arXiv subjects

V. N. Soshnikov

Publications and source records attributed to V. N. Soshnikov.

17 recordsLinked to original sources

arXiv2015

Comments to support the Dipole Dynamical Model (DDM) of Ball Lightning (BL)

I present estimates to justify previously proposed by me heuristic Dipole Dynamical Model (DDM) of Ball Lightning (BL). The movement and energy supplying to the dipole BL are due to the atmospheric electric field. Crucial for the detailed analysis of BL is using the new relation of balance of the force of atmospheric electric field (per unit mass of electron cloud) and dipole forces electrons-ions within BL dipole (per unit mass of BL) as the first necessary condition for the existance of BL as an integer. This model is unique because, unlike existing static models, fundamental condition for the existence of Ball Lightning is its forward motion. The virial theorem limiting BL power does not apply to BL which is not closed system like the Sun or Galaxy systems and is strongly dependent part of the infinitely extended in time and space large system. Stability of BL is due to two free parameters with the fundamental role of thermodynamic non-equilibrium, ionization, recombination and translational movement with energy loss by radiation and also excess volumetric positive charge. Stability of BL is not related to the presence of any external shells. Polarization degree of BL plasma is characterized by polarizability factor γ. An example is presented of calculating the stability of an option of BL. There is also a possible connection of stability BL with statistical distributions of the atmospheric electric field in time and space. Destruction of BL can also occur due to arising kinematical instability at its accelerating (or decelerating) movement. Maximal energy density in BL DDM does not exceed the value Espec<(10(8) - 10(9)) J/m(3) decreasing with the growing BL radius. Resulting indefinitely long BL lifetime is also discussed. BL has no outer shell and no any inner rigid or elastic microstructure elements.

physics.gen-ph↗

arXiv2015

Logical contradictions of Landau damping

Landau damping/growing at boundary condition of excitation of a harmonic wave in collisionless ion-electron-neutrals plasma contradicts to the law of energy conservation of a wave damping/growing in space. There is also no criterion of a choice either damping or growing solution in difference from always non-damping in the direction of propagation Vlasov waves. Variety of other incongruities as consequence of Landau damping is specified also. Absence of explicit positivity and finiteness of wave solutions for electron distribution function near singularity point leads to need of imposing additional cutting off constraints with resulting positivity and finiteness of the electron distribution function at the singularity points and finiteness of the complex dispersion integral. Landau damping as a real physical phenomenon of collisionless damping does not exist. A relation is established for the real dispersion equation with real waves (see Appendices 2,4) between the averaged over period wave damping decrement and the collisional energy-exchange term of kinetic equation. Collisionless Vlasov-Landau damping is explained finally by the usual wrong use of nonlinearly complex wave functions leading to complex dispersion equation. All used solution of the complex dispersion equation for the simultaneously existing collisionless both exponentially damping and growing nonlinear complex waves is entirely, quantitatively and in its logical sense, different from the solution of initially real dispersion equation for real either damping or growing waves and should be discarded (see Appendices 2,4,5,6). Collisionless damping is caused by unreasonable use of wave functions with complex frequency or complex wave number leading to complex dispersion relation with unphysical binomial virtual complex roots. Thus finding roots of the complex dispersion equation has only abstract mathematical interest.

physics.gen-ph↗

arXiv2014

Solving non-linear equations of longitudinal and transverse electron waves in collisionless Maxwellian plasma

We have considered an expansion of solutions of the non-linear equations for both longitudinal and transverse waves in collisionless Maxwellian plasma in series of non-damping overtones of the field E(x,t) and electron velocity distribution function f=f(0) +f(1) where f(0) is background Maxwellian electron distribution function and f(1) is perturbation. The electrical field and perturbation f(1) are presented as a series of non-damping harmonics with increasing frequencies of the order n and the same propagation speed. It is shown presence of recurrent relations for arising overtones. Convergence of the series is provided by a power law parameter series convergence. There are proposed also successive procedures of cutting off the distribution function f(1) to the condition of positivity f near the singularity points where kinetic equation becomes inapplicable. In this case, at poles absence the solution reduces to non-damping Vlasov waves (oscillations). In the case of transverse waves, dispersion equation has two roots, corresponding to the branches of fast electromagnetic and slow electron waves. There is noted a possibility of experimental testing appearing exotic results with detecting frequencies and amplitudes of n-order overtones.

