Observation of coherent undulator radiation in THz region

Accepted Manuscript Observation of coherent undulator radiation in THz region Shigeru Kashiwagi, Taro Abe, Hirotoshi Saito, Fujio Hinode, Ken Kanomata, Sadao Miura, Toshiya Muto, Ikuro Nagasawa, Ken-ichi Nanbu, Shingo Ninomiya, Nobuyuki Nishimori, Yuki Saito, Ken Takahashi, Hiroyuki Hama PII: DOI: Reference:

S1350-4495(17)30835-6 https://doi.org/10.1016/j.infrared.2018.08.011 INFPHY 2664

To appear in:

Infrared Physics & Technology

Received Date: Revised Date: Accepted Date:

15 December 2017 1 August 2018 10 August 2018

Please cite this article as: S. Kashiwagi, T. Abe, H. Saito, F. Hinode, K. Kanomata, S. Miura, T. Muto, I. Nagasawa, K-i. Nanbu, S. Ninomiya, N. Nishimori, Y. Saito, K. Takahashi, H. Hama, Observation of coherent undulator radiation in THz region, Infrared Physics & Technology (2018), doi: https://doi.org/10.1016/j.infrared.2018.08.011

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Observation of coherent undulator radiation in THz region Shigeru Kashiwagia,#, Taro Abea, Hirotoshi Saitoa, Fujio Hinodea, Ken Kanomataa, Sadao Miuraa, Toshiya Mutoa, Ikuro Nagasawaa, Ken-ichi Nanbua, Shingo Ninomiyaa, Nobuyuki Nishimorib, Yuki Saitoa, Ken Takahashia and Hiroyuki Hama a a

Research Centre for Electron Photon Science (ELPH), Tohoku University, 1-2-1 Mikamine, Taihaku, Sendai 982-0826, Japan

b

National Institutes for Quantum and Radiological Science and Technology, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan

Abstract The generation of coherent THz radiation from femtosecond electron bunches passing through an undulator was demonstrated with a test accelerator as a coherent terahertz source (t-ACTS) at Tohoku University. The velocity bunching scheme in the traveling wave accelerating structure was employed to generate electron bunches much shorter than the THz wavelength. The electron bunch length was measured with the spectrum analysis method for coherent transition radiation. A 2.5-m long undulator with 25 periods and peak magnetic field of 0.41 T was utilized to generate the tunable coherent undulator radiation ranging from 2.6 to 3.6 THz at the t-ACTS. The measured frequency spectrum and spatial distribution of the coherent undulator radiation are presented. PACS: 41.60.Ap, 41.60.-m, 52.59.Ye Keywords: Electron beam, coherent radiation, undulator radiation

1.

Introduction

The relativistic and femtosecond electron bunches passing through an undulator are capable of generating high intensity, coherent, and narrowband radiation in the THz wavelength region. The coherent THz undulator radiation having polarization control ability can be used for various types of scientific investigations and applications such as circular dichroism spectroscopy of biomolecules [1]. A test accelerator as a coherent terahertz source (t-ACTS) is currently under development at the Research Center for Electron Photon Science (ELPH) in Tohoku University [2–4], wherein extremely short electron bunches are used to generate intense coherent THz radiation. The accelerator system consists of a specially designed S-band radio frequency (RF) gun [5], alpha-magnet with an energy slit, 3-m-long S-band accelerating structure, and 2.5-m terahertz undulator. The t-ACTS injector system can deliver small emittance and short electron beams by implementing the velocity bunching scheme, where a traveling wave structure is utilized as a bunch compressor [6]. Short electron bunches were employed to generate coherent undulator radiation in the THz wavelength region in the present study.

_________________________________________

#

Corresponding author: [email protected], Tel: +81-22-743-3434; fax:+81-22-743-3402.

2.

Undulator radiation from short electron bunch

The radiation spectrum from the electron bunch can be written as

is the number of electrons in the bunch, I is the radiation intensity,  is the radiation frequency, and  is the

where

solid angle of the radiation. The three-dimensional form factor is defined by

and

are the wave vector toward the observation point and the three-dimensional charge distribution of the

electron bunch, respectively. If the form factor is sufficiently large, the radiation intensity from the electron bunch is proportional to the square of the electron number

. By assuming Gaussian charge distribution in both the

longitudinal and transverse directions with rotational symmetry about the z-axis, the charge distribution function is given by

where

and

are the transverse and longitudinal beam sizes, respectively. The three-dimensional form factor can

be expressed as

where

and

for the observation angle

with respect to the z-axis.

