A charged particle has an electric field surrounding it as a result of its charge. Moving a charged particle creates a magnetic field because of its motion.
The acceleration of the charged particle is caused by applying a force and pushing or pulling on the charged particle.
As the particle is accelerated, the acceleration causes a disturbance or a change in the electric and magnetic field that exist around the charged particle. That change in the electric and magnetic filed causing an oscillation or vibration of these fields and these vibrations radiate outward in all directions.