A THz radiation driven IFEL as a phaselocked prebuncher for a Plasma Beat-Wave Accelerator

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1 A THz radiation driven IFEL as a phaselocked prebuncher for a Plasma Beat-Wave Accelerator P. Musumeci 1, S. Ya. Tochitsky, C. E. Clayton, C. Joshi, C. Pellegrini 1, J.B. Rosenzweig 1 1 Department of Physics, Department of Electrical Engineering, University of California at Los Angeles, 45 Hilgard avenue, Los Angeles, CA 995 Abstract To obtain a high quality electron beam with small energy spread in the laser driven plasma accelerator, the electrons have to be prebunched at the scale of the plasma wavelength. We study the feasibility of an experiment where an inverse free electron laser (IFEL) is used to bunch the electron beam before the injection into a plasma beatwave accelerator. It is suggested to drive the IFEL prebuncher by a THz seed radiation phase-locked to the electromagnetic beatwave through difference frequency generation process in a nonlinear crystal. Design and numerical simulations for this experiment are presented. 1. Introduction In recent years advanced high gradient accelerator experiments have taken place successfully. Proof-of-principle demonstrations using laser or electron driven plasma waves and non-plasma based structures have shown gradients much higher than conventional accelerators [1]. The focus of the current research in this field is now shifting from increasing the energy gain in short distances to delivering high quality electron beams that could be used for different applications. One of the main characteristics of any usable electron beam is the energy spread. So far all schemes for high gradient acceleration have shown 1 % energy spread. This is physically due to the experimental difficulties related to the generation and the injection of an electron beam in the high gradient accelerating field wave with a typical period of 1-3 µm. It is obvious that if the injected electron beam samples all the phases of the accelerating field, the energy spectrum at the output will be continuous. The goal of future experiments is to reduce the energy spread by reducing in some way the electron bunch length, either at the stage of electron generation, or by compressing the bunch length and synchronizing the electrons to the accelerating structure. Injection of prebunched electrons that are synchronized to the high gradient electric field wave is commonly called phase locking. The experimental challenges in acceleration of phase-locked electrons have been individuated and studied []. Recently some positive experimental results in this field have been reported. At Brookhaven National Lab, by use of the Inverse Free Electron Laser (IFEL) interaction microbunching of the electron beam on the optical scale has been demonstrated [3]. Later, in the frame of STELLA collaboration, the timed injection of these microbunches in an IFEL accelerator has been successfully realized [4]. At the Neptune Laboratory at UCLA, there is an ongoing experiment on Plasma Beat Wave Accelerator (PBWA) of electrons [1]. The experiment uses two lines of a CO laser (1.6 and 1.3 µm) to excite a relativistic plasma beat wave with acceleration gradient ~3 GeV/m. The plasma wavelength is 34 µm, requiring a bunch length of about 5-6 µm. In phase I of the experiment, currently underway, a long (>34 µm) electron bunch will be injected in the plasma structure and accelerated up to 1 MeV. Then in phase II, prebunched phase-locked electrons will be injected to achieve small energy spread. Several methods for phase-locked injection have been considered including FIR driven IFEL []. It was recognized that the main drawback of such a scheme is the need of a high-power (>1 MW) seed radiation at the wavelength of 34 µm. All feasible solutions of this issue were based on an FEL source that seriously complicates the experiment. For example, a classical FEL oscillator-amplifier scheme was suggested by Lampel et al for a 1 µm driven PBWA [5]. In this paper we address the challenge of generating such micro-bunches with characteristic length shorter than the plasma beat wavelength, phase locked with the accelerating structure. It is suggested to use the IFEL interaction between the relativistic electrons from the Neptune photoinjector and a high power electromagnetic beat-wave. We propose to generate 1 MW of 1 THz radiation by difference frequency generation (DFG) in a nonlinear crystal, mixing the two CO lines. Co-propagating the radiation with the

