Scale $d\sigma/d\Omega$ to try to match the heating profile from I92¶

Oxygen aurora model v0.1¶

Updates from v0.0:¶

Analytical calculation of O-O DSCS
Fix units error in Fig 3 of Ishimoto et al (1992).
Add missing $2\pi$ factor in O-O DSCS

What's included:

Initial precipitating neutral atom source at 1000 km
Elastic collisions of fast $O$ on atmospheric $O$
- differential scattering cross section from Ishimoto et al. (1992).
Inelastic collisions:
- Excitation to $O(^1D)$
- excitation cross section from Ishimoto et al. (1994).
MSIS neutral density (assumed to be entirely $O$)

What's not included:

Charge exchange of precipitating $O^+$ to create fast $O$
- Assumes $\sigma_{\textrm{chg ex}} >> \sigma_{\textrm{other things}}$ (Kozyra et al. 1982)
Ionization collisions
Stripping collisions
Collisions with ambient $N_2$, $O_2$, $He$
Thermal velocities of ambient particles (assumed to be at rest)
Loss of $O(^1D)$
Long lifetime of $O(^1D)$
Excitation of other particles and states (e.g., $O(^1S)$ or $N_2$-band states)
Gravity
Magnetic field
Momentum transfer in inelastic collisions (forward-scattering assumed)
Incident atoms in excited states initially

In [63]:

DSCS_FACTOR = 2*pi

In [89]:

figure(figsize=(5,5))

rh = array(rh_all[-1])
# Create subsampled track
s = 10
idx = range(0,shape(rh)[0],s) + [-1]
plot(rh[idx,0]/1e3,rh[idx,2]/1e3,'k-',linewidth=2) # Particle track

for i in range(len(rh_all)-1):
#for i in range(2):
    rh = array(rh_all[i])
    if len(rh) > 0:
        idx = range(0,shape(rh)[0],s) + [-1]
        plot(rh[idx,0]/1e3,rh[idx,2]/1e3,'-',linewidth=0.5) # Particle track

title('Example Path')
xlabel('x [km]')
ylabel('z [km]')
#xlim((min(rh[:,0]/1e3)-10, max(rh[:,0]/1e3)+10));
ylim((75,1100))
clear_output()
#xlim((350,360));
#mpld3.display()

In [91]:

print '%i secondaries' % len(rh_all)

414 secondaries

In [92]:

idx_esc = (final_alt >= 1100e3)
e_tot = sum(final_e) + 1.96*len(excited_alt)
e_esc = sum(final_e[idx_esc])
e_heat = sum(final_e[~idx_esc])
e_exc = 1.96*len(excited_alt)
#print 'Escape energy: %f eV (%.2f %%)' % (e_esc, 100*e_esc/e_tot)
#print 'Heat energy: %f eV (%.2f %%)' % (e_heat, 100*e_heat/e_tot)
#print 'Excitation energy: %f eV (%.2f %%)' % (e_exc, 100*e_exc/e_tot)
#print 'Total energy: %f eV' % (e_tot)

print 'Energy partition for %.0f keV monoenergetic flux' % (e_0/1e3)
print '\tPrimary simulated particles: %i' % N_particles
print '\tTotal simulated particles:   %i' % len(final_e)
print ''
print '                 My model      Ishimoto et al. 1992'
print 'Heat:             %05.2f %%             78 %%' % (100*e_heat/e_tot)
print 'Escape:           %05.2f %%             17 %%' % (100*e_esc/e_tot)
print 'Ionization:                            5 %'
print '1D Excitation:    %05.2f %%                  ' % (100*e_exc/e_tot)

Energy partition for 1 keV monoenergetic flux
	Primary simulated particles: 5
	Total simulated particles:   30222

                 My model      Ishimoto et al. 1992
Heat:             72.48 %             78 %
Escape:           27.49 %             17 %
Ionization:                            5 %
1D Excitation:    00.04 %

Heating¶

In [97]:

alt_i92 =       xy[1::2]
heat_rate_i92 = xy[0::2]

semilogx(heat_rate,alt/1e3,'k-', label='My model')
semilogx(heat_rate_i92, alt_i92, 'g-', linewidth=2, label='Ishimoto92')
legend(loc='best');
xlim((1e0, 1e6));
ylim((0,600));
xlabel('Heating rate [eV/cm^3/s]');
ylabel('Altitude [km]');

In [98]:

print '                         My model      Ishimoto et al. 1992'
print 'Peak Heating Altitude     %.0f km             %.0f km' % \
                        (alt[argmax(heat_rate)]/1e3, alt_i92[argmax(heat_rate_i92)])

                         My model      Ishimoto et al. 1992
Peak Heating Altitude     222 km             280 km

Excitation¶

In [90]:

semilogx(prod_rate,alt/1e3,'k.-',markersize=2)

xlabel('$O(^1\!D)$ production rate [$cm^{-3} s^{-1}$]');
ylabel('Altitude [km]');

In [94]:

brightness_R = sum(prod_rate*d_alt*1e2)*1e4*1e-10
print 'Column brightness if all of those O(1D) immediately emitted: %f R' % brightness_R

Column brightness if all of those O(1D) immediately emitted: 87.131340 R

In [ ]:

Scale $d\sigma/d\Omega$ to try to match the heating profile from I92¶

Oxygen aurora model v0.1¶

Updates from v0.0:¶

O-O elastic collision cross section¶

The DSCS used in Ishimoto 1992¶

O-O excitation cross section to O(1D)¶

Excitation cross section¶

Neutral density¶

Run entire tree of particles¶

Path Visualizations¶

Heating¶

Excitation¶