prof'], dx=dpsi) * np.sign(self.bcentr)
except:
hold = integ.cumulative_trapezoid(self.PROFdict['q_prof'], dx=dpsi) * np.sign(self.bcentr)
psitor = np.append(0, hold)
psitorN1D = (psitor - psitor[0])/(psitor[-1] - psitor[0])
return {'psitorN1D': psitorN1D, 'psitor1D': psitor}
# --------------------------------------------------------------------------------
# (R,Z) and B-fields on a single flux surface
def getBs_FluxSur(self, psiNVal):
R_hold = np.ones(self.thetapnts)
Z_hold = np.ones(self.thetapnts)
for thet in enumerate(self.theta):
try:
Rneu, Zneu = self.__comp_newt__(psiNVal, thet[1], self.rmaxis, self.zmaxis,
self.psiFunc)
except RuntimeError:
Rneu, Zneu = self.__comp_bisec__(psiNVal, thet[1], self.rmaxis, self.zmaxis,
self.Zlowest, self.psiFunc)
R_hold[thet[0]] = Rneu
Z_hold[thet[0]] = Zneu
Bp_hold = self.BpFunc.ev(R_hold, Z_hold)
fpol_psiN = self.PROFdict['ffunc'](psiNVal)*np.ones(np.size(Bp_hold))
fluxSur = eq.FluxSurface(fpol_psiN[0:-1], R_hold[0:-1], Z_hold[0:-1], Bp_hold[0:-1],
self.theta[0:-1])
Bt_hold = np.append(fluxSur._Bt, fluxSur._Bt[0]) # add last point = first point
Bmod = np.append(fluxSur._B, fluxSur._B[0]) # add last point = first point
return {'Rs': R_hold, 'Zs': Z_hold, 'Bp': Bp_hold, 'Bt': Bt_hold, 'Bmod': Bmod,
'fpol_psiN': fpol_psiN, 'FS': fluxSur}
# --------------------------------------------------------------------------------
# Shaping of a single flux surface
def get_FluxShape(self, psiNVal):
FluxSur = self.getBs_FluxSur(psiNVal)
b = (FluxSur['Zs'].max()-FluxSur['Zs'].min())/2
a = (FluxSur['Rs'].max()-FluxSur['Rs'].min())/2
R = (FluxSur['Rs'].max()+FluxSur['Rs'].min())/2
d = (FluxSur['Rs'].min()+a) - FluxSur['Rs'][np.where(FluxSur['Zs'] == FluxSur['Zs'].max())]
c = (FluxSur['Rs'].min()+a) - FluxSur['Rs'][np.where(FluxSur['Zs'] == FluxSur['Zs'].min())]
return {'kappa': (b/a), 'tri_avg': (c+d)/2/a, 'triUP': (d/a), 'triLO': (c/a), 'aminor': a, 'aspect': R/a, 'radius': R}
# --------------------------------------------------------------------------------
# (R,Z) and B-fields for all flux surfaces given by 1-D normalized poloidal flux array psiN1D
def get_allFluxSur(self, rerun = False):
if not rerun:
if self.FluxSurfList is not None: return self.FluxSurfList
FluxSurList = []
getRZ_failed = False
try: R, Z = self.__get_RZ__(self.theta, self.PSIdict['psiN1D'], quiet=True)
except: getRZ_failed = True
if getRZ_failed: print('getRZ failed, using backup method')
for i, psiNVal in enumerate(self.PSIdict['psiN1D']):
if getRZ_failed:
R_hold,Z_hold = self.flux_surface(psiNVal, 0, theta = self.theta)
else:
R_hold = R[i, :]
Z_hold = Z[i, :]
Bp_hold = self.BpFunc.ev(R_hold, Z_hold)
fpol_psiN = self.PROFdict['fpol'][i] * np.ones(self.thetapnts)
# eq.FluxSurface requires theta = [0:2pi] without the last point
fluxSur = eq.FluxSurface(fpol_psiN[0:-1], R_hold[0:-1], Z_hold[0:-1], Bp_hold[0:-1], self.theta[0:-1])
Bt_hold = np.append(fluxSur._Bt, fluxSur._Bt[0]) # add last point = first point
Bmod = np.append(fluxSur._B, fluxSur._B[0]) # add last point = first point
FluxSur = {'Rs':R_hold, 'Zs':Z_hold, 'Bp':Bp_hold, 'Bt':Bt_hold,