2 electron beam inside a short undulator achieves the bunching at the required wavelength. Moreover, because the electromagnetic radiation is generated from the same laser that excites the relativistic plasma wave, phase-locking is achieved. In the first part of the paper we illustrate the scheme, then after a study of the microbunching dynamics we present the simulation results and discuss the optimization of the experiment. In the last section we focus on possible design of GaAs nonlinear mixer for generating the required power of THz electromagnetic wave.. Inverse Free Electron Laser interaction as an efficient prebuncher at Neptune Laboratory The Neptune Laboratory at UCLA is an advanced accelerator laboratory dedicated to the study of laser plasma acceleration and high brightness electron beam. There are two main components at the laboratory: the most powerful in the world, TW-class CO laser system and a state-of-the-art photoinjector. A two wavelength 1 TW CO laser is used to drive the plasma beat-wave structure. A standard master oscillatorpower amplifier approach is used to amplify 1 ps pulses up to 1 J as presented elsewhere [6]. The electron source for the Neptune Linac is a 1.6 cell S-band RF gun driven by 66 nm photocathode laser followed by a plane-wave transformer (PWT) linac section. The electrons are accelerated inside the PWT up to 1 MeV with a small energy spread (.5%). An emittance compensation solenoid and quadrupoles for transporting and focusing the electrons are important components of the system. Small transverse emittance (6 mm-mrad) and 1 µm rms spot sizes at the interaction point are obtained. There is also a magnetic chicane for manipulations on the electron longitudinal phase space [7]. In Fig.1 we show proposed solution for the PBWA phase II experiment on injecting an electron beam prebunched on the scale of the plasma wavelength and phase locked with the accelerating structure. As shown in the picture, using a salt (NaCl) beamsplitter, a small fraction (~4 %) of the high power CO laser is split and then sent into a non-linear crystal. Here, by difference frequency mixing, as discussed in the last section of this paper, we should generate up to 1 MW of 1 THz radiation. This 34 µm wave originates from the mixing of the same two wavelengths that drive the plasma beat wave, so that it has a well-defined phase relationship with the accelerating structure. Absolute phase can then be adjusted using a delay line. The THz beam is made collinear with the electron beam and is sent through a planar undulator using a mirror with a hole. This off-axis parabolic mirror has also the function of focusing the radiation to a spot size of 7 mm located at the end of a.5 m long undulator. The electron beam coming from the linac is microbunched on the scale of 34 µm by the IFEL interaction going through the undulator magnetic field, then it is focused with the final focus triplet at the interaction point (IP) and finally it is accelerated by the relativistc plasma beatwave excited by the main fraction of the TW CO laser beam. The distance between the end of the undulator and the IP is less than 1 m. Note that for the 1 µm STELLA experiment where tolerances are tighter because of the shorter wavelength, the IFEL accelerator was located.3 m downstream of the IFEL prebuncher [4]. Fig.1: Experimental layout for THZ Inverse Free Electron Laser microbunching.

