Table of contents

The theoretical description of the nonlinear photoionization of atoms and ions exposed to high-intensity laser radiation is underlain by the Keldysh theory proposed in 1964. The paper reviews this theory and its further development. The discussion is concerned with the energy and angular photoelectron distributions for the cases of linearly, circularly, and elliptically polarized laser radiation, with the ionization rate of atomic states exposed to a monochromatic electromagnetic wave and to ultrashort laser pulses of various shape, and with momentum and angular photoelectron spectra in these cases. The limiting cases of tunnel (γ ≪ 1) and multiphoton (γ ≫ 1) ionization are discussed, where c is the adiabaticity parameter, or the Keldysh parameter. The probability of above-barrier ionization is calculated for hydrogen atoms in a low-frequency laser field. The effect of a strong magnetic field on the ionization probability is discussed. The process of Lorentz ionization occurring in the motion of atoms and ions in a constant magnetic field is considered. The properties of an exactly solvable model—the ionization of an s-level bound by zero-range forces in the field of a circularly polarized electromagnetic wave—are described. In connection with this example, the Zel'dovich regularization method in the theory of quasistationary states is discussed. Results of the Keldysh theory are compared with experiment. A brief discussion is made of the relativistic ionization theory applicable when the binding energy of the atomic level is comparable with the electron rest mass (multiply charged ions) and the sub-barrier electron motion can no longer be considered to be nonrelativistic. A similar process of electron-positron pair production from a vacuum by the field of high-power optical or X-ray lasers (the Schwinger effect) is considered. The calculations invoke the method of imaginary time, which provides a convenient and physically clear way of calculating the probability of particle tunneling through time-varying barriers. Discussed in the Appendices are the properties of the asymptotic coefficients of the atomic wave function, the expansions for the Keldysh function, and the so-called 'ADK theory'.

New insight is provided into how runaway electrons are generated in gases. It is shown that the Townsend mechanism of electron multiplication works even for strong fields, when the ionization friction of electrons can be neglected. The non-local electron runaway criterion proposed in the work determines the critical voltage–pd relationship as a two-valued function universal for a given gas (p being the gas pressure, and d the electrode spacing). This relationship exhibits an additional upper branch as contrasted to the familiar Paschen's curves and divides the discharge gap into two regions: one where electrons multiply effectively, and the other which they leave without having enough time to multiply. Experiments on the production of electron beams with subnanosecond pulse duration and an amplitude of tens to hundreds of amperes at atmospheric pressure in various gases are addressed, and the creation of a nanosecond volume discharge with the high density of excitation power and without preionization of the gap by a supplementary source is discussed.

The review covers experimental and theoretical studies of the self-action effects observed for intense wave beams with sawtooth time profiles. For sawtooth waves in quadratic nonlinear media, inertial self-focusing and defocusing processes caused by the formation of acoustic streaming and heating due to nonlinear energy dissipation at shock fronts are discussed. Self-refraction of shock-wave pulses is considered, which leads, in particular, to the saturation of the maximal field achieved by focusing. For cubic nonlinear media, where a sawtooth wave contains both compression and rarefaction shocks, the self-focusing process is studied in the presence of its strong competition with nonlinear damping. New mathematical models, their symmetry properties and exact solutions, and the results of numerical simulation are described. A general picture of the state of the art in this field is given.

Advances in nonequilibrium pattern formation in reaction–diffusion systems are reviewed. Special emphasis is placed on patterns found in the spatially extended Belousov–Zhabotinsky reaction dispersed in aerosol OT water-in-oil microemulsions (BZ–AOT system): Turing patterns, packet and standing waves, antispirals and segmented spirals, and accelerating waves and oscillons. All experimental results are explained theoretically and reproduced in computer simulations.