The interaction of an electron bunch and its synchrotron radiation begins when an electron bunch bends through a magnetic field and emits a cone of synchrotron radiation that has a transverse electromagnetic field. Because of their bent trajectory, electrons in the front of the bunch sense a longitudinal component of the radiation field that can either accelerate or decelerate the electron, depending on its position. The interaction can give rise to a self-amplified instability starting from a small modulation on the bunch profile. This modulation radiates coherently, causing the bunch modulation to increase. Counteracting this effect is the natural energy spread within the bunch, which tends to cause any modulation to smear out. An instability occurs when the runaway amplification beats out the damping effect of the energy spread.

Schematic view of the interaction of an electron bunch with its own synchrotron radiation. The curvature of the electron orbit allows the radiation field to interact with the electron.

Computer simulations of the microbunching instability as the threshold for the instability is passed were the first step. Above the instability threshold, a ripple in the energy distribution is evident in the simulations, along with a small ripple on the bunch profile. As the instability progressed, the disruption in the bunch increased, giving a larger modulation in the bunch profile. Finally, the instability reached saturation and the bunch profile smoothed over, although with an increased length. After radiation damping returned the bunch distribution to its original shape, the instability repeated.

How to Corral T Rays

The ALS was built to produce x rays from a beam of high-energy electrons. The beam is not continuous but consists of a few hundred discrete bunches about a centimeter long into which groups of a few million electrons are clustered. Ordinarily, each electron emits independently, and the total power radiated is proportional to the number of electrons. However, when the wavelength of the emitted radiation is comparable to the length of an electron bunch, the electrons emit in unison rather than as individuals. This coherent emission results in a dramatic increase in the power emitted (proportional to the square of the number of electrons), thereby also generating a wave of enthusiasm among scientists who are potential users of coherent synchrotron radiation (CSR). Because of the high power and because CSR occurs primarily at very long wavelengths in the far infrared portion of the spectrum, where the frequency is around 1 trillion cycles per second (or 1 terahertz, abbreviated THz), it is becoming known by the name T rays. Byrd et al. have used the ALS to observe and explain an instability in the electron beam that potentially prevents the generation of T rays, thereby contributing to the ability to design future electron accelerators (storage rings) optimized to produce them.

Evolution of a microbunching instability illustrated via a computer simulation. The top row shows the electron density in coordinates of relative position along the bunch and fractional energy offset. The bottom row shows the projection of the top row on the longitudinal charge density. The small modulation in the density (left) is amplified until the instability reaches saturation (right).

During the instability, the microbunching resulted in bursts of CSR at the wavelength of the bunch modulation, which for ALS parameters ranges from a few millimeters down to half a millimeter (far infrared or terahertz). To observe these bursts experimentally, the team installed detectors, such as bolometers and heterodyne receivers, at ALS infrared Beamline 1.4.3. With one of the bolometers , the researchers found that the bursts appear above a threshold single-bunch current. As the bunch current increased further, the burst rate and amplitude increased and eventually saturated the detector. At the highest bunch currents achievable at the ALS, the researchers measured a 700-fold enhancement in the power of the CSR emission over the normal incoherent radiation. However, the bursting nature of the signal presents a challenge for its use as a source of CSR.

Examples of bursts of far-infrared synchrotron radiation measured with a bolometer. Each of the bursts is associated with a microbunching of the electron beam caused by interaction with the synchrotron radiation. At larger bunch currents, the burst rate and amplitude increased.

To compare these results with a model recently developed elsewhere, the team measured the bursting threshold as a function of electron beam energy. The data show good agreement with the model. The researchers believe they have good a understanding of this instability and can use the model to predict the performance of future storage rings, particularly sources of CSR.

Comparison of the measured microbunching instability threshold as a function of electron beam energy with that predicted by a model. The comparison shows good agreement between the two.

Research conducted by J.M. Byrd (ALS and University of California, Davis); W.P. Leemans and B. Marcelis (Berkeley Lab); A. Loftsdottir (Berkeley Lab and University of California, Davis); and M.C. Martin, W.R. McKinney, F. Sannibale, T. Scarvie, and C. Steier (ALS).

Research funding: U.S. Department of Energy, Office of Basic Energy Sciences, and Berkeley Lab Laboratory Directed Research and Development.

Publication about this research: J.M. Byrd, W. Leemans, A. Loftsdottir, B. Marcelis, M.C. Martin, W.R. McKinney, F. Sannibale, T. Scarvie, and C. Steier, "Observation of broadband self-amplified spontaneous coherent terahertz synchrotron radiation in a storage ring," Phys. Rev. Lett. 89, 224801 (2002).