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

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