Fast head-tail instability with space charge

The fast head-tail instability with space charge is studied using series expansion techniques, numerical simulations, and a new formulation which allows for precise estimates of growth rates and thresholds. In regimes where they are reliable, all three techniques predict that space charge suppresses the fast head-tail instability. It is found that the series expansion techniques are unreliable for parameter regimes commonly employed in hadron accelerators. The numerical techniques are less prone to error, but the computational requirements become severe as space charge tune shifts increase. The new model has neither of these problems, but it underestimates the benefits of chromaticity, at least in its simplest form.