Stochastic electron beams in the ion-focused regime

The ion-hose instability can catastrophically disrupt a classical electron beam propagating in the ion-focused regime (IFR). Ion hose is driven by a resonant interaction between the smooth electron-betatron and ion-betatron orbits. In a classical beam phase correlations decay secularly in time c(t)/c(t0) ∼ (t0/t)n (0 < n ≤ 2). In a stochastic electron beam the electron orbits are chaotic. Such a beam can be immune to resonant instabilities because phase correlations decay exponentially fast c(t)/c(0) ∼ e-ht thus destroying the coherence of the electron response on the growth time 1/γg if h ∼ γg. Using the same principles we can also envision a stochastic damping cell in which electron phase correlations damp exponentially c(z)/c(0) ∼ e-hz thus centering and conditioning a beam more effectively than a classical phase-mixing cell in which c(z)/c(z0) ∼ (z0/z)n. A triple-Bennett IFR system and the analogous triple-wire damping cell are analyzed. The K-entropy is introduced as a figure-of-merit for such stochastic electron beam systems