Figure 1 shows the three-dimensional form factor as a function of the ratio between the radiation wavelength the bunch length

for different transverse sizes

The angular spread

and transverse size

and observation angles

and

.

of the undulator radiation at the undulator center are expressed in

terms of the undulator and electron beam parameters as follows:

where

,

,

, and

are the period length, the number of periods of the undulator, and the transverse size and

angular spread of the electron beam, respectively. The undulator and typical electron beam parameters for the generation of coherent undulator radiation at t-ACTS are ,

, and

,

,

with the betatron function

, . The angular spread and

transverse size of the undulator radiation for the THz wavelength of 300 m are governed by the diffraction property of the undulator radiation and are given by

and

.

Therefore, the undulator radiation in the THz region is diffraction limited and has sufficient spatial coherence. The form factor in the case of the t-ACTS is shown in Fig. 1. When the length of the electron bunch is compressed to one-tenth of the radiation wavelength, the three-dimensional form factor is approximately 0.72 and the undulator radiation has spatial and temporal coherence. The electrical radiation field of a moving electron is derived from the Lienard–Wiéchert potential [7, 8]. In order to obtain the undulator radiation field, the electron trajectory in an undulator was calculated with the Runge–Kutta

method. The undulator magnetic field distribution necessary for the electron trajectory calculation was derived from a three-dimensional magnetic field calculation program based on a magnetic charge method [9]. The undulator radiation field calculated for a single electron was used to obtain the undulator radiation field of an electron bunch with longitudinal Gaussian distribution of 

The spectrum of the undulator radiation was derived by the Fourier

transform of the electrical field. The electron energy, K-value, and the number of undulator periods were 30 MeV, 3.88, and 25, respectively. The wavelength of the fundamental radiation was approximately 120 m (2.5 THz). Figures 2 and 3 show the electrical fields and spectra of the undulator radiation, respectively. Although the radiation spectrum has higher harmonics for a single electron (Fig. 3(a)), the higher harmonics are suppressed for the Gaussian electron bunch of 

(Fig. 3(b)) The temporal profile of the undulator radiation field is almost a sinusoidal

wave for the Gaussian electron bunch of

 as shown in Fig. 2(b). The coherent undulator radiation has a

periodic structure corresponding to the number of undulator periods. If the bunch length is longer than the radiation wavelength, the periodic structure of the undulator radiation is smeared and it disappears.

3.

Experimental setup

Figure 4 shows the beam line layout of the t-ACTS accelerator system. The beam diagnostic section is the part between the accelerating structure and the undulator. The beam emittance and Twiss parameters were measured by using the beam profile monitors with the phosphor screen or the aluminum-coated mirror. The aluminum-coated mirror allows the generation of transition radiation and reflects the undulator radiation. One Michelson interferometer (M1) was installed to measure the spectrum of the coherent transition radiation (CTR) emitted from the short electron bunches, whereas the electron beam bunch length was deduced from the radiation spectrum. An additional Michelson interferometer (M2) was installed to measure the characteristics of the undulator radiation. A CVD diamond with a thickness of 300 m was employed as an output vacuum window for the THz radiation. In the velocity bunching scheme, the bunch length of the electron beam after compression depends strongly on the longitudinal phase space distribution of the electron bunch and the phase of the beam injection into the accelerating structure. To manipulate the longitudinal phase space distribution, a special S-band thermionic cathode RF gun, which is called an independently tunable cells (ITC) RF gun, was developed. The phase of the beam injection into the accelerating structure was adjusted to produce a short electron bunch by maximizing the radiation power of the CTR at the diagnostic section. From the spectrum analysis of the CTR, the bunch length of the electron beam was estimated to be compressed to approximately 80 fs [10]. To produce the THz undulator radiation, the electron beam energy should be lower, whereas the K-value and period length of the undulator should be large. We developed the THz undulator, which is a planer Halbach-type undulator comprising solely of permanent magnet (Nd-Fe-B) blocks with TiN coating [11, 12]. The longitudinal magnetized blocks were installed at both ends of the undulator in order to align the injection axis with the oscillation axis of the beam. The undulator gap changed horizontally because of which the electron beam oscillated in the vertical plane. The period length and the number of periods were 100 mm and 25, respectively. Each magnet block size was 110×65×25 mm3 (width × height × longitudinal). The gap could be changed in the range of 54~110 mm, and the minimum gap was limited by the installation of the beam pipe. The peak of the magnetic field strength was approximately 0.41 T at the 54-mm gap. This undulator produced terahertz radiation of wavelength 300~136 μm (1.0~2.2 THz) with the 19-MeV electron beam.

