Initial frequency shift of large amplitude plasma wave

A distribution function which is an exact solution to the collisionless Boltzmann equation is obtained in an expansion form in terms of the potential phi(x, t). A complex nonlinear frequency shift ωsub( n)(t) is obtained by use of the Poisson equation and the expansion. The theory is valid for arbitrary phi0 and v sub(p) as long as ωsub(p) >> γsub( l), and in the initial phase defined by 0 < t < t sub(c) where phi0, v sub(p), ωsub(p), γsub( l) and t sub(c) are the initial value of phi, the phase velocity, the Langmuir frequency, the linear Landau damping coefficient and the time for the first minimum of the amplitude oscillation. The ωsub( n)(0) does not vanish and Reωsub( n)(0)/γsub( l) > 1 holds even for e phi0/T << 1 when k lambda sub( d) << 1, lambda sub( d) being the Debye length. It is shown that ωsub( n)(t) is dominant over the Morales and O'Neil's one1 in the initial phase for v sub( p) > v sub( t). The theory reproduces main features of experimental results and that of simulations. (author)