def test_Bqs():
nfp = 2
_, _, ma, _ = get_24_coil_data(nfp=nfp, ppp=100)
eta_bar = -2.25
qsf = QuasiSymmetricField(eta_bar, ma)
iota = qsf.iota
assert (abs(iota - 0.038138935935663) < 1e-6)
Bqs = qsf.B
matlab_Bqs = np.asarray(
[[0, 0.988522982100515, -0.151070559206963],
[-0.010321587904285, 0.988472377058748, -0.151049080152652],
[-0.020641457945632, 0.988320578381101, -0.150984650088425]])
assert np.all(np.abs(Bqs[:3, :] - matlab_Bqs) < 1e-6)
dBqs_by_dX = qsf.dB_by_dX
assert np.allclose(dBqs_by_dX[0, :, :].T, dBqs_by_dX[0, :, :])
matlab_dBqs_by_dx = np.asarray(
[[0.000000000000000, -1.125930207500723, 0.616014274297893],
[0.030176925011424, -1.125619099754597, 0.615869343228699],
[0.060336364146126, -1.124686016345258, 0.615434630935356]])
assert np.all(np.abs(matlab_dBqs_by_dx - dBqs_by_dX[:3, 0, :]) < 2e-6)
matlab_dBqs_by_dy = np.asarray(
[[-1.125930207500723, -0.000000000000000, -0.000000000000000],
[-1.125619099754597, -0.022146228771976, 0.010281638036739],
[-1.124686016345258, -0.044277063777819, 0.020556281775495]])
assert np.all(np.abs(matlab_dBqs_by_dy - dBqs_by_dX[:3, 1, :]) < 2e-6)
matlab_dBqs_by_dz = np.asarray(
[[0.616014274297891, -0.000000000000000, -0.000000000000000],
[0.615869343228698, 0.010281638036739, -0.008030696239448],
[0.615434630935353, 0.020556281775495, -0.016059300368306]])
assert np.all(np.abs(matlab_dBqs_by_dz - dBqs_by_dX[:3, 2, :]) < 2e-6)
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_dcoilcoeffs(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()
coil_dofs = stellerator.get_dofs()
h = 1e-2 * np.random.rand(len(coil_dofs)).reshape(coil_dofs.shape)
dJ = stellerator.reduce_coefficient_derivatives(
J.dJ_by_dcoilcoefficients())
assert len(dJ) == len(h)
deriv = np.sum(dJ * h)
err = 1e6
for i in range(5, 10):
eps = 0.5**i
stellerator.set_dofs(coil_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_iota():
nfp = 2
_, _, ma, _ = get_24_coil_data(nfp=nfp, ppp=20)
eta_bar = -2.25
qsf = QuasiSymmetricField(eta_bar, ma)
iota = qsf.iota
assert (abs(iota - 0.038138935935663) < 1e-6)
def test_taylor_test_sigma_by_coeffs():
nfp = 2
(_, _, ma, eta_bar) = get_24_coil_data(nfp=nfp, ppp=20)
qsf = QuasiSymmetricField(eta_bar, ma)
ma_dofs = ma.get_dofs()
np.random.seed(1)
h = 1e-1 * np.random.rand(len(ma_dofs)).reshape(ma_dofs.shape)
qsf.solve_state()
dJ = qsf.dsigma_by_dcoeffs
deriv = dJ @ h
err = 1e6
eps = 0.01
while err > 1e-8:
eps *= 0.5
ma.set_dofs(ma_dofs + eps * h)
qsf.clear_cached_properties()
Jhp = qsf.sigma
ma.set_dofs(ma_dofs - eps * h)
qsf.clear_cached_properties()
Jhm = qsf.sigma
deriv_est = (Jhp - Jhm) / (2 * eps)
err_new = np.linalg.norm(deriv_est - deriv) / np.linalg.norm(deriv)
assert err_new < 0.26 * err
err = err_new
print("err_new %s" % (err_new))
assert eps < 1e-2
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_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_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_sigma():
nfp = 2
_, _, ma, _ = get_24_coil_data(nfp=nfp, ppp=40)
eta_bar = -2.25
qsf = QuasiSymmetricField(eta_bar, ma)
sigma = qsf.sigma
sigma_matlab = np.asarray([
-0.000000000000000,
-0.056185092625620,
-0.112382986380741,
-0.168606294739314,
