The Abraham-Lorentz force gives the recoil force, $\mathbf{F_{rad}}$, back on a charged particle $q$ when it emits electromagnetic radiation. It is given by:
$$\mathbf{F_{rad}} = \frac{q^2}{6\pi \epsilon_0 c^3}\mathbf{\dot{a}},$$
where $\mathbf{\dot{a}}$ is the rate of change of acceleration.
If a particle has a constant acceleration, $\mathbf{\dot{a}}=0$, then there is no reaction force acting on it. Therefore the particle does not lose energy.
Does this mean that a constantly accelerating charged particle does not emit electromagnetic radiation?
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