Slowing Down Time and Contracting Space to Build Better Machines
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Lawrence Berkeley National Laboratory
Jean-Luc Vay (left) and Cameron Geddes (right), the minds behind the magic.
Nowadays, scientists don't have to tinker with small metal parts to build models of their machines. Instead, their models can be created on supercomputers. They can even put those models into simulated action. The simulations allow scientists to see if their machines will work before they actually build them; visualize improvements; and check whether experimental results are theoretically sound.
Scientists at the U.S. Department of Energy's (DOE's) Lawrence Berkeley National Laboratory are taking their simulations to the next level. They are using Einstein's special theory of relativity, a theory which describes the slowing of time and the contraction of space, to write computer codes that run a million times faster than conventional simulations for selected applications.
The machine they are simulating—which is under construction by the Lab's LOASIS program—is a compact particle accelerator called The Berkeley Lab Laser Accelerator (BELLA). The search for new particles in the universe largely depends on accelerators like Large Hadron Collider at CERN in Switzerland. These high-energy machines smash particles together at speeds high enough to create new particles from the energy of the collisions. Ever higher energies are needed to expand our understanding of the fundamental workings of the universe. BELLA is a prototype for a new technology that could extend the reach of accelerators to higher energies while reducing their size and cost. Scientists Jean-Luc Vay and Cameron Geddes of Berkeley Lab's Accelerator and Fusion Research Division are making simulations of BELLA to see it in action.
BELLA will be what is called a "laser-plasma" accelerator. Here's how it works: A pulse of laser light shoots through a meter of plasma. Plasma is basically a hot gas of electrically charged particles—negative electrons and positive ions. As the laser light moves through the plasma, it creates a wake by pushing the electrons aside. The process is similar to how a speedboat creates a wake on water. In this case, the wake is a wave of electrons that flows over positive ions. The positive ions in the plasma remain in place since they are heavier. The wave of negatively charged electrons in turn sets up electric fields. Those waves of electrons, and the resulting electric fields, are collectively referred to as the "wakefield." Once this wakefield is in place, scientists can accelerate other particles by having them "ride the wakefield" like surfers on a wave.
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Lawrence Berkeley National Laboratory
Image of a wakefield through a plasma, a snapshot from a simulation of BELLA.
Such accelerators can push particles thousands of times harder than conventional machines, accelerating particles over very short distances, which saves both space and materials.
So far, so good…but why do we need to slow down time to make simulations of this process? Well the laser light is moving at an incredibly fast speed, and it is also oscillating; that is how light moves. But computers simulating the light moving through the plasma have to perform their calculations in finite chunks of time called timesteps. The speed of the oscillating light requires too many timesteps; the calculations for the simulations can take days or even weeks.
So how did scientists manage to speed up the calculations? They looked at things in a different light. Literally, they looked from the perspective of the laser light itself! That was the key: to change the frame of reference used in the physics equations for their calculations. Their approach is known as the "boosted frame" method.
From the perspective of a person in the laboratory, the laser light moves fast through a stationary plasma. But from the laser light's perspective, the laser light remains still while the plasma quickly flows past it. The laser light's perspective is similar to what you experience while sitting in a train. You may feel as though you are not moving while trees outside fly past you.
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A simulation of laser-plasma acceleration from the perspective of a person in the laboratory. The oscillations of laser light are the red and blue disks at right; the fields in the wake are colored from pale blue to orange. Other particles accelerated in the wake are shown in white at right. Video credit: Lawrence Berkeley National Laboratory.
This is where Einstein's mind-boggling special theory of relativity comes into play. The basis of Einstein's theory is that space and time are relative and interdependent concepts. The first idea is called time dilation: A clock in motion with respect to an observer runs slow compared to the observer's clock. In our boosted frame, the observer is now on the laser light, and the plasma is now in motion. So time in the plasma seems to run slow.
Additionally, there is the concept of length contraction: An object in motion relative to an observer will be shortened along the direction of motion. So the plasma appears to be shortened, while conversely the oscillations of the light are lengthened. While we don't feel the effects of time dilation and length contraction when we travel in cars or planes, they are proven to be real effects for objects moving near the speed of light!
Jean-Luc Vay explains further: "In addition, we have used a third effect of special relativity which is that it not only stretches time and contracts space, but actually mixes the two. So the oscillating light that looks like a repetitive spatial pattern for an observer in the lab looks like a cycling repetition in time for an observer moving with the laser light. Together with novel numerical techniques, the transformation allows us to reach 10 thousand to 1 million times speedup of the calculations."
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Simulation of the laser-plasma system in the boosted frame. Video Credit: Lawrence Berkeley National Laboratory.
"There was a lot of skepticism when we first proposed the idea in 2007," says Vay, "as the common belief was that the number of time steps needed to model a physical system was independent of the choice of the virtual observer in the simulation. We have now established that it is not the case and the effect is real."
Cameron Geddes expresses the impact of their work: "This is a real-world application of Einstein's special theory of relativity. We're taking advantage of computer simulations using Einstein's theory to help build a new class of machines. That's very powerful!"
BELLA is being built by the LOASIS program, funded by DOE's Office of Science. For more information about the Office of Science, visit science.energy.gov.
This article was written by Abigail Pillitteri, a writer for the Office of Science.
