def test_minimum_distance_taylor_test():
nfp = 2
(coils, currents, ma, eta_bar) = get_24_coil_data(nfp=nfp)
currents = len(coils) * [1e4]
stellarator = CoilCollection(coils, currents, nfp, True)
coils = stellarator.coils
np.random.seed(2)
J = MinimumDistance(coils, 0.1)
coil_dofs = stellarator.get_dofs()
h = np.random.rand(len(coil_dofs)).reshape(coil_dofs.shape)
dJ = stellarator.reduce_coefficient_derivatives(J.dJ_by_dcoefficients())
deriv = np.sum(dJ * h)
err = 1e8
for i in range(1, 5):
eps = 0.1**i
stellarator.set_dofs(coil_dofs + eps * h)
Jp = J.J()
stellarator.set_dofs(coil_dofs - eps * h)
Jm = J.J()
deriv_est = 0.5 * (Jp - Jm) / eps
err_new = np.linalg.norm(deriv_est - deriv)
print("err_new %s" % (err_new))
assert err_new < 0.55**2 * err
err = err_new
print("deriv_est %s" % (deriv_est))
def test_biot_savart_same_results_as_matlab():
num_coils = 6
nfp = 2
coils, currents, ma, eta_bar = get_24_coil_data(nfp=nfp, ppp=20)
currents = num_coils * [1e4]
coil_collection = CoilCollection(coils, currents, nfp, True)
bs = BiotSavart(coil_collection.coils, coil_collection.currents)
points = np.asarray([
[1.079860105000000, 0., 0.],
[1.078778093231020, 0.041861502907184, -0.006392709264512],
])
matlab_res = np.asarray([
[0, -0.044495549447737, 0.005009283509639],
[0.002147564148695, -0.044454924339257, 0.004992777089330],
])
bs.compute(points, use_cpp=True)
print(bs.B, "\n", matlab_res)
assert np.allclose(bs.B, matlab_res)
J = SquaredMagneticFieldNormOnCurve(ma, bs)
J0 = J.J()
assert abs(0.5 * J0 - 0.007179654002556) < 1e-10
J = SquaredMagneticFieldGradientNormOnCurve(ma, bs)
J0 = J.J()
assert abs(0.5 * J0 - 0.014329772542444) < 1e-10
if __name__ == "__main__":
ax = None
for i in range(0, len(coils)):
ax = coils[i].plot(ax=ax, show=False)
ma.plot(ax=ax)
def test_magnetic_field_objective_by_dcurvecoeffs(gradient):
nfp = 2
(coils, _, ma, _) = get_24_coil_data(nfp=nfp, ppp=20)
currents = len(coils) * [1e4]
stellerator = CoilCollection(coils, currents, nfp, True)
bs = BiotSavart(stellerator.coils, stellerator.currents)
if gradient:
J = SquaredMagneticFieldGradientNormOnCurve(ma, bs)
else:
J = SquaredMagneticFieldNormOnCurve(ma, bs)
J0 = J.J()
curve_dofs = ma.get_dofs()
h = 1e-1 * np.random.rand(len(curve_dofs)).reshape(curve_dofs.shape)
dJ = J.dJ_by_dcurvecoefficients()
deriv = np.sum(dJ * h)
err = 1e6
for i in range(5, 10):
eps = 0.5**i
ma.set_dofs(curve_dofs + eps * h)
Jh = J.J()
deriv_est = (Jh - J0) / eps
err_new = np.linalg.norm(deriv_est - deriv)
print("err_new %s" % (err_new))
assert err_new < 0.55 * err
err = err_new
def test_taylor_test_coil_currents(objective):
num_coils = 6
nfp = 2
(coils, _, ma, _) = get_24_coil_data(nfp=nfp, ppp=20)
currents = len(coils) * [1e4]
stellerator = CoilCollection(coils, currents, nfp, True)
bs = BiotSavart(stellerator.coils, stellerator.currents)
bs.set_points(ma.gamma)
qsf = QuasiSymmetricField(-2.25, ma)
J = BiotSavartQuasiSymmetricFieldDifference(qsf, bs)
