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June, 2007
Terahertz Radiation from Tabletop Accelerators: A Tool for Measurement and Experiment

The nickname "tabletop accelerator" may be a metaphor, but laser wakefield accelerators are still remarkably compact by comparison with traditional particle accelerators whose length is measured in kilometers.

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Wim Leemans and Jeroen van Tilborg with the LOASIS laser wakefield acceleration experiment. (Photo Roy Kaltschmidt, CSO)

Since 1995, Wim Leemans and his LOASIS group (Laser Optics and Accelerator Systems Integrated Studies) in Berkeley Lab's Accelerator and Fusion Research Division have been leaders in the development of laser wakefield accelerators. Recently these compact accelerators have boosted beams of electrons to energies of a billion electron volts in only a few short centimeters — although to do it they require lasers with paths many meters long.

"The basic laser wakefield concept is to use an intense laser pulse to punch through a plume of helium or hydrogen gas, forming a plasma in which strong electric fields trap and accelerate bunches of electrons," says researcher Jeroen van Tilborg.

Now in Berkeley Lab's Chemical Sciences Division, van Tilborg was introduced to laser wakefield accelerators in 1999 as an undergraduate from the Netherlands, when he spent a three-month student internship at LOASIS. Leemans invited van Tilborg to do his doctoral work at Berkeley investigating the then-unanswered question of the "time domain" of the electron bunches.

At the time, says van Tilborg, "Many characteristics of the system were well understood, such as the charge, electron bunch energy, and bunch divergence of the electron bunches that make up the beam. What was difficult to measure directly was the precise duration of the bunch — in other words, its length."

Leemans suggested that one approach might be to use the coherent radiation emitted when the electron bunch leaves the plasma and enters the surrounding vacuum. This so-called transition radiation, in the terahertz range (a terahertz is a trillion cycles per second, abbreviated THz), should contain all the time information about the length of the bunch. The challenge was to detect and measure it.

Van Tilborg was excited by the project, but UC Berkeley would not recognize the master's degree he was awarded in 2001, so rather than start over he pursued doctoral studies at Technische Universiteit Eindhoven (the Eindhoven University of Technology, the Netherlands) under Marnix van der Wiel, with Leemans as his co-advisor. Subsequent research for his thesis was done in the LOASIS group.   

Energy in transition

"Any time a bunch of electrons goes from one medium to another with different dielectric properties — say from vacuum through a metal foil, or from plasma to vacuum — transition radiation is emitted," van Tilborg says (the term dielectric refers to a medium's insulating properties). "The radiation is broad-spectrum, consisting of many wavelengths. In fact, the radiation pulse is so short and so broadband it is just a few field cycles long."

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A laser (yellow) forms plasma (green) in a gas plume, and wakefields accelerate bunches of electrons (purple). When an electron bunch encounters the plasma-vacuum boundary, transition radiation (red) is emitted at terahertz frequencies. (After van Tilborg)

Not all the radiation produced is available for analysis. "Wavelengths shorter than the bunch length interfere destructively — they cancel each other out," van Tilborg explains. "Wavelengths longer than the bunch itself add constructively, however, and the profile of the bunch can be determined by analyzing the spectrum of this coherent radiation." 

In the kind of setup for wakefield acceleration that van Tilborg was working in, the electron bunches that leave the plasma quickly blow apart once in vacuum. For this reason, the coherent radiation has to be emitted as near as possible to the creation of the electron bunches. Luckily, the plasma-vacuum boundary, located only a fraction of a millimeter from where the electron bunches are produced, serves as the radiation emitter. Mirrors placed outside the electrons' (and the laser's) path can reflect the terahertz signal to detectors.

Van Tilborg used two kinds of detectors to capture and study the terahertz radiation. The first was a liquid-helium-cooled bolometer, or thermal detector, to measure the energy of the terahertz pulse falling upon it. With this detector van Tilborg proved that in fact terahertz pulses are produced at the plasma-vacuum boundary. He demonstrated the radial polarization of the pulse and showed that its energy increased as the square of the charge — the more electrons in the bunch, the greater the terahertz pulse energy.

Pumps and probes

"In this early stage, we also used a few tricks to get an approximate measure of the duration of the electron bunch," van Tilborg says.

The technique called semiconductor switching uses a pump pulse — in this case, a slice of the same laser beam that goes on to create the plasma and accelerate the electrons — and a probe pulse, the terahertz radiation. A silicon wafer (the semiconductor) is placed in front of the bolometer; normally terahertz radiation penetrates the silicon wafer to be registered by the bolometer.

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In a semiconductor-switching experiment, a terahertz pulse is directed by mirrors to a silicon wafer that acts as a switch. Normally the wafer transmits the THz pulse, but reflects it when excited by a pump laser beam, whose timing can be adjusted relative to the arrival of the pulse. The bolometer measures how much energy is transmitted through the semiconductor switch. (After van Tilborg)

But when the pump laser pulse strikes the wafer, it almost instantaneously excites a plasma in the surface layers of silicon, momentarily reflecting the probe terahertz pulse. (The plasma consists of negative and positive charge carriers, but while the negative charge carriers are electrons, in semiconductors the positive charge carriers are holes, that is, the absence of electrons.)

