Abstract
We investigate the regime of a high-gain free-electron laser starting from noise. In the first part, we neglect the radiation propagation and we formulate a linear theory of the N-particle free-electron laser Hamiltonian model, quantizing both the radiation field and the electron motion. Quantum effects such as frequency shift, line narrowing, limitation for bunching and energy spread, and minimum uncertainty states are described. Using a second-quantization formalism, we demonstrate entanglement between the recoiling electrons and the radiation field. In the second part, we describe the field classically but we include propagation effects (i.e. slippage) and we demonstrate the novel regime of SASE with high temporal coherence and discrete spectrum. Furthermore, we describe quantum purification'' of SASE: the classical chaotic spiking behavior disappears and the spectrum becomes a series of discrete very narrow lines which correspond to transitions between discrete momentum eigenstates ( which originate high temporal coherence).
Highlights
The quantum dynamics of an free-electron laser (FEL) is determined by a ‘‘quantum FEL parameter,’’ [1,2], defined in terms of the classical parameter, introduced by Bonifacio, Pellegrini, and Narducci [3] as mcR ; (1)@k which represents the ratio between the classical momentum spread and the one-photon recoil momentum
We show that the discrete gain spectrum of the quantum regime shown in Fig. 2, can give rise to ‘‘quantum purification’’ of the selfamplified superradiant emission (SASE) spectrum
Our results demonstrate that the intrinsic quantum mechanical properties of the momentum and position operators imply a very general minimum uncertainty relation between energy spread and bunching, yielding a quantum limitation to the maximum bunching which can be obtained in an FEL
Summary
The quantum dynamics of an free-electron laser (FEL) is determined by a ‘‘quantum FEL parameter,’’ [1,2], defined in terms of the classical parameter, introduced by Bonifacio, Pellegrini, and Narducci [3] as mcR. We describe classically the field and we include propagation/slippage effects using a selfconsistent system of Schrödinger-Maxwell equations This allows us to provide a quantum description of selfamplified superradiant emission (SASE). Other treatments assume that SASE is just steady-state instability starting from noise [5,6] This approach does not give the correct temporal structure and spectrum of SASE radiation as described in [4]. [7,8,9] it has been shown that, due to propagation, there exists the steady-state instability of [3], and a superradiant instability, with peak intensity proportional to n2 , where n is the electron density This superradiant instability, entirely due to slippage, is the heart of SASE, so that all the treatments which claim to describe. The classical continuous noisy spectrum is recovered when, for > 0:4, the lines overlap
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