[en] Presented is the algorithm for determination of emission current density and singularity function while solving the problem on focusing the relativistic electron beam in cylindrical air waveguide. Algorithms are built up in such a way that their accuracy is not lower than the accuracy of determination of other characteristics of the whole problem. Computer memory necessary for calculation on real nets (10-20 points for the unit of waVeguide length) constitutes 10-15 thousand words. Shown is effectivity of the proposed algorithm

[en] The development of wave collapse (WC) results in many cases in the formation of a long-living hot spot that draws continuously waves from the surrounding space. This important and widespread mechanism of nonlinear dissipation of wave energy in strong-turbulent processes has been lately studied intensively in the model of nonlinear Schroedinger equation (NLS) that describes the various types of WC in the d-dimensional space for sufficiently intensive initial conditions. For 4 ≤ sd < 2s+2 the short-living collapses (strong collapse with fixed energy trapped into singularity at sd=4 and weak collapse with continuously decreasing energy at sd > 4) take place. However, for sd ≥ 2s+2, a small-size dissipative zone (hot spot or black hole), which absorbs quasisteadily energy, is formed as a result of a weak collapse. This effect of long collapse, named as a superstrong wave collapse (SWC) is critically important for understanding of many macroscopic displays of strong wave turbulence (optical, plasma, and others). The SWC can be developed in the four different regimes. Note that the SWC phenomena may exist in the NLS independently of s at d>2. This means that the convenient and widely used model of forced damped NLS for studies of strong (collapsing) wave turbulence in nonlinear media can not take into account this significant effect for d≤2. Since long 3D computations of turbulence with multiple collapses are extremely expensive, there is an important problem of crating of the SWC models in lower dimensions

[en] The problem of the acceleration of impurity aluminum ions in a hydrogen plasma which is expanding into vacuum is solved by numerical simulation. Particular emphasis is placed on the role played by Coloumb collisions during the ion acceleration. The motion of the major plasma species is assumed to be collisionless, obeying the Vlasov kinetic equation. For the impurity component, the self-consistent-field effects and collisions with the ions of the major species and the electrons are taken into account. The conditions under which collisions play a governing role in the acceleration of the impurity ions are determined. Under these conditions, a steady-state energy spectrum is formed for the impurity ions comparatively rapidly. This spectrum then changes slowly as a result of ion acceleration by the self-consistent field. It is also shown that the dependence of the average energy of the various components on the charge weakens with increasing charge and with increasing plasma density

[en] It was shown recently that mode conversion phenomena has a profound influence on the emission of radiation from a nonuniformly magnetized plasma. Whenever the emitting layer is localized due to gradients of the external magnetic field, mode conversion leads to the Generalized Kirchhoff's Law (GKL) A₁/E₁ = A₂/E₂ = A₃/E₃ = I, where A_j represents the absorbed fraction on the j-th wave branch, E_j is the corresponding emitted energy along j-th branch and I is some fundamental constant depending upon basic plasma parameters. As the relations between emission and absorption were deduced from qualitative thermodynamic arguments using only the law of equipartition of energy and the reciprocity relations, they do not depend on details of the source or sink if their distributions fall off quickly enough as |z|→∞. In order to understand the main physical processes underlying the GKL it is important to obtain the explicit expressions for A_j and E_j from the governing mathematical model. In this paper the authors have considered a model based on the fourth-order mode-conversion-tunneling equation, and have discovered new important properties of linearly independent solutions of the adjoint problem. Using the properties obtained and the results of a cited reference they have found a general but simple expressions for absorbed and emitted wave power. They considered the N-point approximation for relating sink and source, since due to the fluctuation-dissipation theorem any absorber is also an emitter and vice versa. In the general case of arbitrary N, any of N-1 source points may be chosen arbitrary, since the GKL only imposes two conditions. Thus the GKL is consistent with nearly any N-point model. On the other hand, they believe that the GKL can give the information about the distributed source when additional physical considerations are involved. 4 refs

[en] Whereas direct calculations of emission from a source model in both homogeneous and weakly inhomogeneous media have been previously executed, there are no previous theories of the source distribution function from nonuniformly magnetized plasmas where mode conversion phenomena must be taken into account. Whenever the emitting layer is localized due to gradients of the external magnetic field, mode conversion leads to the Generalized Kirchhoff's Law (GKL) E₁/A₁ = E₂/A₂ = E₃/A₃, where A_j represents the absorbed fraction on the j-th wave branch and E_j is the corresponding emitted energy along j-th branch. Recently integral expressions for A_j and E_j in terms of arbitrary localized sink and source distributions have been obtained. The GKL relating absorption to emission along each branch of coexisting in the inhomogeneous mode conversion layer affects the shape of source distribution through a functional of the emissivity. Moreover, E_j/A_j ≡ I_bb, where I_bb is a black body radiated power. Accordingly, the distributed emission source function should be an extremal of the emissivity functional. The authors have developed the corresponding variational analysis with nontrivial GKL constraints. As a result they have discovered the correct representation of the ratio of source and sink distributions in the form of an expansion in linearly independent adjoint wave solutions of the absorption problem. Finally, unknown coefficients have been found numerically by further maximization taking account of both source boundedness and the GKL constraints. Calculations performed for a broad variety of plasma parameters will be presented

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[en] The dynamics of elementary cell of turbulence (collapsing cavity) is investigated both in the model of nonlinear Schroedinger equation and in total kinetic description (particle simulation). Electron acceleration due to Langmuir turbulence is studied in different physical situations. The long-time evolution of the soliton turbulence is investigated. (author) 31 refs

[en] The theory of an inhomogeneous source of cyclotron emission from a three-branch mode-conversion layer in a non-uniformly magnetized plasma is presented. The physical formulation of the problem is based on the generalized Kirchhoff's law that relates, branch by branch, the emission to the absorption. A variational principle for the integral of the emitted power is formulated. A regular analytical procedure for solving the variational problem with non-trivial generalized Kirchhoff's law constraints for obtaining a continuous source distribution is developed. Examples at harmonics of both the electron-and ion-cyclotron frequencies are given and analysed for both relativistic and non-relativistic plasmas. (author)

[en] Recent results on determining the spatial profile of the emission source distribution from a cyclotron mode conversion layer are extended to the five branch wave coupling case which occurs when the X-mode is coupled to the O-mode. A variational problem for an inhomogeneous source is formulated and solved. Computations demonstrate that the basic features, including a highly localized emitter, are generally similar to those of the three branch mode conversion problem