PBPL Publications: 2009-00025 PUBLICATION HELICAL ELECTRON-BEAM MICROBUNCHING BY HARMONIC COUPLING IN A HELICAL UNDULATOR

Microbunching of a relativistic electron beam into a helix is examined analytically and in simulation. Helical microbunching is shown to occur naturally when an e beam interacts resonantly at the harmonics of the combined field of a helical magnetic undulator and an axisymmetric input laser beam. This type of interaction is proposed as a method to generate a strongly prebunched e beam for coherent emission of light with orbital angular momentum at virtually any wavelength. The results from the linear microbunching theory show excellent agreement with three-dimensional numerical simulations. Helical Electron-Beam Microbunching by Harmonic Coupling in a Helical Undulator E. Hemsing, P. Musumeci, S. Reiche, R. Tikhoplav, A. Marinelli, J. B. Rosenzweig, and A. Gover Particle Beam Physics Laboratory, Department of Physics and Astronomy University of California Los Angeles, Los Angeles, California 90095, USA Università degli Studi di Roma ‘‘La Sapienza’’, Via Antonio Scarpa 14, Rome, 00161, Italy Faculty of Engineering, Department of Physical Electronics, Tel-Aviv University, Ramat-Aviv 69978, Tel-Aviv, Israel (Received 13 August 2008; published 29 April 2009) Microbunching of a relativistic electron beam into a helix is examined analytically and in simulation. Helical microbunching is shown to occur naturally when an e beam interacts resonantly at the harmonics of the combined field of a helical magnetic undulator and an axisymmetric input laser beam. This type of interaction is proposed as a method to generate a strongly prebunched e beam for coherent emission of light with orbital angular momentum at virtually any wavelength. The results from the linear microbunching theory show excellent agreement with three-dimensional numerical simulations. DOI: 10.1103/PhysRevLett.102.174801 PACS numbers: 41.60.Cr, 42.50.Tx, 42.60.Jf, 42.65.Ky A relativistic electron beam (e beam) that is subject to the free-electron laser (FEL) instability becomes microbunched in density and velocity at the resonant interaction wavelength, and at harmonics. The modulated e beam can then be used to emit radiation in various kinds of radiation schemes that preserve the characteristic frequency and geometry of the microbunching in the e beam. In general, the microbunching interaction generates a purely longitudinal modulation, such that the subsequent radiative process produces emission at, or near, the fundamental transverse optical mode. The range of modulation wavelengths obtainable in modern devices make this technique appealing for the generation of light with wavelengths that span many orders of magnitude. However, in some cases one may wish to produce radiation with the modulated beam that has a specific higher-order phase or intensity structure. Depending on the emission process, the e beam must be prepared with the correct microbunching structure in the modulator. Here we examine a simple modulator arrangement that generates a helically microbunched e beam, such that the electrons are arranged in a helix (or multiply twisted helices) about the longitudinal axis. Such a beam can be used for generation of coherent light that carries orbital angular momentum (OAM) as a result of the imprinted helical e beam density distribution on the optical phase. Light that carries OAM is a subject of intense research for a myriad of applications [1–5]. Coherent OAM modes allow the possibility of light-driven micromechanical devices or the use of torque from photons as an exploratory tool [6]. Laguerre-Gaussian (LG) modes of free-space propagation are of particular interest since they are known to possess a well-defined value of angular momentum l@ per photon due to an azimuthal component of the linear momentum [7]. Emission of OAM light with an e beam may be accomplished through a variety of radiation processes, including harmonic emission from an FEL [8] or through coherent transition radiation [9] or superradiant FEL emission [10,11] with helically microbunched beams. Modes of this type may be particularly relevant for study with modern optical and next-generation x-ray FELs with the ability to probe the structure of matter down to Å length and attosecond time scales. For future FEL light sources, the ability to directly generate intense higher-order LG modes in situ would further extend the experimental and operational capabilities. In this Letter, we propose a scenario for generating a helically microbunched e beam which utilizes harmonic coupling in a helical undulator. We show that microbunching of this type may be easily performed with an axisymmetric EM seed input in the modulator section of an optical klystron [12]. The helical beam can then be used as a source of OAM radiation in a downstream radiator. A linear analysis of the harmonic bunching process is developed in which the input field and density modulation are treated as superpositions of orthogonal modes [13,14], and the beam couples at harmonics via field gradients in the input laser beam. Simple symmetry arguments are employed to clearly delineate the spatial dependence of the harmonic fields that couple to the e beam. The method also illustrates the geometric structure of the resonant phase for arbitrary harmonics, the mode coupling for a cylindrically symmetric e beam, and the resulting density and velocity modulations excited in the e beam during the interaction. Selection rules are also derived for coupling between azimuthal modes in the e beam (l) and in the field (l0) at harmonics (h). These rules apply both to the modulator setup described here and to harmonic radiation in a FEL with a cold beam. The interaction between the e beam and the input radiation field in an undulator operating as a buncher can be described analytically using standard linearized FEL equations in the small-signal regime if the radiation fields are injected with sufficient power (or the interaction length is PRL 102, 174801 (2009) P HY S I CA L R EV I EW LE T T E R S week ending 1 MAY 2009 0031-9007=09=102(17)=174801(4) 174801-1 2009 The American Physical Society short enough) that the total field energy is unaffected by the e beam throughout interaction. The fields are assumed to be dominantly transverse. The electric field is given by the modal expansion