Introduction
In the last few decades, laser-wakefield acceleration (LWFA) has been a vibrant research area for its successful application in low emittance electron beam generation in the gigaelectron volts (GeV) scale (Malka et al., Reference Malka, Faure, Glinec and Lifschitz2006; Wang et al., Reference Wang, Zgadzaj, Fazel, Li, Yi, Zhang, Henderson, Chang, Korzekwa, Tsai, Pai, Quevedo, Dyer, Gaul, Martinez, Bernstein, Borger, Spinks, Donovan, Khudik, Shvets, Ditmire and Downer2013; Leemans et al., Reference Leemans, Gonsalves, Mao, Nakamura, Benedetti, Schroeder, Toth, Daniels, Mittelberger, Bulanov, Vay, Geddes and Esarey2014; Couperus et al., Reference Couperus, Pausch, Kohler, Zarini, Kramer, Garten, Huebl, Gebhardt, Helbig, Bock, Zeil, Debus, Bussmann, Schramm and Irman2017; Dann et al., Reference Dann, Baird, Bourgeois, Chekhlov, Eardley, Gregory, Gruse, Hah, Hazra, Hawkes, Hooker, Krushelnick, Mangles, Marshall, Murphy, Najmudin, Nees, Osterhoff, Parry, Pourmoussavi, Rahul, Rajeev, Rozario, Scott, Smith, Springate, Tang, Tata, Thomas, Thornton, Symes and Streeter2019). However, for the most modest lab scale and portable applications like field manipulation of electrons and ultrafast electron diffraction (UED) (Srinivasan et al., Reference Srinivasan, Lobastov, Ruan and Zewail2003; Calendron et al., Reference Calendron, Meier, Hemmer, Zapata, Reichert, Cankaya, Schimpf, Hua, Chang, Kalaydzhyan, Fallahi, Matlis and Kaertner2018; Schaeffer et al., Reference Schaeffer, Hofer, Knall, Heuer, Constantin and Niemann2018), a compact, relatively inexpensive, high average current source of laser-accelerated electrons is sufficient and much desirable.
Another crucial problem of electron source is related to the beam charge. Take UED for example, large electron charge becomes particularly important since the detection of many irreversible ultrafast processes require high-brightness electrons in one single shot. Whereas the conventional methods for generating ultrafast electron source generally follow a two-step method: firstly, femtosecond laser pulses is used to generate electron pulses from photocathode; then, the generated electron pulses are accelerated by an external static electric field with the field strength up to several tens of kilovolts (Harb et al., Reference Harb, Ernstorfer, Hebeisen, Sciaini, Peng, Dartigalongue, Eriksson, Lagally, Kruglik and Miller2008; Sciaini and Miller, Reference Sciaini and Miller2011). The pulse charge is often limited to the order of only 1 fC in order to minimize the pulse duration broadened by space charge forces, making it almost impossible to perform single-shot measurements with such a low-brightness electron pulse. For electron diffraction in the MeV range, on the other hand, such a high-energy electron source is limited to transmission mode only owing to the picometer-size electron wavelength and the small few mrad diffraction angle (Musumeci et al., Reference Musumeci, Moody, Scoby, Gutierrez, Bender and Wilcox2010). In addition, MeV energy range also suffers from other disadvantages such as small cross section of elastic scattering and high radiation damage to samples (Tokita et al., Reference Tokita, Inoue, Masuno, Hashida and Sakabe2009; Gulde et al., Reference Gulde, Schweda, Storeck, Maiti, Yu, Wodtke, Schafer and Ropers2014). For electrons in hundreds keV energy range, pulse-compressed electrons have been developed to supply hundreds of fC electron charge utilizing radiofrequency (RF) wave to compress the beam pulse. But it also suffers from the big size of the facility and the time jitter between electron beam and RF wave (van Oudheusden et al., Reference van Oudheusden, Pasmans, van der Geer, de Loos, van der Wiel and Luiten2010; Otto et al., Reference Otto, Rene de Cotret, Stern and Siwick2017).
