def synthetic_phase_shift_cyl(d, lmbda):
"""
Synthetic phase shift for a cylindrical simulation
Parameters:
-----------
- d [dict]: dictionary data containing fields (2D ndarrays), at least
- r: radius array [cm] (must be equidistant)
- z: height array [cm] (must be equidistant)
- nele: electron density [cm⁻³]
- lmbda: probe wavelenght [nm]
Returns:
--------
- phase shift: 2D ndarray
"""
Ne = d['nele']
Nc = critical_density(lmbda)
mu = np.sqrt(1 - Ne / Nc) - 1
mu[Ne > Nc] = np.nan
dr = np.diff(d['x'])[0, 0]
mu_dl = abel(mu, dr) / (2 * lmbda * 1e-9 * 1e2)
return np.ma.array(mu_dl, mask=np.isnan(mu_dl))
def synthetic_phase_shift_cyl(d, lmbda):
"""
Synthetic phase shift for a cylindrical simulation
Parameters:
-----------
- d [dict]: dictionary data containing fields (2D ndarrays), at least
- r: radius array [cm] (must be equidistant)
- z: height array [cm] (must be equidistant)
- nele: electron density [cm⁻³]
- lmbda: probe wavelenght [nm]
Returns:
--------
- phase shift: 2D ndarray
"""
Ne = d['nele']
Nc = critical_density(lmbda)
mu = np.sqrt(1 - Ne/Nc) - 1
mu[Ne>Nc] = np.nan
dr = np.diff(d['x'])[0,0]
mu_dl = abel(mu, dr)/(2*lmbda*1e-9*1e2)
return np.ma.array(mu_dl, mask=np.isnan(mu_dl))
def test_abel_gaussian():
n = 500
r = np.linspace(0, 5., n)
dr = np.diff(r)[0]
rc = 0.5 * (r[1:] + r[:-1])
fr = np.exp(-rc**2)
Fn = abel(fr, dr=dr)
Fn_a = np.pi**0.5 * np.exp(-rc**2)
yield assert_allclose, Fn, Fn_a, 1e-2, 1e-3
def test_abel_gaussian():
n = 500
r = np.linspace(0, 5.0, n)
dr = np.diff(r)[0]
rc = 0.5 * (r[1:] + r[:-1])
fr = np.exp(-rc ** 2)
Fn = abel(fr, dr=dr)
Fn_a = np.pi ** 0.5 * np.exp(-rc ** 2)
yield assert_allclose, Fn, Fn_a, 1e-2, 1e-3
def synthetic_shadowgraphy_cyl(d, lmbda, L=10, absorption=True, refraction=False):
"""
Compute angle of refraction for a plasma assuming cylindrical symmetry on an axis
orthogonal to the propagation axis.
Parameters:
-----------
- d [dict]: dictionary data containing fields (2D ndarrays), at least
- r: radius array [cm] (must be equidistant)
- z: height array [cm] (must be equidistant)
- dens: solid density [g.cm⁻³]
- Abar: mean atomic mass [g.mol⁻¹]
- Zbar: mean ionization
- lmbda: probe wavelenght [nm]
- L: distance to detector [cm]
Returns:
--------
- theta: 2D ndarray: refracted angle
Source: Shlieren and shadowgraph techniques. G.Settles
"""
dI = np.ones(d['nele'].shape)
Ne = d['nele']
Nc = critical_density(lmbda)
if refraction:
# this doesn't seem to work so well
Ref = 1 - np.sqrt(1 - Ne/Nc)
Ref[Ne>Nc] = np.nan
dr = np.diff(d['r'])[0,0]
Ref_dl = abel(Ref, dr)
d2Ref_dl = laplace(Ref_dl, dr)
#pval = (np.abs(np.gradient(Ref_dl)[0])/dr + np.abs(np.gradient(Ref_dl)[1])/dr)*180/np.pi
#return d2Ref_dl
dI0 = 1./(1. + d2Ref_dl)
dI *= dI0
if absorption:
from scipy.constants import c
nu_ei = 3e-6*d['nele']*d['Zbar']*10/d['tele']**(3./2)
nu_ei = 1.0
print(Nc)
kernel = nu_ei*(Ne/Nc)/(c*(1 - Ne/Nc)**0.5)
dr = np.diff(d['r'])[0,0]
print(dr)
kappa = kernel
#kappa = abel(kernel, dr)
dI0 = kappa#np.exp(-kappa)
dI *= dI0
return dI
def test_abel_step():
n = 800
r = np.linspace(0, 20, n)
dr = np.diff(r)[0]
rc = 0.5 * (r[1:] + r[:-1])
fr = np.exp(-rc**2)
#fr += 1e-1*np.random.rand(n)
# plt.plot(rc,fr,'b', label='Original signal')
F = abel(fr, dr=dr)
F_a = (np.pi)**0.5 * fr.copy()
F_i = abel(F, dr=dr, inverse=True, derivative=np.gradient)
#sys.exit()
# plt.plot(rc, F_a, 'r', label='Direct transform [analytical expression]')
# mask = slice(None,None,5)
# plt.plot(rc[mask], F[mask], 'ko', label='Direct transform [computed]')
# plt.plot(rc[mask], F_i[mask],'o',c='orange', label='Direct-inverse transform')
#yield assert_allclose, fr, F_i, 5e-3, 1e-6, 'Test that direct>inverse Abel equals the original data'
#yield assert_allclose, F_a, F, 5e-3, 1e-6, 'Test direct Abel transforms failed!'
