Jennifer Nicholls, Michelle C. Storey, PASA, 16 (2), in press.
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Title/Abstract Page: An Analytic Approximation to
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Calculation of the average drift angle
To calculate how far the electrons drift before they have lost sufficient energy to be indistinguishable from the ambient population of mildly relativistic electrons we integrate
with respect to time, from t=0 to tf and then average over .
The integral over time is
. With given by equation (28), the integral becomes
term so the average over becomes
(32) |
Bringing this all together gives the average angle through which the electrons drift in time tf:
For a given system the pitch-angle-average drift angle depends only on the equatorial radius, and initial Lorentz factor. An electron with very large drifts a very large distance before losing sufficient energy to thermalise regardless of its equatorial radius, for two reasons: its drift speed is initially very large and it lives for a very long time, which is why
as
. Conversely, an electron with a small initial Lorentz factor will not drift far due to a low initial drift speed and short lifetime. For an electron of given Lorentz factor the drift speed is inversely proportional to both the magnetic field strength and the radius of curvature of the field, both of which decrease with equatorial radius. Hence an electron of given Lorentz factor will drift faster the further it is away from the star. As its lifetime also increases with decreasing field strength, an electron far from the star will drift further than one close to the star.
Next Section: Application to V471 Tau
Title/Abstract Page: An Analytic Approximation to
Previous Section: The Lorentz Factor
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