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 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