yield assert_allclose, fr, F_i, 5e-2, 1e-6, 'Test that direct>inverse Abel equals the original data'
yield assert_allclose, F_a, F, 5e-3, 1e-6, 'Test direct Abel transforms failed!'
def test_abel_step():
n = 800
r = np.linspace(0, 20, n)
dr = np.diff(r)[0]
rc = 0.5 * (r[1:] + r[:-1])
fr = np.exp(-rc ** 2)
# fr += 1e-1*np.random.rand(n)
# plt.plot(rc,fr,'b', label='Original signal')
F = abel(fr, dr=dr)
F_a = (np.pi) ** 0.5 * fr.copy()
F_i = abel(F, dr=dr, inverse=True, derivative=np.gradient)
# sys.exit()
# plt.plot(rc, F_a, 'r', label='Direct transform [analytical expression]')
# mask = slice(None,None,5)
# plt.plot(rc[mask], F[mask], 'ko', label='Direct transform [computed]')
# plt.plot(rc[mask], F_i[mask],'o',c='orange', label='Direct-inverse transform')
# yield assert_allclose, fr, F_i, 5e-3, 1e-6, 'Test that direct>inverse Abel equals the original data'
# yield assert_allclose, F_a, F, 5e-3, 1e-6, 'Test direct Abel transforms failed!'
yield assert_allclose, fr, F_i, 5e-2, 1e-6, "Test that direct>inverse Abel equals the original data"
yield assert_allclose, F_a, F, 5e-3, 1e-6, "Test direct Abel transforms failed!"
def synthetic_radiography_cyl(d,
species,
nu,
spect_ip,
hdf5_backend='pickle',
transform=None):
"""
Postprocess simulation to produce Xray
Parameters:
-----------
- d [dict]: data with all the fields
- species [dict]: of species
- nu [ndarray]: array of frequences [eV]
- spect_ip [ndarray]: normalized spectra on ip
- hdf5_backend: pytables or h5py
- transform: a optional function
def transform(d, op):
# do something with d, op
return d, op
Returns:
--------
- trans [ndarray]: transmissions
"""
spect_ip = spect_ip[np.newaxis, np.newaxis, :]
dnu = np.diff(nu)[0]
nu = nu #[np.newaxis, np.newaxis, :]
species_keys = sorted(species.keys())
# projected density
dr = np.diff(d['r'])[0, 0]
pd = {key: abel(d['dens'] * d[key], dr) for key in species}
# getting the opacitoy
op = {
key: hedp.opacity.henke.cold_opacity(species[key], pd[key], nu,
hdf5_backend)
for key in species
}
#if 'tube' in op:
# op['tube'][550:700,:37] = 1e-9
if transform is not None:
d, op = transform(d, op)
op_int = hedp.math.add_multiple(*[op[key] for key in species])
tm = np.sum(spect_ip * np.exp(-op_int), axis=-1) * dnu
return tm
def synthetic_radiography_cyl(d, species, nu, spect_ip, hdf5_backend='pickle', transform=None):
"""
Postprocess simulation to produce Xray
Parameters:
-----------
- d [dict]: data with all the fields
- species [dict]: of species
- nu [ndarray]: array of frequences [eV]
- spect_ip [ndarray]: normalized spectra on ip
- hdf5_backend: pytables or h5py
- transform: a optional function
def transform(d, op):
# do something with d, op
return d, op
Returns:
--------
- trans [ndarray]: transmissions
"""
spect_ip = spect_ip[np.newaxis, np.newaxis, :]
dnu = np.diff(nu)[0]
nu = nu#[np.newaxis, np.newaxis, :]
species_keys = sorted(species.keys())
# projected density
dr = np.diff(d['r'])[0,0]
pd = {key: abel(d['dens']*d[key], dr) for key in species}
# getting the opacitoy
op = {key: hedp.opacity.henke.cold_opacity(species[key], pd[key], nu, hdf5_backend) for key in species}
#if 'tube' in op:
# op['tube'][550:700,:37] = 1e-9
if transform is not None:
d, op = transform(d, op)
op_int = hedp.math.add_multiple(*[op[key] for key in species])
tm = np.sum(spect_ip * np.exp(-op_int), axis=-1)*dnu
return tm
def test_abel_zeros():
# just a sanity check
n = 64
x = np.zeros((n, n))
assert (abel(x, inverse=False) == 0).all()
def test_abel_zeros():
# just a sanity check
n = 64
x = np.zeros((n, n))
assert (abel(x, inverse=False) == 0).all()
