Laser Wake Field Acceleration (LWFA)
A. Pukhov and J. Meyer-ter-Vehn, Appl. Phys. B74, 355 (2002)|
The largest electric fields for acceleration of particles can be produced by separation of electrons and ions in dense plasma. Strong laser pulses propagating in plasma generate such charge separation through the excitation of wakefields. Wakes with electric fields 6 orders of magnitude larger than in conventional accelerators appear to be feasible. In principle this would allow to reduce the size of accelerators from kilometers to millimeters. Problems arising with plasma accelerators are the generation of extended stable wakefields, controlled synchronised injection of particles into the wave buckets, and the generation of mono-energetic beams. Here we describe a new regime of LWFA, in which ultra-short few-cycle laser pulses, fitting into one wave bucket, drive the plasma plasma wave so hard that it breaks already after the first oscillation. Under these conditions, large amounts (nano-Coulombs) of background electrons can be trapped and accelerated with sharply peaked spectra. In the original LWFA concept (Tajima, Dawson, PRL 43, 267 (1979)), the wavebreaking limit was considered as the upper limit of LWFA operation. In what follows, we present two cases in which the wave-breaking limit is exceeded by different amounts. Pulses with these parameters have not yet achieved so far, but are expected to become available in the near future. |
Case I : The highly non-linear broken-wave regime
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Energy spectrum, beam emittance, conversion efficiency
Different from the exponential energy spectrum of electron beams generated in self-focussed plasma channels, the prsent form of acceleration leads to a plateau-like spectrum with a slight peak at energies around 45 MeV. We find 109 relativistic electrons with energies above 5 MeV. The normalized emittance is comparable and better than for conventional accelerators. 15% of the incident laser energy is transferred to the relativistic electron bunch. |
Long and short laser pulses interact differently
Plotting longitudinal vs transverse energy gain
there is a distinct difference between long and short (relative
to the plasma wavelength) laser pulses. While long pulses overlapping
with the accelerated electrons lead to self-focussing
and direct laser acceleration,
the few-cycle pulses discussed here do not overlap with the accelerated
electrons and experience only the longitudinal wakefield.
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Case II : The solitary bubble regime
In this second case, a laser intensity significantly
above the wave-breaking limit ( a=eA/mc2=10 ) has been
chosen such that the wakefield breaks completely after the first oscillation
and only a single wakefield bubble survives which is practically void of
electrons. Part (c) of the figure below shows electron trajectories
in a comoving frame. Yellow electrons are only slightly perturbed by the
laser pulse, blue electrons are scattered away, while red electrons hit
by the central part of the laser pulse form the mantle of the bubble and
are predominantly trapped in the bubble. The trapping is so efficient that
after a certain propagation distance there are more trapped electrons
in the bubble than were initially in the same volume. At this point beam-loading
effects set in and the bubble starts to stretch; after 500 laser cycles the
extension is 35 λ and after 700 laser cycles 40 λ. This stretching has a
significant effect on the energy spectrum.
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Evolution of peaked energy spectrum
It is seen that the energy spectrum, having a flat spectrum after 350 cycles, develops a sharp peak at later times. After 750 cycles, it contains about 3.5 x 10 10 electrons in the energy interval between 300 and 360 MeV. |
Profiles along the bubble axis at 700 fsHere we show distributions of different quantities along the bubble axis after 700 laser cycles. The laser pulse, initially 10 cycles long, has shortened and has steepened, forming an optical shock at the front. The electron density in the accelerating bunch is almost 5 times the background plasma density,. It may surprise that this huge charge accumulation has almost no effect on the longitudinal Ez field, shown in frame (c). The reason for this is that the Coulomb field of a charge, though isotropic when at rest, is reduced by a factor γ-2 in the direction of motion for a relativistic particle. The energy distribution along the bubble axis in frame (d) consists of two distint regions: (1) the front edge with highest energies represents the early phase of bubble evolution where its size is fixed, (2) the electrons more to the left have been injected at later time when the bubble was already expanding.
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Electron pulse and conversion efficiency
Here we show the accelerated electron bunch in a perspective view with
the driving laser pulse depicted as a white cloud. 1.8 J (15%) of the incident
12 J laser energy are found in 3x1010 electrons with energy peaked
around 300 MeV.
The acceleration takes place over a distance less than
1 mm.
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Analytical estimates for Laser Wakefield AccelerationJ. Meyer-ter-Vehn, A. Pukhov, Rel. Las. Plas. Interaction, part I: Analytical ToolsA. Pukhov and J. Meyer-ter-Vehn, Rel. Las. Plas. Interaction, part II: Particle-in-Cell Simulation in Relativistic Optics , eds. G. A. Mourou, C. P. J. Barty, M. D. Perry (Springer Verlag, under preparation) Laser wakefield excitation
Wakefield acceleration
Wave breaking
Scaling of broken-wave regime favours few-cycle pulsesA. Pukhov and J. Meyer-ter-Vehn, Appl. Phys. B74, 355 (2002)
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Generation of relativistic ionsD. Habs, G. Pretzler, A. Pukhov and J. Meyer-ter-Vehn, Progress in Particle and Nuclear Physics 46, 375 (2001).1 kJ, 15 fs pulses incident on 30 μm plastic foil may result in 10 14 , 4-5 GeV protons. 
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Here we show the wakefield evolution of a 20 mJ, 6.6 fs laser
pulse, simulated with the 3D-PIC code VLPL. Electron density is plotted
in four frames (snapshots at different times) with colour representing
p z/mc. A typical plasma wave is seen trailing
the laser pulse with green wave crests moving to the right and low-density
plasma in between moving to the left. In frame (a) the laser pulse
is also shown explicitly and is seen to fit into the first wave bucket.
A prominent feature is the red stem of high-energy electrons growing
out of the rear vertex of the the first wave bucket. These electrons originate
from wavebreaking which occurs at this vertex first and spills electrons
into the wave trough where they are strongly accelerated by the electric
field in the wake. When the wave arrives at the rear side of the thin plasma
layer, this wave trough opens and releases a bunch of relativistic electrons
which is just a few μm long. You may look at this process in more detail
in the movie: