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We consider the motion of a charge in a large amplitude electrostatic wavewith a triangular wave form relevant to an oscillating model of a pulsarmagnetosphere. The (one-dimensional) orbit of a particle in such a wave isfound exactly in terms of Weierstrass functions.  The result is used to discuss linear acceleration emission (at both low andhigh frequencies) in an oscillating model for pulsars. An explicit expressionfor the emissivity is derived in an accompanying paper (Melrose & Luo 2009),and used here to derive an expression for the absorption coefficient at lowfrequencies. We show that absorption can be negative, corresponding to maseremission. For the large amplitude required to trigger pair creation in anoscillating model, the rate of the maser growth is too small to be effective.Effective growth requires smaller amplitudes, such that the maximum Lorentzfactor gained by acceleration in the wave is $\lapprox10$.

Linear acceleration emission: 1 Motion in a large amplitude electrostatic wave