Radiation force on a charged emitting particle

Maxwell equations allows us to calculate the electromagnetic fields based on the motion of charged particles. On the other hand, to see how particles are affected by those fields, you add the Lorentz force, which is an approximation at low speeds, so it is modified relativistically.
The modification is $dvec{p}/dt=q(vec E + vec v$ x$ vec B) $ with $vec{p}=gamma m_0 vec{v}$, which results in extra terms that slows the particle.

The Lorentz force generalization introduce terms opposing the speed and the acceleration that modify the classical path.

For instance, a charged particle moving in a circle in a magnetic field will end up spiraling inwards and losing energy. Because the magnetic force does not do work, is this change in energy dues to the emitted radiation?

On the other hand, you can calculate the radiation force using a different argument and you reach a different conclusion, that the force is a function of jerk. Is this a second mechanism that emits energy and must be introduced ad hoc in the Lorentz force, in addition to the relativistic modification?