Sub-picosecond electron bunch length measurement using coherent transition radiation at SXFEL

Sub-picosecond electron bunch length measurement using coherent transition radiation at SXFEL 1 2 first-author 1 1 1 corresp Corresponding author, wangdong@sinap.ac.cn Corresponding author, wangdong@sinap.ac.cn wangdong@sinap.ac.cn Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China University of Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China Longitudinal electron bunch length plays a significant role in single-pass free-electron lasers (FEL), as the high-gain FEL process depends strongly on the high peak current of electron bunches. Longitudinal electron bunch length was measured by detecting the interferogram of coherent transition radiation generated by electron bunches using a THz interferometer and a Golay Cell (spectral range: 0.02–20 THz) at Shanghai X-ray free-electron laser. The detailed process of measurement and data analysis are discussed herein. Furthermore, the electron bunch length was estimated based on the dispersive strength <math id="M1"><mrow><msub><mi>R</mi><mrow><mn>56</mn></mrow></msub></mrow></math> of the bunch compressor and the energy spread <math id="M2"><mi>δ</mi></math> of electron bunches, which were obtained via experiments. The comparison showed that the measured bunch length was consistent with the estimated bunch length. Electron bunch length THz interferometer Coherent transition radiation Beam diagnostics 1 INTRODUCTION 1 Shanghai X-ray free-electron laser (SXFEL) test facility was constructed at the Zhangjiang campus of Shanghai Institute of Applied Physics (SINAP) in 2016. This test facility, driven by an 840 MeV electron linac with a photocathode RF gun, aims at generating free-electron laser (FEL) radiation of wavelength 8.8 nm using a two-stage cascaded high-gain harmonic generation scheme and will be upgraded to a user facility in the following two years. Electron beam peak current is one of the most important parameters to achieve excellent FEL performance. In practical experiments, electron bunches pass through a series of bunch compressors before they enter the undulator. Thus, a high-resolution measurement of sub-picosecond electron bunch length is necessary to characterize beams and set bunch compressor parameters [ 1 1 ]. Table 1 Table 1 presents the main beam parameters at the exit of the SXFEL linac. 1 1 Parameters 1 1 SXFEL 1 1 Energy (MeV) 1 1 840 1 1 Normalized emittance (mm mrad) 1 1 ≤2.5 1 1 Bunch length (FWHM) (ps) 1 1 0.4-1 1 1 Peak current (A) 1 1 ≥500 1 1 Bunch charge (pC) 1 1 500 Transverse RF deflecting structure (TDS), electro-optical (EO) sampling, and coherent radiation measurement are standard diagnostic tools for the measurement of FEL electron bunch length. By adding a vertical streak to the electron bunch and measuring the deflected vertical bunch profile downstream, TDS can be used to measure the longitudinal bunch length with a time resolution of 50 fs in actual experiments [ 2 2 ]. EO sampling is based on the Pockels effect, according to which the optical properties of electro-optic crystals vary proportional to the external electric field strength. By placing an electro-optic crystal very close to the electron beam trajectory and detecting the polarization modulation of a co-propagating short laser pulse travelling through the crystal, EO sampling can achieve a time resolution of less than 50 fs [ 3 3 ]. Coherent radiation measurement is based on the detection of the radiation emitted by electron bunches under different conditions [ 4 4 - 6 6 4-6 ]. Coherent transition radiation (CTR) and coherent synchrotron radiation are the most widely used radiation sources. In contrast to time-domain measurements, CTR-based measurement is a frequency-domain technique, which can achieve a high time resolution in an easy and economical manner. 