def test_toroidal_flux_is_constant(self):
"""
this test ensures that the toroidal flux does not change, regardless
of the cross section (varphi = constant) across which it is computed
"""
s = get_exact_surface()
coils, currents, ma = get_ncsx_data()
stellarator = CoilCollection(coils, currents, 3, True)
bs_tf = BiotSavart(stellarator.coils, stellarator.currents)
gamma = s.gamma()
num_phi = gamma.shape[0]
tf_list = np.zeros((num_phi, ))
for idx in range(num_phi):
tf = ToroidalFlux(s, bs_tf, idx=idx)
tf_list[idx] = tf.J()
mean_tf = np.mean(tf_list)
max_err = np.max(np.abs(mean_tf - tf_list)) / mean_tf
assert max_err < 1e-2
s.fit_to_curve(ma, 0.10, flip_theta=True)
iota = -0.4
tf = ToroidalFlux(s, bs_tf)
ar = Area(s)
ar_target = ar.J()
boozer_surface = BoozerSurface(bs, s, ar, ar_target)
# compute surface first using LBFGS, this will just be a rough initial guess
res = boozer_surface.minimize_boozer_penalty_constraints_LBFGS(tol=1e-10, maxiter=300, constraint_weight=100., iota=iota, G=G0)
print(f"After LBFGS: iota={res['iota']:.3f}, tf={tf.J():.3f}, area={s.area():.3f}, ||residual||={np.linalg.norm(boozer_surface_residual(s, res['iota'], res['G'], bs, derivatives=0)):.3e}")
if "DISPLAY" in os.environ:
s.plot()
# now drive the residual down using a specialised least squares algorithm
res = boozer_surface.minimize_boozer_penalty_constraints_ls(tol=1e-10, maxiter=100, constraint_weight=100., iota=res['iota'], G=res['G'], method='manual')
print(f"After Lev-Mar: iota={res['iota']:.3f}, tf={tf.J():.3f}, area={s.area():.3f}, ||residual||={np.linalg.norm(boozer_surface_residual(s, res['iota'], res['G'], bs, derivatives=0)):.3e}")
if "DISPLAY" in os.environ:
s.plot()
# change the label of the surface to toroidal flux and aim for a surface with triple the flux
print('Now aim for a larger surface')
tf_target = 3 * tf.J()
boozer_surface = BoozerSurface(bs, s, tf, tf_target)
res = boozer_surface.minimize_boozer_penalty_constraints_ls(tol=1e-10, maxiter=100, constraint_weight=100., iota=res['iota'], G=res['G'], method='manual')
print(f"After Lev-Mar: iota={res['iota']:.3f}, tf={tf.J():.3f}, area={s.area():.3f}, ||residual||={np.linalg.norm(boozer_surface_residual(s, res['iota'], res['G'], bs, derivatives=0)):.3e}")
if "DISPLAY" in os.environ:
s.plot()
res = qfm_surface.minimize_qfm_penalty_constraints_LBFGS(
tol=1e-12, maxiter=1000, constraint_weight=constraint_weight)
print(
f"||vol constraint||={0.5*(s.volume()-vol_target)**2:.8e}, ||residual||={np.linalg.norm(qfm.J()):.8e}"
)
res = qfm_surface.minimize_qfm_exact_constraints_SLSQP(tol=1e-12, maxiter=1000)
print(
f"||vol constraint||={0.5*(s.volume()-vol_target)**2:.8e}, ||residual||={np.linalg.norm(qfm.J()):.8e}"
)
# Now optimize at fixed toroidal flux
tf = ToroidalFlux(s, bs_tf)
tf_target = tf.J()
qfm_surface = QfmSurface(bs, s, tf, tf_target)
res = qfm_surface.minimize_qfm_penalty_constraints_LBFGS(
tol=1e-12, maxiter=1000, constraint_weight=constraint_weight)
print(
f"||tf constraint||={0.5*(s.volume()-vol_target)**2:.8e}, ||residual||={np.linalg.norm(qfm.J()):.8e}"
)
res = qfm_surface.minimize_qfm_exact_constraints_SLSQP(tol=1e-12, maxiter=1000)
print(
f"||tf constraint||={0.5*(tf.J()-tf_target)**2:.8e}, ||residual||={np.linalg.norm(qfm.J()):.8e}"
)
# Check that volume is not changed