Ginzburg-Landau Model and Single-Mode Operation of a Free-Electron Laser Oscillator

Abstract

It is shown that the radiation field in a long-pulse, low-gain free-electron laser oscillator obeys the complex Ginzburg-Landau equation. The question of single-mode operation is investigated by analysis and simulation, and the results are compared with experiments at the University of California at Santa Barbara, as well as the Dutch fusion free-electron-maser experiment. It is shown that the intervention of a frequency-dependent reflection coefficient can facilitate the realization of single-mode operation.[S0031-9007(99)08757-8] PACS numbers: 41.60.Cr, 42.65.Tg, 52.35.Mw In a free-electron laser (FEL) oscillator, the intensity of the radiation field is built up over many passes of the radiation in a resonator cavity at the expense of the energy of a relativistic electron beam. Several cavity modes are usually excited due to the interaction of the electron and the optical beam. This paper is motivated by two principal questions: (i) What is the equation governing the nonlinear dynamics of the radiation field when multiple modes are excited. (ii) What are the conditions under which a single-mode state emerges spontaneously from the nonlinear evolution of a broad spectrum of unstable modes competing for the energy of the electron beam?The theory developed in this paper is applicable to lowgain FEL oscillators driven by long-pulse electron beams. These devices exhibit a strong tendency to evolve into a single-mode state [1-3]. The linewidths realized can be very small, making them ideal for demanding applications such as spectroscopy or isotope separation. For such devices, we demonstrate that the radiation field amplitude A͑z, t͒ can be modeled by the complex Ginzburg-Landau equation (GLE),where z is the coordinate along the axis of the undulator, t is time, and c 1 and c 2 are real parameters calculated by the theory. We then apply the model to two different FEL devices-one at the University of California at Santa Barbara (UCSB) [1,2] and the other at the Dutch FOM-Institute for Plasma Physics [3]. Whether singlemode operation was truly realized within the lifetime of the electron pulse in the UCSB experiment has been a source of theoretical controversy in the past [4,5]. Based on a large number of high-resolution simulations of the GLE with random initial conditions, we conclude that, in the absence of frequency selective feedback, a single-mode state was most probably not realized in the UCSB experiment. We also apply the GLE, with some modifications, to the Dutch fusion free-electron maser (FEM) experiment which has recently reported single-mode operation [3]. We show that, although it takes a very long time to realize a single mode in the absence of any frequency discrimination, the intervention of a frequency-dependent reflection coefficient may have facilitated the realization of a single-mode state within the lifetime of the electron beam in the Dutch experiment.In earlier work, we have derived the GLE [6,7] from the FEL amplifier equations in the high-gain Compton regime. In this paper, we derive the ...

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“…The approach that uses the complex Ginzburg-Landau equation (CGLE) in relation to passively modelocked lasers was pioneered by Haus. 5 It is now used extensively to describe pulse behavior in solid-state or fiber-based passively mode-locked lasers, [6][7][8][9] optical parametric oscillators, 10 free electron laser oscillator, 11 etc. The CGLE has also been used to describe transverse soliton effects in wide-aperture lasers.…”

Variational approach to stationary and pulsating dissipative optical solitons

“…The complex Ginzburg-Landau equation (CGLE) is one of the universal models used in describing dissipative systems [3][4][5]. Examples of its application include optical parametric oscillators [6], free-electron laser oscillators [7], spatial and temporal soliton lasers [8][9][10] and all-optical transmission lines [11][12][13][14]. In these systems, there are dispersive elements, linear and non-linear gain, as well as losses.…”