Theory Of Free-electron Laser Research Articles

Visible-infrared self-amplified spontaneous emission amplifier free electron laser undulator

The visible-infrared self-amplified spontaneous emission amplifier (VISA) free electron laser (FEL) is an experimental device designed to show self-amplified spontaneous emission (SASE) to saturation in the near infrared to visible light energy range. It generates a resonant wavelength output from 800\char21{}600 nm, so that silicon detectors may be used to characterize the optical properties of the FEL radiation. VISA is designed to show how SASE FEL theory corresponds with experiment in this wavelength range, using an electron beam with emittance close to that planned for the future Linear Coherent Light Source at SLAC. VISA comprises a 4 m pure permanent magnet undulator with four 99 cm segments, each of 55 periods, 18 mm long. The undulator has distributed focusing built into it, to reduce the average beta function of the 70\char21{}85 MeV electron beam to about 30 cm. There are four FODO cells per segment. The permanent magnet focusing lattice consists of blocks mounted on either side of the electron beam, in the undulator gap. The most important undulator error parameter for a free electron laser is the trajectory walk-off, or lack of overlap of the photon and electron beams. Using pulsed wire magnet measurements and magnet shimming, we were able to control trajectory walk-off to less than $\ifmmode\pm\else\textpm\fi{}50\ensuremath{\mu}\mathrm{m}$ per field gain length.

APS Honors Physics Contributions

APS Honors Physics Contributions

Kick and phase errors in spontaneous and amplified radiation

Two types of magnet errors are considered – the random phase error (RPE), in which the phase errors are evenly distributed along the magnet, and the random kick error (RKE), in which the errors in the derivative of the phase are evenly distributed. We compute the reduction in performance of both spontaneous radiation and high-gain free-electron lasers for both types of errors within the framework of 1-D free-electron laser theory.

Theory of group synchronism in free-electron waveguide lasers fed a sequence of short electron pulses

A theory of free-electron lasers fed a sequence of short electron pulses is developed. It is assumed that the group velocity of the electromagnetic pulse that develops in the cavity is the same as the translational velocity of the particles, and the repetition period of the electron pulses equals the transit time of the electromagnetic radiation in the cavity. Under these conditions of group synchronism, the principal factors governing the feasibility of establishing a stationary pulsed lasing regime are found to be the dispersive spread of the electromagnetic pulse and the channeling properties of an electron bunch. The conditions for self-excitation are found, and the characteristics of the stationary lasing regimes are determined assuming that the cavity has a high Q and using a parabolic equation for the evolution of the electromagnetic pulse shape.

Madey’s and Liouville’s theorems relating to free-electron lasers without inversion

The small-gain regime of free-electron lasers (FEL) without inversion is considered and seeming contradictions with the traditional theory of FEL are resolved. As a result, a generalized Madey's theorem is obtained for the case of a phase shift given to electrons between the two wigglers. It explicitly demonstrates the contribution of interference of radiation from the wigglers. It is shown, by considering the motion in the phase space, that Liouville's theorem applied to the motion of electrons in a two-dimensional (rather than one-dimensional) real space is consistent with a nonzero integral of the gain over electron energies. These conclusions are crucial for the achievement of orders-of-magnitude improvement in the FEL gain in the case of a large electron energy spread.

Masing and single-mode locking in a free-electron maser employing prebunched electron beam.

We report a first demonstration of single-mode selection in a free-electron maser (FEM) using electron-beam prebunching at or near the natural oscillation frequencies of the resonator. The FEM oscillation frequency can be selectively locked to each eigenfrequency of the resonant waveguide cavity within the frequency band of the FEM net gain. When the electron beam is prebunched at a frequency close to an eigenfrequency of the cavity, the oscillation buildup process is sped up and the radiation buildup time is shortened significantly. Measurements are in good agreement with collective (Raman) free-electron laser theory.