The planar undulator produces a natural focusing of the electron beam in the transverse dimension normal to the undulation plane. The focusing strength is inversely proportional to the square of the beam energy. Low-energy electron beams are employed for the generation of undulator radiation in the THz region; therefore, natural focusing is an important issue here. To retain the small beam size of the electron beam in the undulator, the Twiss parameter of the injection beam should be optimized to compensate for the natural focusing.

4.

Observation of coherent undulator radiation

One of the peculiar properties of coherent radiation from an electron bunch is that the radiation intensity is proportional to the square of the number of electrons in the bunch, as described by Eq. (1). The intensity of the undulator radiation was measured by using a pyroelectric detector, and the signal from the detector was recorded as a function of the electron beam current. The beam current was varied by using a mechanical slit located downstream of the accelerating structure. In Fig. 5, the radiation intensity is plotted as a function of the micro-bunch charge; the solid line indicates the expected trend of the coherent radiation. The radiation power clearly increased in proportion to the square of the bunch charge; therefore, we could confirm the generation of coherent undulator radiation. The frequency spectrum of the undulator radiation was measured by a Michelson interferometer (M2). The optical path length in one direction of the interferometer was varied by changing the mirror position; as a result, the interferometer generated the interferogram of the undulator radiations. The entire interferometer system was enclosed and continually purged with dry nitrogen to avoid the strong absorption of the THz wave by the water vapor. Figure 6 (a) shows the measured interferogram, obtained by moving a mirror by 5-

steps over a distance of 5 mm. This

interferogram indicates that the coherent undulator radiation was being produced. As mentioned in Section 2, the electric field distribution of the coherent undulator radiation has a periodic structure corresponding to the number of undulator periods. Therefore, the interference pattern also has a periodic structure that is approximately twice the number of undulator periods, as shown in Fig. 6 (a). Figure 6 (b) shows the frequency spectrum of the coherent undulator radiation. The frequency resolution of the spectrum was 30 GHz in the spectrum measurement. The center frequency of the undulator radiation was approximately 2.88 THz (

), and the frequency spread was 0.13

THz (FWHM). The bandwidth of the undulator radiation was evaluated at approximately

, where

is the

number of undulator periods. The measured bandwidth was approximately 4.5%, which is consistent with the estimation. The frequency change of the undulator radiation was investigated by varying the undulator gap and the frequency of the radiation as a function of the undulator strength parameter, as shown in Fig. 7. The frequency of the undulator radiation

is given by

, where

are the speed of light, the electron beam

energy, period length, and strength parameter of the undulator, respectively. Curve fitting was performed for the measured data to find the beam energy. The relation between the undulator gap and the magnetic field strength was measured before the beam experiment. The beam energy derived from the curve fitting was 31.1 MeV in this measurement. Because the detector was not calibrated in this experiment, the absolute value of the intensity of the undulator radiation could not be measured. We evaluated the intensity of the coherent undulator radiation from the electron beam and the undulator parameters. The radiation wavelength for the fundamental radiation was 115 μm (2.6

THz), and the pulse duration of the radiation was 9.6 ps and included 25 wave cycles. The radiation energies in the micro-pulse and macro-pulse were 25 nJ and 144 μJ, respectively. The spatial distribution of the undulator radiation was measured by scanning the detector position across the radiation axis. For this measurement, the pyroelectric detector was located at 1.8 m from the center of the undulator. The polarization components in both the vertical and horizontal directions were obtained by installing a wire grid polarizer (GS57207, SPECAC; wire diameter of 10 m, period of 25 m) in front of the pyroelectric detector. The frequency of the undulator radiation was approximately 2.7 THz with K = 3.8. Figure 8 shows the measured vertical and horizontal polarized components of the undulator radiation. The radiation intensity of the vertical polarized component was much stronger than the horizontal one. The aspect ratio of the vertically polarized profile shown in Fig. 8(a) was in good agreement with the calculation result. On the other hand, a weak intensity peak on the radiation axis was observed in the measured horizontally polarized profile. Because this peak does not appear on the axis in the calculation of a single electron, it is presumed that the cause is due to the emittance of the electron beam. The polarization properties of the coherent undulator radiation are currently being investigated using three-dimensional calculations.

