Acceleration laser-plasma

acceleration laser-plasma is a research topic aiming at developing sources of particles having new properties. Currently, the acceleration of particles is very developed on conventional particle accelerator . Nevertheless, the accelerating field in these structures radio frequencies is limited to values of about 50 MV/m. to reach higher energies, in order to study new phenomena, the scientists were constrained to build gigantic accelerators (27km for LHC).

There also exists of other methods to accelerate particles. This article presents in particular the mechanisms of acceleration of particles by using the interaction of a laser with the matter. By focusing a laser of power on a target, it is possible to create beams of particles to the particularly original properties (brevity, energy, flux density, load). At the time of this interaction of the laser beam with the matter, of the extreme electric fields are produced. Reaching peak values about TV/m, that is to say more than 10.000 times more intense than the electric fields produced in structures RF of the accelerators, the particles initially at rest, leave the target by undergoing a fulgurating acceleration, about $10^ {22}$ g (g=acceleration of terrestrial gravity). These new sources open the way with many applications: medical, nuclear, chemistry and biology. They should moreover make it possible to study new phenomena on scales of ultra-short times (100 fs).

The experiments of interaction laser-plasma make it possible to accelerate two types of particles: electrons and protons. These two disciplines are presented in the continuation.

Electron beams

Principles and definition of the terms

The American physicists Tajima and Dawson proposed into 1979 to use plasmas created by Laser to accelerate particles. In the case of the acceleration of electrons, the target in which is propagated the laser is a gas. The use of a light gas is preferable (typically helium) because thus the electric field related to the laser ionizes the atoms of gas completely. The intense part of the laser is propagated in a homogeneous medium made up of free electrons and ions, having an overall neutral load. It is what one names plasma.

It should well be understood that the laser directly does not accelerate the particles in the direction of propagation of the luminous impulse. Indeed, the electrons are subjected mainly to the electric field of the laser. In the case of the electromagnetic waves, the electric field is perpendicular to the trajectory of the laser impulse and oscillates at the laser frequency. Thus, the electric field of the laser does not contribute directly to the acceleration of electrons to high energies.

On the other hand, the passage of the laser impulse disturbs the electronic density. This force related to the laser is called the Force pondéromotrice. It corresponds to the frequency low part of the laser variation of intensity. It is named also pressure of radiation of the laser. Following these displacements, the procession of electrons reorganizes under the effect of the Coulomb repulsions. This causes oscillations in the electronic density. The laser thus makes it possible to generate a wave plasma which is propagated in the direction of the laser at a speed equal at the speed of group of the laser in the medium. This wave plasma corresponds primarily to longitudinal electric fields. These fields are adapted to the acceleration of electrons to high energies.

In short, the laser generates a wave plasma in its wake in which the acceleration of particles to high energies is possible. A simple hydrodynamic analogy to include/understand this mechanism is the following one: imagine a boat which moves on the surface of a lake. This boat causes waves in its wake. A surfer could benefit from it to gain speed and to travel at the speed of the wave. In general, acceleration is done by trapping in the structure of wave. Indeed, there exist conditions on the initial speed of the surfer so that the trapping takes place. If it does not make any effort to take the wave, it passes under him and moves away. Contrary, if it goes too quickly, it exceeds the wave.

In scientific terms, one speaks about potentials. Calculations utilizing the Transformation of Lorentz make it possible to determine the potentials minima and maxima according to the intensity of the laser. These calculations are carried out in geometry 1D by supposing the laser field suffisemment weak to carry out limited developments.

The speed of phase of the wave plasma being equal at the speed of group of the laser wave, these speeds are close speed of light in the vacuum (plasma sub-critical). Electrons injected with high speeds can thus be trapped by the wave and be accelerated there. The maximum energy of the electrons is all the more large as the speed of the waves plasma is high, i.e that the electronic density is low. As example, for a plasma with the density of $10^ {19}$ /cm³ and for a wave plasma of relative amplitude of 100%, the electric field is about 100 GV/m, which makes it possible to accelerate with high energies at small distances (millimetre-length).