x0 = stellerator.get_currents()
h = 1e4 * np.random.rand(len(currents))
if objective == "l2":
J0 = J.J_L2()
dJ = stellerator.reduce_current_derivatives(J.dJ_L2_by_dcoilcurrents())
else:
J0 = J.J_H1()
dJ = stellerator.reduce_current_derivatives(J.dJ_H1_by_dcoilcurrents())
assert len(dJ) == len(h)
deriv = np.sum(dJ * h)
err = 1e6
eps = 0.1
while err > 1e-7:
eps *= 0.5
stellerator.set_currents(x0 + eps * h)
bs.clear_cached_properties()
Jh = J.J_L2() if objective == "l2" else J.J_H1()
deriv_est = (Jh - J0) / eps
err_new = np.linalg.norm(deriv_est - deriv)
print("err_new %s" % (err_new))
assert err_new < 0.55 * err
err = err_new
assert eps < 1e-2
def test_quasi_symmetric_difference_same_results_as_matlab():
num_coils = 6
nfp = 2
coils, currents, ma, eta_bar = get_24_coil_data(nfp=nfp, ppp=20)
currents = num_coils * [1e4]
coil_collection = CoilCollection(coils, currents, nfp, True)
bs = BiotSavart(coil_collection.coils, coil_collection.currents)
bs.set_points(ma.gamma)
qsf = QuasiSymmetricField(-2.25, ma)
J = BiotSavartQuasiSymmetricFieldDifference(qsf, bs)
print(0.5 * J.J_L2())
print(0.5 * J.J_H1())
assert abs(3.486875802492926 - 0.5 * J.J_L2()) < 1e-5
assert abs(8.296004257157044 - 0.5 * J.J_H1()) < 1e-5
def test_taylor_test_ma_coeffs(objective):
num_coils = 6
nfp = 2
(coils, _, ma, _) = get_24_coil_data(nfp=nfp, ppp=20)
currents = len(coils) * [1e4]
stellerator = CoilCollection(coils, currents, nfp, True)
bs = BiotSavart(stellerator.coils, stellerator.currents)
bs.set_points(ma.gamma)
qsf = QuasiSymmetricField(-2.25, ma)
J = BiotSavartQuasiSymmetricFieldDifference(qsf, bs)
ma_dofs = ma.get_dofs()
np.random.seed(1)
h = np.random.rand(len(ma_dofs)).reshape(ma_dofs.shape)
if objective == "l2":
J0 = J.J_L2()
dJ = J.dJ_L2_by_dmagneticaxiscoefficients()
else:
J0 = J.J_H1()
dJ = J.dJ_H1_by_dmagneticaxiscoefficients()
assert len(dJ) == len(h)
deriv = np.sum(dJ * h)
err = 1e6
eps = 0.04
while err > 1e-11:
eps *= 0.5
deriv_est = 0
shifts = [-2, -1, +1, +2]
weights = [+1 / 12, -2 / 3, +2 / 3, -1 / 12]
for i in range(4):
ma.set_dofs(ma_dofs + shifts[i] * eps * h)
bs.set_points(ma.gamma)
qsf.clear_cached_properties()
deriv_est += weights[i] * (J.J_L2()
if objective == "l2" else J.J_H1())
deriv_est *= 1 / eps
err_new = np.linalg.norm(deriv_est - deriv) / np.linalg.norm(deriv)
print("err_new %s" % (err_new))
assert err_new < (0.55)**4 * err
err = err_new
assert eps < 1e-3
def test_magnetic_field_in_ncsx_is_correct():
nfp = 3
(coils, ma, currents) = get_ncsx_data(Nt=25, ppp=20)
stellarator = CoilCollection(coils, currents, nfp, True)
dir_path = os.path.dirname(os.path.realpath(__file__))
filepath = os.path.join(dir_path, "..", "pyplasmaopt", "data", "ncsx",
"mgrid_c09r00_modularOnly.nc")
ds = nc.Dataset(filepath)
Br = ds['br_001'][:, :, :] + ds['br_002'][:, :, :] + ds['br_003'][:, :, :]
Bp = ds['bp_001'][:, :, :] + ds['bp_002'][:, :, :] + ds['bp_003'][:, :, :]
