def test_parallel_fieldline(self):
nlines = 4
r0 = np.linalg.norm(self.ma.gamma()[0, :2])
z0 = self.ma.gamma()[0, 2]
R0 = [r0 + i * 0.01 for i in range(nlines)]
Z0 = [z0 for i in range(nlines)]
phis = []
comm = MPI.COMM_WORLD
print('comm.size', comm.size)
res_tys_mpi, res_phi_hits_mpi = compute_fieldlines(
self.bsh,
R0,
Z0,
tmax=1000,
phis=phis,
stopping_criteria=[],
comm=comm)
res_tys, res_phi_hits = compute_fieldlines(self.bsh,
R0,
Z0,
tmax=1000,
phis=phis,
stopping_criteria=[],
comm=None)
for i in range(nlines):
assert np.allclose(res_phi_hits_mpi[i],
res_phi_hits[i],
atol=1e-9,
rtol=1e-9)
def test_poincare_plot(self):
coils, currents, ma = get_ncsx_data(Nt_coils=15)
nfp = 3
stellarator = CoilCollection(coils, currents, nfp, True)
bs = BiotSavart(stellarator.coils, stellarator.currents)
n = 10
rrange = (1.0, 1.9, n)
phirange = (0, 2*np.pi/nfp, n*2)
zrange = (0, 0.4, n)
bsh = InterpolatedField(
bs, UniformInterpolationRule(2),
rrange, phirange, zrange, True, nfp=3, stellsym=True
)
nlines = 4
r0 = np.linalg.norm(ma.gamma()[0, :2])
z0 = ma.gamma()[0, 2]
R0 = [r0 + i*0.01 for i in range(nlines)]
Z0 = [z0 for i in range(nlines)]
nphis = 4
phis = np.linspace(0, 2*np.pi/nfp, nphis, endpoint=False)
res_tys, res_phi_hits = compute_fieldlines(
bsh, R0, Z0, tmax=1000, phis=phis, stopping_criteria=[])
try:
import matplotlib # noqa
plot_poincare_data(res_phi_hits, phis, '/tmp/fieldlines.png')
except ImportError:
pass
def trace_fieldlines(bfield, label):
t1 = time.time()
R0 = np.linspace(ma.gamma()[0, 0], ma.gamma()[0, 0] + 0.14, nfieldlines)
Z0 = [ma.gamma()[0, 2] for i in range(nfieldlines)]
phis = [(i/4)*(2*np.pi/nfp) for i in range(4)]
fieldlines_tys, fieldlines_phi_hits = compute_fieldlines(
bfield, R0, Z0, tmax=tmax_fl, tol=1e-7, comm=comm,
phis=phis, stopping_criteria=[LevelsetStoppingCriterion(sc_fieldline.dist)])
t2 = time.time()
print(f"Time for fieldline tracing={t2-t1:.3f}s. Num steps={sum([len(l) for l in fieldlines_tys])//nfieldlines}", flush=True)
if comm is None or comm.rank == 0:
particles_to_vtk(fieldlines_tys, f'/tmp/fieldlines_{label}')
plot_poincare_data(fieldlines_phi_hits, phis, f'/tmp/poincare_fieldline_{label}.png', dpi=150)
def test_poincare_ncsx_known(self):
coils, currents, ma = get_ncsx_data(Nt_coils=25)
nfp = 3
stellarator = CoilCollection(coils, currents, nfp, True)
currents = [-c for c in currents]
bs = BiotSavart(stellarator.coils, stellarator.currents)
R0 = [np.linalg.norm(ma.gamma()[0, :2])]
Z0 = [ma.gamma()[0, 2]]
phis = np.arctan2(ma.gamma()[:, 1], ma.gamma()[:, 0])
res_tys, res_phi_hits = compute_fieldlines(
bs, R0, Z0, tmax=10, phis=phis, stopping_criteria=[])
for i in range(len(phis)-1):
assert np.linalg.norm(ma.gamma()[i+1, :] - res_phi_hits[0][i, 2:5]) < 1e-4
