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Next Section: Acceleration efficiency Title/Abstract Page: Resonant inverse Compton scattering Previous Section: Limits on particle energies | Contents Page: Volume 15, Number 2 |
Electron positron pair cascades can be started by accelerated
ions in thermal photon fields. A photon can decay into an electron
positron pair in the Coloumb field of a nucleus when the center of
momentum frame energy exceeds the rest mass of the nucleus plus two
electrons, that is
where 
is the mass of the nucleus.
This condition can be satisfied for soft photons from the polar cap
in the presence of accelerated ions. We can estimate the mean free
path of an ion before producing an average one pair. If we believe
one pair per primary particle is enough to short out the electric
field, this mean free path length, represented by 
,
can be identified as the gap length (Figures 3 and 4).
Figure 3: Pair production due to ion colliding with soft photon
from polar cap emission above the polar cap with
. Beside ions, the outflowing
charges may include positrons.
Figure 4: Plots of cumulative number of pairs produced per ion
as a function of distance. Solid, dashed and dotted curves
correspond respectively to 
for the whole star's
surface, 
for the polar cap (but the star's surface
has 
), and for the polar cap (but
the star's surface has 
). The thick and thin
curves are calculated using the potentials (2) and (3), respectively.
We assume 
, 
.
Numerical evaluation of the mean free path for an accelerated ion
traversing an isotropic thermal photon field was given by Protheroe (1984),
and Protheroe & Johnson (1996). The injection rate of pairs for a given
energy of iron nuclei was numerically calculated by Bednarek & Karakula
(1995) for an anisotropic photon field from the polar cap. We calculate
number of pairs produced by iron nuclei accelerated along open field lines
by the potentials given by Eqs. (2) and (3), and the mean free path corresponds
to the average distance at which one pair is produced per ion nucleus.
The mean cumulative number of pairs produced in the radiation field of
the polar cap (or whole neutron star) at temperature T by a nucleus of
energy E traveling along the neutron star magnetic axis from the pole
to distance 
above the polar cap surface is given by,
where 
is the differential photon number density
of photons of energy 
in black body radiation at
temperature T, and 
is the total cross section for
pair production (Protheroe 1997) by a the nucleus at center of
momentum (CM) frame energy squared, s, given by
where 
is the angle between the directions of the nucleus
and photon. Note that 
is determined
by the threshold condition (5). Plots of accumulative number of
pairs produced per ion through interaction with thermal photons
as a function of distance from the polar cap are shown in Figure 4.
for and . Compared to
RICS, in this case we have 
.
Although we use a high B, the process strongly depends on P and T.
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Next Section: Acceleration efficiency Title/Abstract Page: Resonant inverse Compton scattering Previous Section: Limits on particle energies | Contents Page: Volume 15, Number 2 |
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