Back Matter Pages Examples of Nonlinear Processes in an Isotropic Plasma. Specific Nonlinear Processes in a Magnetoactive Plasma. About this book Introduction This volume contains two papers that review certain theoretical problems that have been studied in the Laboratory of Plasma Accelerators and Plasma Physics of the P. The review of R.

Kikvidze and A. Neunzert, "An existence theorem for the unmodified Vlasov equation", Math. Isichenko, "Nonlinear Landau damping in collisionless plasma and inviscid fluid", Phys. Kondrat'ev, "Boundary-value problems for elliptic equations in domains with conical or corner points", Tr. Kozlov, "The generalized Vlasov kinetic equation", Russian Math.

Surveys , , 63 :4, — Kozlov, "The Vlasov kinetic equation, dynamics of continuum and turbulence", Regul. Chaotic Dyn. Kurth, "Das Anfangswertproblem der Stellardynamik", Z. Landau, "On the vibrations of the electronic plasma", Zh.

Lemou, F. Raphael, "The orbital stability of the ground states and the singularity formation for the gravitational Vlasov Poisson system", Arch. Leontovich and B. Kadomtsev eds. Lifshitz and L. Pitaevskii, Course of theoretical physics, Pergamon Internat.

Library Sci. Social Stud. Lions and B. Perthame, "Propagation of moments and regularity for the 3-dimensional Vlasov—Poisson system", Invent. Loeper, "Uniqueness of the solution to the Vlasov—Poisson system with bounded density", J. Pures Appl. Mancini and S. Totaro, "Vlasov equation with non-homogeneous boundary conditions", Math. Marchioro and M. Markov, G. Rudykh, N. Sidorov, and A. Sinitsyn, "Existence of stationary solutions of Vlasov—Maxwell equations and some of their exact solutions", Mat.

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Sinitsyn, "The family of solutions of Vlasov—Maxwell system and their stability", Mat. Sidorov, A. Sinitsyn, and D.

Maslov, "Equations of the self-consistent field", J. Soviet Math. Maslov and M. Fedoryuk, "The linear theory of Landau damping", Math. Mischler, "On the trace problem for solutions of the Vlasov equation", Comm.

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Partial Differential Equations , , 25 , — Mouhot and C. Villani, "On Landau damping", Acta Math. Nazarov and B. Plamenevsky, Elliptic problems in domains with piecewise smooth boundaries, de Gruyter Exp. Neunzert and K. Pfaffelmoser, "Global classical solutions of the Vlasov—Poisson system in three dimensions for general initial data", J. Differential Equations , , 95 :2, — Pokhozhaev, "On stationary solutions of the Vlasov—Poisson equations", Differ.

Rein, "Generic global solutions of the relativistic Vlasov—Maxwell system of plasma physics", Comm. This may be useful for medical applications or for ion beam fast ignition fusion. It accounts for ion acceleration in the electrostatic sheath and Coulomb interaction between heavy and light ions. The model is used to study proton acceleration, and the conditions for a quasimonoenergetic proton beam formation are defined.

Comparison with the hybrid and two-dimensional particle-in-cell kinetic simulations verifies the model results. The electron response includes both collisional and collisionless dissipative effects in a plasma with arbitrary ion charge. The difference between known absorption models and our theoretical RFBR approach which accounts for localized plasma heating with nonlocal heat transport has been discussed. A simple semi-analytical model of femtosecond electron heating and resultant optical absorption is developed to describe the time dependent and integral reflectivity covering the range from cold metal response to hot plasma response.

The model is in good agreement with experimental ultrafast reflectivity measurements over the intensity range studied. This work is a generalization of the nonlocal transport theory by Bychenkov et al. Transport closure relations have been obtained for the complete set of electron and ion fluid equations which are valid over the full range of particle collisionality and for an arbitrary ionic charge.

The well-known limits of collisionless and strongly collisional plasma transport theory have been recovered. Practical fits based on the numerical calculations have been introduced for nonlocal and frequency-dependent ion transport coefficients. The injection scheme requires a concordance of the density scale length and laser intensity. It is shown that at a sloping inhomogeneity of plasma the wave breaking produces stronger singularity of the electron density than at a density discontinuity, but develops slower.

With the help of simulations for a moderate laser intensity, we demonstrate the optimal plasma density gradient, where the electron injection into the wake wave forms the electron beam with low divergence, small energy spread and high energy. In this regime heavy ions expand predominantly in the direction of laser pulse propagation enhancing the longitudinal charge separation electric field that accelerates light ions. The dependence of the maximum proton energy on the foil thickness has been found and the laser pulse characteristics have been matched with the thickness of the target to ensure the most efficient acceleration.

Moreover, the proton spectrum demonstrates a peaked structure at high energies, which is required for radiation therapy. The electron acceleration is studied depending on the initial position of the electron in the focal plane and is compared with the results corresponding to the paraxial approximation for the laser field. The maximum energy acquired by the electron in the laser focus is found.

The dependences of the ejection angle of the electron on its initial position near the focus are analysed. The obtained spatial and energy distributions of light and heavy ions in different charge states demonstrate that the model can be efficiently used to study the ion composition in a multispecies expanding laser plasma. The regular features of the acceleration of ions of different species are investigated. The formation of compression and rarefaction waves in the halo of light ion impurity, as well as their effect on the energy spectrum of the accelerated ions, is analyzed.

An approach is proposed that makes it possible to describe the production of fast ions by laser pulses of a given shape. It is shown that the energy of fast ions can be increased markedly by appropriately shaping the pulse.

The effect of heating of the bulk of the cold target electrons on the ion acceleration is discussed. The expansion is in the form of a collisionless rarefaction wave associated with three types of electrostatic shocks.

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Each shock manifests itself in a potential jump and in the spatial separation of plasma species. The shock front associated with the proton—electron separation sets the maximum proton velocity. Two other shocks are due to the hot—cold electron separation and the light—heavy ion separation. They result in the light ion acceleration and their accumulation in the phase space. These structures open possibilities for control of the number and the energy spectrum of accelerated ions.

Simple analytical models are confirmed in numerical simulations where the ions are described kinetically, and the electrons assume the Boltzmann distribution. RU en change language. Ivanov, S. Shulyapov, P. Ksenofontov, I. Tsymbalov, R. Volkov, A. Brantov, V.

Bychenkov, A. Turinge, A. Lapik, A. Rusakov, R. Djilkibaev, and V. Nedorezov3 Comparative study of amplified spontaneous emission and short pre-pulse impacts onto fast electron generation at sub-relativistic femtosecond laser-plasma interaction Physics of Plasmas, vol. Brantov, G.