An electrostatic undulator with single-polarity feed

The analytical formulae for field and potential in a plane electrostatic undulator with single-polarity feed were derived using an original method of summing infinite series. The system is placed inside a zero-potential metallic housing to simulate its real use in FELs. Such a geometry allows a precise calculation of the transverse velocity of electrons and their change of energy when moving in the undulator. A single-polarity feed can be advantageous in permitting higher field amplitudes, since electrical breakdown inside the undulator is excluded, in contradistinction to opposite-polarity (+V0,−V0) feed of adjacent conductors in usual designs. Also the housing can be placed at a distance much greater than undulator transverse dimensions, thus hampering external discharge. Some peculiarities of particle dynamics and regimes of FEL with such an undulator were analysed.