'Bmod':Bmod, 'fpol_psiN':fpol_psiN, 'FS':fluxSur}
FluxSurList.append(FluxSur)
self.FluxSurfList = FluxSurList
return FluxSurList
# --------------------------------------------------------------------------------
# B-fields and its derivatives in 2-D poloidal plane given by (R,Z) grid
def getBs_2D(self, FluxSurfList=None):
RZdict = self.RZdict
dpsidR_loc = -1*self.dpsidR
dpsidZ_loc = -1*self.dpsidZ
d2psi_dZ2, _ = np.gradient(dpsidZ_loc, RZdict['dZ'], RZdict['dR'])
d2psi_dRdZ, d2psi_dR2 = np.gradient(dpsidR_loc, RZdict['dZ'], RZdict['dR'])
Rs_hold2D = np.ones((self.nw, self.thetapnts))
Zs_hold2D = np.ones((self.nw, self.thetapnts))
Btot_hold2D = np.ones((self.nw, self.thetapnts))
Bp_hold2D = np.ones((self.nw, self.thetapnts))
Bt_hold2D = np.ones((self.nw, self.thetapnts))
dpsidR_hold2D = np.ones((self.nw, self.thetapnts))
dpsidZ_hold2D = np.ones((self.nw, self.thetapnts))
d2psidR2_hold2D = np.ones((self.nw, self.thetapnts))
d2psidZ2_hold2D = np.ones((self.nw, self.thetapnts))
d2psidRdZ_hold2D = np.ones((self.nw, self.thetapnts))
dpsidRFunc = interp.RectBivariateSpline(RZdict['Rs1D'], RZdict['Zs1D'], dpsidR_loc.T)
dpsidZFunc = interp.RectBivariateSpline(RZdict['Rs1D'], RZdict['Zs1D'], dpsidZ_loc.T)
d2psidR2Func = interp.RectBivariateSpline(RZdict['Rs1D'], RZdict['Zs1D'], d2psi_dR2.T)
d2psidZ2Func = interp.RectBivariateSpline(RZdict['Rs1D'], RZdict['Zs1D'], d2psi_dZ2.T)
d2psidRdZFunc = interp.RectBivariateSpline(RZdict['Rs1D'], RZdict['Zs1D'], d2psi_dRdZ.T)
if(FluxSurfList is None):
FluxSurfList = self.get_allFluxSur()
for i in range(self.nw):
R_hold = FluxSurfList[i]['Rs']
Z_hold = FluxSurfList[i]['Zs']
Rs_hold2D[i, :] = R_hold
Zs_hold2D[i, :] = Z_hold
Btot_hold2D[i, :] = FluxSurfList[i]['Bmod']
Bp_hold2D[i, :] = FluxSurfList[i]['Bp']
Bt_hold2D[i, :] = FluxSurfList[i]['Bt']
dpsidR_hold2D[i,:] = dpsidRFunc.ev(R_hold, Z_hold)
dpsidZ_hold2D[i,:] = dpsidZFunc.ev(R_hold, Z_hold)
d2psidR2_hold2D[i,:] = d2psidR2Func.ev(R_hold, Z_hold)
d2psidZ2_hold2D[i,:] = d2psidZ2Func.ev(R_hold, Z_hold)
d2psidRdZ_hold2D[i,:] = d2psidRdZFunc.ev(R_hold, Z_hold)
return {'dpsidZ_2D':dpsidZ_hold2D,'dpsidR_2D':dpsidR_hold2D,'d2psidR2_2D':d2psidR2_hold2D,'d2psidZ2_2D':d2psidZ2_hold2D,
'd2psidRdZ_2D':d2psidRdZ_hold2D,'Bp_2D':Bp_hold2D,'Bt_2D':Bt_hold2D,'Btot_2D':Btot_hold2D,
'Rs_2D':Rs_hold2D,'Zs_2D':Zs_hold2D}
# --------------------------------------------------------------------------------
# normal and geodesic curvature, and local shear in 2-D plane
def get_Curv_Shear(self, FluxSurfList = None, Bdict = None):
curvNorm_2D = np.ones((self.nw,self.thetapnts))
curvGeo_2D = np.ones((self.nw,self.thetapnts))
shear_fl = np.ones((self.nw,self.thetapnts))
if(FluxSurfList is None):
FluxSurfList = self.get_allFluxSur()
if(Bdict is None):
Bdict = self.getBs_2D(FluxSurfList)
for i, psiNVal in enumerate(self.PSIdict['psiN1D']):
fprint_psiN = self.PROFdict['fpfunc'](psiNVal)*np.ones(self.thetapnts)
R = FluxSurfList[i]['Rs']
Bp = FluxSurfList[i]['Bp']
B = FluxSurfList[i]['Bmod']
fpol_psiN = FluxSurfList[i]['fpol_psiN']
kapt1 = (fpol_psiN**2)*(Bdict['dpsidR_2D'][i, :])