In contrast to photocathode or gas plasma, the laser solid-density plasma interaction benefits from its high laser absorption efficiency (Thévenet et al., Reference Thévenet, Leblanc, Kahaly, Vincenti, Vernier, Quéré and Faure2015) and could supply a few nanocoulomb electrons in a single shot. The laser-driven electron sources, thus, show great advantages in terms of brightness when compared with a conventional photocathode-based electron source. However, the heating mechanisms that underly such electron sources like resonant absorption, vacuum heating, J × B heating, and stochastic heating (Gibbon, Reference Gibbon2004) also give rise to large divergence angles and quasi-thermal broad energy spectra (Mordovanakis et al., Reference Mordovanakis, Easter, Naumova, Popov, Masson-Laborde, Hou, Sokolov, Mourou, Glazyrin, Rozmus, Bychenkov, Nees and Krushelnick2009; Tian et al., Reference Tian, Liu, Wang, Wang, Deng, Xia, Li, Cao, Lu, Zhang, Xu, Leng, Li and Xu2012). Directional electron beams have been produced via vacuum laser acceleration with a plasma mirror injector (Thévenet et al., Reference Thévenet, Leblanc, Kahaly, Vincenti, Vernier, Quéré and Faure2015). Unfortunately, the beam collimation also suffers from the ponderomotive force of the laser pulse in vacuum during acceleration, which results in a large divergence angle (hundreds of milliradians) and a halo in the electron beam profile. As a result, despite several attempts have been made to employ laser-accelerated electrons from solid targets as the electron source for UED use, the relatively low electron charge still renders these schemes fall short of an ideal source for UED (Tokita et al., Reference Tokita, Inoue, Masuno, Hashida and Sakabe2009, Reference Tokita, Hashida, Inoue, Nishoji, Otani and Sakabe2010).
In this paper, we present experimentally an optimized electron source form laser-driven wire target. In contrast to the planar solid targets, electrons accelerated from wire targets experience a radial field immediately established on the target surface and gyrate along the wire surface in a helical manner (Tokita et al., Reference Tokita, Otani, Nishoji, Inoue, Hashida and Sakabe2011; Nakajima et al., Reference Nakajima, Tokita, Inoue, Hashida and Sakabe2013; Tian et al., Reference Tian, Liu, Bai, Zhou, Sun, Liu, Zhao, Li and Xu2017). Many electron pulse can, hence, be strongly concentrated and harnessed to form a compact and collimated electron source. By combining the laser-irradiated wire target and an electron filter unit, we develop a simple system that could serve as a convenient electron source with potential for single-shot electron diffraction. Our scheme embraces both the merits of compactness and potential high charge comparable to those based on LWFA.
Methods
Concept and implementation
The experimental implementation of our laser wire-based electron diffraction device is schematically depicted in Figure 1a and consists of two functional units: one for electron pulse generation and one for filtering electrons that would satisfy the demand of single-shot electron diffraction. In general, the laser–solid interaction could result in a rather wide energy spectrum. As a result, to achieve the desirable electron beam for electron diffraction, a component responsible for narrowing energy spread is indispensable. Here, a pair of dipole magnets and several apertures are utilized to narrow the energy and angular spread in the proposed scheme. The collimated electrons from the target are spatially filtered by an entrance aperture and guided to the pair of dipole magnets, which allow the wire target to traverse it. In the dipole magnets, the path of electrons with different energy deviates. And a filter tube comprised of two apertures in the exit of the magnets therefore enables the spatial as well as energy filter of the electrons.
Fig. 1. Schematic representation of the proposed setup for electron diffraction using laser-irradiated wire target. (a) A pair of magnets and several apertures function as the electron filter. (b) Schematic of the layout for measuring electrons at the entrance of the magnets. The obtained single-shot saturated ring zone on the IP indicates a vast number of electrons are collimated in a small divergence by the wire target. (c) Three-dimensional profile of the electron beam near the wire target corresponding to the data obtained in (b) with dose N in electrons/0.04 mm2, where the inset shows the two-dimensional dose map of the central part of the beam. The dashed white circle in the inset represents the half-maximum height contour of the beam.
