A weak microwave instability with potential well distortion and radial mode coupling

In attempts to minimize the impedance of an accelerator by smoothing out its vacuum chamber, improvements are typically first made by reducing the inductive part of the impedance. As the inductance is reduced, however, the impedance becomes increasingly relatively resistive, and as a consequence, the nature of potential well distortion changes qualitatively. An inductive impedance lengthens the bunch (above transition) while maintaining more or less a head-tail symmetry of the bunch longitudinal distribution. A resistive impedance does not change the bunch length as much, but tends to cause a large head-tail asymmetry