Simulating Tomorrow's Accelerators at Near the Speed of Light

As conventional accelerators like CERN's Large Hadron Collider grow ever more vast and expensive, the best hope for the high-energy machines of the future may lie in "tabletop" accelerators like BELLA (the Berkeley Lab Laser Accelerator), now being built by the LOASIS program at the U.S. Department of Energy's Lawrence Berkeley National Laboratory (Berkeley Lab). BELLA, a laser-plasma wakefield accelerator, is remarkably compact. In just one meter a single BELLA stage will accelerate an electron beam to 10 billion electron volts, a fifth the energy achieved by the two-mile long linear accelerator at the SLAC National Accelerator Laboratory.

But realizing the promise of laser-plasma accelerators crucially depends on being able to simulate their operation in three-dimensional detail. Until now such simulations have challenged or exceeded even the capabilities of supercomputers.

A team of researchers led by Jean-Luc Vay of Berkeley Lab's Accelerator and Fusion Research Division (AFRD) has borrowed a page from Einstein to perfect a revolutionary new method for calculating what happens when a laser pulse plows through a plasma in an accelerator like BELLA. Using their "boosted-frame" method, Vay's team has achieved full 3-D simulations of a BELLA stage in just a few hours of supercomputer time, calculations that would have been beyond the state of the art just two years ago.

Not only are the recent BELLA calculations tens of thousands of times faster than conventional methods, they overcome problems that plagued previous attempts to achieve the full capacity of the boosted-frame method, such as violent numerical instabilities. Vay and his colleagues, Cameron Geddes of AFRD, Estelle Cormier-Michel of the Tech-X Corporation in Denver, and David Grote of Lawrence Livermore National Laboratory, publish their latest findings in the March, 2011 issue of the journal Physics of Plasma Letters.

Space, time, and complexity

The boosted-frame method, first proposed by Vay in 2007, exploits Einstein's Special Theory of Relativity to overcome difficulties posed by the huge range of space and time scales in many accelerator systems. Vast discrepancies of scale are what made simulating these systems too costly.

"Most researchers assumed that since the laws of physics are invariable, the huge complexity of these systems must also be invariable," says Vay. "But what are the appropriate units of complexity? It turns out to depend on how you make the measurements."

Laser-plasma wakefield accelerators are particularly challenging: they send a very short laser pulse through a plasma measuring a few centimeters or more, many orders of magnitude longer than the pulse itself (or the even-shorter wavelength of its light). In its wake, like a speedboat on water, the laser pulse creates waves in the plasma. These alternating waves of positively and negatively charged particles set up intense electric fields. Bunches of free electrons, shorter than the laser pulse, "surf" the waves and are accelerated to high energies.

"The most common way to model a laser-plasma wakefield accelerator in a computer is by representing the electromagnetic fields as values on a grid, and the plasma as particles that interact with the fields," explains Geddes, a member of the BELLA science staff who has long worked on laser-plasma acceleration. "Since you have to resolve the finest structures -- the laser wavelength, the electron bunch -- over the relatively enormous length of the plasma, you need a grid with hundreds of millions of cells."

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