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The second term in the radiation formula, Eq.(69), is new. Under what circumstance does it dominate? Consider
the circumstance where the magnetic dipole oscillates with proper
. By averaging the emitted
radiation over one cycle, one finds
Thus the criterion for ``violent'' acceleration is that its inverse,
the Fermi-Walker length of the accelerated point object be small compared to the emitted wavelength,
Recall that (proper acceleration) is the time it takes for the
oscillator to acquire a relativistic velocity relative to an inertial
frame. Also recall that is the time for one oscillation cycle.
Consequently, the criterion for ``violence'' is that
When this condition is fulfilled, the Larmor contribution to the
radiation is eclipsed by the Rindler contribution.