3 3. IFEL Bunching dynamics and simulation results In an IFEL [8], relativistic particles are moving through an undulator magnet; an electromagnetic wave is propagating parallel to the beam. The undulator magnet produces a non zero transverse velocity (wiggling motion) in a direction parallel to the electric vector of the wave, so that energy can be transferred between the particle and the wave. The Inverse Free Electron Laser dynamics is usually described in terms of the energy of the electron (γ) and the phase of the coupling between the wiggling motion and the electromagnetic wave (ψ). The equations of the motion for a single electron moving in a plane linearly polarized electromagnetic wave in a planar undulator magnetic field, are: γ = z ee mc JJ ( K) K sin( ψ ) ψ = k z w + k K K + l k + KK l γ JJ ( K) cos( ψ ) where k w is the undulator wave number, K is the undulator dimensionless parameter (eb/ mck w ), K l is the radiation dimensionless parameter (ee /mck) and JJ is the Bessel factor due to the planar geometry. The IFEL acts as a longitudinal lens and microbunches the electrons on the scale of the electromagnetic wavelength. 1/ bunch length (fraction of wavelength) Full IFEL equations Harmonic oscillator approximation Distance (normalized units) Fig.: Rms microbunch length as a function of normalized distance for a harmonic oscillator and an IFEL. To understand a fundamental limitation of an IFEL-microbuncher it is instructive to study the difference between the IFEL longitudinal lens compression and an ideal case of a harmonic oscillator type of interaction (Fig.). In the ideal case, the electron density evolves under linear transformation and the minimum bunch length is obtained after 1/4 of the synchrotron period with a final bunch length that depends only upon the initial energy spread. In the IFEL case, the equations are not linear and the corrections to the linear motion (expansion of the sine term in the equation for γ) are important. The IFEL reaches optimum bunching 5% later than the harmonic oscillator (at 3/8 of the calculated synchrotron period) and the minimum microbunch length is set now by the aberrations, or non-linearities of the potential (Fig.). They cause an effective emittance growth, or diluition in the longitudinal phase space. This is the limit of the IFEL as a longitudinal lens. Nevertheless, bunch lengths on the order of 1/1 the wavelength can easily be obtained, and that is well within the goals for the Phase II of PBWA. At the Neptune Laboratory, in order to achieve efficient microbunching in the small experimental area available, we need to optimize parameters of the THz IFEL. We considered here a planar permanent magnet undulator. The requirement that the undulator should geometrically match the THz beam propagating in free space with the electron beam limits the minimum gap or the maximum achievable

4 magnetic field. The undulator length sets the duration of the IFEL interaction. Obviously the choice of the undulator length depends strongly on the available electromagnetic power. For 1 MW of THz radiation and a magnetic field of.6 T, we achieve maximum bunching through the Inverse Free Electron Laser interaction after ~.5m. As it is shown in the Fig.3, having more electromagnetic power or a longer undulator doesn t significantly increase the performance of the system. The IFEL buncher efficiency reaches the limit mentioned above, considering the effects of the non-linearities and the longitudinal emittance dilution. Microbunch length (µ) FIR radiation power (MW ) Undulator length (m ) 1. Fig.3: Electron microbunch length versus electromagnetic power and undulator length. We note that the undulator requirements to get optimum bunching having 1 MW of FIR radiation available to drive the IFEL are not very demanding from the magnet construction point of view (Table1). A planar permanent magnet undulator with the Halbach scheme will easily produce these characteristics. Table 1: Undulator parameters Magnetic field.6 T Undulator wavelength 6 cm Magnet gap cm K parameter 3.1 Undulator length.54 m Our preliminary calculations are well confirmed by full 3D simulations. The results are shown in Fig. 4. The simulations are performed using TREDI [9], a 3d Lienerd-Wiechert based, 4 th order Runge Kutta, Lorentz solver code to track the electrons through the undulator magnetic field and the laser field. The input electron beam has the parameters typically running at Neptune laboratory, 4 ps (rms) long, emittance 6 mm-mrad, charge 3 pc. The radiation is assumed to be a 1 MW THz wave, focused in vacuum to 7 mm focal spot. Fig.4 shows a snapshot of the electron longitudinal phase space at the end of the undulator. The longitudinal microbunching on the scale of the plasma wavelength is evident within the 4 ps (rms) long beam envelope. Fig.4b presents the phase histogram over the 34 µm wavelength. The microbunches have a width of ~3 µm - much smaller than the plasma wavelength - which should allow us to load electrons into the best accelerating fields, giving a relatively monochromatic output spectrum. Obviously because the

