Synchrotrons and free-electron lasers are the most powerful sources of X-ray radiation. They constitute invaluable tools for a broad range of research1; however, their dependence on large-scale radiofrequency electron accelerators means that only a few of these sources exist worldwide. Laser-driven plasma-wave accelerators2,3,4,5,6,7,8,9,10 provide markedly increased accelerating fields and hence offer the potential to shrink the size and cost of these X-ray sources to the university-laboratory scale. Here, we demonstrate the generation of soft-X-ray undulator radiation with laser-plasma-accelerated electron beams. The well-collimated beams deliver soft-X-ray pulses with an expected pulse duration of 10 fs (inferred from plasma-accelerator physics). Our source draws on a 30-cm-long undulator11 and a 1.5-cm-long accelerator delivering stable electron beams10 with energies of 210 MeV. The spectrum of the generated undulator radiation typically consists of a main peak centred at a wavelength of 18 nm (fundamental), a second peak near 9 nm (second harmonic) and a high-energy cutoff at 7 nm. Magnetic quadrupole lenses11 ensure efficient electron-beam transport and demonstrate an enabling technology for reproducible generation of tunable undulator radiation. The source is scalable to shorter wavelengths by increasing the electron energy. Our results open the prospect of tunable, brilliant, ultrashort-pulsed X-ray sources for small-scale laboratories.


Resolving the structure and dynamics of matter on the atomic scale requires a probe with ångstrøm resolution in space and femtosecond to attosecond resolution in time. Third-generation synchrotron sources produce X-ray pulses with durations of typically a few tens of picoseconds and can achieve 100 fs by using complex beam-manipulation techniques12,13. They have already proven their capability of imaging static structures with atomic (spatial) resolution1 and upcoming X-ray free-electron lasers hold promise for also extending the temporal resolution into the atomic/sub-atomic range14,15,16,17,18. Both of these sources consist of an electron accelerator and an undulator, which is a periodic magnetic structure that forces the electrons to oscillate and emit radiation19. Whereas current facilities require a kilometre-scale accelerator, new laser-plasma accelerators offer the potential for a marked reduction in size and cost as well as pulse durations of a few femtoseconds.

Femtosecond-laser-driven plasma accelerators have produced quasi-monoenergetic electron beams2,3,4,5,6,7 with energies up to 1 GeV (refs 8, 9, 20, 21) from centimetre-scale interaction lengths. The concept is based on an ultra-intense laser pulse, which ionizes atoms of a gas target and excites a plasma wave. This trails the pulse at nearly the speed of light and generates longitudinal electric fields, which are more than three orders of magnitude larger than in conventional accelerators22. Plasma electrons can become trapped and accelerated in these fields to a well-defined ultra-relativistic energy, which is indicative of an electron bunch length confined to a fraction of the plasma wavelength (in our case 15 μm). This intuitive picture is confirmed by particle-in-cell simulations, which have revealed characteristic bunch lengths of the order of 3 μm, corresponding to bunch durations of 10 fs (ref. 23).

Driving short-period undulators with these electron beams holds promise for brilliant ultrashort X-ray sources on a university-laboratory scale. So far, undulator radiation from laser-plasma-accelerated electrons has been reported only in the visible to infrared part of the electromagnetic spectrum24. Here, we demonstrate the reproducible generation of tunable, ultrashort undulator radiation in the soft-X-ray range by propagating electrons with energies of 210 MeV through a specifically designed undulator with a period of 5 mm. The duration of this short-wavelength pulse is dominated by that of the electron bunch and hence estimated to be 10 fs, about three orders of magnitude shorter than that of typical pulses produced by synchrotron sources1 (for more details on electron-bunch duration and elongation during beam transport, see Supplementary Information). Detection of undulator radiation in some 70% of consecutive driver-laser shots indicates a remarkable reproducibility for a first proof-of-concept demonstration experiment. It can be attributed to a stable electron-acceleration scheme10 and the use of magnetic lenses11 to guide the electron beam through the undulator.

Undulators have a sinusoidal transverse magnetic field with an amplitude B0 and period λu that define the deflection parameter19 KB0·λu. In the rest frame of the relativistic electrons moving through this field, λu is contracted by the Lorentz factor γ, which is defined as the total electron energy E in units of the electron rest energy moc2. The undulator field causes the electrons to oscillate transversely with an amplitude proportional to K, and as a result of this acceleration to emit radiation. In the laboratory frame, this emission occurs in a narrow cone in the forward direction. The measured wavelength is once more reduced by γ because of the Doppler shift, which varies with the detection angle Θ. Taking into account the reduced longitudinal electron velocity caused by the transverse quivering motion, the detected wavelength for the nth harmonic is

In our experiment, the electron accelerator is driven by pulses from a 20 TW (850 mJ in 37 fs) laser system (see the Methods section). Focused into a hydrogen-filled gas cell with a length of 15 mm (Fig. 1), they produce stable electron beams showing a quasi-monoenergetic energy spectrum with a stable peak in the range of 200–220 MeV and 7 pC of charge in the whole spectrum.

