a stop on the left side wall at a point slightly higher than point b the particle will then accelerate down the wall pass through point a and pass through point b with a positive radial velocity thus escaping the magnetic ring in order to capture the externally injected electron either it must be slowed radially or the potential walls must be raised the acceleration acting on the particle can be varied when the particle is at or near point a to increase the integral of the force between points a and b that is the difference in potential between points a and b from the equation for a radial it is clear that an increase in the magnetic field decreases a radial thus increasing the potential difference between points a and b which would make it possible to capture the particle this has been generally the approach of the prior art for large diameter rings however for magnetic rings under 1 m in radius the time available to make this change is generally on the order of 10 nanoseconds or less which would require very fast time varying magnets thereby being extremely expensive or even infeasible it is the change in potential that captures the particle for a particle with a relativistic energy v u2248 c the speed of light the energy lost through radiation such as synchrotron radiation or through collisions will result in a decreased effective mass while the velocity remains approximately equal to the speed of light the decreased mass lowers the centripetal force making it easier to contain the particle however synchrotron radiation does not cause a significant energy loss per orbit for electrons below 100 mev using a material target allows a significant change in a radial and thus u radial even.