2 MEASUREMENT THEORY AND EXPERIMENTAL SETUP 1 2.1 Autocorrelation bunch length measurement theory 2 Transition radiation is generated owing to the dielectric constant change when a relativistic electron passes through the interface between vacuum and aluminum foil. For the incidence of 45° in our experiments, the backward transition radiation is emitted perpendicular to the electron trajectory and its angular spectral energy can be expressed approximately as [ 7 7 ] <math display="block" id="M3"><mrow><msub><mi>I</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><msup><mtext>d</mtext><mn>2</mn></msup><mi>E</mi></mrow><mrow><mtext>d</mtext><mi>Ω</mi><mtext>d</mtext><mi>ω</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><mi>e</mi><mn>2</mn></msup><msup><mi>β</mi><mn>2</mn></msup></mrow><mrow><msup><mrow><mtext>4π</mtext></mrow><mn>2</mn></msup><mi>c</mi></mrow></mfrac><msup><mrow><mo stretchy="false">(</mo><mfrac><mrow><mi>cos</mi><mi>θ</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>β</mi><mi>sin</mi><mi>θ</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mi>sin</mi><mi>θ</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>β</mi><mi>cos</mi><mi>θ</mi></mrow></mfrac><mo stretchy="false">)</mo></mrow><mn>2</mn></msup><mo>,</mo></mrow></math> where <math id="M4"><mi>θ</mi></math> is the angle between the backward transition radiation and vertical direction of electron beam trajectory and <math id="M5"><mi>β</mi></math> is the ratio of the speed of electron to that of light. <math id="M6"><mrow><msub><mi>I</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow></math> is frequency-independent, which makes transition radiation ideal for spectral analysis. As shown in Fig. 1 Fig. 1 , the angular distribution is a narrow, slightly asymmetric double cone, centered around zero and reaches maximum at <math id="M7"><mrow><mi>θ</mi><mo>≈</mo><mn>1</mn><mo>/</mo><mi>γ</mi></mrow></math> , where <math id="M8"><mi>γ</mi></math> is the Lorentz factor and <math id="M9"><mrow><mi>γ</mi><mo>=</mo><mn>1</mn><mo>/</mo><msqrt><mrow><mn>1</mn><mo>−</mo><msup><mi>β</mi><mn>2</mn></msup></mrow></msqrt></mrow></math> . When an electron bunch passes through the interface, the electrons radiate coherently at wavelengths equal to or longer than the bunch length. The energy spectrum of CTR can be expressed as follows [ 8 8 , 9 9 ]: <math display="block" id="M10"><mrow><msub><mi>I</mi><mrow><mtext>coherent</mtext></mrow></msub><mo stretchy="false">(</mo><mi>ω</mi><mo>,</mo><msub><mi>σ</mi><mtext>z</mtext></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mi>I</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">[</mo><mi>N</mi><mo>+</mo><mi>N</mi><mo stretchy="false">(</mo><mi>N</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><msub><mi>F</mi><mtext>b</mtext></msub><mo stretchy="false">(</mo><mi>ω</mi><mo>,</mo><msub><mi>σ</mi><mtext>z</mtext></msub><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>,</mo></mrow></math> where <math id="M11"><mi>N</mi></math> is the number of electrons, <math id="M12"><mrow><msub><mi>I</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow></math> is the single-electron transition radiation energy spectrum, and <math id="M13"><mrow><msub><mi>F</mi><mtext>b</mtext></msub><mo stretchy="false">(</mo><mi>ω</mi><mo>,</mo><msub><mi>σ</mi><mtext>z</mtext></msub><mo stretchy="false">)</mo></mrow></math> is the bunch form factor, which is the absolute square of the Fourier transform of the normalized longitudinal electron bunch distribution, expressed as follows: <math display="block" id="M14"><mrow><msub><mi>F</mi><mtext>b</mtext></msub><mo stretchy="false">(</mo><mi>ω</mi><mo>,</mo><msub><mi>σ</mi><mtext>z</mtext></msub><mo stretchy="false">)</mo><mo>=</mo><msup><mrow><mrow><mo>|</mo><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>ω</mi><mo>,</mo><msub><mi>σ</mi><mtext>z</mtext></msub><mo stretchy="false">)</mo></mrow><mo>|</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><msup><mrow><mrow><mo>|</mo><mrow><mstyle displaystyle="true"><mrow><msubsup><mo>∫</mo><mrow><mo>−</mo><mi>∞</mi></mrow><mi>∞</mi></msubsup><mrow><mi>ρ</mi><mo stretchy="false">(</mo></mrow></mrow></mstyle><mi>t</mi><mo>,</mo><msub><mi>σ</mi><mtext>z</mtext></msub><mo stretchy="false">)</mo><msup><mtext>e</mtext><mrow><mo>−</mo><mi>i</mi><mi>ω</mi><mi>t</mi></mrow></msup><mtext>d</mtext><mi>t</mi></mrow><mo>|</mo></mrow></mrow><mn>2</mn></msup><mo>,</mo></mrow></math> where <math id="M15"><mrow><mi>ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo>,</mo><msub><mi>σ</mi><mtext>z</mtext></msub><mo stretchy="false">)</mo></mrow></math> denotes the normalized longitudinal charge distribution as a function of time t, with root mean square (rms) bunch length <math id="M16"><mrow><msub><mi>σ</mi><mi>z</mi></msub></mrow></math> . For an electron bunch at SXFEL, its bunch charge is 500 pC, and the number of electrons <math