Notes

# -*- coding: utf-8 -*-
#import numpy
import math,pylab
#from scipy.fftpack import fft, fftshift
import matplotlib.pyplot as plt
"""
Arvydas Sepetys LID
"""
"""
Assumtions:

"""

###########
"""
Tm - melting temp, K
Alpha_1064/532 - absorption coef for 1064nm/532nm
c- specific heat/specific heat capacity, J/(kgK)
kth - thermal conductivity, W/(mK)
rho - density, kg/m^3
R_1064/532 - refelctivity for wavelengths
k_1064/532 - optical extinction coefficient for wavelengths
Cv - specific evaporation heat, J/Kg
"""
###########
# Tungsten (W) props
W = {'Tm': 3695, 'Alpha_1064': 4.4231e5, 'Alpha_532': 6.468e5,
'c':132, 'kth': 170, 'rho': 19250, 'R_1064': 0.60267, 'R_532':0.49487, 'k_1064':3.7450, 'k_532':2.7382, 'Cv':4482160}
# Lithium (Li) props
Li = {'Tm': 453.69, 'Alpha_1064': 5.9483e5, 'Alpha_532': 5.6017e5,
'c':3570, 'kth': 85, 'rho': 534, 'R_1064': 0.94159, 'R_532':0.88227, 'k_1064':5.0364, 'k_532':2.3715, 'Cv':21022900}
#Hydrogen
H = {'rho': 1000, 'c': 14300, 'kth': 0.1805}


############
I = 5 # % spectroscopical data collection limit
T0 = 298 # ambient temperature

#LASER props
wlen1= 1064e-9 #laser wavelength in nm
wlen2= 532e-9 #laser wavelength in nm 2nd harmonics
#E = 1.1 # laser energy J
E = 0.4# laser energy J
t = float(6)/float(1000000000) #pulse length s
#t= float(1.5)/float(1000) #1.5ms

def find_h(I,dic,wlen):
"""
I - spectroscopical data collection limit ()collection limit lower intensity
dic - of sample
wlen - wavelength
"""
mp = 1000000000 # multiplyer to go from nm to m
nu=4*math.pi*dic['k_'+str(int(wlen*mp))]/wlen
d = -math.log(float(I)/float(100))/nu
return d #in m

def find_h2(I,dic,wlen):
"""

""""""
I - spectroscopical data collection limit ()collection limit lower intensity
dic - of sample
wlen - wavelength
"""
mp = 1000000000 # multiplyer to go from nm to m
d = -math.log(float(I)/(float(100)*(1-dic['R_'+str(int(wlen*mp))])))/(dic['Alpha_'+str(int(wlen*mp))])
return d #in m


def find_r0_LIDS(dic_particles, dic_sample, wlen, E, T0,t):
"""
dic_particles - desorbing aprticles
dic_sample - sample properties
wlen- laser wavelength
E- laser energy in J
T0- room temperature(ambient temperature)
t- pulse length
"""
mp = 1000000000 # multiplyer to go from nm to m
D=float(dic_particles['kth'])/float(dic_particles['rho']*dic_particles['c'])
# diffusion coefficient for diffusing particles
r=math.sqrt((E*(1-dic_sample['R_'+str(int(wlen*mp))]))/(math.pi*(dic_sample['Tm']-T0)*
dic_sample['rho']*dic_sample['c']*math.sqrt(2*D*t)))
DD = math.sqrt(2*D*t) #thermal diffusion depth
AL = 1/dic_sample['Alpha_'+str(int(wlen*mp))] #absorption length
return r, DD, AL

def find_r0_LIDS2 (dic_particles, dic_sample, wlen, El, T0,t):
"""
dic_particles - desorbing aprticles
dic_sample - sample properties
wlen- laser wavelength
El- laser energy in J
T0- room temperature(ambient temperature)
t- pulse length
#IF optical absorption length alpha^-1 (AL) small compared to thermal diffusion length (2Dt)^1/2 (DD)
"""

mp = 1000000000 # multiplyer to go from nm to m
D=float(dic_particles['kth'])/float(dic_particles['rho']*dic_particles['c'])
# diffusion coefficient for diffusing particles
#D=float(dic_sample['kth'])/float(dic_sample['rho']*dic_sample['c'])
A= 2*dic_sample['Alpha_'+str(int(wlen*mp))]*math.sqrt(D*t)*math.sqrt(1/math.pi)*(1-dic_sample['R_'+str(int(wlen*mp))])*El
r = math.sqrt(A/(dic_sample['Tm']*dic_sample['kth']*t*math.pi))
DD = math.sqrt(2*D*t) #thermal diffusion depth

