def pyoculusPoincare(stel,
qvfilename,
Rbegin=1.55,
Rend=1.62,
nPpts=50,
nPtrj=5):
from axisOptFuncs import importCoils, getFourierCurve
from pyoculus.solvers import PoincarePlot
import matplotlib.pyplot as plt
_, current = importCoils("coils." + qvfilename)
outputFile = qvfilename + "_coil_coeffs.dat"
coils, currents = getFourierCurve(outputFile, current)
bs = BiotSavart(coils, currents)
sbsp = SimsgeoBiotSavart(bs, R0=sum(stel.rc), Z0=0, Nfp=stel.nfp)
params = dict()
Rbegin = 1.01 * sum(stel.rc)
params["Rbegin"] = Rbegin
params["Rend"] = Rend
params["nPpts"] = nPpts
params["nPtrj"] = nPtrj
p = PoincarePlot(sbsp, params)
poincare_output = p.compute()
p.plot(s=1)
plt.savefig("poincarePyoculus_" + qvfilename + '.pdf',
bbox_inches='tight',
pad_inches=0)
iota = p.compute_iota()
p.plot_iota()
plt.savefig("iotaPyoculus_" + qvfilename + '.pdf',
bbox_inches='tight',
pad_inches=0)
plt.show()
def coils2simsgeo(qvfilename, NFP, nPCoils, accuracy):
print("Convert resulting coils to SIMSGEO curves")
from axisOptFuncs import importCoils, cartesianCoils2fourier, getFourierCurve, export_coils
coilsCartesian, current = importCoils("coils." + qvfilename)
outputFile = qvfilename + "_coil_coeffs.dat"
cartesianCoils2fourier(coilsCartesian, outputFile, nPCoils, accuracy)
coils, currents = getFourierCurve(outputFile, current)
filename = "coils." + qvfilename + "2"
export_coils(coils, filename, currents, NFP)
return coils, currents
def getResidue(stel,
axis,
qvfilename,
guess=1.6,
pp=3,
qq=8,
sbegin=1.58,
send=1.62):
from axisOptFuncs import importCoils, getFourierCurve
from pyoculus.solvers import FixedPoint
_, current = importCoils("coils." + qvfilename)
outputFile = qvfilename + "_coil_coeffs.dat"
coils, currents = getFourierCurve(outputFile, current)
bs = BiotSavart(coils, currents)
sbsp = SimsgeoBiotSavart(bs, R0=sum(stel.rc), Z0=0, Nfp=stel.nfp)
fp = FixedPoint(sbsp, {"Z": 0.0})
#sbegin=1.01*sum(stel.rc)
output = fp.compute(guess=guess, pp=pp, qq=qq, sbegin=sbegin, send=send)
residue = output.GreenesResidue
print(residue)
def CoilsBonAxis(axis, qvfilename, NFP):
from axisOptFuncs import importCoils, getFourierCurve, plot_stellarator
from simsopt.geo.biotsavart import BiotSavart
from numpy import sqrt, dot
import matplotlib.pyplot as plt
_, current = importCoils("coils." + qvfilename)
outputFile = qvfilename + "_coil_coeffs.dat"
coils, currents = getFourierCurve(outputFile, current)
print("Look at resulting coils")
plot_stellarator("coils_FOURIER_", qvfilename, coils, NFP, axis,
"quasisymmetry_out." + qvfilename + ".nc")
print("Plot on-axis B from these coils")
bs = BiotSavart(coils, currents)
bs.set_points(axis.gamma())
Bfield = bs.B()
Bstrength = [sqrt(dot(Bfieldi, Bfieldi)) for Bfieldi in Bfield]
plt.figure()
plt.plot(Bstrength)
plt.xlabel('phi')
plt.ylabel('B')
plt.savefig("Bonaxis" + qvfilename + '.pdf',
bbox_inches='tight',
pad_inches=0)
def optaxiscoil(qvfilename, stel, iotaTarget, nIterations=30, nquadrature=150):
from simsopt.core.least_squares_problem import LeastSquaresProblem
from simsopt.solve.serial_solve import least_squares_serial_solve
from simsopt.geo.curverzfourier import CurveRZFourier
from axisOptFuncs import getFourierCurve, plot_stellarator, export_coils
from numpy import sqrt, dot
from os import remove
from glob import glob
import matplotlib.pyplot as plt
outputFile = qvfilename + "_coil_coeffs.dat"
current = 3.11049660e+05
coils, _ = getFourierCurve(outputFile, current)
axis = CurveRZFourier(nquadrature, len(stel.rc) - 1, stel.nfp, True)
axis.set_dofs(concatenate((stel.rc, stel.zs[1:])))
obj = objaxiscoil(coils, current, axis, stel)
term = [(obj.iota, iotaTarget, 1e4), (obj.devBonAxis, 0, 1e0),
(obj, 'max_elongation', 0, 1e1), (obj.stdBonAxis, 0, 1e5),
(obj.residue, 0, 1e5)]
prob = LeastSquaresProblem(term)
obj.all_fixed()
# obj.set_fixed('rc(1)', False)
# obj.set_fixed('zs(1)', False)
# obj.set_fixed('rc(2)', False)
# obj.set_fixed('zs(2)', False)
obj.set_fixed('rc(3)', False)
obj.set_fixed('zs(3)', False)
obj.set_fixed('rc(4)', False)
obj.set_fixed('zs(4)', False)
obj.set_fixed('rc(5)', False)
obj.set_fixed('zs(5)', False)
#obj.set_fixed('etabar', False)
#obj.set_fixed('current', False)
#obj.fixed[obj.nAxisFour:obj.nAxisFour+(obj.ncoils+1)*obj.nCoilFour]=False
################################################
rcInit = obj.stel.rc
zsInit = obj.stel.zs
plt.figure()
plt.plot(obj.BonAxis())
plt.xlabel('phi')
plt.ylabel('B')
################ OPTIMIZE ####################
least_squares_serial_solve(prob, max_nfev=nIterations) #, method='lm')
################################################
for f in glob("residuals_2021*.dat"):
remove(f)
for f in glob("simsopt_2021*.dat"):
remove(f)
################################################
rcFinal = obj.stel.rc
zsFinal = obj.stel.zs
rcDelta = [
100 * (rcf - rcInit[count]) / rcInit[count]
for count, rcf in enumerate(rcFinal)
]
zsDelta = [
100 * (zsf - zsInit[count]) / zsInit[count]
for count, zsf in enumerate(zsFinal)
]
print('Initial rc = [',
','.join([str(elem) for elem in rcInit]), ']')
print('Final rc = [',
','.join([str(elem) for elem in rcFinal]), ']')
print('Initial zs = [',
','.join([str(elem) for elem in zsInit]), ']')
print('Final zs = [',
','.join([str(elem) for elem in zsFinal]), ']')
print('Percentage change in rc = [',
','.join([str(elem) for elem in rcDelta]), ']')
print('Percentage change in zs = [',
','.join([str(elem) for elem in zsDelta]), ']')
print('Target iota = ', iotaTarget, ', final iota = ', obj.stel.iota)
################################################
print("Plot on-axis B from these coils")
plt.plot(obj.BonAxis())
plt.savefig("optimizedBonaxis_" + qvfilename + '.pdf',
bbox_inches='tight',
pad_inches=0)
################################################
print("Plot final coils and axis")
plot_stellarator("coils_axis_Optimized_", qvfilename, obj.coils, obj.nfp,
obj.axis)
filename = "coils." + qvfilename + "Optimized"
export_coils(obj.coils, filename, obj.currents, obj.nfp)
return obj.stel, obj.axis