Generation of High-Power, Tunable Terahertz Radiation from Laser Interaction with a Relativistic Electron Beam

PHYSICAL REVIEW ACCELERATORS AND BEAMS 20, 050701 (2017) Generation of high-power, tunable terahertz radiation from laser interaction with a relativistic electron beam Zhen Zhang,* Lixin Yan, Yingchao Du, Wenhui Huang, and Chuanxiang Tang Department of Engineering Physics, Tsinghua University, Beijing 100084, China † Zhirong Huang SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA (Received 6 February 2017; published 5 May 2017) We propose a method based on the slice energy spread modulation to generate strong subpicosecond density bunching in high-intensity relativistic electron beams. A laser pulse with periodic intensity envelope is used to modulate the slice energy spread of the electron beam, which can then be converted into density modulation after a dispersive section. It is found that the double-horn slice energy distribution of the electron beam induced by the laser modulation is very effective to increase the density bunching. Since the modulation is performed on a relativistic electron beam, the process does not suffer from strong space charge force or coupling between phase spaces, so that it is straightforward to preserve the beam quality for terahertz (THz) radiation and other applications. We show in both theory and simulations that the tunable radiation from the beam can cover the frequency range of 1–10 THz with high power and narrow-band spectra. DOI: 10.1103/PhysRevAccelBeams.20.050701 I. INTRODUCTION which copropagates with the electron beam inside an undulator can create energy modulation on the scale of High-brightness electron beams have been used to drive the laser wavelength. The energy modulation can be free-electron lasers (FELs) [1–3], high-intensity terahertz converted into density modulation by letting the beam (THz) radiation [4,5], advanced accelerators [6–8] and beyond. The precise manipulation of the beam phase-space pass through a longitudinally dispersive element, e.g., a magnetic chicane. However, the typical laser wavelength is distribution is often desired to advance the development in ∼800 the above-mentioned fields. Recently, there has been great usually nm, which is much shorter than the THz interest in the generation and control of high frequency wavelength. In this case, the concept of difference fre- structure in the current profile of relativistic electron beams. quency can be used to approach THz range with two The bunched beam at picosecond (ps) and sub-ps scale can wavelengths of energy modulation in two separated undu- – be used to produce intense narrow-band THz radiation [5,9] lator sections [25 27]. and resonant wakefield excitation [10–13]. Besides, in For the laser-based modulation method, since it is FELs, sub-ps bunched beams have been applied to generate performed directly on a relativistic electron beam, the multicolor x rays [14] based on the sideband effect [15]. process will not suffer from the strong space charge force There are several methods proposed and studied or coupling between transverse and longitudinal phase for the generation of ps and sub-ps bunching in electron spaces, which is critical to preserve the beam quality for beams, including exchanging transverse modulation to further applications. For example, in resonant wakefield longitudinal distribution [16,17], direct modulating the excitation, the transverse focus size of the electron beam drive laser [18–21] and converting wakefield induced needs to match the plasma density [16], which puts a chal- energy modulation to density bunching [22–24]. As the lenging constraint on the transverse normalized emittance. development of the state-of-the-art laser technologies, In this paper, we propose a method based on the slice laser-based manipulation of the electron beam has been energy spread modulation (SESM), rather than energy implemented widely. An external-injected laser pulse modulation, to generate sub-ps density bunching in a relativistic electron beam. The slice energy spread of the *zhen‑[email protected] beam will be modulated in a laser heater [28,29] if the laser † [email protected] intensity envelop varies periodically. The laser heater has been used widely in the FEL facilities [30–33].Thenaftera Published by the American Physical Society under the terms of dispersive section, strong density bunching can be obtained the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to whose wavelength depends on the scale of laser envelope the author(s) and the published article’s title, journal citation, variation, not the laser wavelength. Similar methods have and DOI. been adopted to generate THz radiation in a storage ring [5] 2469-9888=17=20(5)=050701(9) 050701-1 Published by the American Physical Society ZHANG, YAN, DU, HUANG, TANG, and