5 .1 Bunching in IFEL. Histogram of phase distribution.5 deltap/p % z (m) Fig. 4: Simulation results for THz IFEL microbunching phase THz IFEL driving radiation is locked in phase with the plasma beatwave, all these microbunches are phaselocked with the accelerating structure. We also analyzed the relevance of diffraction, spectral bandwidth and space charge, that are usually not included in the simple analytic treatment of the IFEL interaction, but that are potentially critical for the IFEL interaction. It is important to take into account effect of the diffraction of the long wavelength (34 µm) electromagnetic radiation. Including diffraction effects in the analysis is necessary any time the radiation Raleigh range is shorter than the undulator length [1]. Slow variation of electric field amplitude and phase along the undulator effectively change the resonant condition along the undulator. With a 7 mm spot size, the Raleigh range for THz radiation is 5 cm, so that in our case this effect is not very important. If less FIR power is available, a guiding system rather than tighter focusing should be implemented to avoid this diffraction effect. As was reported by Corkum et al. [11], significant broadening of the 1 µm radiation in the bulk of nonlinear material could be observed due to high non-linearity. This, of course, could result in broader than Fourier transformed limited bandwidth of THz radiation. We simulated the effects of spectral sidebands to the bunching process. As it is shown in Fig.5a, the bunching efficiency starts to decrease when the spectrum becomes larger than 1 GHz FWHM. This frequency interval is more than 1 times greater than the Fourier limited spectral width for 1 ps pulses. Estimations have shown that at pump intensity ~3 GW/cm one should not expect spectral broadening above 5 GHz. More detailed study of this issue is required. Another question is what happens when we increase the number of electrons in the microbunches. The longitudinal space charge fields counters the IFEL bunching force, so that the IFEL interaction has to stay on for a longer period of time to get to the optimum bunching point. No significant effect is seen for charge up to 3 pc (Fig.5b) Relative undulator length Spectral width (GHz) Relative undulator length Charge (pc) Fig. 5: Undulator length for the optimum bunching as a function of (a) the spectral width of radiation and (b) the electron beam charge. Optimization of the system in our case means getting more electrons with a smaller phase spread in order to have better energy spread after acceleration in the PBWA. Further improvement in this respect (excluding

6 adiabatic capture or undulator tapering from the consideration) is possible with additional modulation of the e-beam injected in the IFEL structure. Here we briefly consider several options. One approach is to have pre-bunched electrons generated at the cathode with a modulated UV laser as described in []. Another possibility is to utilize the Neptune magnetic chicane in order to pre-compress the electron beam. In this case the problem of the jitter of the RF clock with respect to the laser beatwave clock has to be addressed. The results of the simulations for these options are shown in Fig.6. 1 Histogram of phase distribution.4 Histogram of phase distribution %.5 % phase phase Fig. 6: Phase distribution for: a) electrons prebunched at the photocathode through UV driving laser modulation. b) electron beam precompressed in the magnetic chicane. 4. THZ radiation source The key element of a laser-driven IFEL prebuncher is a high-power source of optical radiation. We propose to use difference frequency mixing process in a nonlinear crystal to produce high-power driving THz radiation (>1 MW) for the IFEL buncher. It is known that low DFG efficiency is a serious problem for the FIR spectral range. The highest FIR power generated by now using this method is a few kw [1]. At the same time 1 ps, two-wavelength CO laser pulses from the Neptune Lab system are naturally very well suited for producing high-power FIR radiation. Nonlinear frequency conversion efficiency increases significantly for short pulses: first owing to the power increase and second, this power can be coupled into a crystal because of the higher surface damage threshold for shorter pulses. Three methods to generate high-power 34 µm radiation by CO laser difference frequency mixing in a nonlinear crystal have been considered. They are: standard birefringent phase matching, quasi-phase matching with periodic structures, and noncollinear phase matching in isotropic materials. FIR generation by difference frequency mixing is possible in the birefringent materials ZnGeP, AgGaSe and Te, which are transparent for both MIR (1 µm) and FIR (34 µm) radiation. Collinear phase-matched DFG has been reported in ZnGeP [13,14]. Our calculations have shown that up to 39 MW/cm can be generated in FIR with a 1 cm long crystal at 5 GW of incident power. However, serious difficulties are encountered in growing large-aperture ZnGeP crystals that makes achieving a 1 MW power level at 34 µm very challenging. Another problem is that this material requires Type II interaction for DFG. The later hinders it s application for a high-power, two-wavelength CO laser system. There are some cubic nonlinear semiconductors such as InSb, GaAs, etc., which can be used for FIR DFG with CO lasers. But these crystals being cubic lack birefringence. Therefore other methods for phasematching in isotropic crystals must be considered. Even in isotropic crystals waves are propagating in phase over the coherence length (L c ), the distance over which the relative phase changes by π. For FIR difference frequency mixing the coherence length is relatively long. For example, L c is 7 µm in the case of GaAs. This allows for the generation of FIR radiation in thin InSb [15] and GaAs [16] slabs. However, the DFG efficiency is very low because of the short L c. Quasi-phase matching is a technique for phase matching nonlinear optical interactions in which the relative phase is corrected at regular intervals using a stack of plates or periodically grown structure. This technique progressed significantly during the last decade and it has a bright future for the FIR region where production of structures is much easier. Unfortunately GaAs structures until now have had the status of experimental devices and are not available.

