V. F. Kovalev

Group analysis and renormgroup symmetries

An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries based on modern group analysis are described. An application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model.An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described. Application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model.

High-energy ion generation by short laser pulses

This paper reviews the many recent advances at the Center for Ultrafast Optical Science (CUOS) at the University of Michigan in multi-MeV ion beam generation from the interaction of short laser pulses focused onto thin foil targets at intensities ranging from 1017 to 1019 W/cm2. Ion beam characteristics were studied by changing the laser intensity, laser wavelength, target material, and by depositing a well-absorbed coating. We manipulated the proton beam divergence using shaped targets and observed nuclear transformation induced by high-energy protons and deuterons. Qualitative theoretical approaches and fully relativistic two-dimensional particle-in-cell simulations modeled energetic ion generation. Comparison with experiments sheds light on ion energy spectra for multi-species plasma, the dependences of ion-energy on preplasma scale length and solid density plasma thickness, and laser-triggered isotope yield. Theoretical predictions are also made with the aim of studying ion generation for high-power lasers with the energies expected in the near future, and for the relativistic intensity table-top laser, a prototype of which is already in operation at CUOS in the limits of several-cycle pulse duration and a single-wavelength spot size.

Particle Dynamics during Adiabatic Expansion of a Plasma Bunch

The renormalization-group approach is used to obtain an exact solution to the self-consistent Vlasov kinetic equations for plasma particles in the quasi-neutral approximation. This solution describes the one-dimensional adiabatic expansion of a plasma bunch into a vacuum for arbitrary initial particle velocity distributions. Ion acceleration is studied for two-temperature Maxwellian and super-Gaussian initial electron distributions, which predetermine distinctly different ion spectra. The solution found is used to describe the acceleration of ions of two types. The relative acceleration efficiency of light and heavy ions as a function of atomic weights and number densities is analyzed. The solutions obtained are of practical importance in describing ion acceleration during the interaction of an ultrashort laser pulse with nanoplasma, for example, cluster plasma or plasma produced when thin foils are irradiated by a laser.

Ion Acceleration during Adiabatic Plasma Expansion: Renormalization Group Approach

The renormalization group approach is applied to derive an exact solution to self-consistent Vlasov kinetic equations for plasma particles in the quasineutral approximation. The solution obtained describes the one-dimensional adiabatic expansion into vacuum of a plasma bunch with arbitrary initial velocity distributions of the electrons and ions. The ion acceleration is investigated for both a Maxwellian two-temperature initial electron distribution and a super-Gaussian initial electron distribution.

Symmetries of Integro-Differential Equations: A Survey of Methods Illustrated by the Benny Equations

Classical Lie group theory provides a universal tool for calculatingsymmetry groups for systems of differential equations. However Liesmethod is not as much effective in the case of integral orintegro-differential equations as well as in the case of infinitesystems of differential equations.This paper is aimed to survey the modern approaches to symmetriesof integro-differential equations. As an illustration, an infinitesymmetry Lie algebra is calculated for a system of integro-differentialequations, namely the well-known Benny equations. The crucial idea is tolook for symmetry generators in the form of canonical Lie–Bäcklundoperators.

Laser triggered Coulomb explosion of nanoscale symmetric targets

Approximate kinetic solutions are found for Coulomb explosions of nanostructures in plane (thin foils), cylindrical (nanowires/tubes) and spherical (nanospheres/shells) geometries. The distribution function, mean velocity, density distribution, as well as the energy spectra for accelerated ions are derived. The proposed kinetic model describes physics of multiple flows that occur during Coulomb explosion. Comparison with particle-in-cell numerical simulations shows good agreement with analytical results.

Coulomb Explosion in a Cluster Plasma

The energy spectra of particles in a cluster plasma produced during the Coulomb explosion of spherically symmetric clusters with an arbitrary initial density distribution are investigated. A relationship is found between the energy spectrum of the ions and the density profile of the atoms in the cluster.

Kinetic Description of the Coulomb Explosion of a Spherically Symmetric Cluster

The particle distribution function is calculated for the Coulomb explosion of a spherically symmetric charged cluster formed through the interaction of intense ultrashort laser pulses with a cluster gas. The particle density and mean velocity distributions as well as the energy spectra of the accelerated particles are obtained. These characteristics are analyzed in detail for a cold cluster plasma, where the kinetic effects determine the physics of multiple flows emerging after the turnover of the cluster particle velocity profile. We find the boundaries of the multiple-flow regions and study the characteristics of an exploding cluster as a function of its initial density profile. The energy spectra of the accelerated ions are obtained for a cluster plasma with a specified cluster size distribution.

Renormalization Group in Mathematical Physics and Some Problems of Laser Optics

An original approach to constructing special type symmetries for boundary value problems, RENORMGROUP SYMMETRIES, is reviewed here. It is applied to a system of geometric optics equations. New solutions to the laser beam self-focusing problem are presented.

Relativistic Coulomb Explosion of Spherical Microplasma

The nonlinear problem of the expansion of a uniform spherical cluster, which consists of ions with a charge sufficient to accelerate relativistic energies has been solved precisely. It has been shown that relativistic non-linearity is responsible for the formation of an expanding shell-type structure. The space-time and energy characteristics of the relativistically exploding cluster have been found.