Bz = ds['bz_001'][:, :, :] + ds['bz_002'][:, :, :] + ds['bz_003'][:, :, :]
Rs = np.linspace(0.436, 2.436, 5, endpoint=True)
phis = np.linspace(0, 2 * np.pi / 3, 4, endpoint=False)
Zs = np.linspace(-1, 1, 9, endpoint=True)
gammas = [coil.gamma for coil in stellarator.coils]
dgamma_by_dphis = [
coil.dgamma_by_dphi[:, 0, :] for coil in stellarator.coils
]
currents = stellarator.currents
avg_rel_err = 0
max_rel_err = 0
for i, phi in enumerate(phis):
for j, Z in enumerate(Zs):
for k, R in enumerate(Rs):
x = R * np.cos(phi)
y = R * np.sin(phi)
Bxyz = np.zeros((1, 3))
xyz = np.asarray([[x, y, Z]])
cpp.biot_savart_B_only(xyz, gammas, dgamma_by_dphis, currents,
Bxyz)
trueBx = np.cos(phi) * Br[i, j, k] - np.sin(phi) * Bp[i, j, k]
trueBy = np.sin(phi) * Br[i, j, k] + np.cos(phi) * Bp[i, j, k]
trueBz = Bz[i, j, k]
trueB = np.asarray([[trueBx, trueBy, trueBz]])
err = np.linalg.norm(Bxyz - trueB) / np.linalg.norm(trueB)
avg_rel_err += err
max_rel_err = max(max_rel_err, err)
assert err < 2e-2
print('avg_rel_err', avg_rel_err / ((len(phis) * len(Zs) * len(Rs))))
print('max_rel_err', max_rel_err)
def test_poincareplot(nparticles=12, nperiods=20):
nfp = 2
coils, currents, ma, eta_bar = get_24_coil_data(nfp=nfp,
ppp=20,
at_optimum=True)
currents = [
1e5 * x for x in [
-2.271314992875459, -2.223774477156286, -2.091959078815509,
-1.917569373937265, -2.115225147955706, -2.025410501731495
]
]
# coils, currents, ma, eta_bar = get_24_coil_data(nfp=nfp, ppp=20, at_optimum=False)
# currents = 6 * [1]
coil_collection = CoilCollection(coils, currents, nfp, True)
bs = BiotSavart(coil_collection.coils, coil_collection.currents)
rphiz, xyz, _, _ = compute_field_lines(bs,
nperiods=nperiods,
batch_size=8,
magnetic_axis_radius=1.1,
max_thickness=0.6,
delta=0.02)
nparticles = rphiz.shape[0]
try:
import mayavi.mlab as mlab
if not __name__ == "__main__":
mlab.options.offscreen = True
for coil in coil_collection.coils:
mlab.plot3d(coil.gamma[:, 0], coil.gamma[:, 1], coil.gamma[:, 2])
colors = [(0.298, 0.447, 0.690), (0.866, 0.517, 0.321),
(0.333, 0.658, 0.407), (0.768, 0.305, 0.321),
(0.505, 0.447, 0.701), (0.576, 0.470, 0.376),
(0.854, 0.545, 0.764), (0.549, 0.549, 0.549),
(0.800, 0.725, 0.454), (0.392, 0.709, 0.803)]
counter = 0
for i in range(0, nparticles, nparticles // 5):
mlab.plot3d(xyz[i, :, 0],
xyz[i, :, 1],
xyz[i, :, 2],
tube_radius=0.005,
color=colors[counter % len(colors)])
counter += 1
mlab.view(azimuth=0, elevation=0)
if __name__ == "__main__":
mlab.show()
else:
mlab.savefig("/tmp/poincare-particle.png", magnification=4)
mlab.close()
except ModuleNotFoundError:
pass
import matplotlib.pyplot as plt
plt.figure()
for i in range(nparticles):
plt.scatter(rphiz[i, range(0, nperiods * 100, 100), 0],
rphiz[i, range(0, nperiods * 100, 100), 2],
s=0.1)
# plt.show()
plt.savefig("/tmp/poincare.png", dpi=300)
plt.close()
assert True # not quite sure how to test this, so we just check that it runs.