To effectively optimize the filtered electron beam in terms of electron charge and transverse coherence that determine the diffraction image quality, the magnets could adjust in field strength as well as their separated distance. For energy separation using the magnet pairs, neighboring magnets are set to identical magnetic field strength with opposite direction and the following filter tube is optically aligned by a small He–Ne laser beam parallel to the wire. Since a vast number of electrons from the laser–solid interaction (up to hundreds of pC or even a few nC, depending on the laser intensity) are collimated into the first magnet by the wire target regardless of energy difference, a tailored filter tube would keep enough electron charge for single-shot electron diffraction with adequate transverse coherence. In this work, electron pulse that enters the entrance hole of the first magnet carries approximately ~10 pC electron charge. However, a significant improvement in electron charge, as well as divergence angle, could be expected when a laser pulse of large intensity is applied. Electron charges of several hundred pC and even over a few nC in the center spot have been reported when applying 5 × 1018 and ~1019 W/cm2 pulse intensity, respectively (Tokita et al., Reference Tokita, Otani, Nishoji, Inoue, Hashida and Sakabe2011; Nakajima et al., Reference Nakajima, Tokita, Inoue, Hashida and Sakabe2013), while simultaneously, most of the electron energy still falls in the range of around 100–300 keV. In such scenario of several nC initial charge, a mere 0.001% portion of the electrons filtered out could satisfy the electron charge demand of an ideal diffraction electron source (van Oudheusden et al., Reference van Oudheusden, de Jong, van der Geer, ‘t Root, Luiten and Siwick2007).
Laser-driven electron collimation along the wire target
Laser–solid interaction at relativistic intensities produces substantial fast electrons in the sub-MeV range. A small fraction of the hot electrons is emitted into the vacuum and give rise to a charge-neutralizing disturbance propagating away from the interaction region. An interesting case to consider is the wire target. Once applied to a wire target, a transient radial charging field would be generated by this sudden charge separation, which could, in turn, drive back the ejected electrons to move along the wire. With adequate laser intensity, the electric field of the transient field has been experimentally demonstrated its capability of transporting electrons along the wire surface over a distance as far as over 1 m (Nakajima et al., Reference Nakajima, Tokita, Inoue, Hashida and Sakabe2013). Electrons emitted from wire targets are thus far more concentrated in space than planar targets.
For diffraction utility, an image plate (IP; Fujifilm BAS-SR2025) placed opposite the wire allows assessing of the electron distribution and charge amount. The electron pattern in Figure 1b shows a typical image taken at a traveling distance of 40 mm from the irradiated spot. Electron emission angle and dose distribution can thereby be retrieved from the pattern. Figure 1c displays the three-dimensional dose map of the electron beam. Since the most of these electrons are constricted in close vicinity to the wire with a small divergence angle, a blocking aperture is placed in the entrance of the filter stage to preclude the influx of outer electrons and meanwhile modulate the divergence of the electrons that are allowed in.
Electron filter approach: analytical description by the transverse coherence length
For experimental validation of the proposed scheme, the spatial resolution of the electron source for diffraction is quantified by the transverse coherence length L c as follows (van Oudheusden et al., Reference van Oudheusden, de Jong, van der Geer, ‘t Root, Luiten and Siwick2007):
$$L_{\rm c} = \displaystyle{\hbar \over {mc}}\displaystyle{{{\rm \sigma} _x} \over {{\rm \varepsilon} _{{\rm n},x}}},$$where m is the electron mass, c is the speed of light, 
$\hbar$ is Planck's constant, σx is the rms bunch radius, and ɛn,x is transverse normalized emittance. At the sample, the transverse coherence length L c of at least several unit cell dimension is required to ensure good quality of the diffraction pattern. A radical increase in L c can be achieved by lengthening the filter tube or using a smaller radius, though at the dispense of a shrinking electron number. As a result, the trade-off between electron charge and the transverse coherence length is made by carefully adjust the magnets as well as the shape (namely its length, radius, and distance related to the wire) of the filter tube with the help of particle tracing simulations.