id="M17"><mi>N</mi></math> is large, i.e., approximately 10 9 –10 10 . As the intensity of coherent radiation is proportional to the square of the number of radiating electrons, the energy spectrum of CTR can be approximated as <math display="block" id="M18"><mrow><msub><mi>I</mi><mrow><mtext>coherent</mtext></mrow></msub><mo stretchy="false">(</mo><mi>ω</mi><mo>,</mo><msub><mi>σ</mi><mtext>z</mtext></msub><mo stretchy="false">)</mo><mo>≈</mo><msup><mi>N</mi><mn>2</mn></msup><msub><mi>I</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><msub><mi>F</mi><mtext>b</mtext></msub><mo stretchy="false">(</mo><mi>ω</mi><mo>,</mo><msub><mi>σ</mi><mtext>z</mtext></msub><mo stretchy="false">)</mo><mo>.</mo></mrow></math> As the energy spectrum of CTR produced by SXFEL electron bunches is in the THz regime, a THz Michelson interferometer was used to measure the autocorrelation function of CTR, which can be expressed as follows: <math display="block" id="M19"><mrow><mi>i</mi><mo stretchy="false">(</mo><mi>τ</mi><mo stretchy="false">)</mo><mo>∝</mo><mstyle displaystyle="true"><mrow><mo>∫</mo><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi>τ</mi><mo stretchy="false">)</mo><mtext>d</mtext><mi>t</mi></mrow></mrow></mstyle><mo>,</mo></mrow></math> where <math id="M20"><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></math> denotes the CTR radiation in time domain and <math id="M21"><mi>τ</mi></math> denotes the time delay. It can be mathematically proven that the Fourier transformation of autocorrelation function <math id="M22"><mrow><mi>i</mi><mo stretchy="false">(</mo><mi>τ</mi><mo stretchy="false">)</mo></mrow></math> is the bunch form factor <math id="M23"><mrow><msub><mi>F</mi><mtext>b</mtext></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow></math> , or the energy spectrum of CTR, as follows: <math display="block" id="M24"><mrow><mi>F</mi><mo stretchy="false">[</mo><mstyle displaystyle="true"><mrow><msubsup><mo>∫</mo><mrow><mo>−</mo><mi>∞</mi></mrow><mi>∞</mi></msubsup><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mrow></mstyle><mo>⋅</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi>τ</mi><mo stretchy="false">)</mo><mtext>d</mtext><mi>t</mi><mo stretchy="false">]</mo><mo>=</mo><mi>F</mi><mo stretchy="false">[</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>⋅</mo><msup><mi>F</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy="false">[</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>=</mo><msup><mrow><mrow><mo>|</mo><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><mo>|</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><msub><mi>F</mi><mtext>b</mtext></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>,</mo></mrow></math> where <math id="M25"><mi>F</mi></math> denotes the Fourier transform of a function. From Eq. (4), the information of bunch length is contained in the energy spectrum of CTR. By analyzing the measured autocorrelation function, the bunch length can be determined. 2.2 Experimental setup for bunch length measurement at SXFEL 2 In the experiment, the photocathode RF electron gun is driven by a laser with full width at half maximum (FWHM) pulse duration of 8 ps, and is operated at a repetition rate of 10 Hz. The electron beam energy at the exit of the photocathode RF electron gun is 5 MeV. The beams are further accelerated in accelerating structure 1 (ACC1) to 150 MeV before they enter the bunch compressor 1 (BC1). After BC1, the compressed beams enter accelerating structure 2 (ACC2) and are accelerated to approximately 650 MeV. Subsequently, the beams enter bunch compressor 2 (BC2) where an Al foil is located between the second and third bending magnets of BC2 for CTR-based bunch length measurement. The dispersive strength of BC2 is small, and the bunch length is mainly compressed in BC1. The schematic layout of SXFEL linac is illustrated in Fig. 2 Fig. 2 , showing the position of Al foil for CTR-based bunch length measurement. Our measuring system consists of a bunch length interferometer system (BLIS, RadiaBeam) and a Golay Cell used as the THz radiation detector. The CTR-based bunch length measurement has been developed in many leading FEL laboratories worldwide during the last few decades. Many THz radiation detectors have been employed in this measurement, such as pyroelectric detectors, liquid-helium-cooled bolometers, Golay Cells, and liquid-nitrogen-cooled