7 µm Θ=.38 Fig. 7: Schematic wave vector diagram for noncollinear DFG (a) and optical scheme of a GaAs nonlinear optical device (b). Internal FIR power versus pump power density on the 1.3 µm line calculated in assumption of equal power on each line (c). Another approach to obtain phase-matched FIR DFG in isotropic nonlinear materials is noncollinear mixing of two laser beams. This is possible in any crystal which possesses anomalous dispersion between the incident CO laser radiation and FIR difference frequency radiation. Zernike [15] and Aggarwal et al.[17] have demonstrated noncollinear mixing of two CO laser beams in liquid helium cooled semiconductor samples. By using a 1 cm long GaAs crystal of folded geometry, up to 4kW in the 1 µm region was generated [1]. Several reasons make GaAs the best candidate for generation of high-power 34 µm radiation using a noncollinear DFG scheme. It has a relatively high value for the electro-optic nonlinear coefficient d=43 pm/v. GaAs with high resistivity (> 1 8 Ωcm) is transparent in the FIR beyond µm at room temperature as well as in the 1 µm region of the CO laser [18]. High-quality, single crystals with a diameter of 15 cm and length up to 1 cm are commercially available. The expected surface damage threshold could reach 1 GW/cm for 1 ps CO laser pulses. We present results of calculations for a FIR nonlinear device made of GaAs below. For noncollinear phase-matched mixing of two laser lines of frequencies ω 1 and ω (ω 1 >ω ) to generate the difference-frequency radiation at ω 3, the conditions of photon energy and momentum conservation require that where r k 1, r k and r k 3 are the respective vectors for radiation of frequencies ω 1 (1.3 µm), ω (1.6µm), ω 3 (33 µm). Fig 7a. shows the direction of propagation of the incident beams and that of the difference frequency radiation inside the crystal. According to Aggarwal et al. [17], angles θ and ϕ are given by k k 3 Θ Sin( 1 (n ω ) (n1 ω n ω ) Θ) = 4n n ω ω 1 1 k 1 ϕ=1.6 b a ϕ µm FIR 34 µm ω 3 = ω 1 ω and r k 3 = r k 1 r k Internal FIR Power Density, MW/cm 1/ ; Cosϕ = c ω 1+( )Sin (.5Θ) ω ( ω 1 ω L = 5 cm L = 3 cm L = 1 cm 1.3 µm Power Density (P 1.3 =P 1.6 ), GW/cm ω 3 )Sin (.5Θ) 1

8 Refractive indices for insulating GaAs are n 1 n =3.8 at 1 µm region, and n 3 =3.61 at 34 µm [18]. For these values of refractive index we obtain Θ=.7 and ϕ=1.64. The corresponding external phasematching angle is.38 degrees. The angle at which FIR radiation propogates inside the crystal is greater than the critical angle for total internal reflection. Therefore, as it shown in Fig.7b, the output face of the GaAs crystal has to be cut at 1 degrees to release the newborn radiation. We also calculated the 34 µm power produced inside of a GaAs crystal for different interaction lengths L using standard Boyd and Kleinman relations [19]. For an isotropic material, the interaction length is limited only by the pulse length because of group velocity dispersion. For 