Most commonly, there is a beam circulating in a synchrotron, in the form of a particle train which only partially fills the arc.
An ejection kicker magnet does the opposite, diverting a circulating beam so it leaves the synchrotron.
This means that it has the entire tail-to-head gap in the synchrotron to function, and the switch-off time is essentially irrelevant.
The magnets are powered by a high voltage (usually in the range of tens of thousands of volts) source called a power modulator which uses a pulse forming network to produce a short pulse of current (usually in the range of a few nanoseconds to a microsecond and thousands of amperes in amplitude).
Because a kicker magnet applies a particular lateral impulse to the beam, to achieve a fixed deflection angle the strength of the kick must be accurately matched to the momentum of the particles.