-0.224867254805832,
-0.281177536480886,
-0.337548048436650,
-0.393988739822343,
-0.450508396607183,
-0.507114431454616,
-0.563812666008344,
-0.620607104459419,
-0.677499697256753,
-0.734490093823280,
-0.791575383149675,
-0.848749821160578,
-0.906004543788638,
-0.963327264754031,
-1.020701957136678,
-1.078108517951100,
-1.135522415096348,
-1.192914316262969,
-1.250249699643717,
-1.307488446623194,
-1.364584417023181,
-1.421485007964753,
-1.478130697985200,
-1.534454578727070,
-1.590381877307561,
-1.645829473387029,
-1.700705415991899,
-1.754908446313264,
-1.808327533997705,
-1.860841435865964,
-1.912318287526287,
-1.962615239972233,
-2.011578154939745,
-2.059041374503194,
-2.104827582059986,
-2.148747773417560,
-2.190601358069108,
-2.230176411822216,
-2.267250102609442,
-2.301589311429245,
-2.332951469797540,
-2.361085633687722,
-2.385733811557786,
-2.406632560578662,
-2.423514860486942,
-2.436112268528834,
-2.444157351739409,
-2.447386384385629,
-2.445542288955833,
-2.438377788865210,
-2.425658730435253,
-2.407167521167246,
-2.382706621428404,
-2.352102018033593,
-2.315206601494947,
-2.271903364568463,
-2.222108338719867,
-2.165773187697747,
-2.102887383784994,
-2.033479902503788,
-1.957620385304120,
-1.875419736514573,
-1.787030139750048,
-1.692644499001194,
-1.592495329566807,
-1.486853142563567,
-1.376024382731296,
-1.260348991572805,
-1.140197675702519,
-1.015968963133882,
-0.888086127997064,
-0.756994057124279,
-0.623156120721537,
-0.487051094933613,
-0.349170167713112,
-0.210014042374294,
-0.070090136929009,
0.070090136929009,
0.210014042374294,
0.349170167713112,
0.487051094933614,
0.623156120721537,
0.756994057124279,
0.888086127997064,
1.015968963133882,
1.140197675702519,
1.260348991572805,
1.376024382731296,
1.486853142563567,
1.592495329566807,
1.692644499001194,
1.787030139750048,
1.875419736514573,
1.957620385304121,
2.033479902503789,
2.102887383784994,
2.165773187697748,
2.222108338719868,
2.271903364568463,
2.315206601494947,
2.352102018033593,
2.382706621428404,
2.407167521167246,
2.425658730435254,
2.438377788865211,
2.445542288955834,
2.447386384385629,
2.444157351739409,
2.436112268528835,
2.423514860486943,
2.406632560578662,
2.385733811557786,
2.361085633687722,
2.332951469797541,
2.301589311429245,
2.267250102609442,
2.230176411822216,
2.190601358069108,
2.148747773417560,
2.104827582059986,
2.059041374503194,
2.011578154939746,
1.962615239972234,
1.912318287526287,
1.860841435865964,
1.808327533997705,
1.754908446313264,
1.700705415991898,
1.645829473387029,
1.590381877307561,
1.534454578727070,
1.478130697985200,
1.421485007964753,
1.364584417023181,
1.307488446623194,
1.250249699643717,
1.192914316262969,
1.135522415096348,
1.078108517951100,
1.020701957136678,
0.963327264754031,
0.906004543788638,
0.848749821160577,
0.791575383149675,
0.734490093823280,
0.677499697256752,
0.620607104459418,
0.563812666008344,
0.507114431454616,
0.450508396607183,
0.393988739822343,
0.337548048436650,
0.281177536480886,
0.224867254805832,
0.168606294739314,
0.112382986380741,
0.056185092625620,
])
assert all(np.abs(sigma - sigma_matlab) < 1e-8)
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.