AL = 1/dic_sample['Alpha_'+str(int(wlen*mp))] #absorption length
return r, DD, AL

def find_r0_LIAS(I,dic,wlen,El):
"""
I - spectroscopical data collection limit ()collection limit lower intensity
dic - sample dictionary
wlen - wavelength
El- laser energy
"""
mp = 1000000000 # multiplyer to go from nm to mmp
h=find_h(I, dic,wlen) # penetration depth of wavelegnth till spectroscopically useful data
r=math.sqrt(El/(dic['rho']*math.pi*h*(dic['c']*(dic['Tm']-T0)+dic['Cv'])))
#print 'V = ' + str(h*math.pi*r**2)
return r #in m

def find_Tz_LIDS(dic_particles,dic_sample,El,wlen, z,t,tx ):
"""
dic_particles - desorbing particles dictionary
dic_sample - sample dictionary
El - laser energy, J
wlen- laser wavelength
z- depth, m
t - pulse length, s
tx - measurement time,s
"""

mp = 1000000000 # multiplyer to go from nm to m
D=float(dic_particles['kth'])/float(dic_particles['rho']*dic_particles['c'])
# diffusion coefficient for diffusing particles
T=(El*(1-dic_sample['R_'+str(int(wlen*mp))])*math.exp(-z**2/(4*D*tx)))/(math.sqrt(dic_sample['rho']**2*dic_sample['c']**2*math.pi*D*tx))
if tx<=t:
return z,T, tx # temperature at depth z in K at time tx
else:
return 0,0,0
print 'tx >= t_laser'

def r_des():
"""
nu - preexponential factor
x - order of desorption
N- concentration
Ea - activation energy for desorption
R - universal gas constant, 8.314 Jmol^-1 K^-1
T- temperature
"""
r_des=nu*N**x*exp(-Ea/(R*T))
return r_des


def show_data_LID(r1,DD1,AL1, r2, DD2, AL2):
print '|----------------------------------------+------------------------------------------|'
print '| First Harmonics, 1064 nm | Second Harmonics, 532 nm |'
print '|----------------------------------------|------------------------------------------|'
print '| Maximum spot radius r = '+ "%.5f" % (r1*100) + ' cm | Maximum spot radius r = '+ "%.7f" % (r2*100) + ' cm |'
print '| Estimated thermal diffusion length: | Estimated thermal diffusion length: |'
print '| D ='+ "%.3e" % DD1 + ' m | D ='+ "%.3e" % DD2 + ' m |'
print '| Absorption length (alpha):'+ "%.3e" % AL1 + 'm | Absorption length (alpha):'+ "%.3e" % AL2 + 'm |'
print '|----------------------------------------+------------------------------------------|'

def show_data_LIA(r1,r2,E,t):

print '|----------------------------------------+------------------------------------------|'
print '| First Harmonics, 1064 nm | Second Harmonics, 532 nm |'
print '|----------------------------------------|------------------------------------------|'
print '| Maximum spot radius r = '+ "%.5f" % (r1*100) + ' cm | Maximum spot radius r = '+ "%.7f" % (r2*100) + ' cm |'
print '| Energy density : ' + "%.3e" %(E/(math.pi*(r1*100)**2)) + ' J/cm^2 | Energy density : ' + "%.3e" %(E/(math.pi*(r2*100)**2)) + ' J/cm^2 |'
print '| Power density : ' + "%.3e" %(E/(t*math.pi*(r1*100)**2)) + ' W/cm^2 | Power density : ' + "%.3e" %(E/(t*math.pi*(r2*100)**2)) + ' W/cm^2 |'
print '|----------------------------------------+------------------------------------------|'
print ''


print 'Pulse length t = '+ str(t) + 's, Energy E = ' + str(E) +'J'
r1,DD1,AL1 = find_r0_LIDS(H, W, wlen1, E, T0, t)
r2,DD2,AL2 = find_r0_LIDS(H, W, wlen2, E, T0, t)
print '------------>>>H desorption from W<<<-------------P=' + "%.3e" %(E/t) + 'W, with t = ' + str(t) +'s'
show_data_LID(r1,DD1,AL1, r2, DD2, AL2)
r1,DD1,AL1 = find_r0_LIDS(Li, W, wlen1, E, T0, t)
r2,DD2,AL2 = find_r0_LIDS(Li, W, wlen2, E, T0, t)
print ''
print ''
print '------------>>>Li desorption from W<<<-------------P=' + "%.3e" %(E/t) + 'W, with t = ' + str(t) +'s'
show_data_LID(r1,DD1,AL1, r2, DD2, AL2)
print ''
print 'Pulse length t = '+ str(t) + 's, Energy E = ' + str(E) +'J'
print '------------>>>W abalation <<<-------------P=' + "%.3e" %(E/t) + 'W, with t = ' + str(t) +'s'
r1 = find_r0_LIAS(I,W,wlen1,E)
r2 = find_r0_LIAS(I,W,wlen2,E)
show_data_LIA(r1,r2,E,t)
print '------------>>>Li abalation <<<-------------P=' + "%.3e" %(E/t) + 'W, with t = ' + str(t) +'s'
r1 = find_r0_LIAS(I,Li,wlen1,E)
r2 = find_r0_LIAS(I,Li,wlen2,E)
show_data_LIA(r1,r2,E,t)

#print 'W LIAS r='+str(r1*100) + ' cm, S= ' + str((r1*100)**2*math.pi) + 'cm^2'
#print 'Li LIAS r='+str(find_r0_LIAS(I,Li,wlen1,E)*100) + ' cm'

print str(find_h2(I, W, wlen1)) + ' - optical penetration depth for wlen = ' + str(wlen1) + ' m, when 5% of initial light intensity remains'
print 'z,T,tx'
print find_Tz_LIDS(H,W,E,wlen1, (find_h2(I, W, wlen1))/1000,t,float(5)/float(1000000000) )