Figure 1: Experimental set-up.
Figure 1

A laser pulse (red) is focused into a gas cell, in which plasma waves accelerate electrons (yellow) to energies of several hundred megaelectronvolts. The electron beam is collimated by a pair of quadrupole lenses. Plasma radiation and the laser beam are blocked by a 15 μm aluminium foil. The electrons propagate through an undulator and emit soft-X-ray radiation into a narrow cone along the forward direction (blue). The radiation is collected by a spherical gold mirror and characterized by a transmission grating in combination with an X-ray CCD camera. Stray light is blocked by a slit in front of the grating. The pointing, divergence and spectrum of the electron beam are diagnosed by phosphor screens.

For electron-beam transport from the plasma accelerator to the undulator, we use a pair of miniature permanent-magnet quadrupole lenses, which has proven to be a critical system component for stable, reproducible operation of the undulator source for two reasons. First, they reduce the angular shot-to-shot fluctuations of the electron beam by an order of magnitude. Second, the lenses also act as an effective energy-band-pass filter for the undulator radiation and thus lower the photon-energy bandwidth and fluctuations. These benefits arise from the chromaticity of the lenses, which means that only electrons with a particular energy are collimated, whereas the divergence of electrons with different energies markedly increases (Fig. 2a). As each individual electron emits its radiation in a narrow cone along its propagation direction, the whole photon beam has the approximate size and divergence of the emitting electron bunch. For that reason, it is possible to control the on-axis photon flux with the magnetic lenses by focusing the electron beam. In future applications, a small spot size on the target can therefore be achieved even for hard X-ray beams without the need for lossy optical focusing elements. For our set-up, a slightly convergent electron beam at 210 MeV yields the highest on-axis photon flux at the detector, whereas deviations of a few tens of megaelectronvolts cause this flux to drop sharply (Fig. 2b). Thus, the magnetic lenses limit the energy range of electrons that primarily contribute to the undulator radiation and therefore define an ‘effective’ electron spectrum (Fig. 2c).

Figure 2: Effect of the magnetic lenses.
Figure 2

a, Divergence of electrons traversing the magnetic lens assembly with energies of 190 MeV (red), 215 MeV (yellow) and 240 MeV (blue). b, Simulated normalized on-axis flux of the fundamental undulator emission versus electron energy 260 cm downstream from the undulator exit (at the position of the detector). The narrow bandwidth of 9% FWHM is due to the energy-dependent electron-beam divergence introduced by the magnetic lenses. c, Measured electron spectrum (blue) corresponding to the undulator spectrum of Fig. 3. The effective electron spectrum (green) is determined by the product of the measured spectrum (blue) and the system response curve (red in b,c). It has a bandwidth of 6% FWHM and a peak at 207 MeV.

The influence of the electron-beam divergence on the angular flux of the undulator radiation at the position of the detector was computed with the code SRW (ref. 25), taking into account all beamline components (see the Methods section) to generate a ‘system response’ curve (Fig. 2b). An effective electron spectrum can be determined by multiplying this system response curve with the measured electron spectrum (shown in Fig. 2c). This effective band-pass filtering reduces the shot-to-shot fluctuations of the spectral width and mean photon energy of the undulator emission as well as the bandwidth of an individual shot significantly below those of the corresponding electron spectra. For example, the fundamental spectrum of a single shot, shown in Fig. 3, shows a bandwidth of 22% (full-width at half-maximum, FWHM) at an observation angle of Θ=0 (after deconvolving the instrument function deduced from the zeroth diffraction order), whereas a bandwidth of 65% would be expected without the filtering of the lenses. In 70% of consecutive laser shots we observed undulator spectra, whereas in the remaining 30% the amount of charge in the effective electron spectrum was insufficient to produce enough radiation. The average charge within the effective electron spectrum was 0.6±0.3 pC, which produced 70,000±25,000 photons in the undulator fundamental, integrated over a detection cone of K/(2γ)=±0.7 mrad, leading to a bandwidth of 30% FWHM. The observed spectra show a fundamental wavelength at 18 nm and a second harmonic peak at 10 nm with shot-to-shot standard deviations of about 5%. The wavelength of the second harmonic is slightly longer than half the fundamental owing to its emission characteristics. In contrast to the fundamental, its flux distribution is peaked off-axis19 (Θ>0) with correspondingly longer wavelengths according to equation (1). Owing to the horizontally focusing mirror, these components are propagated through the slit onto the detector, shifting the peak of the observed on-axis spectrum to longer wavelengths.