mercury-cadmium-telluride (MCT) photoconductive detectors [ 10 10 - 13 13 10-13 ]. It is known that the spectrum of CTR is determined by the bunch form factor, and a shorter electron bunch is radiated at higher frequency components. Pyroelectric detectors have a narrow spectrum coverage of 0.02–3 THz, and cannot cover the spectrum emitted by electron bunches with bunch length less than 150 fs. The spectrum coverage of Golay Cell is 0.02–20 THz, which is adequate for the measurement of electron bunch length ranging from 20 fs to 2 ps with a Gaussian shape [ 14 14 ]. In contrast to liquid-helium-cooled bolometers, whose spectrum coverage is 0.15–20 THz, Golay Cells are room-temperature detectors. MCT photoconductive detectors are used for electron bunches with bunch length less than 20 fs [ 13 13 ]. As the designed electron bunch length at SXFEL is 0.4–1 ps, a Golay Cell is selected for the present experiments. By using an Al foil—tilted by 45° facing the electron beam direction—as a radiator in the electron path, the backward transition radiation was emitted perpendicular to the beam axis with the divergence angle <math id="M26"><mrow><mo>≈</mo><mn>1</mn><mo>/</mo><mi>γ</mi></mrow></math> . As the beam energy at BC2 is approximately 650 MeV, the generated CTR was treated as a quasi-parallel light. The experimental setup for bunch length measurement is illustrated in Fig. 3 Fig. 3 . A Martin–Puplett-type THz interferometer with transmission wire grids as beamsplitters was used in the experiment. All the components of BLIS were pre-aligned by the manufacturer and the alignment of the system was verified during the installation. The incoming CTR wave was split into two parts by the 45°-beamsplitter (BS1). The transmitted part was split again by the 90°-beamsplitter (BS2) and recombined with the other initially reflected component, which was reflected by a front surface mirror (M1) in the delay stage. Subsequently, the auto-correlated THz wave was fed to the Golay cell using a focusing mirror (FM1). After the measurement of CTR by the Golay cell, the signal from the detector was amplified by a lock-in amplifier, which was triggered with 10 Hz using a camera trigger. By moving the delay stage, which was controlled by the computer, the interferograms of CTR were obtained by recording the data from the lock-in amplifier. The step length of the delay stage was set to 0.25 μm, with 10 steps per second. As the shot-to-shot fluctuations of the intensity of the incoming pulse could be ignored, no reference detectors were employed in the experiment. 3 RESULTS AND DISCUSSION 1 The obtained interferograms were functions of the position of the movable mirror, which can be converted to a time delay. By analyzing the interferograms of CTR, the rms bunch length can be determined. We assumed that the longitudinal charge distribution of electron bunches at the exit of the photocathode RF electron gun was an ideal Gaussian distribution, the distribution remained unchanged during the accelerations in ACC1 and ACC1, and the electron bunches were compressed linearly in BC1. As BC2 was a small chicane, its effect could be ignored. The longitudinal bunch distribution <math id="M27"><mrow><mi>ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></math> with rms bunch length <math id="M28"><mrow><msub><mi>σ</mi><mtext>z</mtext></msub></mrow></math> at the Al foil can be expressed as <math display="block" id="M29"><mrow><mi>ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>2</mn><mi>π</mi></mrow></msqrt><msub><mi>σ</mi><mtext>z</mtext></msub></mrow></mfrac><msup><mi>e</mi><mrow><mo>−</mo><msup><mi>t</mi><mn>2</mn></msup><mo>/</mo><mn>2</mn><msub><mi>σ</mi><mtext>z</mtext></msub><msup><mrow/><mn>2</mn></msup></mrow></msup><mo>,</mo></mrow></math> and thus, the interferogram <math id="M30"><mrow><mi>i</mi><mo stretchy="false">(</mo><mi>τ</mi><mo stretchy="false">)</mo></mrow></math> becomes [ 15 15 ] <math display="block" id="M31"><mrow><mi>i</mi><mo stretchy="false">(</mo><mi>τ</mi><mo stretchy="false">)</mo><mo>∝</mo><mstyle displaystyle="true"><mrow><msubsup><mo>∫</mo><mrow><mo>−</mo><mi>∞</mi></mrow><mrow><mo>+</mo><mi>∞</mi></mrow></msubsup><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi>τ</mi><mo stretchy="false">)</mo><mtext>d</mtext><mi>t</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><msqrt><mi>π</mi></msqrt><msub><mi>σ</mi><mtext>z</mtext></msub></mrow></mfrac></mrow></mrow></mstyle><msup><mi>e</mi><mrow><mo>−</mo><msup><mi>τ</mi><mn>2</mn></msup><mo>/</mo><mn>4</mn><msub><mi>σ</mi><mtext>z</mtext></msub><msup><mrow/><mn>2</mn></msup></mrow></msup><mo>.