kapt2 = (Bdict['d2psidR2_2D'][i, :]*Bdict['dpsidZ_2D'][i, :]**2) + ((Bdict['dpsidR_2D'][i, :]**2)*Bdict['d2psidZ2_2D'][i, :])
kapt3 = (2*Bdict['dpsidR_2D'][i,:]*Bdict['d2psidRdZ_2D'][i,:]*Bdict['dpsidZ_2D'][i,:])
curvNorm_2D[i,:] = (kapt1 + Bdict['Rs_2D'][i,:]*(kapt2-kapt3))/(R**4 * Bp * B**2)
kap2t1 = Bdict['d2psidRdZ_2D'][i,:]*(Bdict['dpsidR_2D'][i,:]**2 - Bdict['dpsidZ_2D'][i,:]**2)
kap2t2 = Bdict['dpsidR_2D'][i,:]*Bdict['dpsidZ_2D'][i,:]*(Bdict['d2psidR2_2D'][i,:] - Bdict['d2psidZ2_2D'][i,:])
kap2t3 = Bdict['dpsidZ_2D'][i,:] * R**2 * B**2
# curvGeo_2D[i, :] = -1*fpol_psiN*(Bdict['Rs_2D'][i, :]*(kap2t1 - kap2t2 + kap2t3))/(R**5 * Bp * B**3)
# maybe no -1 up front?
curvGeo_2D[i, :] = fpol_psiN*(Bdict['Rs_2D'][i, :]*(kap2t1 - kap2t2) + kap2t3)/(R**5 * Bp * B**3)
coeft1 = fpol_psiN / (R**4 * Bp**2 * B**2)
coeft2 = ((Bdict['d2psidR2_2D'][i, :] -
Bdict['d2psidZ2_2D'][i, :]) * (Bdict['dpsidR_2D'][i, :]**2 -
Bdict['dpsidZ_2D'][i, :]**2) +
(4*Bdict['dpsidR_2D'][i,:] * Bdict['d2psidRdZ_2D'][i,:] * Bdict['dpsidZ_2D'][i,:]))
sht2 = fpol_psiN * Bdict['dpsidR_2D'][i,:] / (R**3 * B**2)
sht3 = fprint_psiN * Bp**2 / (B**2)
shear_fl[i, :] = coeft1 * coeft2 + sht2 - sht3
return {'curvNorm_2D': curvNorm_2D, 'curvGeo_2D': curvGeo_2D,
'localShear_2D': shear_fl, 'Rs_2D': Bdict['Rs_2D'], 'Zs_2D': Bdict['Zs_2D']}
# --------------------------------------------------------------------------------
# 1-D parallel current density profile
def cur_density(self, FluxSurfList=None, get_jtor=True):
import scipy.constants
mu0 = scipy.constants.mu_0
PSIdict = self.PSIdict
PROFdict = self.PROFdict
Bsqrd_prof = np.ones(self.nw)
if(FluxSurfList is None):
FluxSurfList = self.get_allFluxSur()
for i, psi in enumerate(PSIdict['psiN1D']):
Bsqrd_prof[i] = FluxSurfList[i]['FS'].Bsqav()
# parallel current calc
# <jpar> = <(J (dot) B)>/B0 = (fprime*<B^2>/mu0 + pprime*fpol)/B0
jpar1D = (PROFdict['fprime']*Bsqrd_prof/mu0 + PROFdict['pprime']*PROFdict['fpol']) / self.bcentr/1.e6 * np.sign(self.Ip)
# <jtor> = <R*pprime + ffprime/R/mu0>
# jtor1D = np.abs(self.Rsminor*PROFdict['pprime'] +(PROFdict['ffprime']/self.Rsminor/mu0))/1.e6
if get_jtor:
jtor1D = self. jtor_profile(FluxSurfList)
else:
jtor1D = 0
return {'jpar': jpar1D, 'jtor': jtor1D, 'Bsqrd': Bsqrd_prof}
# --------------------------------------------------------------------------------
# 1-D toroidal current density profile
def jtor_profile(self, FluxSurfList=None):
import scipy.constants
mu0 = scipy.constants.mu_0
PSIdict = self.PSIdict
PROFdict = self.PROFdict
jtor1D = np.ones(self.nw)
if(FluxSurfList is None):
FluxSurfList = self.get_allFluxSur()
# get flux surface average
for i, psi in enumerate(PSIdict['psiN1D']):
jtorSurf = PROFdict['pprime'][i]*FluxSurfList[i]['Rs'] + PROFdict['ffprime'][i]/FluxSurfList[i]['Rs']/mu0
f_jtorSurf = eq.interpPeriodic(self.theta[0:-1], jtorSurf[0:-1], copy = False)
jtor1D[i] = FluxSurfList[i]['FS'].average(f_jtorSurf)
# <jtor> = <R*pprime + ffprime/R/mu0>
jtor1D = np.abs(jtor1D)/1.e6 * np.sign(self.Ip)
return jtor1D
