Collisionless damping of plasma waves as a real physical phenomenon does not exist

Abstract

Trivial logic of collisionless plasma waves is reduced to using complex exponentially damping/growing wave functions to obtain a complex dispersion equation for their wave number 1 k and the decrement/increment 2 k (for a given real frequency  and complex wave number k  k1  ik2 ), whose solutions are ghosts 1 2 k , k which do not have anything to do at 2 k  0 with the real solution of the dispersion equation for the initial exponentially damping/growing real plasma waves with the physically observable quantities 1 2 k , k , for which finding should be added, in this case, the second equation of the energy conservation law. Using a complex dispersion equation for the simultaneous determination of 1 k and 2 k violates the law of energy conservation, leads to a number of contradictions, is logical error, and finally also the mathematical error leading to both erroneous statement on the possible existence of exponentially damping/growing harmonic wave solutions and to erroneous values 1 k and 2 k . Mathematically correct conclusion about the damping/growing of virtual complex waves of collisionless plasma is wrongly attributed to the actual real plasma waves.