Logical contradictions of Landau damping

Abstract

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.