This is far more efficient than lasers which are heavily attenuated by vapour from the target and are energetically inefficient. Using nuclear warheads to destroy asteroids would create highly unpredictable results and even worsen planetary damage. It is a very short step from electric ion propulsion systems such as Deep Space 1 to developing powerful electromagnetic ion beams several orders of magnitude more powerful. There are large inquiries circulating for very high purity Xenon and Krypton. These gases are inert and very ionisable.
High purity is required to avoid corrosion of the hollow cathodes where the ions are formed.
These ions are accelerated by electromagnets to extremely high velocities. Some ground based accelerators achieve .999 light speed. The statistics are staggering. Furthermore the ion beam can be highly controlled and could be used to accurately control the trajectory of an asteroid. The beam will hardly be attenuated in the near vacuum of space.