A Helical Undulator Wave-guide Inverse Free- Electron Laser

A Helical Undulator Wave-guide Inverse Free- Electron Laser J. Rosenzweig*, N. Bodzin*, P. Frigola*, C. Joshi ℵ, P. Musumeci*, C. Pellegrini*, S. Tochitsky ℵ, and G. Travish* *UCLA Dept. of Physics and Astronomy, 405 Hilgard Ave., Los Angeles, CA 90095 ℵ UCLA Dept. of Electrical Engineering, 405 Hilgard Ave., Los Angeles, CA 90095 Abstract. 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 4 : a single 0.3-0.6 TW line of 10.6 µm CO 2 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 Z r, 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 Z r 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 CO 2 laser pulse has already been experimentally tested at Neptune 8, 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 15 W/cm 2 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 13 W/cm 2, 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 a u = eb u k u m e 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 w 0, 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 ω c /k u c) 1, where ω c = eb s γm e c, and k u = 2π /λ u. 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 ( ω c /k u c) 2 ] 1 ; this effect is negligible for our parameters. Thus the main effect 2 of the solenoid is to increase the field s net focusing strength k β = 1 k u a u 2 γ minimizing the betatron beam size, σ β = ε n /γk β. 2 + ω 2 c, 2c This effect of electrons sampling regions of smaller laser field can be controlled by matching into a larger value of w, as the CO 2 laser may supply more total power than we have assumed. As such, we have performed an initial 1D analysis of the longitudinal beam dynamics, ignoring 3D effects on the electron-laser coupling. TABLE 1. Parameters for study of helical undulator waveguide IFEL experiment at Neptune. Parameter Value Undulator Field, B u 1.7 kg Undulator Period, λ u 1.7-11 cm Solenoid Guide Field, B z 0.5 T Undulator Length, L u 80 cm Undulator Gap, a 2 mm Input Power, P 50 GW Matched Laser Spot Size, w >250 µm TABLE 2. Electron beam parameters for Neptune helical undulator waveguide IFEL experiment. Parameter Value Normalized emittance, ε n 5 mm-mrad Matched rms beam size, σ β 175 µm Beam centroid offset (start-end) 27 300 µm Injection energy 14.5 MeV Extraction energy 100 MeV Trapping fraction 63% The one-dimensional, undulator period-averaged equations of motion integrated to give the longitudinal dynamics are dθ dz = k 1+ 1 2 k r 0 2 k 0 + k ( z) k 0 u 1 1+ a 2 u ( z) + a 2 L ( z) + 2a u ( z)a L ( z)cos( θ), 1/ 2 γ 2 dγ dz = k a ( z)a ( z) 0 u L sin( θ). γ Here k 0 = ω /c is the free-space wave-number of the laser radiation, k r 1/w is the radial wave-number associated with the waveguide mode, and a L = ee L /k 0 m e c 2 is the

normalized vector potential of the circularly polarized laser, and energy loss by synchrotron radiation [1] is ignored. Note that the change in the phase velocity due to the presence of the wave-guide is non-negligible. The design case, where the full laser power of 50 GW is used, is shown in Fig. 3(a). The wavelength is linearly varied to give a final resonant energy of 100 MeV (107 MeV/m average acceleration), with over 61% of the electrons trapped in the accelerating bucket. Figure 3(b) shows the longitudinal phase space obtained by use of only 15 GW, with the trapping fraction degraded to 42%. FIGURE 3. Simulation results showing the final longitudinal phase space for the design power of 50 GW (a), and the phase space for the design power derated by a factor of 0.3 (b).

