Abstract
The effects of initial conditions, nonlinearity and resonant particles, which are not included in the usual formula in terms of the dielectric permittivity for wave energy density, are derived from a rigorous solution of the initial value problem to second order in the amplitude of electron waves propagating parallel to a static magnetic field in a homogeneous collisionless plasma. Wave energy is found to propagate at two speeds, the group velocity and the velocity of resonant electrons. Energy conservation is derived.
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