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permittivity.py
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from numpy import sqrt
from math import pi
import numpy as np
import h5py
import util
#Fundamental Constants
epsilon0 = 8.85e-12 #Permittivity of Free Space
mu0 = 4*pi*1e-7 #Permeability of Free Space
c0 = 1./sqrt(epsilon0*mu0) #Speed of Light in Vacuum
#Functions
def eps2m(eps_c): #Return complex refractive index (m) from complex relative permittivity (eps_c)
eps_r = eps_c.real
eps_i = eps_c.imag
n_sq = (1/2.) * (sqrt(eps_r**2 + eps_i**2) + eps_r )
k_sq = (1/2.) * (sqrt(eps_r**2 + eps_i**2) - eps_r )
n = sqrt(n_sq)
k = sqrt(k_sq)
m = n + 1j*k
return m
def m2eps(m):
eps_c = m**2
return eps_c
def cond2eps_im(sigma, f):
w = 2*pi*f
return sigma/(w*epsilon0)
def sigma_from_p(p, sigma): #p: porosity, sigma: conductivity for p = 0
v = 1 - p #volume filling factor
return sigma*v*(0.68 + 0.32*v)**2
def alpha(eps_c, f):
m_c = eps2m(eps_c)
k = m_c.imag
w = 2*pi*f
return 4*w*k/c0
def pureice(x, z):
n_vacuum = 1.
n_ice = 1.78 + 1e-5j
n_material = n_vacuum
if z >= 0:
n_material = n_ice
else:
n_material = n_vacuum
return n_material
def pureice_1d(z, k = 0):
n_ice = 1.78 + 1j*k
N = len(z)
return n_ice * np.ones(N)
def southpole(z):
A=1.78
B=-0.43
C=-0.0132
return A+B*np.exp(C*z)
def rho2n(rho):
eps_r = (1 + 0.835*rho)**2
return eps2m(eps_r)
def poro2n(poro,eps_r0):
eps_r = eps_r0*poro*(0.68 + 0.32*poro)**2
return eps2m(eps_r)
def glacier(z, data_file):
glacier_data = h5py.File("share/" + data_file + ".h5", 'r')
eps_data = glacier_data.get("eps-data")
z_arr = eps_data[:,0]
eps_r = eps_data[:,1]
nprof = eps2m(eps_r)
zmax = glacier_data.attrs["max-depth"]
n_medium = 1.0
if z < 0:
n_medium = 1.0
elif z >= 0 and z < zmax:
ii = util.findNearest(z_arr, z)
n_medium = nprof[ii]
elif z >= zmax:
n_medium = 1.78
return n_medium
def glacier_layer(z, data_file, z_layer, eps_layer):
n_medium = glacier(z, data_file)
if z > z_layer:
n_medium = eps2m(eps_layer)
return n_medium
def pure_ice_glacier(x, z, z_layer, eps_layer):
n_vacuum = 1.
n_ice = 1.78 + 1e-5j
n_material = n_vacuum
if z >= 0:
n_material = n_ice
elif z > z_layer:
n_medium = eps2m(eps_layer)
elif z < 0:
n_material = n_vacuum
return n_material
freq_test = 1.35e9 #100 MHz
sigma_solid_pure_ice = 8.7e-6 #uS/m
P_surface = 0.9
sigma_pure_snow = sigma_from_p(P_surface, sigma_solid_pure_ice)
P_sinter = 0.4
sigma_III_snow = 3.889e-3 #conductivity of TypeII
sigma_sinter = sigma_from_p(P_sinter, sigma_III_snow)
#print('Type III, sinter ice P = 0.4', sigma_sinter)
#print('Type III snow, P = 0', sigma_III_snow)
#print('Type III Snow, P = 0.9', sigma_pure_snow)
eps_i_sinter = cond2eps_im(sigma_sinter, freq_test)
eps_sinter = 2.2 + 1j*eps_i_sinter
m_sinter = eps2m(eps_sinter)
#print(sigma_pure_snow)
eps_i_ice = cond2eps_im(sigma_solid_pure_ice, freq_test)
#print(eps_i_ice)
eps_snow = 1.2 + 0.015j #Permittivity of Enceladus Snow (Type III)
m_snow = eps2m(eps_snow) #
eps_ice = 3.2 + 1j*eps_i_ice
m_ice = eps2m(eps_ice)
#print('Snow, eps_r =', eps_snow, 'n = ', m_snow, 'alpha = ', alpha(eps_snow, freq_test))
#print('Ice, eps_r =', eps_ice, 'n =', m_ice, 'alpha = ', alpha(eps_ice, freq_test))
