In this way we find the average particle energy change per single collision with a cloud
m if v << u, if v < u, if v > u, if v >> u.
The Eq. 4.4.11 implies an important conclusion which is at variance with the commonly accepted opinion that the energy gain in the statistical acceleration mechanism is owed to the difference between the frequencies of the head-on and overtaking collisions (the second term in Eq. 4.4.11). In the actuality the acceleration in the non-relativistic range is mainly (by more than 75%) owing to the difference between the energy loss and gain in the head-on and overtaking collisions (the first term in Eq. 4.4.11).
The mean relative change of the kinetic energy may be obtained as
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