[en] Self-fosusing thresholds are derived for multiple laser beams in the presence of a beat-excited plasma wave. The effects of relativistic electron ''quiver'' motion and the interaction of the beams with the plasma wave are included self-consistently. When the plasma wave is driven resonantly to large amplitude, transfer of the pump energy into sidebands causes the beams to defocus more rapidly. Consequently, relativistic focusing occurs above an irradiance threshold of Iλ²∼2x10¹⁷ W cm^-2 μm², instead of the usual power threshold for double-frequency illumination P∼4√2x10⁹(ω₀/ω_p)² W. Numerical solusions show that self-trapping of the laser energy is possible only for relatively small amplitude plasma waves. Comparisons are made with ''cascade focusing,'' which occurs when the plasma wave is driven below the plasma frequency. The threshold for the latter is up to ten times lower than for relativistic focusing. Numerical studies in this case indicate that self-trapped solutions do not exist, but the rate of beam collapse can be controlled by choosing an appropriate density mismatch

[en] The following lecture notes offer a short, elementary introduction to the field of high-intensity laser interactions with matter. The material starts with basic phenomena such as ionization, plasma characterization and thresholds for non-linear behaviour. In the latter sections, topics relevant to laser-based particle acceleration are covered in detail, including wave propagation in underdense plasmas and fast electron heating in overdense (solid) plasmas. The notes are concluded with a short summary of plasma simulation techniques, including a work-through tutorial using a particle-in-cell code.

[en] Recent theoretical and experimental research with short-pulse, high-intensity lasers is surveyed with particular emphasis on new physical processes that occur in interactions with low-and high-density plasmas. Basic models of femtosecond laser-solid interaction are described including collisional absorption, transport, hydrodynamics, fast electron and hard x-ray generation, together with recently predicted phenomena at extreme intensities, such as gigagauss magnetic fields and induced transparency. New developments in the complementary field of nonlinear propagation in ionized gases are reviewed, including field ionization, relativistic self-focusing, wakefield generation and scattering instabilities. Applications in the areas of x-ray generation for medical and biological imaging, new coherent light sources, nonlinear wave guiding and particle acceleration are also examined. (author)

[en] A method is presented for the solution of the 2D wave-envelope equations describing beat-wave excitation. The code includes self-focussing, radial plasma-wave fields, and density inhomogeneity. The time evolution of injected particle beams is followed in 3D over distances up to an accelerator stage length. An example of the code's application is given using parameters in the vicinity of anticipated experiments. (orig.)

[en] Non-linear Langmuir waves are examined in the context of the beat-wave accelerator. With a background of immobile ions the waves in one dimension are subject to the relativistic non-linearity of Rosenbluth, M.N. and Liu, C.S., Phys. Rev. Lett., 1972, 29, 701. In two or three dimensions, other electron non-linearities occur which involve electric and magnetic fields. The quasi-linear equations for these non-linearities are developed and solved numerically in a geometry representative of laser-driven beat waves. (author)

[en] In the reply to the comment the authors summarise that there seems to be different ways of looking at cascade focusing of laser radiation in the BWA

[en] The 2D wave-envelope equationf for the beat-wave--cascade system are studied analytically and numerically. An expression for the mean square width of the cascade envelope is obtained, and is used to predict the long-term behavior of the waves. The amplitude or a resonantly driven plasma wave falls significantly over a stage length due to enhanced diffraction of the cascade envelope. Conversely, detuning the pumps from the plasma frequency can lead to focusing of the envelope and a corresponding increase in plasmon amplitude of up to 200% over the same distance

[en] This paper reports on experimental investigations on relativistic self-focusing and self-channeling of a terawatt laser pulse (0.7 TW ≤ P ≤ 15 TW) in an underdense plasma. The authors present results obtained with picosecond (τ = 1 ps) and subpicosecond (τ = 0.4 ps) pulses. In the ''long pulse'' regime, modifications in the laser propagation are observed for P < P_c, the critical power for self-focusing. By contrast, self-guiding of subpicosecond pulses is observed for P ∼ P_c. Using a paraxial envelope model describing the laser propagation and taking into account the plasma response to the ponderomotive force, it is shown that a maximum laser intensity of 5--15 times that reached in vacuum may be achieved when P is in the (1.25--4) x P_c range. It is also demonstrated that ion motion may significantly reduce the effective P_c

[en] We present two-dimensional wave-envelope studies of the interaction between a plasma beat-wave and the laser pumps which drive it. A new method of focusing is demonstrated which requires the plasma wave to be driven slightly below its resonant frequency. Test particles are employed to investigate possible means of extending the accelerator stage length. copyright 1989 American Institute of Physics

[en] We present experimental measurements of the absorption of ultrashort laser pulses by 15 μm diameter methanol micro-droplets. The droplet absorbs up to 70% of the incidence laser energy in the presence of a prepulse at intensities of about 1.5*10¹⁶ W/cm². In the absence of a prepulse, the absorption is only about 20 per cent. Simultaneous measurements of X-ray yield (12 keV to 350 keV) and the absorption in the droplet plasma, shows that our earlier measurements of efficient generation of hard X-rays from the droplet plasma is due to the increased absorption in the droplets in the presence of optimum prepulse. One dimensional Particle-in-cell simulations, mimicking the mass-limited droplet density profile, demonstrate the effectiveness of the large scale-length droplet plasma in providing optimal conditions for resonant laser absorption energy and generation of hot electrons. (authors)