Simulation
Numerical simulations of the electron beam were carried out for electron beam optimization in the filter stage using particle tracking code ELEGANT (Borland, Reference Borland2000). The space charge effect was ignored in the simulation. Emitted electrons from the laser–wire interaction were approximated by the Gaussian distribution with initial full-width at half-maximum (FWHM) spatial size and temporal span hypothesized to be identical to the laser pulse. It is assumed in the simulation that the electron beam produced at the laser spot has a uniform energy and angular distribution. Also, helical movement is not included in the simulation here because, on the one hand, the angular momentum of the filtered electrons is rather small when compared to the forward momentum. On the other hand, the emittance of the selected electrons from after the whole filter system is determined by the filter tube at the end of the system which further undermines the effect brought by the helical motion. In accordance to the experimental results under present laser and wire parameters, the initial electron beam was set with a momentum distribution of peak momentum of 419 keV/c (E = 150 keV) and an FWHM 
${\rm \delta} p/p = 33\%$. When the entrance blocking aperture has a diameter of 3 mm, the electron beam that enters the first magnet has a root-mean-square (rms) radius of 1.06 mm.
The optimized position of the first magnet, at z = 40 mm, has been chosen such that the small portion of energetic electrons with broad emitting angle is stopped by the first aperture from entering the filter unit. The two magnets have a width of 30 mm, whereas their magnetic field strength and separation distance are chosen in accordance with the quality of the injected electron beam. The quality of the filtered electron beam is determined by a combined action of the magnets and filter tube. Longer tube length with narrow radius contributes to smaller transverse emittance and energy spread though at the cost of a reduction in electron number. When aiming for single-shot diffraction with a transverse coherence length of L c ≥ 1 nm, about 0.1 pC charge is necessary for sufficient diffraction quality (Tao et al., Reference Tao, Zhang, Duxbury, Berz and Ruan2012).
Figure 2 shows the bunch evolution in the optimized setup for selected energy of 150 and 250 keV. The locations of the magnets and the filter tube are also shown in the figure. For energy selection of 150 and 250 keV, magnetstrengths are respectively set to 25 and 20 mT. The second magnet M2 is located contiguous to the M1 (d1 = 0 mm) in both cases and produces an equal magnetic field with M1 but in the reversed direction. When leaving the magnets, the bunch emittance drops abruptly in the filter tube by several order of magnitude to 10−2 due to the energy filter by the magnets and filter tube. Here, filter tubes of 0.3 mm diameter, length d2 = 150 mm and 0.4 mm diameter, length d2 = 250 mm are used, respectively, for 150 and 250 keV energy selection. Snapshots of the phase-space distribution in transverse x–y plane, phase-space, and the longitudinal phase-space at the sample place are plotted in Figure 3.
Fig. 2. The bunch transverse normalized emittance ɛn,x (solid line) and rms radius σx (dashed line) evolution in the optimized filter unit for selected energy of (a) 150 and (b) 250 keV. The insets present the layout of the filter tube with the outcome ɛn,x and σx.
Fig. 3. (a–f) Phase-space distribution projections for selected energy of 150 (row 1) and 250 keV (row 2). The distribution is color-coded by energy with blue to red for lower to higher energies.
We list the beam parameters at the sample position for both 150 and 250 keV in Table 1. At the sample, the filtered bunch for 150 keV is characterized by a transverse rms size of 0.22 mm, a normalized emittance of 0.04 mm mrad, a relative rms momentum spread of 1.1%, and a transverse coherence length of 1.1 nm. The portion of filtered electrons is 0.004% of the initial electrons. Similar results are produced with 250 keV energy though with less portion of 0.002% filtered out. If the initial bunch charge carries a few nC, the filtered electron charge could thereby well satisfy the charge demand for single-shot electron diffraction.
