Demonstration Scheme for a Laser-Plasma-Driven Free-Electron Laser

Laser-plasma accelerators are prominent candidates for driving next-generation compact light sources, promising high-brightness, few-femtosecond x-ray pulses intrinsically synchronized to an optical laser, and thus are ideally suited for pump-probe experiments with femtosecond resolution. So far, the large spectral width of laser-plasma-driven beams has been preventing a successful free-electron laser (FEL) demonstration using such sources. In this paper, we study the application of an optimized undulator design and bunch decompression to large-energy-spread beams in order to permit FEL amplification. Numerically, we show a proof-of-principle scenario to demonstrate FEL gain in the vacuum ultraviolet range with electron beams from laser-plasma accelerators as currently available in experiments.

Popular Summary

The doors to new scientific investigations and applications in physics, chemistry, biology, and medicine that can be opened by x-ray laser pulses of high brilliance and femtosecond durations seem limitless. But, the fact that the current free-electron laser (FEL) sources for such x-ray pulses are costly devices embedded in large-scale research facilities poses a severe limit on scientific progress. Having a tabletop x-ray FEL source at their disposal must be the dream of every x-ray scientist. Great effort is, therefore, being put into developing such compact sources. The most prominent candidate is arguably a FEL driven by an electron accelerator generated by the interaction of an intense laser with a gas plasma. The major difficulty that stands in the way is the large spread in the energies of the electrons in the accelerated beam produced in this class of devices, which makes the essential process in a FEL—the coherent self-amplification of the emission of x-ray radiation from the electrons—ineffective. The commonly held view was that a laser-plasma-driven FEL is not yet realizable today. In this theoretical work, we challenge this view with the design of a first proof-of-principle FEL experiment entirely based on currently available laser-plasma generated beams and demonstrate realistic laser emission gains.

An essential structural and functional component of a free-electron laser source is the undulator, a series of periodically placed, alternating magnets that cause electrons to wiggle back and forth to produce radiation. The central concept in our design is an undulator that is optimized to accept unusually high energy spreads. By increasing the undulator magnetic field, the wiggle amplitude of the beam electrons can be modified such that it partially compensates for the large spread in energies. Another critical parameter in the self-amplification process central to FELs is the length of interaction of the beam electrons with the radiation field they emit. As laser-plasma accelerators tend to generate very short electron bunches, decompressing the beam can increase the interaction length. By using a magnetic chicane, our design achieves bunch decompression and significantly reduces the requirement on the electron beam charge. As the result of these two new design features, experimentally detectable FEL gains appear possible with the electron beams generated by the currently operational laser-plasma devices.

We expect proof-of-principle experimental demonstrations to become possible in the near future.

Figure 1

Total emitted power (log scale) normalized to the spontaneous radiation level, scanning bunch charge, and rms energy spread in a range of $Q=10–40\mathrm{pC}$, corresponding to beam currents $I=2.4–9.6\mathrm{kA}$, Pierce parameters $\rho =1.4–2.3\%$, and ${\widehat{\sigma }}_{\gamma }\approx 0–1.0\%$, respectively. Data are obtained from time-dependent Genesis simulations, with each data point averaged over 10 runs with different shot-noise seeds, and error bars marking the standard deviation of the fluctuation in shot-to-shot power. The black dashed line indicates an amplification by an order of magnitude above the spontaneous background. With the optimized undulator, FEL gain is possible even for very-large-energy-spread beams.

Figure 2

Scan of the undulator parameter $K$ by changing the undulator gap size, for an electron bunch of $Q=40\mathrm{pC}$ and different uncorrelated energy spreads. Error bars mark 1 standard deviation of the fluctuation in power originating from runs with different shot-noise seeds, with each data point averaged over 10 runs. Large undulator parameters are required to permit FEL gain for beams of broad spectral width. This dependency weakens as indicated by the flat curve for ${\widehat{\sigma }}_{\gamma }=0.25\%$ if the FEL is no longer dominated by the energy spread.

Figure 3

Normalized power (log scale), for a chirped bunch, $\alpha =1\%/{\sigma }_z$, with a slice-energy spread of ${\widehat{\sigma }}_{\gamma ,s}=0.5\%$. About 20 pC in ${\sigma }_z=0.5\mu \mathrm{m}$ are sufficient to demonstrate FEL gain.

Figure 4

Normalized power (log scale) for a stretched bunch of initially ${\sigma }_z=0.5\mu \mathrm{m}$, 1% energy chirp over ${\sigma }_z$, and a slice-energy spread of ${\widehat{\sigma }}_{\gamma ,s}=0.5\%$. The solid line is the average over 10 runs and the error bars mark 1 standard deviation of the shot-to-shot power fluctuation. FEL performance is significantly enhanced compared to the initial bunch length. Dots represent individual runs of different shot-noise seeds to illustrate the spread in power, which originates from the self-amplified spontaneous emission FEL starting from noise. The rms variation in pulse energy relates to the number of modes $M$ in the FEL pulse and scales with $M^{-1/2}$ [33]. As the bunch length is comparably short, only a few modes are supported, leading to large shot-to-shot fluctuations.

Figure 5

Normalized power (linear scale) for a stretched ${\sigma }_z=2.5\mu \mathrm{m}$, $Q=5\mathrm{pC}$ bunch, for a varying linear undulator taper. As before, dots mark individual runs and the solid line is the average over different shot-noise seeds. The blue area indicates 1 standard deviation of the spread in power.