We present a summary of the beatwave particle acceleration program developed at Ecole Polytechnique. In dedicated experiments, plasma formation, plasma wave generation and saturation, and particle acceleration were successively studied and understood in detail. A maximum energy gain of 1.3 MeV was obtained, which is compatible with an accelerating gradient of 0.7 GV/m.

In a plasma, some of the energy of a high-power laser beam can be transferred to a longitudinal plasma wave with a high phase velocity. This wave can in turn accelerate relativistic charged particles to very high energies. Several mechanisms have been proposed to generate these intense electric fields and some of them have already been tested experimentally. Using the beat wave method, electric fields of 1 - 10 have been produced and electrons have been accelerated with an energy gain from 1 MeV to more than 30 MeV. Some preliminary experiments have shown that electrons can be accelerated in plasma waves generated by the wakefield method. In the case of self-modulated wakefield, electric fields larger than 100 trap electrons and eject them from the plasma with an energy up to 100 MeV. The perspectives in the near future are the production of intense and short electron beams of a few MeV and the acceleration of electrons up to 1 GeV. To reach an energy of 1 TeV and get closer to the parameters required by the high-energy physicists, one will have to test some new methods to be able to guide the laser beam over large distances.

We present a general, paraxial study of triple focusing (i.e., stigmatic and non-dispersive) index-free dipole magnets. The transcendental equations which describe such magnets lead to a second-degree polynomial equation which we solve analytically. The two solutions of this equation correspond to magnets having either one or no intermediate focal points in the vertical direction. The first-order optical properties of the physical solutions are studied.

The beating between two colinear Nd-YLF (lambda = 1.053 mu m, tau = 90 ps) and Nd-YAG (lambda = 1.054 mu m, tau = 160 ps) lasers in a homogeneous plasma (n(c) = 10(17) cm(-3)) generates intense relativistic plasma waves associated with a high longitudinal electric field of the order of 1 GV m(-1). In the conditions of the experiment, these electron plasma waves couple with ion waves in the regime of modulational instability as it has been demonstrated by electric field amplitude and saturation time measurements by Thomson scattering.When 3 MeV energy electrons are injected into the plasma, several hundreds of electrons accelerated up to 3.7 MeV are observed in correlation with the Thomson scattering signal associated to the plasma waves. This result is in agreement with a numerical simulation which takes into account the relative focussing geometry of electron and laser beams.

We present an experiment for demonstrating the principle of plasma beat-wave acceleration. The beating of two Nd-laser pulses creates a relativistic plasma wave in a deuterium plasma. Electrons at an energy of 3 MeV are injected into the plasma. We observe several hundred electrons accelerated up to 3.7 MeV. This paper is mainly devoted to the description of the experimental apparatus. In the design of the apparatus, we gave particular attention to efficient electron injection and to background noise suppression. We present also some preliminary results of electron acceleration experiments.