VIOLENT ACCELERATION

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 frequency $\omega_0=2\pi/\lambda_0$. By averaging the emitted radiation over one cycle, one finds

$$(\pm)~\frac{\xi'^2}{\xi^2} \frac{2}{3}\left[ \left(\frac{d^... ... \left[1+ \frac{1}{(2\pi)^2}\frac{\lambda_0^2}{\xi'^2} \right]$$

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,

$$\frac{\lambda_0}{\xi'}\equiv \frac{\lambda_0\times (\textrm{proper~acc'n})}{c^2} \gg 2\pi$$

or equivalently

$$\frac{(\textrm{proper~acc'n})}{c} \gg~\omega_0~.$$ (71)

Recall that $c/$(proper acceleration) is the time it takes for the oscillator to acquire a relativistic velocity relative to an inertial frame. Also recall that $2\pi/\omega_0$ is the time for one oscillation cycle. Consequently, the criterion for ``violence'' is that

$$\left( \begin{array}{c} \textrm{time for oscillator}\\ ... ...ity} \end{array} \right) \ll (\textrm{oscillation period})~.$$ (72)

When this condition is fulfilled, the Larmor contribution to the radiation is eclipsed by the Rindler contribution.