def test_poincare_tokamak(self):
# Test a simple circular tokamak geometry that
# consists of a superposition of a purely toroidal
# and a purely poloidal magnetic field
R0test = 1.0
B0test = 1.0
qtest = 3.2
Bfield = ToroidalField(R0test, B0test)+PoloidalField(R0test, B0test, qtest)
nlines = 4
R0 = [1.05 + i*0.02 for i in range(nlines)]
Z0 = [0 for i in range(nlines)]
nphis = 4
phis = np.linspace(0, 2*np.pi, nphis, endpoint=False)
res_tys, res_phi_hits = compute_fieldlines(
Bfield, R0, Z0, tmax=10, phis=phis, stopping_criteria=[])
# Check that Poincare plot is a circle in the R,Z plane with R centered at R0
rtest = [[np.sqrt((np.sqrt(res_tys[i][j][1]**2+res_tys[i][j][2]**2)-R0test)**2+res_tys[i][j][3]**2)-R0[i]+R0test for j in range(len(res_tys[i]))] for i in range(len(res_tys))]
assert [np.allclose(rtest[i], 0., rtol=1e-5, atol=1e-5) for i in range(nlines)]
def test_poincare_toroidal(self):
logger = logging.getLogger('simsopt.field.tracing')
logger.setLevel(1)
# Test a toroidal magnetic field with no rotational transform
R0test = 1.3
B0test = 0.8
Bfield = ToroidalField(R0test, B0test)
nlines = 10
R0 = [1.1 + i*0.1 for i in range(nlines)]
Z0 = [0 for i in range(nlines)]
nphis = 10
phis = np.linspace(0, 2*np.pi, nphis, endpoint=False)
res_tys, res_phi_hits = compute_fieldlines(
Bfield, R0, Z0, tmax=100, phis=phis, stopping_criteria=[])
for i in range(nlines):
assert np.allclose(res_tys[i][:, 3], 0.)
assert np.allclose(np.linalg.norm(res_tys[i][:, 1:3], axis=1), R0[i])
assert validate_phi_hits(res_phi_hits[i], nphis)
if with_evtk:
particles_to_vtk(res_tys, '/tmp/fieldlines')
def test_poincare_caryhanson(self):
# Test with a known magnetic field - optimized Cary&Hanson configuration
# with a magnetic axis at R=0.9413. Field created using the Biot-Savart
# solver given a set of two helical coils created using the CurveHelical
# class. The total magnetic field is a superposition of a helical and
# a toroidal magnetic field.
coils = [CurveHelical(200, 2, 5, 2, 1., 0.3) for i in range(2)]
coils[0].set_dofs(np.concatenate(([np.pi/2, 0.2841], [0, 0])))
coils[1].set_dofs(np.concatenate(([0, 0], [0, 0.2933])))
currents = [3.07e5, -3.07e5]
Btoroidal = ToroidalField(1.0, 1.0)
Bhelical = BiotSavart(coils, currents)
bs = Bhelical+Btoroidal
ma = CurveXYZFourier(300, 1)
magnetic_axis_radius = 0.9413
ma.set_dofs([0, 0, magnetic_axis_radius, 0, magnetic_axis_radius, 0, 0, 0, 0])
R0 = [np.linalg.norm(ma.gamma()[0, :2])]
Z0 = [ma.gamma()[0, 2]]
phis = np.arctan2(ma.gamma()[:, 1], ma.gamma()[:, 0])
res_tys, res_phi_hits = compute_fieldlines(
bs, R0, Z0, tmax=2, phis=phis, stopping_criteria=[])
for i in range(len(res_phi_hits[0])):
assert np.linalg.norm(ma.gamma()[i+1, :] - res_phi_hits[0][i, 2:5]) < 2e-3