A Helical Undulator Wave-guide Inverse Free- Electron Laser

With recent success in high gradient, high-energy gain IFEL experiments at the UCLA Neptune Laboratory, future experiments are now being contemplated. The Neptune IFEL was designed to use a tightly focused, highly diffracting, near-TW peak power 10 micron laser. This choice of laser focusing, driven by power-handling limitations of the optics near the interaction region, led to design and use of a very complex undulator, and to sensitivity to both laser misalignment and focusing errors. As these effects limited the performance of the IFEL experiment, a next generation experiment at Neptune has been studied which avoids the use of a highly diffractive laser beam through use of a waveguide. We discuss here the choice of low-loss waveguide, guided mode characteristics and likely power limitations. We also examine a preferred undulator design, which is chosen to be helical in order to maximize the acceleration achieved for a given power. With the limitations of these laser and undulator choices in mind, we show the expected performance of the IFEL using 1D simulations. Three-dimensional effects are examined, in the context of use of a solenoid for focusing and acceleration enhancement. In the last year, a very high energy-gain inverse free-electron[1] laser (IFEL) experiment was performed at the UCLA Neptune Lab, in which 14.5 MeV electrons [2] were accelerated to over 35 MeV [3]. This experiment is unique in the power of the laser source: a single 0.3-0.6 TW line of 10.6 μm CO2 light. With such high power and limited laboratory space, the handling of the beam required use of small f/# optics. Thus the laser beam used may have very high intensities, but at the cost of a very short focus — short Rayleigh range Zr, in our case a design of less than 3 cm. With this tight focus, there was a significant challenge in dealing with a large Guoy phase shift which ran into tens of degrees per undulator period. In addition, with a tightly focused TW beam and moderate injection energy, we designed for a very large fractional acceleration. Thus, the undulator was strongly tapered in order to keep the beam captured and accelerating in the IFEL ponderomotive bucket. The design of the tapered IFEL undulator had a specially tailored magnetic field at the focus to evade the effects of the Guoy phase shift, by shifting the phase of the electron’s transverse oscillation smoothly, while also accommodating a quickly diffracting laser spot. This magnet system was analyzed extensively to understand and optimize longitudinal dynamics issues, producing an experiment where a large percentage of the beam was to accelerate from 14.5 MeV injection to a narrow band near 55 MeV in 50 cm. It was found more difficult than anticipated to achieve Zr above 1.5 cm, and thus the laser power was mismatched to the acceleration program of of the undulator. In practice, the second half of the undulator was not “turned on” effectively due to this effect. In addition a high sensitivity to relative laser/electron beam alignment was observed. The diffraction-dominated IFEL experiment performed last year at Neptune thus yielded many lessons, both positive (significantly larger acceleration than previous experiments [5,6,7]) and negative, and concerning both physics and technology issues. A follow-on experiment that attempts to use the techniques mastered in the first IFEL experiment, while avoiding the problems listed above is discussed here — a waveguide IFEL. This scenario is designed to mitigate issue encountered in the first experiment, and should yield 100 MeV electrons at the end of an 80 cm undulator. To begin the discussion of implementing a waveguide for an far-IR IFEL experiment, we note that the guiding the CO2 laser pulse has already been experimentally tested at Neptune , on metallic wall pipes, which have shown the ability to propagate up to 10 TW in ps laser pulses previously [9]. Good performance in 2 mm ID capillary pipes for short pulses was obtained for very high intensities, before plasma formation closed the capillary to radiation propagation. Unfortunately, in the far IR, wall losses are an issue for propagation over the 10’s of cm needed for an IFEL experiment; orders of magnitude of attenuation would be expected in 80 cm. Thus we have investigated the use of very low loss, so-called “leaky guides” [10] (Fig. 1), which we had originally examined in the context of a far-IR guided SASE-FEL experiment [11]. Initial low power tests on a 2 mm ID guide showed no measurable loss over 30 cm, with matching obtained from an f/18 final focus. FIGURE 1. A typical, ultra-low loss, leaky waveguide geometry: inner layer of AgI, followed by Ag, and smooth glass capillary. High power behavior of these guides is now under investigation at Neptune. For our pulse length ( € ≥100 ps FWHM), it has been proposed that one may be able to guide up to 10 W/cm in these guides without damage. For the sake of a conservative approach, however, we have restricted the present design study to one in which the peak intensity in the guide does not exceed € 5×10 W/cm, with a guide of 2 mm ID. To increase the coupling of the electrons to the laser fields, which are assumed to be limited by breakdown in the guide, and match the waveguide geometry optimally, a helical undulator (with circularly polarized laser) is proposed. In order to make sure that the beam stays well within the guide and samples only a small region where the field does not vary much radially, we also include in the design a strong solenoid guide-field. These features are generally favored in long wavelength FEL and IFEL experiments, but also provide significant benefits in this far-IR design. The additional positive effect of using the solenoid field is to enhance the beam rotation velocity [12], and couple the beam motion more strongly to the laser field. FIGURE 2. Design study layout of Neptune IFEL wavelength-tapered undulator, bifilar windings shown in blue and red, solenoid windings (partially shown) in yellow. A design study of the beam dynamics of such an IFEL, with 15-50 GW of total laser power (assuming matched-mode propagation) has yielded an experimental scenario, summarized in Table 1. The undulator which delivers this type of performance is a wavelength tapered (1.8 – 15.6 cm), constant field (1.7 kG) bifilar helical-magnet 80 cm in length. These parameters give the undulator a normalized strength which slews from € au = eBu kume c=0.28 to 2.46. We assume the undulator is embedded in a large solenoid, as indicated in a first-pass engineering design shown in Fig. 2. The maximum beam offset should be kept to below the laser w0, so we may expect one-dimensional behavior from the IFEL interaction through most of the undulator. We note that some loss of coupling may occur near the end of the undulator, where the amplitude of the helical motion grows. The addition of the focusing solenoid field increases the rotational velocity by a factor of € ≈ 1−ωc /kuc ( ) −1 , where € ωc = eBs γme c , and € ku = 2π /λu . In our case this enhancement factor is less than 5% throughout the undulator. While this rotational velocity gives rise to a proportionally larger acceleration gradient, it also results in a slightly larger radial offset of the design orbit, € R∝ 1− ωc /kuc ( ) 2 [ ] −1 ; this effect is negligible for our parameters. Thus the main effect of the solenoid is to increase the field’s net focusing strength € kβ 2 = 1 2 kuau γ 