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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