# --------------------------------------------------------------------------------
# Flux surface enclosed 2D-Volume (Area inside surface) and derivative (psi)
def volume2D(self, FluxSurfList = None):
V = np.zeros(self.nw)
psi = self.PSIdict['psiN1D']
if(FluxSurfList is None):
FluxSurfList = self.get_allFluxSur()
for i in range(1, self.nw):
rsq = (FluxSurfList[i]['Rs'] - self.rmaxis)**2 + (FluxSurfList[i]['Zs'] - self.zmaxis)**2
try: V[i] = 0.5 * integ.simps(rsq, self.theta)
except: V[i] = 0.5 * integ.trapz(rsq, self.theta)
# dV/dpsi
dV = np.zeros(self.nw)
for i in range(1, self.nw - 1):
dV[i] = (V[i+1] - V[i-1]) / (psi[i+1] - psi[i-1])
dV[0] = (-V[2] + 4*V[1] - 3*V[0]) / (psi[2] - psi[0])
dV[-1] = (V[-3] - 4*V[-2] + 3*V[-1]) / (psi[-1] - psi[-3])
return {'V':V, 'Vprime':dV}
# --------------------------------------------------------------------------------
# compute and return all of the above
def get_all(self):
paramDICT={'Rs1D':self.RZdict['Rs1D'], 'Zs1D':self.RZdict['Zs1D'], 'theta':self.theta,
'psi2D':self.PSIdict['psi2D'], 'psiN1D':self.PSIdict['psiN1D'], 'psiN_2D':self.PSIdict['psiN_2D']}
# Prepare all flux surfaces
FluxSurList = self.get_allFluxSur()
# 2-D B-field properties
Bdict = self.getBs_2D(FluxSurList)
# returns 'dpsidZ_2D', 'dpsidR_2D', 'd2psidR2_2D', 'd2psidZ2_2D', 'd2psidRdZ_2D',
# 'Bp_2D', 'Bt_2D', 'Btot_2D', 'Rs_2D', 'Zs_2D'
paramDICT['Rs_2D'] = Bdict['Rs_2D']
paramDICT['Zs_2D'] = Bdict['Zs_2D']
paramDICT['Btot_2D'] = Bdict['Btot_2D']
paramDICT['Bp_2D'] = Bdict['Bp_2D']
paramDICT['Bt_2D'] = Bdict['Bt_2D']
# 2-D local shear
SHEARdict = self.get_Curv_Shear(FluxSurList, Bdict) # returns 'curvNorm_2D', 'curvGeo_2D', 'localShear_2D'
paramDICT['curvNorm_2D'] = SHEARdict['curvNorm_2D']
paramDICT['curvGeo_2D'] = SHEARdict['curvGeo_2D']
paramDICT['localShear_2D'] = SHEARdict['localShear_2D']
# 1-D current density
Jdict = self.cur_density(FluxSurList) # returns 'jpar', 'jtor'
paramDICT['jpar1D'] = Jdict['jpar']
paramDICT['jtor1D'] = Jdict['jtor']
# q profile
qprof1D = self.PROFdict['qfunc'](self.PSIdict['psiN1D'])
paramDICT['qprof1D'] = qprof1D
# pressure profile
press1D = self.PROFdict['pfunc'](self.PSIdict['psiN1D'])
paramDICT['press1D'] = press1D
# toroidal field profile
btor1D = self.PROFdict['ffunc'](self.PSIdict['psiN1D'])/self.Rsminor
paramDICT['btor1D'] = btor1D
# toroidal flux
paramDICT['psitorN1D'] = self.getTorPsi()['psitorN1D']
return paramDICT
# --------------------------------------------------------------------------------
# returns arrays R and Z of N points along psi = const. surface
def flux_surface(self, psi0, N, theta=None):
if (theta is None):
theta = np.linspace(0, 2 * np.pi, N + 1)[0:-1]
else:
N = len(theta)
r = np.zeros(theta.shape)
# get maximum r from separatrix in g-file
Rsep = self.g['lcfs'][:,0]
Zsep = self.g['lcfs'][:,1]
idxup = Zsep.argmax()
idxdwn = Zsep.argmin()
rup = np.sqrt((Rsep[idxup] - self.rmaxis)**2 + (Zsep[idxup] - self.zmaxis)**2)
rdwn = np.sqrt((Rsep[idxdwn] - self.rmaxis)**2 + (Zsep[idxdwn] - self.zmaxis)**2)
rmax = max([rup, rdwn])
# iterate
for i in range(N):
r[i] = self.__bisec__(psi0, theta[i], b=rmax)
R = r * np.cos(theta) + self.rmaxis
Z = r * np.sin(theta) + self.zmaxis
