Super-radiation and super-regeneration

The transient behavior of a two-level spin system coupled to an electric circuit is investigated by using the equations of Bloembergen and Pound. The equations are solved, in the limit where the circuit ringing time is very short compared with all other characteristic times, for two cases: 1) the spin-lattice and spin-spin relaxation times both infinite, with an externally applied driving field, and 2) the spin-lattice relaxation time infinite but the spin-spin relaxation time finite, in the absence of an external field. In case 1), it is shown that the motion of an initially inverted magnetization under the action of an applied signal consists roughly of two stages: in the first stage, the effect of radiation damping is unimportant and the motion of the system is determined principally by the applied signal via the ordinary Bloch equations, whereas in the second stage, the motion is essentially the same as if the applied signal had been turned off and only radiation damping were present. In case 2), it is shown that a delayed peak in the emitted radiation should be observed under certain conditions. The delayed peak condition is identical with that derived by Bloom. Curves are presented showing the peak power and the time at which the delayed peak occurs as functions of the relevant parameters. In connection with the ordinary maser behavior of a two-level spin system, it is shown that for values of the parameters typical of steady-state maser amplification, the effects of radiation damping should be unimportant. Finally, systems are examined for which the radiation damping time is much shorter than all other characteristic times (super-regenerative systems). It is indicated how such systems might be operated as one-shot multivibrators or as linear amplifiers. For the latter type of operation, an expression for the gain is derived which is found to be similar to that encountered in ordinary circuit theory.