</mo></mrow></math> The FWHM of this Gaussian interferogram was <math id="M32"><mrow><mn>4</mn><msqrt><mrow><mi>I</mi><mi>n</mi><mn>2</mn></mrow></msqrt><msub><mi>σ</mi><mtext>z</mtext></msub></mrow></math> . In Fig. 4 Fig. 4 , the measured interferograms of CTR at different accelerating phases in the linac are shown. The FWHM of these interferograms were 2.194 ps, 1.704 ps, 1.294 ps, and 0.711 ps at the phases of 25°, 30°, 35°, and 45°, respectively, which indicated that the rms bunch lengths <math id="M33"><mrow><msub><mi>σ</mi><mi>z</mi></msub></mrow></math> were 659 fs, 512 fs, 389 fs, and 213 fs, respectively. In order to verify the reliability of this CTR-based measurement, the energy spread of electron bunches was measured by an energy spectrometer after BC1. The bunch length was estimated by applying the following formula [ 16 16 ]: <math display="block" id="M34"><mrow><msub><mi>σ</mi><mtext>z</mtext></msub><mo>≈</mo><mrow><mo>|</mo><mrow><mn>1</mn><mo>+</mo><mi>h</mi><msub><mi>R</mi><mrow><mn>56</mn></mrow></msub></mrow><mo>|</mo></mrow><msub><mi>σ</mi><mi>i</mi></msub><mo>,</mo></mrow></math> where <math id="M35"><mrow><msub><mi>σ</mi><mi>i</mi></msub></mrow></math> is the rms bunch length before BC1, <math id="M36"><mrow><msub><mi>R</mi><mrow><mn>56</mn></mrow></msub></mrow></math> is the dispersive strength of BC1, and <math id="M37"><mi>h</mi></math> is the energy chirp of the electron beam. In this case, <math id="M38"><mi>h</mi></math> can be estimated using the following equation: <math display="block" id="M39"><mrow><mi>h</mi><mo>≈</mo><mi>δ</mi><mo>/</mo><msub><mi>σ</mi><mi>i</mi></msub><mo>,</mo></mrow></math> where <math id="M40"><mi>δ</mi></math> is the energy spread of electron bunches. In our experiments, the factor <math id="M41"><mrow><msub><mi>R</mi><mrow><mn>56</mn></mrow></msub></mrow></math> and FWHM pulse length of the laser driven by the photocathode RF electron gun were −37.32 mm and 8 ps, respectively. We assumed that the FWHM electron bunch length was 8 ps with a Gaussian shape before BC1. The measured energy spread at different accelerating phases is presented in Table 2 Table 2 . 1 1 Accelerating phase 1 1 25º 1 1 30º 1 1 35º 1 1 40º 1 1 45º 1 1 50º 1 1 Energy spread 1 1 0.85% 1 1 1.09% 1 1 1.5% 1 1 2.0% 1 1 2.4% 1 1 3.0% In Fig. 5 Fig. 5 , the measured and estimated bunch lengths are plotted against the accelerating phases in the linac, and the results are very close to each other. The bunch length could not be further compressed after a phase of 45°, which indicated that the electron bunches were over-compressed in BC1. 4 CONCLUSION 1 CTR-based measurement of electron bunch length was investigated using a THz interferometer and a Golay Cell used as the detector at SXFEL. The electron bunch length was determined by analyzing the measured interferograms of CTR generated by electron bunches. The electron bunch length was also estimated based on the dispersive strength of the bunch compressor and the energy spread of electron bunches, which were obtained via experiments. The comparison showed that the measured bunch length was consistent with the estimated bunch length, which indicated that the results of this frequency-domain bunch length measurement technique are reliable. To improve the accuracy of this technique, the frequency response of the measuring system will be investigated as the subsequent step. 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Lett ., 25 : 2440 - 2443 ( 2008 ). doi: 10.1088/0256-307X/25/7/030 http://doi.org/10.1088/0256-307X/25/7/030 Experimental characterization of sub-picosecond electron bunch length with coherent diffraction radiation We thank Dr. Jin-Feng Yang and Dao Xiang for their useful discussions and encouragement. 10.1007/s41365-018-0399-8 This work was supported by the National Program on Key Basic Research Project (No. 2016YFA0401900) and the Ministry of Science and Technology of China. 2017-09-25 2018-01-15 2018-01-27 2018-04-05 2018-05-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2018 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-018-0399-8 http://dx.doi.org/10.1007/s41365-018-0399-8 . 2018 Nuclear Science and Techniques 05 29