def abel_inversion_single(freq_samp,
time_delay,
current_ind,
pos_antenna=1.15,
other_method=False):
"""
TODO
.. math:: R_c(\omega_{pe}) = R_{ant} - c/\omega \int_0 ^{\omega_{pe}}
t_g \quad 1 / \sqrt{\omega_{pe}^2 - \omega^2} \\text{d} \omega
Parameters
----------
freq_samp
time_delay
current_ind
pos_antenna
other_method
Returns
-------
"""
fpe = freq_samp[current_ind]
density = plasma_density(fpe)
if current_ind < 1:
return pos_antenna, density
if other_method:
# Method: TODO
freqs_used = freq_samp[:current_ind + 1]
times_used = time_delay[1:current_ind + 1]
temp_arr = np.arcsin(freqs_used[1:] / fpe) - np.arcsin(
freqs_used[:-1] / fpe)
integral = np.dot(temp_arr, times_used)
r_vacuum = pos_antenna
else:
# Naive Abel Inversion
freqs_used = freq_samp[:current_ind]
times_used = time_delay[:current_ind]
temp_arr = 1 / np.sqrt(np.power(fpe, 2) - np.power(freqs_used, 2))
integral = simps(times_used * temp_arr, x=freqs_used)
r_vacuum = distance_vacuum(time_delay[0]) / 2 + pos_antenna
radius = speed_of_light * integral / np.pi + pos_antenna
return radius, density
def CalcInvPerfO(fpro, gdel, vacd=0.0, initpts=32):
"""Inverts an O-mode groupd delay into a density profile.
Group delay is not initialized
Parameters
------------
fpro: array
Probing frequencies
gdel: array
Group delays. Must be the same size as "fpro"
vacd: float
Vaccuum distance to the antenna: where the plasma is believed to start.
initpts: int
How many points to be used in the initialization
Returns
------------
rad: array
Radius
dens: array
Density
fpro: array
The actual probing frequency used to calculate the density profile
gdel: array
The actual group delay used to calculate the density profile
"""
k3 = speed_of_light / np.pi
# Initialization points
init0_f = 0.0
vac_gdel = 2.0 * vacd / speed_of_light
init0_g = vac_gdel
init1_f = fpro[0]
init1_g = gdel[0]
# Automatically initializes GD, if Fprobe starts at zero this does nothing
initf = np.linspace(init0_f, init1_f, num=initpts, endpoint=False)
initg = np.linspace(init0_g, init1_g, num=initpts, endpoint=False)
fpro = np.concatenate((initf, fpro))
gdel = np.concatenate((initg, gdel))
# Converts the density
dens = plasma_density(fpro)
# Gets the integral done
summa = []
# for i in range(np.size(dens)):
# inte = []
# for j in range(i):
# inte.append( gdel[j] * 1.0/(np.sqrt(fpro[i]*fpro[i]-fpro[j]*fpro[j])) )
# summa.append(np.trapz(inte, x=fpro[0:i]))
# rad = konst.c/np.pi * np.array(summa)
II = np.zeros_like(fpro)
for j in range(1, len(gdel)):
for i in range(1, j + 1):
II[j] = II[j] + gdel[i] * (np.arcsin(fpro[i] / fpro[j]) -
np.arcsin(fpro[i - 1] / fpro[j]))
rad = k3 * II
return rad, dens, fpro, gdel