Step 1: Understanding the Concept:
A cyclotron is a device used to accelerate charged particles outwards from the center along a spiral path.
A fundamental characteristic of a standard non-relativistic cyclotron is that the time period of revolution and the orbital frequency do not depend on the speed or kinetic energy of the particle.
Step 2: Key Formula or Approach:
The orbital cyclotron frequency of a charged particle of mass and charge moving in a uniform magnetic field is given by the formula:
Step 3: Detailed Explanation:
Looking closely at the formula for the cyclotron frequency , we can observe that it is determined solely by the charge , the magnetic field strength , and the rest mass .
The formula entirely lacks any variable related to the particle's velocity , orbital radius , or kinetic energy .
Therefore, even if the particle accelerates and its kinetic energy is doubled, the frequency of revolution strictly remains unchanged (assuming the speeds remain safely non-relativistic).
Step 4: Final Answer:
The cyclotron frequency remains .