Published on 29 April 2016
Research

A team coming from three members of Université Paris-Saclay has developed a new technique to accelerate particles. This method proved to be very effective: the energy gain could reach 200%!

LHC just announced the potential discovery of a new particle, thanks to the increase in the particule accelerator’s beams energy. To further increase this energy (i.e. to speed the particles further up), an accelerator should get bigger than the already impressive LHC’s 27 km. However, alternatives can be found.

At the heart of Laboratoire d’Optique Appliquée (LOA), researchers from ENSTA ParisTech, CNRS and École Polytechnique, three members of Université Paris-Saclay, have succeeded in increasing their particles’ energy with an innovative technique. They published the experience last October in Physical Review Letters and their theoretical point of view was presented on April 13th in the journal Physics of Plasma (AIP Publishing).

Victor Malka and his team used a laser wakefield acceleration with a peculiar plasma density profile. This acceleration method involves heating a gas with a laser. The interaction between the laser and the gas creates a plasma wave which propagates at high speed, close to the speed of light. Plasma electrons, trapped in this wave’s wake, are effectively accelerated like a surfer who would use the waves created by a boat to gain speed. The electrons become increasingly relativistic (their speed gets closer to the speed of light) and the associated energy gain is then limited by the electrons catching up with the laser pulse. Indeed, the laser pulse’s velocity (known as the group velocity) is lower than the speed of light in vacuum. This is called “dephasing”.

In conventional laser wakefield accelerators, dephasing is reduced by decreasing the plasma density. But this technique has some major drawbacks, such as more difficulty to self-guide¹ the laser. An alternative, chosen by LOA team, is to tailor the plasma density to keep particles in phase with the accelerating part of the wave.

This "rephasing" is done by suddenly increasing the plasma density at a specific location. The curve representing the plasma density along the propagation direction then presents a "step", from a low plateau to a plateau of higher value, with a sharp transition. If the transition is significant enough, researchers showed a gain of energy of about 25%. At most, particles get 1/3 more energy than in the absence of rephasing. A numerical simulation, based on the experiment’s parameters, confirmed this impressive result.

During the experiment, the researchers have even highlighted a significant gain up to 75%. Indeed, the model assumes that the laser intensity is constant along its spread. In fact, a relativistic phenomenon occurs and increases the intensity of the laser, producing accelerators fields more intense so more effective. But to represent this phenomenon, simulations digital expensive are necessary: they will be carried out in the future.

To improve this new method, physicists were then considered another profile, where the density is increased only locally, in 'saw-tooth '. In this case, the gain of energy for each jump of density is lower (around 20%) but it is possible to perform many consecutive rephasages. The total energy gain can then reach 200%. A feat that most comprehensive numerical simulations and new experiences have yet to confirm.

## What does this equation mean?

$\Delta\gamma$ corresponds to the obtained energy gain, the value the scientists want to optimize. By this equation, we see that this gain depends on three factors:

 $z_{boost}$ is the position of the density change $L_d$ is the distance on which the electrons are able to gain speed. This “dephasing length” depends on which laser is used and the wave speed, among others. $\Delta\gamma_{max}(n_0)$ is the maximum gain achieved without rephasing

The last two elements are constant in the system: we consider that we can’t tune them to optimize the gain.

The gain will then be maximum if  $1+\frac{z_{boost}}{L_d}-\frac{3}{4}\frac{z_{boost}^2}{L_d^2}$ is maximum, i.e. if the density change (as a step or sawtooth alike) is correctly positioned relatively to the dephasing length.

Ultimately, the gain is maximum at the position $z_{boost}=\frac{2}{3}L_d$ and the gain is then

$\Delta\gamma=\frac{4}{3}\Delta\gamma_{max}(n_0)$

Particles thus gain at most 1/3 more energy than in the absence of rephasing

¹ The propagation of a laser pulse involves two opposite effects. The optical Kerr effect tends to focus the beam while the ionization of the environment defocuses it. If they offset each other, these two phenomena can lead to the propagation of high intensity laser pulses over long distances. The laser is then said to be “self-guided”. Source: https://tel.archives-ouvertes.fr/tel-01188199/document

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