return R, Z
# --------------------------------------------------------------------------------
def get_j2D(self):
mu0 = 4 * np.pi*1e-7
jR = np.zeros(self.RZdict['Rs2D'].shape)
jZ = np.zeros(self.RZdict['Rs2D'].shape)
jtor = np.zeros(self.RZdict['Rs2D'].shape)
for i in range(self.nw):
jR[:, i] = -deriv(self.Bt_2D[:, i], self.RZdict['Zs2D'][:, i])
jtor[:, i] = deriv(self.B_R[:, i], self.RZdict['Zs2D'][:, i])
for i in range(self.nh):
jZ[i, :] = deriv(self.Bt_2D[i, :], self.RZdict['Rs2D'][i, :])
jtor[i, :] -= deriv(self.B_Z[i, :], self.RZdict['Rs2D'][i, :])
jZ += self.Bt_2D/self.RZdict['Rs2D']
jR /= mu0
jZ /= mu0
jtor /= mu0
Zsep = self.g['lcfs'][:,1]
idx = np.where((self.PSIdict['psiN_2D'] > 1.0) | (abs(self.RZdict['Zs2D']) > abs(Zsep.max())))
jR[idx] = 0
jZ[idx] = 0
jtor[idx] = 0
jpar = (jR*self.B_R + jZ*self.B_Z + jtor*self.Bt_2D) * np.sign(self.Ip)
jpar /= np.sqrt(self.B_R**2 + self.B_Z**2 + self.Bt_2D**2)
jtot = np.sqrt(jR**2 + jZ**2 + jtor**2)
jtor *= np.sign(self.Ip)
return {'R':self.RZdict['Rs2D'], 'Z':self.RZdict['Zs2D'], 'j2D':jtot, 'jpar2D':jpar,
'jR2D':jR, 'jZ2D':jZ, 'jtor2D':jtor}
# --------------------------------------------------------------------------------
def plot(self, fig = None, c = None):
"""
fig: integer number of figure window to use, e.g. 1
c: string of color code, e.g. 'k' or 'r'
"""
import matplotlib.pyplot as plt
if c is None: c = 'k'
R1d = self.RZdict['Rs1D']
Z1d = self.RZdict['Zs1D']
Rs, Zs = np.meshgrid(R1d, Z1d)
levs = np.append(0.01, np.arange(0.1, 1.1, 0.1))
if fig is None: plt.figure(figsize=(6, 10))
else: plt.figure(fig)
plt.plot(self.rmaxis, self.zmaxis, c+'x', markersize = 5, linewidth = 2)
cs1 = plt.contour(Rs, Zs, self.PSIdict['psiN_2D'], levs, colors = c)
cs1.collections[0].set_label('EFIT')
plt.plot(self.g['lcfs'][:,0],self.g['lcfs'][:,1], c, lw = 2, label = 'EFIT Bndy')
if fig is None:
plt.plot(self.g['wall'][:,0],self.g['wall'][:,1], 'k--')
plt.xlim(self.g['wall'][:,0].min()*0.97, self.g['wall'][:,0].max()*1.03)
plt.ylim(self.g['wall'][:,1].min()*1.03, self.g['wall'][:,1].max()*1.03)
plt.xlabel('R [m]')
plt.ylabel('Z [m]')
plt.gca().set_aspect('equal')
plt.title('Shot: ' + str(self.g['shot']) + ' Time: ' + str(self.g['time']) + ' ms', fontsize = 18)
# --------------------------------------------------------------------------------
def plotProfile(self, what = 'all', fig = None, c = None, label = ''):
"""
what: keyword of what profile to plot. default is 'all' and plots all 6 relevant profiles
fig: integer number of figure window to use, e.g. 1
c: string of color code, e.g. 'k' or 'r'
label: string that becomes the label for the plot in the legend
"""
import matplotlib.pyplot as plt
if c is None: c = 'k'
psi = self.PSIdict['psiN1D']
if what in ['p','P','Pres','pres','pressure','Ptot','ptot','Press','press','Pressure']:
ylabel = 'p$_{tot}$ [kPa]'
y = self.PROFdict['pres']*1e-3
elif what in ['q','qprof','q_prof']:
ylabel = 'q'
y = self.PROFdict['q_prof']
elif what in ['j','jtor','current density','J']:
ylabel = "j$_{tor}$ [MA/m$^2$]"
y = self.jtor_profile()
elif what in ['I','Ip','current']:
