Plasma Electron Accelerators

Particle Accelerators are among the largest scientific structures built by mankind – such as the Large Hadron Collider at CERN with its 27 km circumference. They have been the engineering marvels enabling progress in our fundamental understanding of nature – think the Higgs particle. Yet, their size has become as the most pressing problems. In order to drive scientific progress further and further, particles must gain more and more kinetic energy.

27 kilometers long and up to 175 meters underground: The LHC is the largest particle accelerator in the world. © cern

It comes down to what we call the acceleration field E which is given in units of Volts per meter and, multiplied by the charge q of the accelerated particle, gives us the energy which we can reach with a given accelerator structure. So we can either increase the voltage in our accelerator or increase the number of accelerating stages. For years, physicists have tried to do both.

Unfortunately, it seems we have hit a barrier that hinders us from increasing the electric field beyond roughly hundred Million Volts per meter, as known materials cannot sustain much stronger fields. So we are doomed to add more and more acceleration stages to increase our final particle energy, making future accelerators huge.

But there’s hope in unforeseen places! What if we break apart materials to its atomic constituents, separating the positively charged cores of atoms from their surrounding negatively charged electrons, creating strong charge imbalances. Easily put, if we have to break things anyways, why not go all the way? Indeed, such a state of matter in which electrons are spatially well separated from the atomic nuclei, which we call ions, is called a plasma. The separated charges can create fields up to Teravolts per meter, which is 10,000 larger than the aforementioned 100,000,000 V/m, giving you a staggering 1,000,000,000,000 Volts per meter of electric field.

There are several ways to create plasmas with such high field strengths. One is to use ultra-short laser pulses of extreme intensity. They can create electromagnetic fields strong enough to accelerate electrons to relativistic energies, for which their kinetic energy is much higher than the energy equivalent of their rest mass, given by the famous Einstein relation E=m_0 c^2.

Pulses of a few ten femtoseconds – a femtosecond is 0,000000000000001 seconds – push their way through a gas like a plow pushing its way through the snow, separating the plasma electrons from the ions. This creates an accelerating field that follows the laser pulse through the gas. And one can use this field to accelerate electrons from the surrounding plasma, effectively reaching electron energies over a few millimeters of plasma that would require a hundred meters long conventional accelerator. So by increasing the electric field by a factor of 10,000 we could make it 10,000 times smaller!

But with any new great technique problems arise. Two of the most famous ones can be expressed by two length scales. The depletion length defines the length at which the laser pulse energy has effectively been converted into electron energy and we can no longer sustain the accelerating field.

The dephasing length comes from the fact that the laser pulse in a gas is slower than the electrons accelerated by it. Yes, you heard right, our electrons become faster than the laser light, but this is no magic as the laser light travels through a medium, in which it is slower than the speed of light in vacuum without any gas. This in turn means that at one point the electrons outrun the laser pulse, at which the laser pulse no longer drives the acceleration.

One can increase the laser pulse energy, but this comes at the cost of having to reduce the plasma density, reducing the number of electrons available for acceleration. And one still is faced with overcoming the dephasing length. This can be achieved by replacing the laser pulse with an ultra-short bunch of electrons, which is difficult to create by conventional accelerators.

All in all, there is much work to do. Particle accelerators have matured for over 100 years, while plasma acceleration has been around for about 20 years. It is still undecided what the future of particle acceleration is, but it sure will be small, compact and come with ultra-high acceleration gradients.

Dr. Michael Bussmann, 2018

Junior Group Leader Computational Radiation Physics
Laser Particle Acceleration
Helmholtz-Zentrum Dresden-Rossendorf






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