physics.plasm-ph↗

arXiv2014

Purely electrical nature of ball lightning (BL), its elementary equations, calculated parameters and conditions of BL possible experimental generation

The nature of ball lightning (BL) is pure electric and can be described by simple equations following to elementary considerations of equality of translational acceleration and velocity of the ions and electrons, a spherical-like dipole BL as a whole and balance of the energy influx of atmospheric electricity and radiation losses. From these equations follows a linear relationship between the size of BL and the tension of the atmospheric field E. A typical size of the fireball (FB) r ~ 5 cm corresponds to the calculated electron temperature T(e) ~ 8000K at a pressure p = 1 at with a horizontal component of the electric field E a few kV/cm. I estimate the energy of BL and characterize the conditions of its possible experimental generation. The estimation is given of the surface tension of BL. The possibility of the "hot" and the most realistic thermodynamic non-equilibrium "cold" BL is discussed. Here we presented preliminary evaluations preceding the more detailed work in Arxiv.org [11].

physics.plasm-ph↗

arXiv2008

Collisionless damping of electron waves in non-Maxwellian plasma

In this paper we have criticized the so-called Landau damping theory. We have analyzed solutions of the standard dispersion equations for longitudinal (electric) and transversal (electromagnetic and electron) waves in half-infinite slab of the uniform collisionless plasmas with non-Maxwellian and Maxwellian-like electron energy distribution functions. One considered the most typical cases of both the delta-function type distribution function (the plasma stream with monochromatic electrons) and distribution functions, different from Maxwellian ones as with a surplus as well as with a shortage in the Maxwellian distribution function tail. It is shown that there are present for the considered cases both collisionless damping and also non-damping electron waves even in the case of non-Maxwellian distribution function.

physics.plasm-ph↗

arXiv2008

Non-linear equations for electron waves in Maxwellian low-collision ion-electron plasmas

The before described general principles and methodology of calculating electron wave propagation in homogeneous isotropic half-infinity slab of Maxwellian plasma with indefinite but in principal value sense taken integrals in characteristic equations, and the use of 2D Laplace transform method are applied to an evaluation of collision damping decrements of plane electron longitudinal and transverse waves. Damping decrement tends to infinity when the wave frequency tends to electron Langmuir frequency from above values. We considered recurrent relations for amplitudes of the overtones which form in their sum the all solution of the plasma wave non-linear equations including collision damping and quadratic (non-linear) terms. Collisionless damping at frequencies more the Langmuir one is possible only in non-Maxwellian plasmas.

physics.plasm-ph↗

arXiv2007

Interrelation of fast and slow electron waves at propagation of electromagnetic waves in Maxwellian collisionless plasma

It is shown in linear approximation that in the case of one-dimensional problem of transverse electron waves in a half-infinite slab of homogeneous Maxwellian collisionless plasma with the given boundary field frequency two wave branches of solution of the dispersion equation are simultaneously realizing. These are the branch of fast forward waves determined mainly by Maxwell equations of electromagnetic field, as well as the branch of forward and backward slow waves determined in the whole by kinetic properties of electrons in the collective electrical field. The physical nature of wave movements is revealed. A relation is found between electric field amplitudes of fast and slow waves. Multiform dividing the coupled slow waves into standing and traveling parts leads to a necessity of additional requirements to a selection of the type of a device analyzing these waves and its response interpretation.

physics.plasm-ph↗

arXiv2007

On some peculiarities of electric field pulse propagation in electron Maxwellian plasma and its back response

In the spirit of continued study of general plasma wave properties we investigated the boundary problem with the simplest form of electric field pulse at the edge x=0 of half-infinite uniform plasma slab with Maxwellian electron distribution function. In the case of longitudinal electric field pulse its traveling velocity is essentially other than in the case of harmonic waves; there is also no back response. In the case of transverse field pulse there takes place the bimodal propagation rate of the non-damping fast pulse signal and non-damping weak slow sign reversed pulse signals; some very weak response (echo) arises with a time delay in the near coordinate zone of formation of the asymptotical regime.

physics.plasm-ph↗

arXiv2007

Strong collisionless damping of the low-velocity branch of electromagnetic wave in plasmas with Maxwellian-like electron velocity distribution function

