Course of Theoretical Physics, Volume 2 by L D Landau & E.M. LIFSHITZ

Author:L D Landau & E.M. LIFSHITZ [LANDAU, L.D. & LIFSHITZ, E.M.]
Language: eng
Format: epub
ISBN: 9781483293288
Publisher: Elsevier
Published: 1975-09-15T00:00:00+00:00

We are interested in the time average of the loss of angular momentum for a stationary motion, just as before, we considered the time average of the energy loss. Writing

and noting that the time derivative (first term) vanishes on averaging, we finally obtain the following expression for the average loss of angular momentum of a radiating system:‡

(75.7)

Radiation damping occurs also for a single charge moving in an external field. It is equal to

(75.8)

For a single charge, we can always choose such a system of reference that the charge at the given moment is at rest in it. If, in this reference frame, we calculate the higher terms in the expansion of the field produced by the charge, it turns out that they have the following property. As the radius vector R from the charge to the field point approaches zero, all these terms become zero. Thus in the case of a single charge, formula (75.8) is an exact formula for the reaction of the radiation, in the system of reference in which the charge is at rest.

Nevertheless, we must keep in mind that the description of the action of the charge “on itself” with the aid of the damping force is unsatisfactory in general, and contains contradictions. The equation of motion of a charge, in the absence of an external field, on which only the force (75.8) acts, has the form

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