Frequency response to an electron energy shift

In a free electron laser (FEL) oscillator, the optical pulse evolves through mode competition as a result of mirror losses, desynchronism, and amplification by the electron beam. The finite time for this evolution determines the optical response to an electron beam energy change. The ability of the FEL operating frequency to follow modulations in electron energy has been demonstrated experimentally [l-3] and theoretically [4]. Using a self-consistent FEL theory with dimensionless parameters [5], a longitudinal multimode simulation follows the evolution of the optical pulse over many passes of a FEL oscillator. The optical frequency response to an electron energy shift is summarized in Fig. 1. The characteristic response time II, measures the number of passes for the optical frequency centroid to reach l/e of its new steady-state position after an electron energy shift is imposed at steady-state saturation. The parameters in the simulation are chosen so that the optical pulse reaches steady-state saturation fields without the trapped-particle instability and the growth of optical sidebands. The current density j can be related to the weak-field, single-mode gain, G = 0.135 j, and the energy loss at each pass is given by l/Q. The pulse length, cr:, and desynchonism, d. are measured in terms of the slippage distance, NA. For small Q and low desynchronism d, the optical pulse resides predominantly in the region of the electron pulse. Within the bulk of the optical pulse, strong-field saturation limits changes in the optical fields and the frequency remains unchanged. In the back of the optical pulse where the fields are weak and the interaction with the energy-shifted electron beam changes the optical frequency. Desynchronism d transfers these changes toward the front of the pulse at each pass. The centroid of the optical power spectrum shifts linearly with the number of passes during the middle of the response. In Fig. 1, for a given Q and oz = 2 the response time n, falls off as l/d. For large Q and small uz, the bulk of the optical pulse resides in an exponentially decaying profile outside the interaction region. in the short interaction region, changes

Three-dimensional coupled-mode theory of free-electron lasers in the collective regime.

An analytical three-dimensional model is presented for free-electron lasers (FELs) operating in the small-signal linear regime. The excitation of radiation and space-charge waves is found by expanding the total electromagnetic field in terms of transverse eigenmodes in a waveguide of arbitrary cross section and solving the evolution of their amplitudes from a set of coupled excitation equations. Coupled-mode theory is employed to derive dispersion relations for the space-charge waves and for the gain. The eigenmodes of the FELs (``supermodes'') and the gain for each of them are derived after diagonalization of the coupled-mode system. It is found that for the case of degenerate coupled modes (equal axial wave numbers), the normal modes satisfy the well known FEL gain dispersion equation with a modified gain parameter. The gain of the supermode, calculated according to the presented coupled-mode theory, is higher than the gain of the individual modes if calculated on the basis of a single-mode model. We demonstrate the formalism by finding the gain of the ${\mathrm{TE}}_{01}$, and the coupled ${\mathrm{TE}}_{21}$ and ${\mathrm{TM}}_{21}$ modes excited simultaneously in a rectangular waveguide.

Operation of the sapphire Cerenkov laser

First operation of a sapphire-based Cerenkov free electron laser is reported. It is a tunable source of coherent millimeter and submillimeter radiation. The phase velocity of light in sapphire is about one-tenth of that in free space so that Cerenkov radiation is obtained at modest electron beam energies. In addition to its role as a Cerenkov coupler, the sapphire forms a high Q resonator obviating external mirrors. The spontaneous Cerenkov emission is well-confined by this resonator and can build to watts of power. Measured tuning and threshold currents are presented and compared with the predictions of free electron laser theory.

Free-electron laser supermodes for bunches with longitudinal energy-position correlation

In this note the theory of Free-Electron Laser (FEL) supermodes is extended to cover particle distributions with a correlation between energy and longitudinal position in a Gaussian bunch. This extension is important for FEL’s in storage rings, because wake forces stemming from discontinuities in the vacuum chamber as well as the FEL process itself give rise to such correlations.

Advantages of the “kinetic” amplification regime in a free electron laser with optical undulator

The theory of free electron lasers (FELs) with optical undulators is studied. It is shown that by taking the length of the optical undulator much longer than the traditionally accepted “hydrodynamic” length, a gain much higher than the standard one can be provided. Estimations show that a slight improvement of existing accelerators is sufficient for oscillations in the soft X-ray range.

Recent advances in free electron laser theory

Free electron lasers (FELs) have advanced to the stage where the experiments may be considered to have verified the essential FEL theories. The future research in FELs will be strongly tied to applications. There exist many types of lasers and optical techniques to obtain the required laser characteristics in the optical regime. FELs can make significant impact in the IR, UV and X-ray regimes, where conventional lasers are limited. Competition with other sources also requires FELs to be compact and user oriented. The theory developments addressing some of these issues will be presented in this article.

