Smith-Purcell effect using femtosecond electron beam
K. Kan #,A), J. YangA), A. OgataA), T. KondohA), T. ToigawaA), K. NorizawaA), H. KobayashiA), Y. YoshidaA),
M. HangyoB), R. KurodaC), H. ToyokawaC)
A)
Institute of Scientific and Industrial Research, Osaka University, Osaka, JapanB)
Institute of Laser Engineering, Osaka University, Suita, OsakaC)
National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, Japan

Abstract
In this paper, Smith-Purcell effect, which utilizes metallic grating and electron bunch, was investigated for a new
device of terahertz (THz)-wave generation. Electron bunches and metallic gratings realized monochromatic or
multimode THz-wave generation at a frequency of <0.7 THz.

フェムト秒電子ビームを用いたスミス・パーセル効果の研究
1.

linac was used for the Smith-Purcell radiation (SPR).

Introduction

Ultrashort, e. g. femtosecond [ 1 ] or picosecond,
electron bunches are used in accelerator physics
applications such as free electron lasers (FELs), laserCompton X-ray, and pulse radiolysis [2]. On the otherhand, electron bunches with short bunch lengths are also
useful for electro-magnetic (EM) radiation production interahertz (THz) range because the inverse of 1 ps bunch
length corresponding to the frequency of 1 THz. A shorter
electron bunch can emit EM radiation of higher frequency
according to the bunch form factor, which is described by
the Fourier coefficients of the bunch distribution [3].
Furthermore, the radiation intensity at lower frequency
than the inverse of the bunch length is proportional to theelectron number, e. g. ≈109 at 1 nC. As the result, anintense THz-wave can be generated by such electronbunches. In the studies on EM radiation emitted fromelectrons, Cherenkov radiation (CR) has been studied
since the 1930s [4] and radiation yield dependence on
wavelength and angular distribution was reported. In the1990s, the bunch form factor [3] and angular distributionof coherent transient radiation (CTR) from electron
bunches were measured experimentally. Recently, notonly monochromatic THz-wave [5] but also multimodeone [ 6 , 7 ] of <0.4 THz were generated by coherent
Cherenkov radiation (CCR). Another THz-wave
generation method, which utilized a periodic electron
bunch distribution, generated narrow-band THz-wave up
to ≈0.86 THz for a bunch length diagnostic [8]. Alike
THz-wave generated by a laser, that generated by anaccelerator would be useful to a probe light, whichmonitors conductivity due to quasi-free electrons, or
imaging for medical and security use.
In this study, Smith-Purcell effect [9], which utilizes
metallic grating and electron bunch, was investigated for a
new device of THz-wave generation. Electron buncheswith ≈0.2 ps bunch length from a photocathode RF gun2.

Experimental arrangement

The photocathode RF gun linac and SPR measurement
system are shown in Fig. 1. The details of the linac arediscussed in references [10,11,12]. Figure 1(a) shows thelinac system. The electron bunch was generated by a 1.6cell S-band (2856 MHz) RF gun with a copper cathodeand a Nd:YLF picosecond laser. The pulse width of theUV pulse from the laser was measured to be 5 ps in
FWHM as a Gaussian distribution. The UV light wasprojected onto the cathode surface at an incident angle ofapproximately 2° along the electron beam direction. The
beam energy at the gun exit was 4.2 MeV. The
picosecond electron bunch produced by the RF gun wasaccelerated up to ~32 MeV by a 2 m long S-bandtravelling-wave linac with an optimal energy-phasecorrelation for the bunch compression, in which the headelectrons of the bunch have more energy than the bunch
tail. Finally, the energy-phase-correlated electron bunch iscompressed into femtosecond by rotating the phase space
distribution in the magnetic bunch compressor, which isconstructed with two 45°-bending magnets (B1 and B2),
four quadrupole magnets (Q3, Q4, Q5, and Q6), and two
sextupole magnets (S1 and S2). The femtosecond electron
bunch was obtained by adjusting the energy modulation in
the linac, e. g., compressed bunch length of ~0.2 ps in rms
measured by a streak camera at a bunch charge of ~40 pC
and a linac phase of 97.5°.
In the experiment, the bunch charge was fixed to 210
pC. The femtosecond electron bunch was used in SPR
measurement, which utilized metallic gratings as shown in
Fig 1(b). The grating was made of aluminum andfabricated by a numerical control machining. The period
length of the grating was 2 mm. The grating had
rectangular structures and dips, of which depths was 1 mm.
The total lengths of the grating were 300 mm in order toinvestigate the dependence of THz-wave on a radiation
angle easily. THz-wave produced by SPR was analyzed- 123 -Figure 1: (a) Photocathode RF gun linac. Q denotes a quadrupole magnet; B, a bending magnet; S, a sextupolemagnet. (b) SPR measurement system. OAP denotes an off-axis parabolic mirror; M, a plane mirror; BS, a beam
splitter.
by a Michelson interferometer. Electron beam generates
image charge in a grating, resulting in dipole radiation at aradiation angle. A plain mirror (M1), which rotated along
the vertical axis,
was set 50 mm away from the approximate center of thegrating for directing THz-wave at a radiation angle. Whenthe mirror (M1) rotated, THz-wave at a radiation angle ofθ was selected for the next off-axis parabolic mirror(OAP1) with a focal length of 191 mm. The THz-waveproduced by SPR was separated by a beam splitter (BS)made of 0.15 mm-thick n-type Si. One of the THz-wave
was reflected by a moving mirror (M2). Finally, theseparated THz-waves joined together at a 4.2K siliconbolometer (Infrared Laboratories Inc.). The frequency
spectra of SPR were analyzed by the fast Fouriertransform (FFT) of an interferogram with 128 points and
0.5 ps time step, in which the bolometer output as afunction of the moving mirror position was recorded.
Interferogram was obtained by an oscilloscope using 20
sweeps of the peak-to-peak output from the bolometer.
The measured THz-wave at various radiation angles are
not radiated from the same point because of the rotatedmirror (M1).