After approximate replacing of Maxwellian distribution exponent with the rational polynomial fraction we have obtained precise analytical expression for and calculated the principal value of logarithmically divergent integral in the electron wave dispersion equation. At the same time our calculations have shown the presence of strong collisionless damping of the electromagnetic low-velocity (electron) wave in plasmas with Maxwellian-like electron velocity distribution function at some small, of the order of several per cents, differences from Maxwellian distribution in the main region of large electron densities, however due to the differences in the distribution tail, where electron density itself is negligibly small.

physics.plasm-ph↗

arXiv2007

Damping of plasma-electron oscillations and waves in low-collision electron-ion plasmas

Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is applied to low-collision electron-ion plasmas. Taking into account Coulomb collisions in the limit m_e << m_i, \bar{v_i} << \bar{v_e}, and T_e m_e << T_i m_i, results in the expression for longitudinal high-frequency plasma-electron oscillation/wave decrement essentially depending on oscillation frequency ω. This expression is quite different from the used one for low-frequency plasma sound, which can be derived using expansion in asymptotically divergent series in δ/ω_0, k v_i/ω_0, where δis imaginary part of the frequency ω=ω_0+iδ, and does not reduce to simple expression with some collision frequency δ\simν^{eff}_{e_i}.

physics.plasm-ph↗

arXiv2007

Collisionsless amplifying of longitudinal electron waves in two-stream plasma

To better understanding the principal features of collisionless damping/growing plasma waves we have implemented a demonstrative calculation for the simplest cases of electron waves in two-stream plasmas with the delta-function type electron velocity distribution function of each of the streams with velocities v(1) and v(2). The traditional dispersion equation is reduced to an algebraic 4th order equation, for which numerical solutions are presented for a variant of equal stream densities. In the case of uniform half-infinite slab one finds two dominant type solutions: non-damping forward waves and forward complex conjugated exponentially both damping and growing waves. Beside it in this case there is no necessity of calculation any logarithmically divergent indefinite integrals. The possibility of wave amplifying might be useful in practical applications.

physics.plasm-ph↗

arXiv2004

Some notes on ideology of waves in plasmas

Our last three papers provide an occasion to make some brief notes on ideology of waves in plasmas and to rehabilitate Vlasov prescription to calculate relevant logarithmically divergent integrals in the principal value sense. In this approach asymptotical solutions of plasma oscillations are selected according to self-consistent boundary physical conditions. Landau damping is absent in this case by definition. Boundary electrical field together with conditions of absence of unphysical backward and kinematical waves define single-valued dependence of boundary distribution function on electron velocity \vec{v} in the case of transversal waves and on the surface break of the normal electrical field in the case of longitudinal oscillations. We have proposed physically more justified modified iteration procedure of collisional damping calculation and demonstrated some results of damping decrements calculations in a low-collision electron-ion plasma. Dispersion smearing of both longitudinal and transversal high-frequency waves, for which the smearing decrement δ_x is proportional to Δω/(ω\sqrt{ω^2-ω_L^2}), might be the main cause of waves amplitude damping in collisionless plasmas imitating Landau damping.

physics.plasm-ph↗

arXiv2002

Damping of electromagnetic waves in low-collision electron-ion plasmas

Using previously developed method of two-dimensional Laplace transform we obtain the characteristic equations k(ω) for electromagnetic waves in low-collision fully ionized plasma of a plane geometry. We apply here a new, different from the one used in our previous paper, iteration procedure of taking into account the Coulomb collisions. The waves are collisionally damping in the same extent as electromagnetic waves. Despite the different from previous paper form of the dispersion (poles) equation, the obtained decrements for fast and slow wave modes coincide with results obtained in our earlier paper, if one neglects the terms of higher orders in v^2/c^2, (v and c are electron and light velocities). We point out how one can determine mutually dependent boundary conditions allowing to eliminate simultaneously both the backward and kinematical waves for transversal as well as for longitudinal oscillations.

physics.plasm-ph↗

arXiv2002

Damping of transversal plasma-electron oscillations and waves in low-collision electron-ion plasmas

Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is here applied to consider transversal oscillations and waves in low-collision quasi-neutral (n_i \simeq n_e) Maxwellian electron-ion plasmas. We obtain two branches of electron waves: the ubiquitous one of high-frequency and high-velocity oscillations and the unusual low-velocity one. Taking into account Coulomb collisions in the limit m_e << m_i, \bar{v_i} << \bar{v_e}, and T_e m_e << T_i m_i results in expressions for transversal plasma-electron oscillation/wave decrements with a damping of the low-velocity electron branch \sim n_i^{1/3}/\bar{v}_e^{4/3}, where n_i is the ion density and \bar{v}_e is the mean electron velocity. It ought to rehabilitate Vlasov principal value prescription for relevant integrals, but to supplement it with representation of an asymptotical solution as a sum of exponents (not a single one). "Non-damping" kinematical waves in low-collision plasma transform in the damping ones at reasonably chosen iteration process.

physics.plasm-ph↗

arXiv1997

Landau damping: is it real?

