Since their discovery in 1896 [1], x-rays have fundamentally revolutionized science, medicine and technology. Each successive generation of x-ray machines has opened up new frontiers in science, such as the first radiographs and the determination of the structure of DNA. State-of-the-art x-ray sources, such as synchrotrons, can now produce coherent high-brightness beams of x-rays with energies greater than kiloelectronvolt, which promise a new revolution in imaging complex systems on the nanometer and femtosecond scale. We have recently demonstrated the use of a new generation of laser-driven plasma accelerators, which accelerates high-charge electron beams to high energy in short distances, to produce directional, spatially coherent, intrinsically ultrafast beams of hard x-rays [2]. This reduces the size of the synchrotron source from the tens of meters to the centimeter scale, simultaneously accelerating and wiggling the electron beam. The resulting x-ray source is 1,000 times brighter than previously reported plasma wigglers and thus has the potential to facilitate a myriad of uses across the whole spectrum of light-source applications.

Theory and Experimental Setup
The experiment was carried out at the University of Michigan's Center for Ultrafast Optical Science, which houses one of the most powerful laser systems in the world, the 300 TW Hercules laser. The compact x-ray synchrotron is based on focusing this pulsed high power laser into a millimeter-sized plume of helium gas. The laser is focused down to a size smaller than the diameter of a human hair, achieving intensities of 2×1019 watts per square centimeter. At this intensity, the helium gas is ionized immediately, separating electrons from the atomic nuclei and creating so-called plasma. A sketch of the setup is shown in figure 2. As the laser propagates through the plasma, it drives a plasma wave in its wake, i.e. it displaces electrons from the almost stationary ions, setting up large accelerating electrostatic fields. Background electrons can become trapped and ride the plasma wave much like a surfer on an ocean, to gain energy from the wave. It was demonstrated a few years ago, that this scheme can produce a high quality beam of directional electrons with energy of the order of 100 megaelectronvolt and very small relative energy spread of order a few percent [3-5].

The plasma wave not only accelerates electrons along the propagation direction of the laser but also provides a transverse field to wiggle them around. It is this wiggling motion that causes the electrons to emit light in the form of ­x-rays. The plasma wave therefore mimics the processes of acceleration and radiation generation that are found in a conventional synchrotron accelerator and insertion device, but on a microscopic scale.

Results
To diagnose the electron and x-ray beams, a set of diagnostics was deployed, as indicated in figure 2. The electron beam was deflected with a permanent magnet and dispersed to measure the energy spectrum.

For example, for an plasma density of 8×1018 cm-3 on the 5 mm diameter gas jet, electron beams of W = (230 ± 70) MeV with ∆W/W = (25 ± 10) % energy spread at full-width at half-maximum (FWHM), with a root-mean-square (rms) divergence of 1.5 × 1.8 mrad2 and an rms pointing fluctuation of 4.8 × 4.7 mrad2 were obtained.

With the electron beam deflected away from laser axis by the spectrometer magnet, a bright (undeviated) beam of x-rays was also observed co-propagating along the laser axis. It was imperative to first prove that this x-ray source originates from the plasma itself. To do this, a grid of silver wires (60 μm diameter, 310 μm separation) was placed a few centimeters from the target. X-rays originating from the interaction region project the outline of the mesh onto an imaging plate, an erasable wide-area x-ray detector. A strongly directional beam of x-rays is evident in figure 3. When ­either the laser power or electron plasma density was reduced to inhibit the electron beam, the x-ray beam also disappeared, showing that the generation of the x-rays is linked to the electron beam. The profile is elliptical, with a FWHM divergence of θx× θy = 4 × 13 mrad2, corresponding to a wiggler parameter K = θx of Kx = 1.5 and Ky = 5 for a simultaneously measured electron beam energy W = 200 MeV. Figure 3, combined with other similar measurements [2] also reveals that each x-ray pulse consists of a total of 108 x-ray photons in a broad synchrotron spectrum with an average energy of 10 keV, whilst the pulse duration is ultrashort, on the order of the pulse duration of the high power laser, which is 30 femtoseconds.

To give an indication of the x-ray source size, microscopic objects were backlit with the x-ray beam. Figure 1 shows x-ray radiographic images of a resolution test target. It consists of a gold foil with a thickness of 20 μm, which has lines and bars etched into it. Even the smallest features of size 3 μm are resolved, indicating that the x-ray source is at most 3 μm, smaller than the size of the plasma wave in which the radiating electrons were trapped and oscillate (20 μm diameter). To quantify the source size more precisely, a half-plane was backlit with the x-ray beam, as shown in the experimental setup (fig. 2). A typical intensity distribution on the detector looks like a half-shadow (fig. 2), whose details convolve information about the x-ray source and the half-plane. When integrated along the edge, the intensity profile takes the shape of a step, as shown in figure 4, which depicts several experimentally measured intensity profiles.