At present, it seems that all the cool kids on the block are playing with laser wakefield accelerators. If you ask them about laser wakefield, they will excitedly jabber on about the coolness of it all. After all the explanations are gone through, you'll realize that these involve a tiny number of electrons moving really fast. Upon asking what laser wakefield accelerators are good for, their voices turn kind of mumbly. You get things like "driving free electron lasers" and "medical imaging," which might well be true, but they'll only work if they can control the accelerated bunches of electrons accurately enough.

And that is what this story is about. A graduate student in our group (I was not involved in the work at all) has just published a paper in Physical Review Letters that is all about control. If you set up the acceleration process just right, you can turn a single big bunch of electrons into a number of tiny bunches that are a few hundred attoseconds (an attosecond is one-quintillionth of a second) in duration.

What's a wakefield?

The basic idea of laser wakefield acceleration is that you spend a huge amount of time making a Big-Ass LaserTM and then you shoot said laser into a gas. The first part of the laser pulse promptly strips electrons from the gas molecules. These free electrons suddenly find themselves exposed to immense electric fields from the laser pulse and race to the outer edges of the laser beam. As the electrons move outwards, they form a bubble that travels behind the laser pulse. This bubble has an enormous electric field that is oriented along the direction of the laser pulse's travel—this is the wakefield, and it is just like the wake from a speed boat.

A few of the electrons get trapped in this laser-driven bubble and are accelerated so that they end up traveling at the speed of light in the plasma (which is just shy of the speed of light in vacuum). Over the course of a few centimeters, the electrons go from a standing start to having an energy of a gigaelectron volt (GeV)—doing this with a normal linear accelerator would take a accelerator tunnel on the order of a 100 meters.

This sounds pretty cool, but one of the problems with this scheme is that the electrons in the bubble end up all over the place: they enter the bubbles at different times and end up in different positions in the bubble, meaning that they are smeared out over a huge energy range. Consequently, they have different speeds, and the bunch of accelerated electrons falls apart rapidly. That's not good, since many of the envisioned applications for laser wakefield require that those bunches stick together.

Building better bunches

This is where our research group comes in. We have our own laser wakefield scheme. Instead of letting nature decide where the electrons end up, we use a small linear accelerator to create a bunch of electrons that have a relatively high speed already (3 MeV). This bunch arrives at the plasma just as the laser pulse does and the timing between the two pulses determines where the electrons end up in the bubble. In principle, this allows us to create bunches of electrons that all have nearly the same energy, so that the bunches stick together.

There is a caveat though: we haven't gotten it to work yet. By choosing to control where the electrons end up, we have given ourselves a gigantic headache, referred to as synchronization. That electron bunch has to arrive at the plasma within about a picosecond of the laser pulse. Given that both have to travel over several meters, and both are basically going at the speed of light, this implies that we have to control the path length difference between the two to within 0.1 percent of the total length. Not easy to do.

But, while the experimental program struggles, we have had our theorists doing a lot of modeling and we know the system really well now. Or we thought we did until one of our graduate students turned up a remarkable finding. He wanted to see how the bunch held together after the acceleration process had finished, so he extended the simulations to let that occur.

Remarkably, the bunch did hold together—since they're moving at nearly the speed of light, the electrons are so heavy that their charges can't really push each other away, so as long as they all have the same energy, they should stick together.

But that doesn't mean the bunch remained static. The electrons formed sub-bunches within the main bunch, and these were just 600 attoseconds (10-18s) in duration. Now, if the cool kids have laser wakefield accelerators, the "so cool you could chill a side of beef on me" kids have stuff with the word "attosecond" associated with it. We were pretty excited.

Electrons in an attosecond

So how do you get attosecond bunches of electrons? In the wakefield, there are two important fields: one is the enormous field oriented along the direction of the laser beam that provides the acceleration; the second is smaller, but also important. It points inwards, and keeps the electrons focused in the bubble.

Now, any electron that is off-axis upon entering the wakefield will start to oscillate about the central axis because the inward, focusing field is always forcing electrons back to the center. These shifts, called betatron oscillations, have an oscillation period that depends on how far off-axis the electron was when it started. Essentially, the electrons in the bunch all have the same forward motion, but they are sweeping back and forth through the center at individual times.

By itself, this doesn't really explain why we see bunching. The key is that the external injection scheme sets them all oscillating at the same time, so they stay in phase with each other. After that, it is all just a question of timing. When the electrons all happen to cross the axis at the same, they form a set of bunches that are less than a femtosecond in duration. If this happens to occur just as the bunch leaves the plasma, then the fields that drive the oscillations disappears, stopping it. As a result, the bunch expands, but still keeps its structure.

I could speculate endlessly about the reality of these bunches, but the truth is we will only know when the experiment gets switched on and we start examining real electron bunches. My feeling is that the simulations are good, and that, if we can get the timing right, we will see accelerated electrons. In the meantime, we have to shift labs, and the entire experiment must be disassembled in a couple of months, so we won't be observing attosecond bunches anytime soon.

Physical Review Letters, 2010, DOI: 10.1103/PhysRevLett.105.124801

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