1 ps pulses, the maximum L is approximately 6 cm. The above calculations were done assuming. cm -1 absorption at 34 µm [18] and neglecting absorption at 1 µm. Results are presented in Fig. 7c. Note that hatched section in Fig. 7c indicates our provisional zone for operation where the pump intensity of -4 GW/cm is more than two times less than the damage threshold for GaAs. As can be seen in Fig,7c the 1 MW level could be achieved even for a 1 cm incident area beam with L=5 cm and total pump power density GW/cm. FIR power level could be easily scalable beyond 1 MW by increasing the beam diameter. A typical beam diameter of the Neptune TW two-wavelength CO laser system is 1 cm with an intensity 1 GW/cm [7]. This beam, in combination with available large-aperture GaAs crystals, opens possibility to create a unique high-power 1-1 GW source of coherent radiation in the range of 7 µm mm (.-4 THz) on the base of noncollinear frequency mixing of CO laser lines. 5. Conclusions A feasibility study of phase-locked acceleration of electrons in a plasma based accelerating structure has shown that a THz IFEL microbuncher is a promising scheme. For Neptune PBWA experiment, it is possible to generate high-power (>1 MW) 34 µm radiation by using noncollinear DFG in GaAs. Optimization of the THz driven IFEL parameters demonstrates that requirements for the phased-injection system could be easily achieved. 6. References 1. C. Joshi and P. Corkum, Physics Today, 49, 36 (1996). C.E. Clayton, L. Serafini, IEEE Trans. Plasma Science, 4, 4 (1996). 3. Y. Liu et al., Phys. Rev. Lett., 8, 4418, W. Kimura et al., in Proceedings of Advanced Accelerator Concepts, Santa Fe, NM, 5. M.Lampel, C. Pellegrini, and R.Zhang, in Proc. Particle Accelerator Conf., Dallas, TX, S. Anderson et al, Proc. Particle Accelerator Conf., Chicago, IL, 1 7. S.Ya. Tochitsky, C. Filip, R. Narang, C.E. Clayton, K.Marsh, and C. Joshi, Optics Letters, 4, 1717 (1999). 8. E. D. Courant, C. Pellegrini, W. Zakowicz, Phys. Rev. Lett., 3, 813, L. Giannessi et al., Nucl. Instr. Meth., 393, 434, P. Musumeci, C.Pellegrini, J.B. Rosenzweig, A. Varfolomeev, S. Tomalchev, T. Yarovoi, Proc. Particle Accelerator Conf.,Chicago, IL, P.B. Corkum, P.P. Ho, R.R. Alfano, and J.T. Manassah Optics. Lett. 1, 64 (1985). 1. G.D. Boyd, T. J. Bridges, and C.K.N. Patel, and E. Buehler, Appl.Phys. Lett. 1, 553 (197). 13. V.V. Apollonov, R. Bocquet, A. Boscheron, A.I. Gribenyukov, V.V. Korotkova, C. Rouyer, A.G. Suzdal tsev, Yu. A. Shakir, Int. Journal Infrared M. Waves, 17, 1465 (1996). 14. F. Zernike, Phys. Rev. Lett., 931 (1969). 15. T.J. Bridges, A.R. Strand, Appl.Phys. Lett., 38 (197). 16. R.L. Aggarwal, B. Lax, and G. Favrot, Appl.Phys. Lett., 39 (1973). 17. N. Lee, B. Lax, and R.L. Aggarwal, Optics Commun. 18, 5 (1976). 18. C.J. Johnson, G.H. Sherman, and R. Weil, Appl. Optics, 8, 1667 (1969). 19. G.D. Boyd, D.A. Kleinman, J.Appl.Phys. 39, 3597 (1968).

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