Says van Tilborg, "The arrival time of the terahertz probe can be adjusted, and through a temporal scan, the duration of the electron bunch that created the terahertz radiation can be estimated."  

The main function of the semiconductor switching set-up, however, was to measure the time overlap of the two pulses to femtosecond accuracy. This opens the way to far more precise measurements of the terahertz pulse, using a second experimental approach called electro-optic sampling.

"Now the terahertz pulse becomes the pump, and a circularly polarized, very short laser pulse is the probe," van Tilborg explains. "The terahertz radiation induces birefringence in certain crystals" — a birefringent crystal is one that can modify the polarization of an incident beam into a new polarization state, for example, from circular to elliptical — "so that the polarization state of the probe laser pulse as it leaves the crystal depends on how strongly it has interacted with a given slice of the terahertz electric field."  

By scanning the delay between the laser and terahertz pulses and recording the laser energy transmitted through a polarizer and analyzer, the temporal profile of the terahertz pulses — and thus the electron bunches that created them — could be reconstructed with high precision. This multi-shot technique averaged the properties of several pulses to reconstruct the profile of a typical bunch of accelerated electrons. 

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In an electro-optic sampling experiment, a circularly polarized laser beam passes through a special crystal and a polarization analyzer, with 50-percent power transmission through the analyzer. A terahertz pulse induces birefrigence in the crystal, however. The polarization of the laser pulse and the power transmitted depend on how the two pulses overlap. Adjusting the timing between the pulses allows for precise measurement of the THz pulse profile. (After van Tilborg)

However, van Tilborg says, "because laser wakefield accelerators were not yet perfectly stable from shot to shot, we also wanted to take snapshots of terahertz radiation pulses from single bunches — so that we could get the whole THz waveform in one measurement without averaging."  

To do that van Tilborg devised several different single-shot techniques, all based on the electro-optic effect. The basic concept of these techniques is that the terahertz pump imprints a spatial or spectral signature, or a modulation, on a longer probe laser beam. This modulation can be unraveled in a single measurement with a spectrometer or a cross-correlator.

The data taken during the experiments showed for the first time that the laser-wakefield accelerator delivers bunches shorter than 50 femtoseconds, which were stably synchronized with respect to the laser. In addition, by these and other means, including two-dimensional imaging of the THz pulses with an "electro-optic camera," van Tilborg discovered what averaging had disguised: individual THz pulses were not simple, delivering all their energy at once as depicted by a single peak on a graph, but showed a double peak structure, which was very stable in timing.

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Analysis of single-shot terahertz pulses revealed that not all their energy is delivered at once. Here, measured results (solid lines) of three separate shots are compared to model predictions (circles); the double-peak structure is temporally very stable. Imaging with a 2D electro-optic camera confirmed the presence of a main pulse and secondary structure. (After van Tilborg)

Such a second peak might be formed by a second bunch of accelerated electrons, but tests showed this scenario to be unlikely. A more likely hypothesis (which van Tilborg backed up with mathematical modeling) is that aberrations in the THz beam path lead to the second peak: when focusing optics are not ideally placed, effects on single-cycle pulses, like the coherent THz pulses in van Tilborg’s experiments, can be dramatic.

Terahertz radiation on its own

"Studying the temporal profile of terahertz pulses produced by laser-wakefield-accelerated electron beams yielded two main results," van Tilborg says, "the first being proof of the femtosecond-scale duration of the accelerated electron bunches. That's what we set out to do."

The second result was a demonstration of the unique qualities of the terahertz pulses themselves, "which are one to two orders of magnitude more intense than from conventional sources based on lasers." Van Tilborg says that groups who want to use terahertz radiation for experiments have been just as interested in his findings as those who are building laser-wakefield accelerators.

Van Tilborg's doctoral thesis, Coherent terahertz radiation from laser-wakefield-accelerated electron beams, was published by the Eindhoven University of Technology in 2006 and was recently named the Outstanding Doctoral Thesis in Beam Physics by the American Physical Society's Division of Physics of Beams. Dissertations in the Netherlands, unlike their American counterparts, are not dull "white papers" but resemble high-end trade paperback books, with slick full-color covers designed by their authors.

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And the dissertations are accompanied by another kind of unique document, a list of "Statements" the candidate must defend. Some statements are academic, but others, Van Tilborg says, "are there to show the candidate is not just a geek."

One that van Tilborg chose to defend reflects his side in the eternal struggle of theory and experiment: "Safety is less compromised if an experimental physicist engages in theoretical efforts than if a theorist participates in experiments."  

Van Tilborg is clearly at home in the lab. His tools have benefited all parties interested in laser wakefield accelerators, in terahertz radiation, and a range of events that happen on the scale of the ultrafast.  

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