To calculate linear oscillations and waves in dynamics of gas and plasma one uses as a rule the old classical method of dispersion equation for complex frequencies $ω$ and wave numbers $k$: $ε(ω,k)=0$. This method appears to be inapplicable, f.e., in the case of waves in Maxwellian collisionless plasma when dispersion equation has no solutions. By means of some refined sophistication L.~Landau in 1946 has suggested in this case actually to replace the dispersion equation with another one, having a specific solution (``Landau damping'') and being now widely used in plasma physics. Recently we have suggested a quite new universal method of two-dimensional Laplace transformation (in coordinate $x$ and time $t$ for plane wave case), that allows to obtain asymptotical solutions of original Vlasov plasma equations as inseparable sets of coupled oscillatory modes (but not a single wave like $\exp(-iωt+i k x)$). The mode parameters are defined in this case by double-poles ($ω_n$,$k_n$) of Laplace image $E(ω_n,k_n)$ of electrical field $E(x,t)$. This method allows one to obtain the whole set of oscillatory modes for every concrete problem. It leads to some new ideology in the theory of plasma oscillations, which are considered as a combination of coupled oscillatory modes (characterized by pairs ($ω_n$,$k_n$) and amplitudes) and depend not only on the intrinsic plasma parameters, but also on mutually dependent self-consistent initial and boundary conditions and on method of plasma oscillations excitation.

physics.plasm-ph↗

arXiv1997

General dispersion equation for oscillations and waves in non-collisional Maxwellian plasmas

We propose a new and effective method to find plasma oscillatory and wave modes. It implies searching a pair of poles of two-dimensional (in coordinate $x$ and time $t$) Laplace transform of self-consistent plasma electric field $E(x,t) \to E_{p_1p_2}$, where $p_1 \equiv -i ω$, $p_2 \equiv i k$ are Laplace transform parameters, that is determining a pair of zeros of the following equation $$\frac1{E_{p_1p_2}} = 0 .$$ This kind of conditional equation for searching double poles of $E_{p_1p_2}$ we call ``general dispersion equation'', so far as it is used to find the pair values ($ω^{(n)}, k^{(n)}$), $n=1, 2, ...$ . It differs basically from the classic dispersion equation $ε_l(ω,k) = 0$ (and is not its generalization), where $ε_l$ is longitudinal dielectric susceptibility, its analytical formula being derived according to Landau analytical continuation. In distinction to $ε_l$, which is completely plasma characteristic, the function $E_{p_1p_2}$ is defined by initial and boundary conditions and allows one to find all the variety of asymptotical plasma modes for each concrete plasma problem. In this paper we demonstrate some possibilities of applying this method to the simplest cases of collisionless ion-electron plasma and to electron plasma with collisions described by a collision-relaxation term $-νf^{(1)}$.

physics.plasm-ph↗

arXiv1995

A New Look at the Landau's Theory of Spreading and Damping of Waves in Collisionless Plasmas

The theory of plasma waves and Landau damping in Maxwellian plasmas, Landau's ``rule of pass around poles'' include doubtful statements, particularly related to an artificial ``constructing'' of the dispersion equation, what should allow the possibility of its solution otherwise not existing at all, and the possibility of analytical continuations of corresponding very specific ruptured functions in the one-dimensional Laplace transformation, used by Landau, what is the base of his theory. We represent, as an accessible variant, a more general alternative theory based on a two-dimensional Laplace transformation, leading to an asymptotical in time and space solution as a complicated superposition of coupled damping and {\em non-damping \/} plane waves and oscillations with different dispersion laws for every constituent mode. This theory naturally and very simply explains paradoxes of the phenomenon of plasma echo. We propose for discussion a new ideology of plasma waves (both electron and ion-acoustic waves) qualitatively different from the traditional theory of Landau damping for non-collisional as well as for low-collisional plasmas.

plasm-ph↗