Mechanisms of acceleration

Various methods were proposed to accelerate the electrons by laser. They derive all from the mechanism previously described. They correpondent about at the various crossed stages as the laser duration of the impulses with decreased compared to the Wavelength plasma. Here is a summary:

The beat of waves

This mechanism requires two impulses laser against-propagatives close pulsation ω1 and ω2 to which the difference in frequency is close to the frequency plasma (ωp ~ ω1-ω2). The covering of these two impulses laser generates a resonant beat of waves with the wave plasma. The amplitude of the wave plasma little to reach approximately 30% of the initial density electronic, which limit the accelerating field to some GV/m. In 1993, Clayton and Al obtained an energy of exit of 9.1 MeV for inectés electrons with 2.1 MeV initially in this wave plasma. At that time, the laser duration of the impulses was about 300ps (width with middle height). Experiments in this mode of beat of wave were also led to the UCLA (profit of energy of 30 MeV), to the Polytechnic school and Osaka. The physical mechanisms which limit the amplitude of the waves plasma in this mode are the movement of the ions for long impulses, the relativistic dephasing of the wave plasma for relativistic intensities as well as the growth of instabilities.

The car-resonant wake

The appearance of laser of strong intensity and duration of short impulse (500 fs) containing a strong energy (100 J) gave access to the non-linear behaviors of plasmas. The combined effects of the self focusing and the automodulation of the laser envelope by the electronic disturbance of density cause the modulation of the laser impulse in a laser succession of impulses separated by the wavelength plasma. One thus obtains resonant impulses with the wave plasma, like in the case of the beat of wave previously described. Sprangle et al. , Antonsen et al. , Andreev et al. studied in a theoretical way this mode. They showed that when the duration of the impulse is higher than the period plasma and when the laser power exceeds the critical power for self focusing, a single laser impulse breaks up into a train of resonant impulses with the period plasma.

During the experiments undertaken by Modena et al. , the amplitude of plasma grows until the limit of surge, which corresponds to the moment when the amplitude of the oscillations of the electrons of plasma is so important that the force of recall does not compensate for any more their movement. At this time, the electrons of plasma are automatically injected into the wave plasma and gain kinetic energy. One can take again the hydrodynamic analogy here to explain this mechanism of injection: when a vague approach of the shore, its Crete becomes pricked, the wave grows hollow then breaks. The white scum of vagueness corresponds to the water molecules which gained speed. No external injection is here necessary to produce an electron beam. In the article of Modena et al. , they obtained energies reach 44 MeV. This mode was also reached by the CUOS in the USA and NRL. However, the heating of plasma by these long impulses laser cause the surge before reaching the maximum limit of the electric field calculated for cold plasmas. The electric field reaches 100 typically GV/m.

The forced wake

The development of very intense lasers ( $10^ {18}$ W/cm2), very courts made it possible to reach a new stage and to highlight a more effective mechanism of acceleration: the forced wake. These lasers, of weaker energy, have a higher rate of shooting (10 tir/s instead of a shooting every 20 minutes) and thus they make it possible to consider future applications to these new sources.

Here, the waves are amplified on levels of extreme amplitudes (non-linear mode) producing a very short package of electrons and very energetics. It is not then necessary any more to inject electrons in plasma. They are the electrons of plasma themselves which are made trap. In this mode of short impulse, the heating of plasma is much less important, and the waves can reach higher amplitudes close relations of the value of cold surge. For an electronic density of $2x10^ {19}$ /cm3, the electric field reached in this mode an extreme value about TV/m.

With leasing, electrons were accelerated to 200 MeV in 2 mm of plasma. Thanks to an interaction with the laser impulse reduced, a flux density standardized of 3 pi mm.mrad at summer measured for the electrons with 55 +-2 MeV, which is comparable with the performances of the conventional accelerators.

Electron beams with Maxwellian spectra, produced by short ultra beams were produced in many laboratories in the world: with the LBNL, with the NERL, and in Europe for example with leasing, or the MPQ in Germany.

Mode of the bubble

This last term hiding place a revolution in the field of the acceleration of electrons per interaction laser-plasma: for the first time of the electron beams with a quasi-monoenergetic spectrum were produced. Until now, the electron beams always had a Maxwellian spectrum (exponential decay). The presence of a peak with high energy makes it possible to consider a multitude of applications because its properties are excellent at exit of plasma and remain excellent during the propagation of the beam. It was not the case with a Maxwellian beam: filtering by a Monochromateur would have considerably decreased the flow of electrons with high energy, making fall the output of acceleration.

Actually, these results had been predicted by simulations PEAK 3D which gave rise to this denomination: Mode of the bubble. In this mode, dimensions of the laser are shorter than the wavelength plasma in the three directions of space. Thus, the focused laser impulse resembles a ball of light of a typical ray of 10 microns. The force pondéromotrice of this impulse is so strong that it expels the electrons with its passage. Behind the laser impulse, one then obtains a cavity surrounded by an electronic on-density. With the back of this structure of the electrons are injected towards the cavity and are accelerated in this structure. This cavity is gravitational for the electrons, because it contains the ions whose displacements are negligible on these scales of time. The signature of this mode is the appearance of a quasi-monoenergetic spectrum of electrons. This contrasts with the preceding results. This comes from the combination of different factors:

the injection of the electrons in the cavity is different from the surge observed in the car-modulated wake and the forced wake (that does not come from the surge of the accelerating structure).
the accelerating structure remains stable as a long time during acceleration as the laser is suffisemment intense.
the trapped electrons are behind the laser impulse. They did not interragissent any more with the transverse electric field of the laser.

