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 

wakefield 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:
                            MOVIE (coming soon)

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

gain-plots Plotting  longitudinal vs transverse energy gain Gammas 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.

Case II :   The solitary bubble regime

bubbles 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.

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 fs

Here 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. profiles

Electron pulse and conversion efficiency

3D-bubble 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.

Analytical estimates for Laser Wakefield Acceleration

J. Meyer-ter-Vehn, A. Pukhov, Rel. Las. Plas. Interaction, part I: Analytical Tools
A. 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 pulses

A. Pukhov and J. Meyer-ter-Vehn, Appl. Phys. B74, 355 (2002)

Generation of relativistic ions

D. 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.