from scipy.integrate import cumtrapz
ylabel = "I [MA]"
FluxSurfList = self.get_allFluxSur()
jtor = self.jtor_profile(FluxSurfList)
Vprime = self.volume2D(FluxSurfList)['Vprime']
y = np.append(0, cumtrapz(jtor * Vprime, psi)) # current profile: I = integral(jtor dV) = integral(jtor * dV/dpsi * dpsi) = integral(jtor * dV/dpsi * dpsi/ds * ds)
elif what in ['F','f','fpol','Fpol']:
ylabel = 'F$_{pol}$ [Tm]'
y = self.PROFdict['fpol']
elif what in ['pprime','Pprime','gradP']:
ylabel = "dp/d$\\psi$ [kPa]"
y = self.PROFdict['pprime']*1e-3
elif what in ['ffprime','FFprime']:
ylabel = 'F dF/d$\\psi$ [T$^2$m$^2$]'
y = self.PROFdict['ffprime']
if what in ['all']:
jtor = self.jtor_profile()
fig = plt.figure(figsize = (15,11))
ax1 = fig.add_subplot(321, aspect = 'auto')
ax1.set_xlim(0,1)
ax1.set_ylabel('p$_{tot}$ [kPa]')
ax1.get_xaxis().set_ticklabels([])
ax1.plot(psi, self.PROFdict['pres']*1e-3, '-', color = c, lw = 2)
ax2 = fig.add_subplot(323, aspect = 'auto')
ax2.set_xlim(0,1)
ax2.set_ylabel('q')
ax2.get_xaxis().set_ticklabels([])
ax2.plot(psi, self.PROFdict['q_prof'], '-', color = c, lw = 2)
ax3 = fig.add_subplot(325, aspect = 'auto')
ax3.set_xlim(0,1)
ax3.set_ylabel("dI/d$\\psi$ [MA]")
ax3.set_xlabel('$\\psi$')
ax3.plot(psi, jtor, '-', color = c, lw = 2)
ax4 = fig.add_subplot(322, aspect = 'auto')
ax4.set_xlim(0,1)
ax4.set_ylabel('F$_{pol}$ [Tm]')
ax4.get_xaxis().set_ticklabels([])
ax4.plot(psi, self.PROFdict['fpol'], '-', color = c, lw = 2)
ax5 = fig.add_subplot(324, aspect = 'auto')
ax5.set_xlim(0,1)
ax5.set_ylabel("dp/d$\\psi$ [kPa]")
ax5.get_xaxis().set_ticklabels([])
ax5.plot(psi, self.PROFdict['pprime']*1e-3, '-', color = c, lw = 2)
ax6 = fig.add_subplot(326, aspect = 'auto')
ax6.set_xlim(0,1)
ax6.set_ylabel('F dF/d$\\psi$ [T$^2$m$^2$]')
ax6.set_xlabel('$\\psi$')
ax6.plot(psi, self.PROFdict['ffprime'], '-', color = c, lw = 2)
else:
if fig is None:
fig = plt.figure()
plt.xlim(0,1)
plt.xlabel('$\\psi$')
plt.ylabel(ylabel)
else:
fig = plt.figure(fig)
ax = fig.gca()
ax.plot(psi, y, '-', color = c, lw = 2, label = label)
if len(label) > 0: plt.legend()
fig.tight_layout()
# --------------------------------------------------------------------------------
def help(self):
"""
prints list of all 0D parameters in EFIT
as well as information on available profiles and functions
"""
print('-----------------------------------------------------------------------')
print('------------ List of all parameters in self.g -------------------------')
print('-----------------------------------------------------------------------')
print('shot = ', self.g['shot'])
print('time = ', self.g['time'],'\t\t in ms')
print('--- Grid ---')
print('NR = ', self.nw,'\t\t R grid points')
print('NZ = ', self.nh,'\t\t Z grid points')
print('dR = ', format(self.RZdict['dR'],'.4g'),'\t\t R grid resolution in [m]')
print('dZ = ', format(self.RZdict['dZ'],'g'),'\t\t Z grid resolution in [m]')
print('Xdim = ', format(self.rdim,'g'),'\t\t total R grid length in [m]')
print('Zdim = ', format(self.zdim,'g'),'\t\t total Z grid length in [m]')
print('R0 = ', format(abs(self.R0),'g'),'\t\t center point in R in [m]')
