The total power radiated from an accelerating charge depends on the magnitude of it's acceleration, and is proportional to the square of the accelaration. But there is a certain problem with the definition of such an effect. Because than one is unable to figure out how the charged particle began to move . Suppose for example that we activate an external electic field on a charged particle at rest. The amount of work per time the field is doing on a particle is qEv, where v is the component of velocity parallel to the field. But at the begining, v = 0, so for any supposed initial acceleration of the particle we get a violation of the principle of conservation of energy since the the field did zero work while the charge radiated a finite amount of energy.
So how to resolve this paradox?