5.

Conclusion

We are in the process of developing an accelerator based coherent THz source (t-ACTS) at Tohoku University. Extremely short electron bunches were employed to generate coherent radiation and coherent undulator radiation in the frequency range of 2.6–3.6 THz with the t-ACTS. The experimental results clearly indicated the properties of coherent radiation, such as the radiation intensity being proportional to the square of the bunch charge. The interferogram measured by using the Michelson interferometer characterized it as coherent undulator radiation. The vertical and horizontal polarization components were also measured by using a wire grid polarizer. The intensity of the coherent undulator radiation was evaluated from the electron beam and undulator parameters in the experiment. The radiation wavelength for the fundamental radiation was 115 μm (2.6 THz), and the radiation energies in the micro-pulse and macro-pulse were 25 nJ and 144 μJ, respectively. Further research with regard to coherent undulator radiation will lead to new applications of THz radiation. ACKNOWLEDGMENTS We would like to thank Dr. H. Zen for his useful discussion regarding the measurement system for the THz undulator radiation. This work was partially supported by the Grant-in-Aid for Scientific Research (B) 25286084 and Grant-in-Aid for Challenging Exploratory Research 15K13401, Ministry of Education, Culture, Sports, Science and Technology, Japan. REFERENCES [1] J. Xu et al., Proc. of the SPIE, 5268, (2004) 19–26. [2] H. Hama et al., Energy Procedia 9 (2011) 391–397. [3] S. Kashiwagi et al., Energy Procedia 89, (2016) 346–352. [4] S. Kashiwagi et al., Proc. of LINAC2014, (2014) 1178.

[5] F. Hinode et al., Proc. of IPAC’10, (2010) 1731. [6] L. Serafini and M. Ferrario, AIP Conf. Proc. 581, (2001) 87–106. [7] J.D. Jackson, (1998) [1962]. Classical Electrodynamics (3rd ed.). New York: John Wiley & Sons. [8] K.-J. Kim, AIP Conference Proceedings, 184 (AIP, 1989) 565–632. [9] G. Isoyama, Rev. Sci. Instrum. 60 (1989) 1826. [10] H. Hama et al., Int J Opt Photonic Eng, 2:004, (2017). [11] F. Hinode et al., Nucl Instr. and Meth., A637 (2011) S72–S75. [12] Y. Tanaka et al., Proc. of FEL2011, (2011) 413-416.

Figure 1: Form factor as a function of the ratio of radiation wavelength to bunch length for different transverse beam sizes.

Figure 2: Electrical fields of the undulator radiation from (a) a single electron and (b) a Gaussian bunch of t =100 fs.

Figure 3: Radiation spectrum for (a) a single electron and (b) a Gaussian bunch of t =100 fs.

Figure 4: Beam line layout of the experimental apparatus.

Figure 5: Beam current dependence of the undulator radiation. Solid circles show the radiation power measured using a pyroelectric detector. Solid and dashed lines indicate the expected quadratic and linear dependences, respectively.

Figure 6: (a) Measured interferogram of the coherent undulator radiation; (b) derived frequency spectrum from the interferogram of the undulator radiation with K=3.6.

Figure 7: Radiation frequency as a function of the undulator strength parameter (K-value) fitting by the resonance equation. Vertical error bar indicates the frequency spread (FWHM).

Figure 8: Measured spatial profiles of the undulator radiation using the wire grid. (a) Vertical polarized component; (b) horizontal polarized radiation component. Image size is 20 mm×20 mm.

Highlights

•

Demonstrates of the generation of coherent THz radiation from femtosecond electron bunches.

•

Coherent undulator radiation of wavelength ranging from 2.6 to 3.6 THz produced.

•

This studies is instrumental in developing an enhanced understanding of coherent THz radiation