print('R1 = ', format(self.R1,'g'),'\t\t min grid point in R in [m]')
print('Zmid = ', format(self.Zmid,'g'),'\t\t center point in Z in [m]')
print('--- Shape ---')
print('RmAxis = ', format(self.rmaxis,'g'),'\t R of magnetic axis in [m]')
print('ZmAxis = ', format(self.zmaxis,'g'),'\t Z of magnetic axis in [m]')
print('aminor = ', format(self.g['aminor'],'g'),'\t minor radius in [m]')
print('aspect = ', format(self.g['aspect'],'g'),'\t aspect ratio')
print('kappa = ', format(self.g['kappa'],'g'),'\t elongation')
print('triUP = ', format(self.g['triUP'],'g'),'\t upper triangularity')
print('triLO = ', format(self.g['triLO'],'g'),'\t lower triangularity')
print('Nlcfs = ', len(self.lcfs),'\t\t number of separatrix points')
print('--- Plasma ---')
print('psiAxis = ', format(self.siAxis,'g'),'\t poloidal flux at magnetic axis in [Wb]')
print('psiSep = ', format(self.siBry,'g'),'\t poloidal flux at separatrix in [Wb]')
print('Bt0 = ', format(self.bcentr,'g'),'\t toroidal field at R0 in [T]')
print('Ip = ', int(self.Ip),'\t total plasma current in [A]')
print('helicity = ', self.isHelicity,'\t\t helicity = sign(Bp/Bt) = sign(Ip/Bt0)')
print('--- Wall ---')
print('Nwall = ', len(self.wall),'\t\t number of wall limiter points')
print('-----------------------------------------------------------------------')
print('------------ List of all arrays in self.g -----------------------------')
print('-----------------------------------------------------------------------')
print('Fpol','\t\t\t 1D profile of R * Btor in [Tm] vs. psiN')
print('Pres','\t\t\t 1D pressure profile in [Pa] vs. psiN')
print('FFprime','\t\t 1D profile of Fpol * dFpol/dpsi vs. psiN')
print('Pprime','\t\t\t 1D profile of dPres/dpsi vs. psiN')
print('q','\t\t\t 1D safety factor profile vs. psiN')
print('psiN','\t\t\t 1D array of normalized poloidal flux (psi-psiAxis)/(psiSep-psiAxis)')
print('psiRZ','\t\t\t 2D array or poloidal flux psi in [Wb] on RZ grid')
print('R','\t\t\t 1D array of R')
print('Z','\t\t\t 1D array of R')
print('lcfs', '\t\t\t array of (R,Z) of separatrix')
print('wall', '\t\t\t array of (R,Z) of wall limiter')
print('-----------------------------------------------------------------------')
print('------------ Info on available functionality --------------------------')
print('-----------------------------------------------------------------------')
print('Use the .plot() function to show the poloidal cross section')
print('Use the .plotProfile() function to show all profiles, or')
print(" .plotProfile(keyword) with keyword in ['Fpol','Pres','FFprime','Pprime','q','jtor','Ip']")
print(' to show each profile individually')
print('1D interpolations of profiles are readily available in .PROFdict')
print('2D Interpolations on the R,Z grid are readily available via')
print(' .psiFunc.ev(R,Z), .BRFunc.ev(R,Z), .BZFunc.ev(R,Z), .BpFunc.ev(R,Z), .BtFunc.ev(R,Z)')
print('Further available functions include: strike line locations, flux expansion, Swall cooridante transformations,')
print(' curvature and shear, 2D current density, and more...')
