the elimination of magnetic islands, with both VMEC and SPEC called in
the objective function.
Below, the argument max_nfev=1 in least_squares_mpi_solve causes the
optimization to stop after only a single iteration, so this example
does not take too long to run. For a real optimization, that argument
should be removed.
"""
log()
mpi = MpiPartition()
mpi.write()
vmec_filename = os.path.join(os.path.dirname(__file__), 'inputs',
'input.nfp2_QA_iota0.4_withIslands')
vmec = Vmec(vmec_filename, mpi=mpi)
surf = vmec.boundary
spec_filename = os.path.join(os.path.dirname(__file__), 'inputs',
'nfp2_QA_iota0.4_withIslands.sp')
spec = Spec(spec_filename, mpi=mpi)
# This next line is where the boundary surface objects of VMEC and
# SPEC are linked:
spec.boundary = surf
# Define parameter space:
surf.all_fixed()
surf.fixed_range(mmin=0, mmax=3, nmin=-3, nmax=3, fixed=False)
surf.set_fixed("rc(0,0)") # Major radius
from simsopt.util.mpi import MpiPartition
from simsopt.mhd import Vmec, Boozer, Quasisymmetry
from simsopt.objectives.least_squares import LeastSquaresProblem
from simsopt.solve.mpi import least_squares_mpi_solve
import os
"""
Optimize for quasi-helical symmetry (M=1, N=1) at a given radius.
"""
# This problem has 24 degrees of freedom, so we can use 24 + 1 = 25
# concurrent function evaluations for 1-sided finite difference
# gradients.
mpi = MpiPartition(25)
vmec = Vmec(os.path.join(os.path.dirname(__file__), 'inputs',
'input.nfp4_QH_warm_start'),
mpi=mpi)
# Define parameter space:
surf = vmec.boundary
surf.all_fixed()
max_mode = 2
surf.fixed_range(mmin=0,
mmax=max_mode,
nmin=-max_mode,
nmax=max_mode,
fixed=False)
surf.set_fixed("rc(0,0)") # Major radius
# Configure quasisymmetry objective:
qs = Quasisymmetry(
this example runs fast.
Details of the optimum and a plot of the objective function landscape
can be found here:
https://github.com/landreman/stellopt_scenarios/tree/master/2DOF_vmecOnly_targetIotaAndVolume
"""
# This next line turns on detailed logging. It can be commented out if
# you do not want such verbose output.
log(logging.INFO)
mpi = MpiPartition()
# Initialize VMEC from an input file:
vmec = Vmec(os.path.join(os.path.dirname(__file__), 'inputs',
'input.2DOF_vmecOnly_targetIotaAndVolume'),
mpi=mpi)
surf = vmec.boundary
# Initialize SPEC from an input file:
spec = Spec(os.path.join(os.path.dirname(__file__), 'inputs',
'2DOF_targetIotaAndVolume.sp'),
mpi=mpi)
# Set the SPEC boundary to be the same object as the VMEC boundary!
spec.boundary = surf
# VMEC parameters are all fixed by default, while surface parameters are all non-fixed by default.
# You can choose which parameters are optimized by setting their 'fixed' attributes.
surf.all_fixed()
surf.set_fixed('rc(1,1)', False)
#!/usr/bin/env python
from simsopt.mhd import Vmec, Boozer, Quasisymmetry
from simsopt import LeastSquaresProblem
from simsopt import least_squares_serial_solve
import os
"""
This script solve the problem in
https://github.com/landreman/stellopt_scenarios/tree/master/2DOF_circularCrossSection_varyAxis_targetIotaAndQuasisymmetry
See that website for a detailed description of the problem and plots
of the objective function landscape.
"""
vmec = Vmec(os.path.join(os.path.dirname(__file__), 'inputs', 'input.2DOF_circularCrossSection_varyAxis_targetIotaAndQuasisymmetry'))
# Define parameter space:
vmec.boundary.all_fixed()
vmec.boundary.set_fixed("rc(0,1)", False)
vmec.boundary.set_fixed("zs(0,1)", False)
# Define objective function:
boozer = Boozer(vmec, mpol=32, ntor=16)
qs = Quasisymmetry(boozer,
1.0, # Radius to target
1, 0, # (M, N) you want in |B|
normalization="symmetric",
weight="stellopt_ornl")
# Objective function is 100 * (iota - (-0.41))^2 + 1 * (qs - 0)^2
prob = LeastSquaresProblem([(vmec.iota_axis, -0.41, 100),
The objective function for this example targets quasi-axisymmetry and
the iota profile. First we optimize in a small parameter space, with
m and |n| values up through 1. Then the parameter space is widened to
include m and |n| values up through 2, with the resolution of VMEC and
booz_xform increased at the same time. Then the parameter space is
widened again to include m and |n| values up through 3, and again the
resolution for VMEC and booz_xform is increased.
