Free-Electron Motion Recorded; Physical Constants Proven Incorrect

Scientists at the University of Michigan College of Engineering (UM; Ann Arbor, MI), have observed and recorded the relativistic motion of free electrons in the electromagnetic fields of light. Through these observations, the Thomson cross section—a quantity commonly used as a fundamental physical constant in strong-field theories—has been shown to be variable.

The UM research represents the first time that the instantaneous effects of both light's electric and magnetic fields upon electrons isolated from the overwhelming forces in atoms has been observed. The results confirm several predictions, based on Einstein's theory of relativity, about how electrons behave in extremely high-strength electromagnetic fields, such as those produced by powerful lasers or supernova explosions.

With the discovery, a new field of study called relativistic nonlinear optics can be pursued. This field may yield new technologies that generate x-rays that take snapshots on an atomic scale of ultra-fast chemical, physical, and biological processes like photosynthesis.

The research team was led by Donald Umstadter, associate professor in the UM College of Engineering, who coordinates the high-field science program of the Center for Ultrafast Optical Science where the work was performed. Szu-yuan Chen, an engineering graduate student, conducted the experiment as part of his doctoral thesis. Anatoly Maksimchuk, an assistant research scientist, built the high-power laser system that made the experiment possible.

Experimental Technique
In the experiment, which was designed to test basic aspects of electrodynamic theory formulated over the last century, the researchers focused Maksimchuk's laser onto a supersonic jet of helium. Powered with more than 1 trillion watts, the laser ionized the atoms of the gas, creating a plasma composed only of free electrons and ions.

By observing this plasma, the scientists discovered that the electrons scattered the laser light into colors (frequencies) that differ from, but are harmonically related to, the original beam. Furthermore, the angular direction of the scattered light was observed to be unique to each harmonic. This is the definitive signature of electrons moving in figure-eight patterns due to the combined forces of the light's electric and magnetic fields. The observations were recorded with a digital electronic camera and various filters.

In all previous experiments concerning light scattering by initially stationary free electrons, the effect of light's magnetic field was negligible. Because of this, the electrons had been observed to move in straight lines. The difference in the UM experiment was the ultra-high field strength of the laser light.

Thomson's Theory
Thomson's classic theory of electrodynamics explains that, as light moves past a free electron that is initially at rest, the electron is accelerated by the light's electric field. Although Thomson was aware that light is composed of both electric and magnetic fields, he supposed the magnetic field should have no effect on the electron's motion. Instead, the electron should move back and forth along a straight line in the same direction as the electric field. He also reasoned that the accelerated electron would radiate (scatter) new light waves with the same frequency as the original wave, in a direction at right angles to the light's electric field.

The Thomson cross section—which gives the probability that light will be scattered by a free electron—was assumed to be independent of the strength of the original light, and therefore a fundamental physical constant.

However, contrary to previous studies, the UM experiment demonstrates that the probability of scattering actually depends on the strength of light. Thomson was unaware of relativity, the theory of which was formulated by Einstein several years later. Moreover, the strongest fields of light available in Thomson's day were only equivalent to what can be obtained by focusing a 100-watt light bulb with a magnifying glass.

Light Theory Confirmed
For light with extreme parameters, modifications to electrodynamic theory are required. In the 1920s, Compton showed that the Thomson cross section was not constant for high-frequency light (x-rays) due to quantum mechanical effects.

Later, other theorists asserted that the effects of relativity would need to be incorporated to account for light with low optical frequency but extremely high field strength (as produced in supernova explosions and recently in the laboratory by extremely powerful lasers).

It was predicted that the electrons accelerated by such light would themselves reach nearly the speed of light, causing them to increase in mass, and subjecting them to the influence of light's magnetic field as well as its electric field. Therefore, the instantaneous motion of these electrons should resemble a figure eight, rather than a straight line, due to the combined forces of the light's electric and magnetic fields.

The observations of Umstadter's research team confirm this figure-eight (nonlinear) motion predicted by relativistic theory.

The UM scientists also showed conclusively that, because the speed of the electrons becomes irregular, they broadcast light not at the same frequency (color) as the original light wave (infrared), but at integer multiples of the original beam (green, blue, and so on, called harmonics). And while the first harmonic (infrared light) radiates principally at right angles to the laser's electric field, the second (green) and subsequent harmonics do not. Until now, in the absence of a sufficiently powerful laser, the relativistic predictions could not be tested experimentally.

History Of Optics
The high-power tabletop laser technology that made the experiments feasible was invented at the University of Rochester in 1985 by Professor Gerard Mourou, who has been director of UM's Center for Ultrafast Optical Science since 1988. UM has a history of making major discoveries in this area. Almost 40 years ago, the field of nonlinear optics was begun at UM by Professor Peter Frankin and his colleagues. Frankin was the first to observe harmonic generation from electrons that are bound to atoms.

Thousands of studies in the intervening 40 years have been done on the subject of nonlinear interactions of light with electrons bound to atoms. This research has produced numerous commercial technologies such as fiber optic communication systems.

Relativistic Nonlinear Optics And Future Applications
The findings of Umstadter's team usher in a new research field which could be called relativistic nonlinear optics—the study of light scattering from electrons that are free (not bound to atoms), but that move in nonlinear fashion (relativistically) due only to the intense light field.

A new set of technologies may flow from this discipline, if the results can be extended to the regime of coherent scattering (as was done with bound electrons). Coherent light occurs when the scattering from every electron is in phase with that from all the others.

The most important technologies will probably be developed as coherent harmonics in the x-ray region of the light spectrum are explored. For example, x-rays generated in this way should have extremely short pulses lasting less than a trillionth of a second. These might be used for time-lapse radiography, crystallography, microscopy, and lithography with atomic-scale resolution.

Myriad other nonlinear effects are also predicted to occur as lasers continue to produce record-breaking light intensities.

The UM discovery was featured in the Dec. 17, 1998 issue of the journal Nature. The National Science Foundation and the DOE's Division of Chemical Sciences and Office of Energy Research funded the UM research project.

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