HUANG PHYS. REV. ACCEL. BEAMS 20, 050701 (2017) and multicolor x rays [14]. In this paper, we present detailed where δ0 is the relative energy deviation and I0 is the theoretical analysis on the conversion from SESM to beam current. Due to the laser modulation, the slice energy density bunching and compare it with simulation results. spread is assumed to be We will also provide an example to produce tunable intense narrow-band THz radiation ranging from 1 to 10 THz. σδðz0Þ¼σ¯½1 þ A sinðk0z0Þ; ð2Þ This method is well suited with the configuration of linear accelerator facilities and is of great potential in applications. where σ¯ is the average rms slice energy spread and This paper is organized as follows. In Sec. II, detailed 0 <A<1 is the relative modulation depth. The longi- theoretical analysis on the conversion from SESM to density tudinal phase space is not uniform but integration over δ0 bunching is presented. It is found that the double-horn slice yields uniform current I0. energy distribution from the laser modulation will help An energy chirp is added in the following linac section increase the available bunching factor. In Sec. III,we by δ ¼ δ0 þ hz0, and then the longitudinal dispersion propose a dedicated beam line to generate intense occurs in a magnetic chicane as narrow-band THz radiation based on the SESM method. Simulations are performed to demonstrate the tunable z ¼ z0 þ R56δ ¼ z0 þ R56ðδ0 þ hz0Þ: ð3Þ bunching frequency. Some discussions about the advantages and requirements of the proposed method will be presented in Sec. IV. Lastly, we will give a short summary in Sec. V. Here we ignore the scale of relative energy spread due to the change of beam average energy, which can be absorbed into other parameters. The density modulation appears after II. THEORETICAL ANALYSIS the chicane with the bunching factor as follows: Let us assume the initial beam is uniform in current, but Z σ ðz Þ has a Gaussian slice energy spread δ 0 that is a function 1 −ikz z bðkÞ¼ dδdze fðδ;zÞ: ð4Þ of the longitudinal coordinate 0 within the beam. The I0 distribution can be written as 2 Using the Liouville theorem that fðδ;zÞdδdz ¼ I0 δ0 f0ðδ0;z0Þ¼pffiffiffiffiffiffi exp − ; ð1Þ f0ðδ0;z0Þdδ0dz0 and making a change of variable from 2πσ ðz Þ 2σ ðz Þ2 δ 0 δ 0 δ0 to η ¼ δ0=½1 þ A sinðk0z0Þ, we obtain Z 1 δ2 bðkÞ¼ dδ dz e−ikð1þhR56Þz0−ikR56δ0 pffiffiffiffiffiffi − 0 0 exp 2 2πσδðz0Þ 2σδðzÞ Z 1 η2 −ikð1þhR56Þz0−ikR56η½1þA sinðk0z0Þ ¼ dηdz0e pffiffiffiffiffiffi exp − 2πσ¯ 2¯σ2 Z Z 1 η2 X ¼ pffiffiffiffiffiffi dη −ikR η − dz e−ikð1þhR56Þz0 J ðkR ηAÞe−ink0z0 : ð Þ exp 56 2 0 n 56 5 2πσ¯ 2¯σ n k2R2 σ¯2ð1−bAÞ2 k2R2 σ¯2ð1þbAÞ2 Integration over z0 yields nonvanishing bunching at a − 1 56 − 1 56 b1 ¼ e 2 − e 2 : ð7Þ the wave number kn ¼ nk0=ð1 þ hR56Þ with the bunching 2 factor n Z ð−1Þ η2 The optimal chicane setting to achieve the largest bunching −iknR56η− 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi bn ¼ pffiffiffiffiffiffi dηJnðknR56AηÞe 2¯σ : ð6Þ 2 2πσ¯ factor is to satisfy jk1R56σ¯j ≈ 2 þ 0.5A , and the maxi- mum bunching factor is ∼0.27. Numerical calculation of Eq. (6) can be used to find the It should be noted that there is an assumption for the exact bunching factor and current distribution. above derivations that the beam has a Gaussian slice energy Here we focus only on the fundamental modulation wave distribution. This assumption, however, is not always true if number k1 ¼ k0=ð1 þ hR56Þ, the bunching factor b1 is we use a laser heater to modulate the beam’s slice energy plotted with a solid line for different k1R56σ0 in Fig. 1. The spread. In Ref. [29] it is found that when the laser size is expression of b1 can be simplified if we approximate much larger than the electron beam size, the resulting J1ðxÞ ≈ a sinðbxÞ for jxj < 3 with a ¼ 0.58, b ¼ 0.85, then energy profile is a double-horn distribution, which will not 050701-2 GENERATION OF HIGH-POWER, TUNABLE … PHYS. REV. ACCEL. BEAMS 20, 050701 (2017) TABLE I. Beam parameters before the modulator in the simulations. Parameter Value Units Electron beam Charge 500 pC Beam energy 135 MeV Current profile flattop ÁÁÁ Bunch length ∼10 ps Intrinsic slice energy spread 10−4 ÁÁÁ Normalized emittance 1 mm-mrad rms beam size 200 μm Modulator Laser wavelength 800 nm Undulator period 5 cm FIG. 1. Bunching factor evolution versus k1R56σ¯ with A ¼ 0.9 Period number 10 ÁÁÁ and different slice energy distributions: (solid line) Gaussian Laser waist size 1.5 mm distribution, (dashed line) Gaussian distribution but the bunching Laser stacking separation 0.5 (0.25a)ps factor is calculated by Eq. (7) and (dotted line) double-horn rms laser pulse length 60 (30) fs distribution from laser heater. Laser power 1 (0.26) GW aThe numbers in brackets are the parameters for the 4 THz case.

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