Particle acceleration in plasmas
2.4 Laser guiding
Normally, the acceleration length is limited to twice the Rayleigh length, defined as
(2.5)
where !To is the laser spot size and>. is the laser wavelength. With a typical spot size of 10 ~m and the wavelength of a Neodymium laser (c:::= 1 ~), LR c:::= 0.6 mm. This is mainly due to the fact the the laser beam is focused into a very small spot, in order to reach the required high intensity.
In order to achieve the right conditions for the acceleration, the laser pulse must be trapped and guided through a pre-formed channel. For optical guiding of laser pulses in plasmas, the radial profile of the refractive index must have a maximum on the axis, causing the wavefront to curve inward and the laser beam to converge.
Guiding a laser pulse in a plasma with the required intensity is not easy. A very promising method relies on the ponderomotive self channelling, already described[25]. This method of creating the central depression involves the use of another laser. If a laser pulse with a long duration is sent into a plasma, the laser ponderomotive force expels electrons from the axis and prevents their return, despite the Coulomb attraction, which arises from charge separation. Ifthe laser pulse is long, ions start to move as well, as a result of the Coulomb force and gain momentum during the process. After the pulse is gone, electrons return to neutralise the charge of the ions which keep moving out. This leads to a plasma density depression on the axis[2][42].
For the self channelling to occur, the laser intensity must exceed the critical value of 17(wo/wp)2GW[20]. In this case, the beam extends and forms a second focus. Increasing further the power leads to the formation of multiple foci, which eventually merge into a single channel. A channel formed in this
1e+19 ~-~---r--~----'---~---'----~---'----I
8e+18
NE 6e+18
~
uC'Vi c
Q) 4e+18 C
2e+18
oL~_l--~_l----===~=====::c=====:d
o 10 20 30 40 50
Spot radius (Ilm)
8000 ~-~---r--~--..,--~---,--..,----,--~---,
6000
E
~ .s:::.0,c
~ 4000
.s:::.
'QjCl
>.
0:::ro
2000
40 50
20 30
Spot radius (Ilm)
10
oL---=---.1--~_---L _ _~_ ____L_~~_ _L__~_ _ _ '
o
Graph 2.1: These two graphs show the behaviour of the intensity onto the target and the Rayleigh length for a typical laser pulse of 3J, with a duration of 400 fs and a wavelength of 1 ~m.
way has the advantage of having a small size, usually smaller than 30 J.lm, a high plasma density and the ability to sustain high laser intensities. The short interaction length is then the result of the diffraction.
2.4.1 Experimental results
Many experiments have already reported a laser self channelling by pon- deromotive forces up to twelve times the Rayleigh length[15]. In all the experiments, the laser is focused onto the side of a helium gas supersonic jet a few millimetres long. By focusing the beam onto the side of the jet one can use the highest possible density gradient. The jet provides the right density profile for the laser channelling but not over a long distance and many groups reported this limit[22].
2.4.2 Improved laser guiding
Although to my knowledge no actual experiments have been performed on this topic, previous experience with conventional accelerators indicates that the following type of improved laser guiding should be studied. This is an optical analog of the well known alternating gradient focusing used in most large accelerators (the general principle is made understandable by the in- verted pendulum experiment [63]). In the alternating gradient scheme for electron and heavy ion beams, the diameter of the beam is considerably re- duced by applying a series of converging and diverging magnetic lenses. A
much less well known fact is that in the early sixties a similar beam diameter reduction was obtained with laser light. This was also done with a series of converging and diverging optical lenses at Bell Laboratories. Together with my supervisor, we suggest here that a series of converging and diverging vir- tual capillaries could be used to shrink both the particles beam and the laser beam in laser driven accelerators.
Another improvement not easily realisable with solid state capillaries is the tuning of the central density of the laser channel to the relativistic chang- ing mass of the electrons. This changing mass leads to dephasing of the acceleration process.
Potential applications of Laser Driven Accelerators
Realm Specific application&method Required beam energy
Medicine Positron emission tomography. Tumour differentiation e.g 5 MeV deuteron, 10 and heart disease. Requires local e+production due MeV protons
to short! life ofe+emitters.
ell20 min, N13 (2 min), 015 (110 min)
Proton irradiation: range varies with beam energy, but E <200MeV is well defined by "Bragg peak" in human tissue.
Neutron irradiation for deep tumours. Possibly the neutrons from spallation most effective form or radiation as it destroys both
DNA strands: no mutations.
Hard X-rays. A range of energies could become acces- X-rays energies of same sible from T cubed laser driven accelerators. order as beam energy (line
and bremsstrahlung)
Potential applications of Laser Driven Accelerators
Realm Specific application&method Required beam energy
Biology At higher energies a laser driven accelerator X-ray un- Diamond:
dulator could replace international facilities such as Ebeam ~3GeV(300mAl Grenoble (France) and Diamond (UK).
Solid State Likewise biology, existing neutron spallation sources pharmacology at international facilities could be powered by laser research driven accelerators.
Laser driven Fast ignition from ... eV electrons generated by PW eV T-N fusion laser focused deep in target with gold cone.
Rubbia tho- Proton injection into pure thorium generates neutrons Initial experiment:
rium burner and reactions: 115 MeV protons (2
Th~g2+n~-+Th~g3-+Pa~~3.B-+ugi3 mAl
ugi3+n~ -+ fission+2n~
No isotope separation necessary. Short! life of decay products. Safe (accelerator dependent) reactor.
Particle In the very long term laser driven accelerators might SLAC beam physics compete with LHC and Tevatron. In medium term,
XXXX propose positron or electron driven "after burner."