"""
#log()
mpi = MpiPartition()
mpi.write()
vmec = Vmec(os.path.join(os.path.dirname(__file__), 'inputs', 'input.nfp2_QA'),
mpi=mpi)
vmec.verbose = mpi.proc0_world
surf = vmec.boundary
# Configure quasisymmetry objective:
boozer = Boozer(vmec)
boozer.bx.verbose = mpi.proc0_world
qs = Quasisymmetry(
boozer,
0.5, # Radius to target
1,
0) # (M, N) you want in |B|
# Define objective function
prob = LeastSquaresProblem([(vmec.aspect, 6, 1), (vmec.iota_axis, 0.465, 1),
(vmec.iota_edge, 0.495, 1), (qs, 0, 1)])
can be found here:
https://github.com/landreman/stellopt_scenarios/tree/master/2DOF_vmecOnly_targetIotaAndVolume
"""
# This next line turns on detailed logging. It can be commented out if
# you do not want such verbose output.
log()
# In the next line, we can adjust how many groups the pool of MPI
# processes is split into.
mpi = MpiPartition(ngroups=3)
mpi.write()
# Initialize VMEC from an input file:
equil = Vmec(
os.path.join(os.path.dirname(__file__), 'inputs',
'input.2DOF_vmecOnly_targetIotaAndVolume'), mpi)
surf = equil.boundary
# VMEC parameters are all fixed by default, while surface parameters
# are all non-fixed by default. You can choose which parameters are
# optimized by setting their 'fixed' attributes.
surf.all_fixed()
surf.set_fixed('rc(1,1)', False)
surf.set_fixed('zs(1,1)', False)
# Each Target is then equipped with a shift and weight, to become a
# term in a least-squares objective function. A list of terms are
# combined to form a nonlinear-least-squares problem.
desired_volume = 0.15
volume_weight = 1
from simsopt import LeastSquaresProblem
from simsopt.solve.mpi import least_squares_mpi_solve
import os
"""
This script solve the problem in
https://github.com/landreman/stellopt_scenarios/tree/master/7DOF_varyAxisAndElongation_targetIotaAndQuasisymmetry
See that website for a detailed description of the problem.
"""
# This next line turns on detailed logging. It can be commented out if
# you do not want such verbose output.
log()
mpi = MpiPartition()
vmec = Vmec(
os.path.join(os.path.dirname(__file__), 'inputs',
'input.stellopt_scenarios_7dof'), mpi)
# We will optimize in the space of Garabedian coefficients:
surf = vmec.boundary.to_Garabedian()
vmec.boundary = surf
# Define parameter space:
surf.all_fixed()
surf.fixed_range(mmin=0, mmax=2, nmin=-1, nmax=1, fixed=False)
surf.set_fixed("Delta(1,0)") # toroidally-averaged major radius
surf.set_fixed("Delta(0,0)") # toroidally-averaged minor radius
# Define objective function:
boozer = Boozer(vmec, mpol=32, ntor=16)
qs = Quasisymmetry(
Details of the optimum and a plot of the objective function landscape
can be found here:
https://github.com/landreman/stellopt_scenarios/tree/master/1DOF_circularCrossSection_varyR0_targetVolume
"""
# Print detailed logging info. This could be commented out if desired.
log()
# In the next line, we can adjust how many groups the pool of MPI
# processes is split into.
mpi = MpiPartition(ngroups=2)
mpi.write()
# Start with a default surface, which is axisymmetric with major
# radius 1 and minor radius 0.1.
equil = Vmec(mpi=mpi)
surf = equil.boundary
# Set the initial boundary shape. Here is one syntax:
surf.set('rc(0,0)', 1.0)
# Here is another syntax:
surf.set_rc(0, 1, 0.1)
surf.set_zs(0, 1, 0.1)
surf.set_rc(1, 0, 0.1)
surf.set_zs(1, 0, 0.1)
# VMEC parameters are all fixed by default, while surface parameters
# are all non-fixed by default. You can choose which parameters are
# optimized by setting their 'fixed' attributes.
surf.all_fixed()
from simsopt.mhd import Vmec, Spec, Boozer, Quasisymmetry
from simsopt.mhd.spec import Residue
from simsopt.objectives.least_squares import LeastSquaresProblem
from simsopt.solve.mpi import least_squares_mpi_solve
"""
In this example, we simultaneously optimize for quasisymmetry and
the elimination of magnetic islands, with both VMEC and SPEC called in
the objective function.
"""
log()
mpi = MpiPartition()
mpi.write()
vmec = Vmec(os.path.join(os.path.dirname(__file__), 'inputs', 'input.nfp2_QA_iota0.4_withIslands'), mpi=mpi)
surf = vmec.boundary
spec = Spec(os.path.join(os.path.dirname(__file__), 'inputs', 'nfp2_QA_iota0.4_withIslands.sp'), mpi=mpi)
# This next line is where the boundary surface objects of VMEC and
# SPEC are linked:
spec.boundary = surf
# Define parameter space:
surf.all_fixed()
surf.fixed_range(mmin=0, mmax=3,
nmin=-3, nmax=3, fixed=False)
surf.set_fixed("rc(0,0)") # Major radius
# Configure quasisymmetry objective:
can be found here:
https://github.com/landreman/stellopt_scenarios/tree/master/1DOF_circularCrossSection_varyAxis_targetIota
"""
# Print detailed logging info. This line could be commented out if desired.
log()
# In the next line, we can adjust how many groups the pool of MPI
# processes is split into.
mpi = MpiPartition(ngroups=1)
mpi.write()
# Start with a default surface, which is axisymmetric with major
# radius 1 and minor radius 0.1.
equil = Vmec(os.path.join(os.path.dirname(__file__), 'inputs',
'input.1DOF_Garabedian'),
mpi=mpi)
# We will optimize in the space of Garabedian coefficients rather than
# RBC/ZBS coefficients. To do this, we convert the boundary to the
# Garabedian representation:
surf = equil.boundary.to_Garabedian()
equil.boundary = surf
# VMEC parameters are all fixed by default, while surface parameters
# are all non-fixed by default. You can choose which parameters are
# optimized by setting their 'fixed' attributes.
surf.all_fixed()
surf.set_fixed('Delta(1,-1)', False)
# Each function we want in the objective function is then equipped