Several laboratories obtained quasi-monoenergetic structures: in France, England and in the United States, then in Germany and in Japan with rather different experimental conditions (the duration of impulse was longer than the period plasma). The description of these results appears in the following section.

Experimental results

In this section, only the recent results are described. In September 2004, 3 articles are been published in the nature magazine: electron beams produced by interaction laser-plasma with quasi-monoenergetic peaks were observed for the first time.

the English group of the Rutherford Appleton Laboratory (RAL) obtained a spectrum piqué to 70 MeV containing a load of 22pC
the American group of Lawrence Berkeley National Lab (LBNL) observed an electron beam with 86 MeV + - 2MeV containing a load of 0.3nC
the French group of the Laboratory of Optics Applied (leasing) measured a centered spectrum of electrons with 170MeV + - 20 MeV

These electron beams correspond to very high currents peaks (typically 10 kA). The source of electrons has a very small size, equivalent to the size of focused laser (of a few microns to a few tens of microns in general, according to the optics of focusing used). The divergence of the electron beam varies between 3 mrad with 10 mrad according to the articles. Another essential property of these sources is their short duration. The duration of the package of electrons is estimated at less 100fs in general at the exit of plasma. As the spectrum is piqué with a raised energy, these electrons all travel almost at the same speed and their dispersion is weak. For example, for the measurement taken with leasing, dispersion at 50 fs/m during the propagation was estimated. These packages of electrons can then probe the phenomena ultra-briefs.

In short, these laser installations operating with 10Hz now make it possible to produce electron beams quasi-monoenergetic, short, low-size, of low divergence, weak flux density, strong load.

The current developments aim at increasing the energy of the electrons further (to pass the bar of the 1 GeV), to stabilize the properties of the electron beam tit to shooting, to promote the possible new applications with sources having such properties. The following section describes some of these applications.

Applications of these sources of electrons

In order to promote the various new properties of these sources of electrons, several applications were studied. The examples given below were obtained with leasing:

In medicine for the radiotherapy, this source very collimated could be useful for the treatment of certain cancers with electron beams. From this point of view, simulations Monte Carlo of the deposit of energy in fabrics starting from the quasi-monoenergetic electron beam were carried out. The results show transversely a deposit of energy very fine (even in-depth), very deep. The amount deposited largely exceeds the needs for the radiotherapy. However, it is possible to control the number of electrons accelerated by varying the electronic density. This could mainly become an alternative to the traditional radiotherapy, carried out by x-rays. Indeed, the compact conventional accelerators deliver electrons of 20 MeV, which do not penetrate suffisemment deeply in fabrics (less than 10 cm). And the accelerators of protons are very expensive structures, which limits their exploitation although they are best adapted to the radiotherapy.

In chemistry for the study of chemical reactions (kinetic rapid). The electron beam, very in short and perfectly synchronized with the laser impulse, has all the advantages to conclude this type of study. It should be a tool complementary to traditional sources of electrons controlled well but of which the duration is limited to 1 PS. The experiments carried out made it possible to plot the curve of absorption of a short state of the water molecule, during the solvation of the electrons. It is a question of showing that time characteristic of this state is definitely shorter than than the models predicts. The comprehension of the evolution of the water molecule is important to include/understand the evolution of the alive one.

In biology for the crystallographic study of cellular medium. The interaction of this source with an additional laser beam would allow the generation of flash-X broad spectra and very short duration (<100fs).

In radiobiology for the study of the deposit of amount on very short scales of time. The existing data in this field are limited to scales of time of the microsecond. An lively interest on behalf of the radiobiologists shows the need for exploring this way.

In radiography. By irradiating a dense medium with this electron beam, it is possible to convert the energy of the electrons into gamma ray. This secondary beam inherits the good properties of the source of electrons, which is an asset for the physics of materials. Dimensions of this source (submillimeter) would make it possible to use it to probe defects of small sizes in the matter. Currently radiography gamma is carried out starting from electron beams released by from Linacs. The size of this energy radiation source was estimated at a few hundred microns, which is better than the size produced by conventional accelerators of equivalent energy.

In short, multidisciplinary applications are already considered. Besides they give place to the deposit of several patents.

Notes and references of the article

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