Some Inverse Compton Boost Factors
|
| v / c |
Boost Factor
|
| 0.0 |
1.00
|
| 0.5 |
1.33
|
| 0.9 |
5.26
|
| 0.995 |
102
|
| 0.99995 |
104
|
| 0.9999995 |
106 |
| |
| |
|
Technically Speaking: Inverse Compton Boosts
For highly relativistic electrons, the increase in frequency for a photon by the inverse Compton
process is given by a rather simple formula. If the initial frequency of the photon is
f0,
f / f0
= 1 / [1 - (v / c)2]
where f is the final (boosted) frequency and the quantity on the right side
of the equation is
called the boost factor, since multiplying the original frequency by it gives the
final frequency. The table gives the boost factor for several velocities. Notice that the
velocity must be large relative to the speed of light (relativistic) to give large boosts in
frequency by the inverse Compton process. For non-relativistic velocities the boost factor is
close to one (no increase in frequency).
Let's use the table to do an example. Suppose
that the electron velocity is
v = 0.9999995c. Then the
boost factor is a million and
f = f0 x Boost Factor
= 5 x 1014 Hz x 106
= 5 x 1020 Hz
for an optical photon
of frequency 5 x 1014 Hz. The boosted photon now has a
frequency in the gamma ray region of the spectrum.
|