Electrons "ride the wave" of BELLA's laser pulse (white point), accelerating (blue) to near the speed of light (orange/red is pocket of deceleration.  (Source: Lawrence Berkeley National Laboratory)

In a normal time-frame 3D simulations of the laser in action (seen here) are impossible to simulate at sufficient time scales with current technology.  (Source: Lawrence Berkeley National Laboratory)

By switching your perspective to that of the wavefront, with help from Einstein's theory of relativity, the picture becomes much clearer. Here we see the laser ploughing ahead (blue/red) and the plasma accelerating in its wake (silver ball).  (Source: Lawrence Berkeley National Laboratory)
Accelerator's laser burrows through plasma, relativistically

The SLAC National Accelerator Laboratory, measures in at 2 miles in length and can propel and electron beam with up to 50 billion electron volts (GeV).  But many feel that a respectively tiny tabletop accelerator designed at California's Lawrence Berkeley Laboratory is an even more impressive achievement.

The BErkeley Lab Laser Accelerator (BELLA) uses a laser-plasma wakefield acceleration to achieve 10 GeV of beam power on a compact designs that fits on the table.  You can think of this as the mini-cousin of CERN's famous Large Hadron Collider (LHC), an accelerator which is roughly 700 times as powerful, operating at up to 7 trillion electron volts (TeV)(athough it's worth noting that BELLA's capabilities are significantly different from the LHC's).

Like the SLAC and the LHC, the goal of BELLA is to produce highly energetic collisions, spawning exotic particles and unlocking mysteries of the physics world.  But to properly support and understand your experimental evidence, you have to be able to properly "view" the system in simulated operation, navigating it in three dimensional computer images, in order to understand fully how the device works.

Such 3D views eluded even powerful supercomputers due to the physics driving BELLA.  So a team led by Jean-Luc Vay at Berkeley Lab's Accelerator and Fusion Research Division (AFRD) tapped ideas of late great physicist Albert Einstein to try to solve the puzzle.

I. Mission Impossible: Riding the Laser Wave

BELLA is a fickle tool that operates in a wildly different length scales.  The high-energy laser pulse navigates through a thin plasma tunnel measuring mere centimeters.  The pulse creates a wake of plasma behind it, much like a speedboat.  Electrons are excited by the laser jump on and hitch a ride on the waves, accelerating up to their top collision energy.

The wildly varying scales pose a huge headache for the physicists who tried to simulate it.  Describes [press release] Professor Vay, "Most researchers assumed that since the laws of physics are invariable, the huge complexity of these systems must also be invariable. But what are the appropriate units of complexity? It turns out to depend on how you make the measurements."

Simulations typically use grids, representing the electromagnetic fields inside the device.  The narrow width and large length pose a major challenge, according to the AFRD's Cameron Geddes, who worked on the project.  

Describes Geddes,"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. 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."

To make matters worse, simulators also needed to simulate those hundreds of millions of cells through millions of timesteps, simulating the trajectory of the laser beam.  In full 3D the task appeared impossible, even for a supercomputer.  In grossly simplified 1D (linear) simulations, it still took 5,000 hours of supercomputer processor time at Berkeley Lab's National Energy Research Scientific Computing Center (NERSC) to run a single simulation.

Yet without that simulation the researchers wouldn't be able to fully perfect the device's operation or support/understand their results.

II. Cracking Space-Time

To solve the challenge the team implement an idea that Professor Vay proposed in 2007.  

The laser beam travels at near the speed of light as it zooms through its little plasma tunnel.  To the human perspective it creates wildly varying electromagnetic pulse fields, which are very hard to simulate (require fine time scales and lots of time steps).

But Albert Einstein suggested in the early twentieth century that while outside observers may perceive light speed travelers as moving in outlandish and hard to assess fashion, that the traveler themselves will perceive their actions as moving at a normal speed.  In order to switch from the viewer to the traveler's perspective, you need a math trick called a Lorentz transformation.

Using the Special Theory of Relativity, the researchers were able to crack the puzzle.

From the laser's perspective, time slows, the plasma wave oscillation frequency decreases, and space contracts -- making the plasma shorter.

But despite that insight, the mystery wasn't yet fully solved.  Shifting to the laser's viewpoint caused numerical instabilities, compromising the simulation's results.  If they couldn't solve this problem, the method would be worthless.

So Professor Vay's team attempted to switch from the laser's perspective to the perspective of the electron wavefront, which accelerates along with the laser.  The switch did the trick, eliminating the instabilities.

Thus the trick was not only to shift to a frame of reference closer to light speed, but to shift to the correct frame. 

By shifting from the stationary frame to the correct "boosted" laser frame with the help of Lorentz transformations, the physicists were able to accomplish the seemingly impossible -- create 3D views of BELLA's insides in action.

Describes Professor Vay, "We produced the first full multidimensional simulation of the 10 billion-electron-volt design for BELLA. We even ran simulations all the way up to a trillion electron volts, which establishes our ability to model the behavior of laser-plasma wakefield accelerator stages at varying energies. With this calculation we achieved the theoretical maximum speedup of the boosted-frame method for such systems -- a million times faster than similar calculations in the laboratory frame."

III.  The Future is Laser-Bright

The team looks forward to new challenges, now that they've cracked BELLA's most critical mystery.  Namely, for materials science and biology applications, the simulations will grow more complex and the technique may need to be tweaked slightly in order to properly predict what will happen.  

These predictions will be critical as, along with the experimental evidence they will provide a semi-conclusive picture of how the device works.

In the meantime, Professor Vay and his team can enjoy the prestige generated by their new paper [abstract] in the peer-reviewed journal Physics of Plasmas.  Along with the team leader, the paper's other coauthors were Cameron Geddes, Estelle Cormier-Michel of the Tech-X Corporation in Denver, and David Grote of Lawrence Livermore National Laboratory.

The team was supported by the U.S. Department of Energy's Office of Science.

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