Tutorial on X-Ray Slicing
Electron beam slicing as implemented at third generation synchrotrons is one way to generate femtosecond pulses of X-rays for practical experiments. The idea to use resonant energy exchange between a femtosecond laser pulse and electrons in an insertion device to produce femtosecond X-rays was external pageproposed in 1996 by A. Zholents and M. Zolotorev, and the technique was first external pagepractically demonstrated several years later by Schoenlein, et al. At present, three synchrotrons have implemented this technique: the external pageALS in Berkeley, CA, external pageBESSY in Berlin, Germany, and the external pageSLS.
The papers linked above are the definitive technical references for the technique, and what follows is an informal pictorial introduction to the basic ideas behind slicing aimed toward people who (like me) are not experts in electron beam dynamics. Hopefully is it useful for someone who wants a simple idea of how slicing works and why one might want to do it without delving into a lot of technical details. I also neglect talking about a lot of alternative methods of generating short-pulse X-rays. This discussion assumes some level of rough familiarity with synchrotrons: there are external pageother external pagesources of background material on this subject.
Introduction: Ultrafast X-ray experiments with synchrotrons
Third-generation synchrotrons are amazingly brilliant sources of low-wavelength radiation, providing many orders of magnitude more usable photons for experiments than was even imagined 50 years ago. Time-resolved experiments are particularly demanding in terms of source requirements, and they present a few special difficulties of their own. Broadly speaking, there are two general schemes for achieving time resolution in an experiment: a continuous (or quasi-continuous) source with fast detection, and pump-probe.
Fast detectors
The temporal structure of X-ray output from a synchrotron mirrors the temporal structure of the electrons used to produce the X-rays: typically a train of ~100 ps long bunches spaced at intervals of a couple of nanoseconds that make repeated trips around the storage ring. On certain time scales, this time structure can be approximated as a continuous source of X-rays. Time resolution can then be achieved by exploiting the time resolution of the equipment used to detect the X-rays. This is usually the method used at synchrotrons to observe processes on time scales > 10 ns. Faster time resolutions are possible in special cases: for example, an external pageultrafast X-ray streak camera can resolve the time structure of a single 100 ps long X-ray pulse with 280 fs resolution, but it needs very small input aperture (5 microns) and has limited quantum efficiency in the hard X-ray range (normally < 0.01 for energies > 4 keV).
One important advantage of using fast detectors is that in some cases non-repeatable measurements can be performed, provided sufficient signal per unit time is available. This is essential for studying phenomena which are not easily triggered by an external clock, or which are fundamentally chaotic. Of course, in cases where these "single-shot" measurements are not possible, repetitive measurements can be made and averaged together to give better signal-to-noise ratios.
Pump–probe
For time resolutions faster than 10 ns, the usual procedure in both optical and X-ray spectroscopy is to adopt a "pump-probe" methodology. This scheme relies on having two temporally synchronized signals, called a "pump" and a "probe." The pump excites a sample on a fast time scale, triggering some kind of change. The pump comes a bit later in time and measures some property of the signal on a fast time scale. At some later time the sample is either replaced by another unexcited sample or somehow relaxes to its original state, and the whole process repeats itself, perhaps with a different selection of the pump-probe time delay. By mapping out the results of the probe measurement as a function of the time delay, we get the average time-response of the sample to the pump excitation. The time resolution is set by a convolution of the pump time scale, the probe time scale, and the synchronization uncertainty.
For sub-nanosecond time scales, the pump is typically a short laser pulse or some signal derived from such a pulse. With commercial lasers, it is fairly routine to create intense optical pulses with time scales < 100 fs. Methods have also been developed to syncnhronize the synchrotron beam to a laser with an error approaching 100 fs. The x-ray bunch width of ~100 ps is thus the limiting factor for the time resolution of a pump-probe experiment. For normal, stable operation of storage ring the average temporal width of the bunches cannot be compressed very much beyond this if the ring is to maintain a high average photon output.
Slicing: shorter x-ray pulses
The idea behind slicing is to use the very high electric fields (> 109 V/m) achievable by femtosecond laser pulses to exchange energy with a temporally short (< 100 fs) "slice" of a ~100 ps long electron bunch in the storage ring. The electrons within this slice will then have a larger energy spread than the other electrons in the bunch, and will therefore follow slightly different orbits when passing through dispersive electron optics (e.g. a bend magnet). It is then possible to isolate the x-ray radiation from some of these sliced electrons when they pass through an insertion device or bend magnet placed at a judiciously selected point in the storage ring. Eventually, the sliced electrons will relax back into the main bunch due to damping mechnisms in the storage ring, allowing the process to repeat itself with another laser pulse.
A femtosecond laser pulse: the electric field
The above animation shows the electric field of a femtosecond laser pulse.
This fact that free-space modes of laser radiation have electric fields transverse to the direction of propagation has important consequences. Imagine what would happen if we tried to co-propagate this laser pulse with an electron moving in a straight section of a storage ring. The electron would experience forces perpendicular to its direction of motion, and these forces would nearly average out over the duration of the pulse. In order to have efficient energy exchange between the electric field of the laser and a relativistic electron in the storage ring, we need to have a periodic transverse component of momentum in the electron.
Modulation
Fortunately, third generation synchrotrons are full of devices that do exactly that: undulators and wigglers. Normally, these devices are used only to give energy from electrons to light (usually X-rays), but they can also be used to transfer energy from a very intense light source to the electrons. By constructing and tuning a wiggler, we can achieve highly efficient energy gain from the laser field for some electrons, and highly efficient energy loss for other electrons, the gain or loss depending on the phase of these electrons with respect to the electric field of the laser.
The animation above shows an electron that has the right phase with respect to the laser electric field to achieve maximum energy gain. Note that the force vector exerted by the electric field is always in the same direction as the transverse component of the electron momentum. This causes the energy of the electron to increase. For the purposes of illustration, the transverse motion of the electron is highly exaggerated.
This animation shows an electron only half an optical wavelength away that experiences maximum energy loss from the laser interaction. The force from the electric field is always pointed in the opposite direction of the transverse component of the electron's velocity.
Separation
After the laser modulates the energy of the electrons, these modulated electrons still need to be separated from the rest of the beam. This is done by exploiting dispersion (energy-dependence) of the storage ring electron optics. Simply put, electrons with different energies will travel slightly different paths through some of the electron optics. The simplest example of such a dispersive optic is a magnetic dipole, used for steering the synchrotron beam around the ring. In a constant magnetic field, the turning radius of an electron depends its energy. This causes a spatial and angular separation of the modulated electrons from the rest of the beam.
The animation above shows the separation of the modulated electrons when passing through a simple dipole magnet. The color indicates the energy of the electrons: from red (lowest) to blue (highest).
Provided there is some kind of separation of the modulated portion of the beam from the rest of the electrons, isolating the x-rays generated by these modulated electrons is a matter of using appropriate x-ray optics (slits at different image planes). The result is a femtosecond pulse of x-rays with nearly the temporal width of the laser pulse!