#print(alpha(eps_sinter, freq_test))
eps_meteor = 8.2 + 0.1558j #Taken from Herique et al. (2018) Direct Observations of Asteroid Interior and Regolith Structure: Science Measurement Requirements
eps_vacuum = 1.0
eps_water = 82 + 90.884j #Based on the Conductivity of Salt Water -> 5 S/m
def enceladus_2layer(z, snow_depth=100, water_depth = 500): #Create a flat layer of snow above ice
n_snow = eps2m(eps_snow)
n_ice = eps2m(eps_ice)
n_vacuum = 1.0
n_material = n_vacuum
n_water = eps2m(eps_water)
if z >= 0 and z < snow_depth:
n_material = n_snow
else:
n_material = n_ice
"""
elif z >= snow_depth and z < water_depth:
n_material = n_ice
elif z >= water_depth:
n_material = n_water
"""
return n_material
def enceladus_3layer(z, snow_depth=100, sinter_depth = 150, water_depth = 500): #Create a flat layer of snow above ice
n_snow = eps2m(eps_snow)
n_ice = eps2m(eps_ice)
n_vacuum = 1.0
n_material = n_vacuum
n_water = eps2m(eps_water)
n_sinter = eps2m(eps_sinter)
if z >= 0 and z < snow_depth:
n_material = n_snow
elif z >= snow_depth and z < sinter_depth:
n_material = n_sinter
elif z>= sinter_depth and z < water_depth:
n_material = n_ice
elif z >= water_depth:
n_material = n_water
return n_material
def enceladus_environ(x, z, snow_depth = 100, meteor_list = [], crevass_list = [], aquifer_list=[]): #Creates a 2 layer geometry with added meteorites (spheres), crevasses and aquifers (triangles)
n_ice = eps2m(eps_ice)
n_snow = eps2m(eps_snow)
n_vacuum = 1.0
n_medium = n_vacuum
n_water = eps2m(eps_water)
if z < 0:
m_medium = n_vacuum
if z >= 0 and z < snow_depth:
n_medium = n_snow
elif z > snow_depth:
n_medium = n_ice
numMeteors = len(meteor_list)
numCrevasses = len(crevass_list)
numAquifers = len(aquifer_list)
#Loop over meteorites
for i in range(numMeteors):
meteor_i = meteor_list[i] #must be sphere
if meteor_i.isInside(x,z) == True:
n_medium = eps2m(meteor_i.eps_r)
for i in range(numCrevasses):
crevass_i = crevass_list[i]
if crevass_i.isInside(x,z) == True:
n_medium = eps2m(crevass_i.eps_r)
for i in range(numAquifers):
aquifer_i = aquifer_list[i]
if aquifer_i.isInside(x,z) == True:
n_medium = eps2m(aquifer_i.eps_r)
return n_medium
"""
def enceladus_environ(x, z, snow_depth = 100, sinter_depth = np.nan, meteor_list = [], crevass_list = [], aquifer_list=[]): #Creates a 2 layer geometry with added meteorites (spheres), crevasses and aquifers (triangles)
if sinter_depth != np.nan:
n_medium = enceladus_3layer(z, snow_depth, sinter_depth)
numMeteors = len(meteor_list)
numCrevasses = len(crevass_list)
numAquifers = len(aquifer_list)
#Loop over meteorites
if numMeteors > 0:
for i in range(numMeteors):
meteor_i = meteor_list[i] #must be sphere
if meteor_i.isInside(x,z) == True:
n_medium = eps2m(meteor_i.eps_r)
return n_medium
else:
n_medium = enceladus_2layer(z, snow_depth)
return n_medium
else:
for i in range(numCrevasses):
crevass_i = crevass_list[i]
if crevass_i.isInside(x,z) == True:
n_medium = 1.0
return n_medium
else:
n_medium = enceladus_2layer(z, snow_depth)
return n_medium
for i in range(numAquifers):
aquifer_i = aquifer_list[i]
if aquifer_i.isInside(x,z) == True:
n_medium = eps2m(aquifer_i.eps_r)
else:
n_medium = enceladus_2layer(z, snow_depth)
return n_medium
"""