Abstract

The inherent periodicity of the strong magnetic focusing in a planar wiggler can lead to an FEL-like instability. This instability differs from the conventional FEL in a number of ways: (1) The EM electric field component responsible for the interaction is perpendicular to the wiggler plane. (2) The EM waves couples to the betatron oscillations instead of the plasma oscillations. As such, it relies on transverse gradients in the wiggler field. (3) The “fundamental” mode is at the second harmonic: Δk = 2kw rather than Δk = kw. (4) Coupling goes as the fourth power of the wiggler parameter.The dispersion relation for this instability is derived for two cases: a cold sheet beam and a cold string beam, both in a planar wiggler configuration. An absolute instability is found and its growth rate is given in terms of the beam plasma density and the wiggler parameter.

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