Small signal gain based on analytic models of thin intense electron beams

We develop the free electron laser theory of the effective energy distribution and the small signal gain for a thin electron beam. The assumption of thinness allows us to treat various transverse locations and electron beam trajectory angles as introducing phase shifts that have the same effect as those introduced by a change in energy of the electron. These ideas extend previous work of Colson et al., Dattoli et al., Scharlemann, and others in five important ways. The first is the ability to treat electron beams with three different classes of matching or symmetry conditions: (i) electron beams with separate betatron matching in each plane. (ii) those with aspect ratio matching, and (iii) crossed matched beams. Manifestations of these symmetries include elliptical cross-sections and electron beams that have modulated spatial profiles. For these we derive analytical expressions for effective energy distributions. Second, two emittance parameters for the electron beam are shown to consolidate into a single parameter that describes most of the energy variation of the effective energy distributions. Thus, the effective energy distribution for a 1:4 ribbon electron beam is nearly equivalent to a distribution for a beam of circular cross-section. Third, these calculations extend to energy distributions, angular distributions, and spatial distributions that all follow Gaussian profiles. Fourth, this model incorporates the description of the incident Gaussian optical beam and the above electron beam dynamics into a single influence function kernel. Emittance, energy spread, diffraction, and gain may be interpreted as limiting the length over which the bunching contributions of the propagating electric fields downstream are important. Fifth, three-dimensional profiles of the optical fields are computed. This work is complementary to the recent work of Yu, Krinsky and Gluckstern in that ours always describes the transition from low gain to high gain for a thin beam and not necessarily the high-gain regime itself. Therefore in this work the parameters of the incident optical beam are included, whereas, their work is not concerned with these parameters. The resulting transverse dependence of the fields may be characterized by an optical beam radius. This optical beam width starts out large compared to the thin electron beam and then, in the example given, contracts to a size that becomes so small that the thin-beam assumption is violated.

Space-charge wave theory of free electron lasers

The linear theory of free electron lasers (FELs) is provided from the point of view of space-charge waves. The basic equation describing the space-charge waves in FELs is derived and analyzed. A new kind of hybrid free electron laser with a slow-wave circuit,v which may enhance efficiency with the aid of coupling of the first space harmonic with the space-charge wave, is presented.

Spherical Raman-Nath equation for gyrotron radiation

Based on the structure of the energy levels of a relativistic electron moving in a uniform magnetic field first derived by Schneider, a more rigorous quantum theory of gyrotron radiation is developed. As the result, a difference-differential equation is obtained to describe the evolution of gyrotron radiation. This equation is of the form of the spherical Raman-Nath equation, well known in the quantum theory of free-electron lasers. Therefore, all the mathematical techniques developed for solving the spherical Raman-Nath equation can be used immediately to solve the problem of gyrotron radiation.

Quantum theory of wave propagation and linear amplification in free electron lasers

A quantum field theory of free electron lasers is formulated and evaluated for the case of linear propagation and amplification of thermal noise and radiation emitted spontaneously and from shot noise.

On the theory of parametric free-electron lasers based on opened resonators

The theory of free-electron lasers (FELs) based on opened resonators and modulated electron beams is developed.

Linear theory of a sheet beam free electron laser

The linear theory of a free electron laser based on a sheet beam propagating in a narrow gap is developed. The three-dimensional structure of the radiation field is determined for an infinitely thin sheet beam. Included are the effects of diffraction and space charge. The possibility of diffractive suppression of unwanted modes is discussed.

The study on the gain expression in the single-particle theory of free electron laser

Nonlinear pendulum equation is the fundamental one of the single particle theory in the free electron lasers (FELS). From its solution the gain expression can be derived. In this paper, an exact solution of it has been obtained for the first time, and similar result is also obtained as in the approximation of weak field by Colson.

Free electron laser theory in weak optical fields

In weak optical fields, free electron laser dynamics can be expressed in the form of an integral equation. The integral equation is used to evaluate the gain degradation from various electron beam distributions and determine important design criteria for the accelerator-laser interface.