3.

Results and discussion

3.1

Theoretical description for frequency and radiation
angle

The frequency of n-th mode of SPR, fn, radiated at aradiation angle, θ, can be expressed as [9](1)f n  cn l 1   cos  where c denotes the light speed; l, the period length of thegrating; β, the beam speed as shown in Fig. 1(b).
According to Eq. (1), the frequency of SPR, fn, decreases
with increasing the radiation angle, θ, at the same order, n,
and the period length, l. The frequency of SPR varies ininverse proportion to the period length, l. When the angleof the mirror (M1) varies with the amount of Δθ, theradiation angle of selected SPR varies with the amount of2Δθ because of a reflection.

3.2

Interferogram and frequency spectrum

Figure 2 shows the dependence of SPR on radiation
angle. Figure 2(a) shows the interferograms for threedifferent radiation angles using the 2 mm-period grating.
A periodic oscillation was observed because of frequency
components. In this case, the bolometer output, whichcorresponded to the detected intensity of THz-wave, wasmaximized at a radiation angle of 54°. Figure 2(b) shows
the frequency spectra for three different radiation angles.
All the spectra had discrete components according to Eq.
(1). Some frequencies of the discrete components agreed
to the theoretical calculation. However a spike at a lower
frequency of the fundamental mode was observed at aradiation angle of 54° because of scattering of THz-wave
in the experiment. At a radiation angle of 54°, frequency
spikes up to 2nf order are slightly observed. Intensities ofspikes could not be expected by considering spectral
response according to the order at a radiation angle of110°.

Figure 2: (a) Interferograms for 54, 70, 110° radiation
angles with only offsets adjusted for comparison. (b)Frequency spectra for 54, 70, 110° radiation angles with
only offsets adjusted. The theoretical frequencies (cross)using Eq. (1) were shown.
3.3

Frequency spectra and radiation angles

Figure 3 shows the dependence of SPR on radiation
angle. In the experiment, multimode THz-wave wasobserved with changing the radiation angle, e. g., the 1stand 2nd modes at a radiation angle of 54°, the 2nd mode

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at 110°. In this case, the bolometer output, whichcorresponded to the averaged value of the interferogram,was maximized at a radiation angle of 54°, although theoutput should be considered based on scattering of THzwave, detection efficiency, and spectral response of theinterferometer.

Figure 3: Dependence of frequency spectra of SPR onradiation angle. The color map denotes experimental
data. The theoretical frequencies (lines) using Eq. (1)were shown from the 1st (bottom) to 5th (top) modes.

4.

Conclusions

Smith-Purcell effect, which utilizes metallic grating andelectron bunch, was investigated for a new device ofterahertz (THz)-wave generation. Electron bunches andmetallic gratings realized monochromatic or THz-wave
generation at a frequency of <0.7 THz using a gratingwith a period length of 2 mm. The bolometer output,
which corresponded to the detected intensity of THz-wave,
was maximized at a radiation angle of 54°.

Acknowledgment
We thank the staff of the Radiation Laboratory in theInstitute of Scientific and Industrial Research (ISIR),
Osaka University for the linac operation. We also thank
Masayoshi Ohnishi (ISIR) for the preparation of metallic
gratings. This work was supported by KAKENHIs(23109507, 21226022) and funded research from AIST
(generation of high-power THz-wave).

References[1] G. Berden et al., Phys. Rev. Lett. 99, 164801 (2007).
[2] J. Yang et al., Nucl. Instr. and Meth. A 629, 6 (2011).
[3] T. Takahashi et al., Phys. Rev. E 50, 4041 (1994).
[4] I. E. Tamm et al., Dokl. Akad. Nauk SSSR 14, 107 (1937)[5] A. M. Cook et al., Phys. Rev. Lett. 103, 095003 (2009).
[6] K. Kan et al., Radiat. Phys. Chem. 80, 1323 (2011).
[7] K. Kan et al., Appl. Phys. Lett. 99, 231503 (2011).
[8] P. Piot et al., Appl. Phys. Lett. 98, 261501 (2011).
[9] S. J. Smith et al., Phys. Rev. 92, 1069 (1953).
[10] J. Yang et al., Nucl. Instrum. Methods A 556, 52 (2006).
[11] K. Kan et al., Nucl. Instrum. Methods A 597, 126 (2008).
[12] K. Kan et al., Nucl. Instrum. Methods A 622, 35 (2010).

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