Table 1. The filtered beam parameters for selected energy of 150 and 250 keV
Experimental results and discussion
To experimentally demonstrate the proposed scheme, proof-of-principle experiments are conducted with the setup shown schematically in Figure 1a. A p-polarized laser pulse (central wavelength at 800 nm with FWHM pulse duration of 30 fs) from a commercial 1 kHz Ti:sapphire chirped-pulse amplifier with an 8 mJ pulse energy was focused to an FWHM spot diameter of 4 µm (1/e 2) by an f/2 off-axis parabolic mirror. Taking into consideration of the 60% propagation loss is in our laser path and 70% pulse energy within FWHM radius, it yields a peak intensity of approximate 5 × 1017 W/cm2 on the tungsten wire target (50 µm diameter) at an incident angle of 45° (in the x–z plane on Figure 1, where laser path and wire axis are aligned on the same height). Amplified spontaneous emission is measured to be less than 10−6 of the peak intensity of the laser pulses. The wire target is mounted with one end fixed on a motor and the other end tightened by a small weight. As a result, laser damage to the wire could be ignored since the wire can be moved by the motor to avoid irradiation on the same spot. The whole setup is placed in a vacuum chamber with pressure under 0.1 Pa.
Electron beam qualities like energy spectra, divergence angle, and charge were determined prior to the filter stage. In this measurement, an IP wrapped in a 20-μm Al foil was placed opposite to the target [see Fig. 1b], providing spatially resolved detection of the electron beam. Typically in the conspicuous saturated ring halo like the case shown in Figure 1b, an overall electron charge of around 30 pC was estimated to be confined or collimated within the saturated zone surround the wire target under our experimental parameters. It relays an electron beam with rms radius of 1.06 mm in the 3 mm-diameter entrance aperture. This is equivalent to a half-emitting divergence angle as small as 26 mrad that entered the filter stage. Approximately 36% electrons could enter this first entrance hole, namely about 10 pC (~6.3 × 107 electrons) could enter the filter stage under our experimental parameters.
We present the results for electron filter with the magnets set to 28 mT and a separation distance of 40 mm. The filter tube had 0.3 mm radius and a 135 mm-long drift length. Figure 4a displays a measured electron beam profile obtained in the absence of a sample. The spatial width of the electron beam could be well fitted by a Gaussian function with an FWHM of 0.27 mm. Owing to the weak laser intensity and the resultant small number of electrons in our experimental conditions, six shots were accumulated in the total ~6-fC electron charge estimated in this profile, indicating an average charge of ~1 fC (~6.3 × 103 electrons) in each electron pulse that arrived at the sample. In other words, approximately 0.01% portion of the relayed electrons were filtered by the filter tube for diffraction usage.
Fig. 4. (a) Obtained electron beam pattern at the exit of the filter tube without the sample present. (b) Horizontal beam profile from the measured pattern (black curve) and from ELEGANT simulations. (c) Normalized electron energy distribution before the filter stage (black curve) and that at the exit of the filter tube (blue curve). The dashed red line represents the calculated result.
The energy distribution for electron beams either before or after the filter unit was measured with a magnetic spectrometer. The evident effect of energy narrowing could be seen in Figure 4c where the sharp blue curve represents the filtered electron spectrum in comparison to that before filtering (dark curve). The peak energy before or after the filter stage remained around 150 keV (or 419 keV/c in momentum). And the FWHM momentum spread related to these two places are 33 and 2.9%, respectively. The filtered energy changes with a different horizontal displacement of the filter tube to the wire axis. Hence, the broad initial energy spread provides an abundant source for electron diffraction in the 100–300 keV range. However, the energy distribution of the filtered electrons is not as desirably stable as for multishot experiments. Peak energy fluctuated up to ±30 keV from shot to shot. Possible reasons may arise from fluctuations in laser energy (~2.5%) and alignment of the filter tube. Consequently, this scheme is considered to operate in a single-shot mode only provided that the stability problem had not been well-solved. Nevertheless, since an increase in laser intensity enhances collimated electrons in the central spot dramatically without a significant change in energy spread (Tokita et al., Reference Tokita, Otani, Nishoji, Inoue, Hashida and Sakabe2011; Nakajima et al., Reference Nakajima, Tokita, Inoue, Hashida and Sakabe2013), it suggests that increasing laser intensity could be one possible way to manifold the electron charge that satisfies the requirement for single-shot in a few hundred keV range.