0.7 0.7 0.6 0.6 Trapping fraction 0.5 0.4 0.3 0.2 0.1 Trapped fraction 0.5 0.4 0.3 0.2 0 0.1-0.1 1 10 13 2 10 13 3 10 13 4 10 13 5 10 13 0 0 0.5 1 1.5 2 2.5 Intensity (W/cm 2 z (cm) ) a FIGURE 4. The trapping fraction as a function of (a) on-axis laser intensity and (b) attenuation length in waveguide. As the major uncertainties in the design at this point concern the level of power tolerated in the waveguide, the performance of the IFEL, as measured by trapping fraction (defined as fraction above 80 MeV) was examined as a function of on-axis laser intensity, assuming no attenuation in the guide. As can be seen in Fig. 4(a), the trapping falls precipitously for intensities less than 20% of design, or 10 13 W/cm 2. Additionally we have explored the effect of attenuation in the guide, by assuming an initial intensity of 5 10 13 W/cm 2, and then having the field decay as exp( z /z a ). Here obviously z a is the field attenuation length, which is twice the power attenuation length. In Fig. 4(b), it is shown that the trapping fraction falls quickly for z a < 0.65 m, in which case the power exiting 0.8 m of guide is attenuated to below 10% of its initial value. This result may thus have been anticipated from the study of parametric dependence on power in Fig. 4(a). At present, we are now studying options for undulator construction. The bifilar helical winding approach is straightforward to build at low field, but in our design the current density is high, and the windings should be cryogenically cooled to liquid nitrogen temperatures, or pulsed. Other options include use of iron between the windings to give field enhancement, and a permanent magnet-based system. We note that a solenoid-assisted design requires the absence of iron, and also that this system could not be pulsed. Any design must have a high degree of tunability so that the field profile can be adjusted for correct acceleration program and steering. The undulator and solenoid must also be designed with a proper spin-up quasi-adiabatic transition section. A final design will of course be based on an understanding of the waveguide power-handling capabilities through experiments. Relevant measurements include not only power limits, which are most relevant to next-generation plasma beatwave accelerator experiments at Neptune [13], but mode-matching characteristics. It would be desirable to have a mode-matching horn or funnel which gives a larger mode area inside of the guide. This problem is currently being studied through analytical and computational work.

Future issues that should be addressed in the design of the next-generation Neptune IFEL experiment include the diagnosis of bunching in the system. The possibility of using the harmonics in the coherent undulator-radiation spectrum [14] to deduce the microbunching state of the beam has been studied [3]. New tools for calculating the expected coherent spectra from synchrotron radiation (as well as edge and transition radiation) based on the code TREDI [15] are now being studied at UCLA [16]. ACKNOWLEGMENTS This work is supported by U.S. Dept. of Energy grant DE-FG03-92ER40693. REFERENCES 1. R. Palmer, J. Applied Physics 43, 3014 (1972); E.D.Courant, C. Pellegrini, and W. Zakowicz, Phys. Rev. A 32, 2813 (1985). 2. S.G. Anderson, M. Loh, P. Musumeci, J.B. Rosenzweig and M.C. Thompson, in Proc. of the 9th Workshop on Advanced Accelerator Concepts, 487 (AIP Conf. Proc. 569, 2001). 3. P. Musumeci, et al., these proceedings. 4. S. Y. Tochitsky et al., Opt. Lett. 24, 1717 (1999). 5. A. Van Steenbergen, J. Gallardo, J. Sandweiss, and J. M. Fang, Phys. Rev. Lett. 77, 2690 (1996). 6. R. B. Yoder, T. C. Marshall, and J. L. Hirshfeld, Phys. Rev. Lett. 86, 1765 (2001). 7. W.Kimura et al., Phys. Rev. Lett. 86, 4041 (2001);W.Kimura et al., Phys. Rev. Lett. 92, 054801 (2004). 8. C. Sung, S. Ya. Tochitsky, and C. Joshi, Guiding of 10 µm laser pulses by use of hollow waveguides these proceedings. 9. M Borghesi, et al., Phys. Rev. E, 57, R4899 (1998). 10. Abel, T., Hirsch, J., and Harrington, J. A., "Hollow glass waveguides for broadband infrared transmission," Opt. Lett., vol. 19, pp. 1034-1036, 1994. 11. S. Reiche, J. Rosenzweig, S. Telfer, Proposal for a IR waveguide SASE FEL at the PEGASUS injector, NIM A 475 (2001) 432 435. 12. L. Friedland, Phys. Fluids 23, 2376 (1980. 13. S. Y. Tochitsky et al., Phys. of Plasmas 11, 2875 (2004). 14. Z. Huang and K. J. Kim, Phys. Rev. E 62, 7295 (2000). 15. L. Giannessi and M. Quattromini, Phys. Rev. ST Accel. Beams 6, 120101 (2003). 16. A. Flacco, et al., these proceedings.