velocities are on average 2–4 times higher than that of the neutrals (Odelstad et al.
2018). If both the frequencies are assumed constant with distance and the velocity is
assumed constant, then an analytical solution is available (Galand et al. 2016), i.e.
n i ¼ f e þ f ph
À
Á
n g
r À r 0
v g
:
ð5:35Þ
When gas production rates and therefore neutral densities are high, photoionization dominates but at lower production rates both terms are required.
Johansson et al. (2017) have considered the influence of dust absorption. This will
also be dependent upon the dust optical depth and hence its importance will depend
on the dust production rate. As illustrated in Fig. 4.17, the optical depth at 67P was
quite low at optical wavelengths and so the effect is probably of limited importance
there. However, one needs to be aware that if particles smaller than optical wavelengths are more numerous than we currently believe then these can produce a
significant absorption cross-section for EUV photons and for 67P we have little
knowledge of their column densities. For comets as active as 1P/Halley at the time of
the spacecraft encounters, dust would need to be considered.
For typical electron densities within a cometary coma, the electron flux from the
local plasma overcomes the photoemission from the spacecraft itself and the spacecraft potential becomes negative. This was commonly observed at Rosetta. In the
limit where the plasma electron flux greatly exceeds the flux of electrons from the
spacecraft, the spacecraft potential is expected to have a negative value several times
the electron thermal energy equivalent (Eriksson et al. 2017). An example at 67P
from 10 Jan 2015 presented by Eriksson et al. (2017) shows the spacecraft potential
oscillating between about À5 and À 15 V over a single rotation of the nucleus with
the electron density varying between 100 and 400 cm
À3 at a cometocentric distance
of 27.5 km from the nucleus above the terminator (phase angle of 91
). However, a
cold electron population in the innermost coma of 67P with an electron temperature,
T e , ≲0.1 eV was also identified. This population was insufficient to modify the
spacecraft potential but was clear evidence of electron cooling by collisions with the
cold (e.g. Fig. 3.4), neutral gas molecules (Gan and Cravens 1990). When the neutral
coma and ionosphere becomes dense enough, the neutrals and local ions act as a
large sink for the electron energy input produced by the photoionization resulting in
the cold electron population. As the cometocentric distance increases, the neutral and
ion densities drop faster than the decrease in the electron heating rate and the cold
electron population disappears. Mandt et al. (2016) defined a limit for electron
collisionality (which might be called an electron collisionopause or exobase and
given the symbol, r ce ) as the cometocentric distance at which the mean free path is
equal to that distance. This can be related to the neutral production rate in an
isotropic model. The mean free path is
420
5 The Plasma Environment
2018). If both the frequencies are assumed constant with distance and the velocity is
assumed constant, then an analytical solution is available (Galand et al. 2016), i.e.
n i ¼ f e þ f ph
À
Á
n g
r À r 0
v g
:
ð5:35Þ
When gas production rates and therefore neutral densities are high, photoionization dominates but at lower production rates both terms are required.
Johansson et al. (2017) have considered the influence of dust absorption. This will
also be dependent upon the dust optical depth and hence its importance will depend
on the dust production rate. As illustrated in Fig. 4.17, the optical depth at 67P was
quite low at optical wavelengths and so the effect is probably of limited importance
there. However, one needs to be aware that if particles smaller than optical wavelengths are more numerous than we currently believe then these can produce a
significant absorption cross-section for EUV photons and for 67P we have little
knowledge of their column densities. For comets as active as 1P/Halley at the time of
the spacecraft encounters, dust would need to be considered.
For typical electron densities within a cometary coma, the electron flux from the
local plasma overcomes the photoemission from the spacecraft itself and the spacecraft potential becomes negative. This was commonly observed at Rosetta. In the
limit where the plasma electron flux greatly exceeds the flux of electrons from the
spacecraft, the spacecraft potential is expected to have a negative value several times
the electron thermal energy equivalent (Eriksson et al. 2017). An example at 67P
from 10 Jan 2015 presented by Eriksson et al. (2017) shows the spacecraft potential
oscillating between about À5 and À 15 V over a single rotation of the nucleus with
the electron density varying between 100 and 400 cm
À3 at a cometocentric distance
of 27.5 km from the nucleus above the terminator (phase angle of 91
). However, a
cold electron population in the innermost coma of 67P with an electron temperature,
T e , ≲0.1 eV was also identified. This population was insufficient to modify the
spacecraft potential but was clear evidence of electron cooling by collisions with the
cold (e.g. Fig. 3.4), neutral gas molecules (Gan and Cravens 1990). When the neutral
coma and ionosphere becomes dense enough, the neutrals and local ions act as a
large sink for the electron energy input produced by the photoionization resulting in
the cold electron population. As the cometocentric distance increases, the neutral and
ion densities drop faster than the decrease in the electron heating rate and the cold
electron population disappears. Mandt et al. (2016) defined a limit for electron
collisionality (which might be called an electron collisionopause or exobase and
given the symbol, r ce ) as the cometocentric distance at which the mean free path is
equal to that distance. This can be related to the neutral production rate in an
isotropic model. The mean free path is
420
5 The Plasma Environment