A low level radio frequency (LLRF) control system is designed and constructed at Peking University, which is for the DC-SRF photo injector operating at 2K. Besides with continuous wave (CW), the system is also reliable with pulsed RF and pulsed beam,
the stability of amplitude and phase can achieve 0.13% and 0.1{deg}respectively. It is worth noting that the system works perfectly when the cavity is driven at both generator driven resonator (GDR) and self-excited loop (SEL), the latter is useful in measuring the performance of the cavity.
In this paper we define the radiation field for the wave equation on the Schwarzschild black hole spacetime. In this context it has two components: the rescaled restriction of the time derivative of a solution to null infinity and to the event horizo
n. In the process, we establish some regularity properties of solutions of the wave equation on the spacetime. In particular, we prove that the regularity of the solution across the event horizon and across null infinity is determined by the regularity and decay rate of the initial data at the event horizon and at infinity. We also show that the radiation field is unitary with respect to the conserved energy and prove support theorems for each piece of the radiation field.
