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Riding the Wave of E = mc2
by Caolionn O'Connell

Einstein's Big Idea homepage

I have never been a fan of learning in a classroom. Inside a laboratory or a garage, I always wanted to know more, but never inside a classroom. Since most adults don't work in a classroom, it was always hard for me to see the applicability of idealized problems in an idealized world. I was one of those kids who annoyed the teachers by asking, "When am I ever going to use this? How is this possibly useful? Nobody uses calculus in real life—why are you making me take this class?" I think my calculus teacher, Mr. Schleunes, would be very amused to discover that I became a physicist, which, I am red-faced to admit, actually requires calculus. Regularly.

Did I learn my lesson? No. My introduction to special relativity earned a similar response. Most every lesson on special relativity involves either a spaceship or a train going the speed of light, and exciting physics ensues with changes to time and space. Sure, it was cool and almost mind-bending, but neither spaceships nor trains go the speed of light, so I didn't see this topic as necessary for "life skills." Clearly, I did not anticipate that my specialty in physics would involve speeding particles (electrons) up to the speed of light using new and different techniques. Yeah, eating crow is now also a specialty of mine.

Due to my lack of enthusiasm for class work, it is a little surprising that I should have gone into physics. But once the abstract part of science was explained to me in terms of the concrete components, which we can measure in experiments, then it all seemed to make sense. Calculus was useful (shocking!). How else was I going to know the number of electrons coming into our experiment? A spaceship going the speed of light is not too different than an electron going 99.999999997 percent the speed of light. The physics is still the same, but now we're talking reality. Once the science and the math became useful, then I could understand how powerful calculus is.

"The Equation" at work

This is the point where I mention "The Equation" (I feel it has reached such a stature at this point, caps are required). E = mc2 is incredibly well known, but like calculus and spaceships going the speed of light, it might be a bit surprising to learn we actually use it outside the classroom.

To give a sense of scale, without Einstein and our understanding of The Equation, I wouldn't have a job. Well, I would have a job somewhere, I hope, but I probably wouldn't be having as much fun. One can argue that Einstein's work is the foundation for our experiments in high-energy (or particle) physics. My day-to-day work is concerned with the E side of The Equation. Energy is my business. I and my collaborators are not working on harnessing energy to power your lightbulb (sorry, other more qualified persons are working on that one for you). Rather, we are trying to increase the energies of electrons using different types of particle accelerators.

It makes me feel a bit inadequate, but I haven’t done so bad for a girl who never liked class work.

Our experiment is trying to build particle accelerators using less material, at a cheaper cost, and over smaller distances as compared to existing methods. Then, by colliding these particles at higher and higher energies, we are looking further back in time and better understanding the early universe. We are basically producing mini big bangs. Had I known I could be working on such cool projects in particle physics, I would have been a much better student in Mr. Schleunes's calculus class.

At the Stanford Linear Accelerator Center, where my experiments take place, the accelerator is composed of a copper tube through which the beam of electrons passes. Keep in mind this is not a continuous beam, like a laser, but rather a beam composed of individual bunches of electrons separated in time. Each one of these bunches contains around 20 billion electrons or positrons (the anti-particle for the electron). Using a klystron, a specialized vacuum tube, we generate an electromagnetic wave that we then pump into the copper tubing. Next, we time everything such that the electrons (or positrons) ride the wave at the right point to gain energy.

Surfer girl

To illustrate this in your mind, imagine the bunch of electrons as a surfer (our facility is based in California, after all) and the electromagnetic wave as an ocean wave. The surfer needs to be properly timed so that he or she can catch the wave and ride it. If the surfer is riding the wave at the right spot, then he or she goes faster and faster, just like our electrons. This is how we traditionally accelerate our particles. This works and it works well, but since the accelerator is made of copper, our wave is limited because at some point the copper will begin to melt. In keeping with the analogy, the present system limits our wave to six feet high, but wouldn't it be so much cooler if our electrons could surf a wave that was 60 feet high or 600 feet high and gain more massive amounts of energy (because higher wave amplitude, or height, means more energy)?

This is where my group's experiment comes into play. We want the electrons to ride a wave that is 600 feet high, not the puny (but perfectly good) six-foot-high wave. By replacing the copper tubing with plasma, we think that we can boost electrons to energies 100 times higher. Plasma is just a gas with the outer electron removed and moving about—an ionized gas, if that is a better description for you. This means you don't have the problems of breaking down and melting like you do with copper, since plasma, by definition, is already broken down.

Now we have the chance to see the electrons ride these huge waves and gain more and more energy—enough to rip matter apart. This is how I work with The Equation. Understanding the intrinsic nature of energy and its connection with matter is crucial for these types of experiments. Einstein's insight gave physicists a tool to better explore that connection and do great science, which, in my humble opinion, is a category that includes my experiments.

My work is only a small example of where E = mc2 has led us in physics. Without it as a foundation, particle physics wouldn't exist. Even more incredible, Einstein was a year younger than me when he formulated The Equation. It makes me feel a bit inadequate, but I haven't done so bad for a girl who never liked class work.

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When Caolionn O'Connell is not boosting electrons to nearly the speed of light, she can often be found on trail-running expeditions in her native California.


Particle accelerators like SLAC usually require a large swath of land, but O'Connell hopes that her plasma system, which accelerates electrons to much higher energies in much less space than existing technologies, will one day allow an accelerator of SLAC's energy reach to fit on a laboratory tabletop.

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Caolionn O'Connell completed her Ph.D. dissertation in physics at Stanford University in June 2005. She will be working as a post-doc at Caltech starting this summer. To check in on her life and work, visit her blog at

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