print('Current code version is: ', _VERSION)
# --------------------------------------------------------------------------------
def length_along_wall(self):
"""
Compute length along the wall
return Swall, Swall_max
"""
Rwall = self.g['wall'][:,0]
Zwall = self.g['wall'][:,1]
Nwall = len(Rwall)
Swall = np.zeros(Nwall)
dir = 1
S0 = 0
Swall[0] = np.sqrt((Rwall[0] - Rwall[-1])**2 + (Zwall[0] - Zwall[-1])**2)
if (Swall[0] > 0):
S0 = Zwall[-1]/(Zwall[-1] - Zwall[0])*Swall[0]
if (Zwall[0] < Zwall[-1]): dir = 1; # ccw
else: dir = -1 # cw
for i in range(1,Nwall):
Swall[i] = Swall[i-1] + np.sqrt((Rwall[i] - Rwall[i-1])**2 + (Zwall[i] - Zwall[i-1])**2) #length of curve in m
if ((Zwall[i]*Zwall[i-1] <= 0) & (Rwall[i] < self.g['R0'])):
if (Zwall[i-1] == Zwall[i]): continue
t = Zwall[i-1]/(Zwall[i-1] - Zwall[i])
S0 = Swall[i-1] + t*(Swall[i] - Swall[i-1])
if (Zwall[i] < Zwall[i-1]): dir = 1 # ccw
else: dir = -1 # cw
Swall_max = Swall[-1]
# set direction and Swall = 0 location
for i in range(Nwall):
Swall[i] = dir*(Swall[i] - S0);
if (Swall[i] < 0): Swall[i] += Swall_max
if (Swall[i] > Swall_max): Swall[i] -= Swall_max
if (abs(Swall[i]) < 1e-12): Swall[i] = 0
return Swall, Swall_max
# --------------------------------------------------------------------------------
def all_points_along_wall(self, swall, get_index = False, get_normal = False):
"""
Compute matching point R,Z to given swall along wall
This uses vectorization instead of a for loop and is much faster than the old version
return R,Z
"""
Rwall = self.g['wall'][:,0]
Zwall = self.g['wall'][:,1]
isFloat = False
if isinstance(swall, float) | isinstance(swall, np.float64):
swall = np.array([swall])
isFloat = True
N = len(swall)
swall = swall % self.Swall_max
swall[swall < 0] += self.Swall_max;
idx = -np.ones(N, dtype = int)
use = np.ones(N, dtype = bool)
Nuse = N
# locate discontinuity
idx_jump = np.where(np.abs(np.diff(self.Swall)) > 0.5*self.Swall_max)[0]
if len(idx_jump) == 0: idx_jump = 0
else: idx_jump = idx_jump[0] + 1
# This case occurs only when the wall does not have a point at inboard midplane
k = np.where((swall > self.Swall.max()) | (swall < self.Swall.min()))[0]
if len(k > 0):
idx[k] = idx_jump
use[k] = False
Nuse -= len(k)
swall_k = swall[k]
k2 = np.where(np.abs(swall_k - self.Swall[idx_jump]) > 0.5*self.Swall_max)[0]
if len(k2 > 0):
swall_k2 = swall_k[k2]
swall_k2[swall_k2 < self.Swall[idx_jump]] += self.Swall_max
swall_k2[swall_k2 >= self.Swall[idx_jump]] -= self.Swall_max
swall_k[k2] = swall_k2
swall[k] = swall_k
# locate intervall that brackets swall
s0 = self.Swall[-1]
for i in range(len(self.Swall)):
if Nuse <= 0: break
idxu = -np.ones(Nuse, dtype = int)
uu = np.ones(Nuse, dtype = bool)
s1 = self.Swall[i]
if (abs(s1 - s0) > 0.5*self.Swall_max): #skip the jump around Swall = 0 point
s0 = s1
continue
k = np.where((s1 - swall[use]) * (s0 - swall[use]) <= 0)[0]
idxu[k] = i
uu[k] = False
Nuse -= len(k)
idx[use] = idxu
use[use] = uu
s0 = s1
# set bracket points
R1,Z1,R2,Z2,i = Rwall[idx], Zwall[idx], Rwall[idx-1], Zwall[idx-1], 2
id = np.where((R1 == R2) & (Z1 == Z2))[0]
while len(id) > 0: # if points are identical
R2[id],Z2[id] = Rwall[idx[id]-i], Zwall[idx[id]-i] # works for idx == 0 as well
id = np.where((R1 == R2) & (Z1 == Z2))[0]
i += 1
# linear interplation between bracket points
dR,dZ = (R2-R1), (Z2-Z1)
dx = np.sqrt(dR**2 + dZ**2)
dR,dZ = dR/dx, dZ/dx # dR,dZ is normalized
x = np.abs(swall - self.Swall[idx])
R,Z = (R1 + x*dR), (Z1 + x*dZ)
if isFloat: R,Z,dR,dZ,idx = R[0],Z[0],dR[0],dZ[0],idx[0]
if get_normal: # get normal vector
return R,Z,-dZ,dR # nR,nZ = -dZ, dR
else:
if get_index: return R,Z,idx
else: return R,Z