Figure 3: Single-shot spatially resolved undulator spectrum.
Figure 3

a, Smoothed representation of the zeroth and the ± first diffraction order of the measured undulator spectrum corresponding to the electron spectrum of Fig. 2c. It consists of a fundamental peak at 17 nm and a second harmonic peaked at 9 nm, with a high energy cutoff at 7 nm. The theoretical parabolic dependence of the wavelength on the observation angle Θ is shown by solid lines. An electron energy of 207 MeV corresponding to the peak of the effective electron spectrum of Fig. 2c was used as a parameter. For the different emission characteristics of the second harmonic, our simulation yields an on-axis radiation spectrum peaked at a wavelength of 9.2 nm, which defines the parameter chosen for the corresponding parabola. b, On-axis lineout summed over 10 pixel rows around Θ=0 (blue) and the underlying raw data (red).

Figure 3 shows the spectral and angular distribution of undulator radiation measured in a single shot. The parabolic dependence of the wavelength on the observation angle Θ as predicted by equation (1) (see solid lines in Fig. 3a), is in excellent agreement with the measured data. From the spectrum shown in Fig. 3, we deduce (see the Methods section) that our source delivers 8,200±3,100 photons per shot per mrad2 per 0.1% bandwidth. An analytical estimation for the on-axis peak intensity in units of photons per shot per mrad2 per 0.1% bandwidth for an undulator with a deflection parameter of K<1 is approximately given by19 Nph≈1.744×1014Nu2·E2(GeV)·Qe·K2/(1+K2/2), where Nu is the number of undulator periods, E is the electron energy and Qe is the charge of the electron bunch. According to this estimate, a charge of 1.3 pC in the effective electron spectrum (green curve in Fig. 2c, which produced the undulator spectrum of Fig. 3) corresponds to 9,500±2,100 photons per shot per mrad2 per 0.1% bandwidth. (The error is due to uncertainties in the calibration of the charge measurement and in the lens settings, both of which determine the amount of charge in the effective spectrum.) From the measured electron-beam divergence of 1 mrad and source diameter of 2 μm (derived from numerical simulations23 and plausibility arguments involving the wakefield dimensions), we estimate the normalized electron-beam emittance as ɛn=0.8π mm mrad. For the central energy of the effective electron spectrum, this translates to a root-mean-square (r.m.s.) photon-beam size of 270 μm vertically and 630 μm horizontally in the undulator, with respective r.m.s. divergences of 180 and 170 μrad. Assuming a duration of 10 fs for the undulator radiation pulse, these estimates yield a peak brilliance of 1.3×1017 photons per second per mrad2 per mm2 per 0.1% bandwidth.

Owing to the broad range of electron energies delivered by the plasma accelerator (blue curve in Fig. 2c), the undulator source can be readily tuned to different wavelengths by changing the lens positions and thus shifting the system response (see Supplementary Fig. S2) and effective electron spectrum shown (by the green curve) in Fig. 2c. The correlation between the peak energy of the effective electron spectrum and the detected fundamental wavelength for different lens settings is shown in Fig. 4. The dependence of wavelength on electron energy predicted by equation (1) is in excellent agreement with the measured data.

Figure 4: Undulator wavelength versus electron energy.
Figure 4

Detected fundamental undulator radiation wavelengths plotted against the corresponding maxima of the effective electron spectra (determined by the method of Fig. 2c). The green and blue points correspond to consecutive shots with two different positions of the magnetic lenses, demonstrating the wavelength-tunability of the source (see Supplementary Information). The error bars arise from measurement errors of the electron spectrometer, the X-ray spectrometer, magnetic lens distances and the undulator field. The asymmetric error bars of the blue points are due to a non-zero angle of the electron beam with the spectrometer axis. The red points represent shots that lie outside the stable electron acceleration regime. The theoretical behaviour described in equation (1) is shown as a solid line.

Our experiment paves the way for a new generation of brilliant, compact X-ray sources with the potential for widespread application in university-scale laboratories. Of key importance will be the few-femtosecond duration of emission inherent to laser-wakefield acceleration. This implies orders of magnitude improvement in temporal resolution compared with third-generation synchrotron sources. The remarkable stability of this first laser-driven soft-X-ray undulator source along with anticipated advances in laser-electron acceleration26,27, beam transport and undulator design hold promise for further progress: in the short term, we expect this approach to spawn laboratory-sized undulator radiation sources with ångstrøm wavelengths and sub-10-fs pulse durations for four-dimensional imaging with atomic resolution28. In the long term, these developments may culminate in the emergence of laboratory-scale ultra-brilliant X-ray free-electron lasers29,30 with revolutionary impacts on many fields of science, technology and medicine.