Note here expanded filter tube radius as well as shortened filter tube length were adopted in the experiment compared to the simulation parameters. The adjustment was a trade-off made between the transverse coherence and the low electron charge resultant from our modest laser intensity. Electron loss also took place in the alignment deviation of the wire with the tube axis as well as the inhomogeneity in electron distribution, magnetic field as compared to the uniform assumptions in the simulation. With experimental filter unit parameters, the simulation results predict electron beam profile in good agreement with the experimental one [Fig. 4b] with rms radius of σx = 0.2 mm. The produced transverse normalized emittance of the filtered electron beam is retrieved as ɛn,x = 1.4 × 10−1 mm mrad. The transverse coherence length L c is then given by Eq. (1) with 0.57 nm, a value slightly bigger than the unit cell dimension of a single-crystal Au. However, a radical increase in L c can be easily realized with adjustment in tube geometry and magnets with more initial electrons.
While the experiment shows a proof-of-principle demonstration employing a relatively low-energy laser system, there are still significant improvements that could be made toward single-shot electron diffraction, for example, (i) using a higher intensity laser pulse to create more collimated electrons; (ii) applying a more refined filter arrangement, such as a magnet combined with two apertures to simplify the whole setup to several centimeter scale (Tokita et al., Reference Tokita, Inoue, Masuno, Hashida and Sakabe2009); (iii) adopting more sensitive detection devices such as an electron-multiplying charge-coupled camera or a scintillator plate to obtain a better resolved image; and (iv) combining the setup with laser-based electron pulse compression methods (Tokita et al., Reference Tokita, Hashida, Inoue, Nishoji, Otani and Sakabe2010; van Oudheusden et al., Reference van Oudheusden, Pasmans, van der Geer, de Loos, van der Wiel and Luiten2010) to further reduce the electron chirp. In addition, future studies in the geometric and plasma scale length parameters may also hint on methods that will improve electron qualities from the laser–plasma interaction.
Conclusion
In conclusion, we have demonstrated the optimization of the electron source from intense femtosecond laser interacting with a wire target. By manipulating the energy and spatial distributions of the electron pulse with two magnets served as the filter unit, we have demonstrated with numerical simulations the possibility of utilizing this approach for single-shot UED. A proof-of-principle experiment is conducted to provide an electron beam with 1 fC charge and transverse coherence length approaching 1 nm which indicates the scheme as a promising candidate for single-shot electron diffraction.
Furthermore, in comparison to the traditional dc-accelerated or laser-accelerated UED in the sub-MeV energy range, the extraordinary collimation ability of wire targets amounts to a novel, compact electron source that, unlike conventional sources, can deliver a vast number of electrons with extraordinary small divergence angle regardless of their energy. This wide energy spread from laser–solid interaction also enables the proposed scheme to work in an energy range of a few hundred keV range. Though stability, brightness, and transverse length of the filtered electron pulse still need to be increased to accommodate further applications. However, taking into consideration the modest low pulse energy used in our experiment, radical improvements could be expected through various approaches such as applying higher laser intensity to raise the collimated electron charge and using thinner filtering pinholes. Imaging can, meanwhile, be ameliorated using more effective filtering arrangements and detection devices. We, thus, believe that this development provides a competitive approach for observing irreversible ultrafast phenomena by UED in the near future.
Acknowledgments
This work was sponsored by the National Natural Science Foundation of China (Grant Nos. 11874372, 11922412), the Shanghai Rising-Star Program, the Strategic Priority Research Program (B) (Grant No. XDB16), the Science and Technology on Plasma Physics Laboratory, the Youth Innovation Promotion Association of Chinese Academy of Sciences.
