It is an open question whether a linearly accelerating charge actually radiates. This question gets a decent amount of attention in theoretical circles. To give you a flavor of the debate, assume that a linearly accelerating charge does emit radiation. If I were in a spaceship with rocket motors burning, accelerating the rocket at 9.8m/s^2, and I had a charge sitting on the floor, it would radiate right?
Now if that same spaceship is still on the launchpad on Earth, would that charge on the floor radiate? If it does not, then this violates the strong equivalence principal (general relativity). If is does than what is supplying the energy needed for this charge to continuously radiate?
Here is one reference that you can lookup online:
Radiation from a Uniformly Accelerated Charge
Stephen Parrott
University of Massachusetts at Boston