Undulator radiation calculations are carried out with the code SRW (ref. 25). The effect of the magnetic lenses is taken into account using the Twiss parameters, determined by electron-beam optics with an initial electron source size of 2 μm and divergence of 1 mrad. The calculated near-field is subsequently propagated through the beamline, consisting of a spherical focusing mirror with a 10 m radius of curvature and a slit, onto the detector.

X-ray spectrometer.

The spectrometer consists of a 1,000 lines mm−1 transmission grating with free-standing wires held by a support mesh. The radiation was detected by a Princeton Instruments SX-400 X-ray CCD (charge-coupled device) camera. Owing to a slight rotation of the grating with respect to the CCD camera, the parabolas drawn in Fig. 3a are corrected accordingly. Stray light was blocked by a 700 μm slit in front of the grating. The wavelength calibration was deduced from plasma radiation, when the blocking foil (Fig. 1) was removed, by the spectral cutoff through a 150 nm aluminium filter (17.1 nm) in front of the CCD. To deduce the number of photons emitted by the undulator, the wavelength-dependent reflectivity and efficiency of the gold mirror and the transmission grating as well as the wavelength-dependent quantum efficiency and conversion from CCD counts into detected photons have been taken into account.

Laser-plasma accelerator.

The laser-wakefield accelerator is driven by the ATLAS Ti:sapphire laser system, which delivers pulses of 850 mJ energy on target with a 37 fs FWHM duration at a central wavelength of 800 nm with a repetition rate of 10 Hz. The laser beam is focused by an f/22 off-axis parabola to a spot of 23 μm FWHM (corresponding to a normalized laser-vector potential of a0=1.0) into a 15-mm-long hydrogen-filled gas cell of 200 μm diameter. At a plasma density of np=8×1018 cm−3, electron bunches with an overall charge of 7 pC are injected into the laser wakefield and accelerated to energies of up to 210 MeV (ref. 10). The average beam divergence after collimation with the magnetic lenses is 0.7 mrad with an r.m.s. angular shot-to-shot variation of 0.2 mrad.

Miniature magnetic quadrupole lenses and undulator11.

The magnetic lenses with a field gradient of 500 T m−1 over a radius of 3 mm are positioned 25 cm after the accelerator in a doublet configuration with lengths of 17 mm and 15 mm, respectively. The permanent-magnet (NdFeB) undulator has a length of 30 cm with 5-mm-long periods constructed in a hybrid structure. At a gap of 1.2 mm between the magnetic poles, it has an undulator parameter of K=0.55.


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We thank M. Fieß, R. Ernstorfer, A. Cavalieri, E. Fill and M. Hofstetter for equipment. This work has been financially supported by the DFG through Transregio TR18 and supported by the DFG Cluster-of-Excellence ‘Munich-Centre for Advanced Photonics’ MAP.

Author information


  1. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany

    • Matthias Fuchs
    • , Raphael Weingartner
    • , Antonia Popp
    • , Zsuzsanna Major
    • , Jens Osterhoff
    • , Rainer Hörlein
    • , George D. Tsakiris
    • , Dietrich Habs
    • , Ferenc Krausz
    • , Stefan Karsch
    •  & Florian Grüner
  2. Department für Physik, Ludwig-Maximilians-Universität, Am Coulombwall 1, 85748 Garching, Germany

    • Matthias Fuchs
    • , Raphael Weingartner
    • , Zsuzsanna Major
    • , Stefan Becker
    • , Jens Osterhoff
    • , Isabella Cortrie
    • , Benno Zeitler
    • , Rainer Hörlein
    • , Dietrich Habs
    • , Ferenc Krausz
    • , Stefan Karsch
    •  & Florian Grüner
  3. Forschungszentrum Dresden–Rossendorf, Bautzner Landstraße 128, 01328 Dresden, Germany

    • Ulrich Schramm
  4. University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK

    • Tom P. Rowlands-Rees
    •  & Simon M. Hooker


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M.F., R.W., A.P., Zs.M., S.B., J.O., S.K. and F.G. carried out the experiment. M.F., R.W., A.P., Z.M., S.B., J.O., R.H., G.T., U.S., T.P.R., S.M.H. and S.K. designed and fabricated the components of the experiment. M.F., I.C. and B.Z. analysed the data. D.H., F.K., S.K. and F.G. provided overall guidance to the project.

Corresponding authors

Correspondence to Stefan Karsch or Florian Grüner.

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