Microbunching Plasma-Cascade Instability

Abstract

In this paper we describe a new micro-bunching instability occurring in charged particle beams propagating along a straight trajectory: based on the dynamics we named it a Plasma-Cascade Instability. Such instability can strongly intensify longitudinal micro-bunching originating from the beam’s shot noise, and even saturate it. Conversely, such instability can drive novel high-power sources of broadband radiation or can be used as a broadband amplifier. In this paper we present our analytical and numerical studies of this new phenomenon as well as the results of its experimental demonstration. PLASMA-CASCADE INSTABILITY High brightness intense charged particle beams play critical role in the exploration of modern science frontiers [1]. Such beams are central for high luminosity hadron colliders as well as for X-ray femtosecond free-electron-lasers (FEL). In the future, such beams could be central for cooling hadron beams in high-luminosity colliders, X-ray FEL oscillators, and plasma-wake-field accelerators with TV/m accelerating gradients. Dynamics of high intensity beams is driven by both external factors—such as focusing and accelerating fields—and self-induced (collective) effects: space charge, wakefields from the surrounding environment and radiation of the beam. While external factors are designed to preserve beam quality, the collective effects can produce an instability severely degrading beam emittance(s), momentum spread and creating filamentation of the beam. On the other hand, such instabilities can be deliberately built-in to attain specific results such as the FEL instability, Coherent electron Cooling (CeC) or generation of broad-band high power radiation. The Plasma-Cascade micro-bunching Instability (PCI) occurs in a beam propagating along a straight line. It is driven by variation of the transverse beam size(s) [1]. Conventional micro-bunching instability for beams travelling along a curved trajectory is a well-known and in-depth studied both theoretically and experimentally [2-20]. Space-charge-driven parametric transverse instabilities are also well known (see review [21] and references therein). But none of them include the PCI—a micro-bunching longitudinal instability driven by modulations of the transverse beam size. Figure 1 depicts a periodic focusing structure where the charged particle beam undergoes periodic variations of its transverse size. It is known that small density perturbations in a cold, infinite and homogeneous charged beam will undergo oscillations with plasma frequency, \uf077 p \uf03d c 4\uf070norc [22], where no is the particles density (in beam’s co-moving frame), c is the speed of light and rc \uf03d e 2 / mc is particle’s classical radius. Figure 1: A sketch of four focusing cells with periodic modulations of beam envelope, a(s), and the plasma frequency, ωp. Beam envelope has waists, ao, in the middle of each cell where plasma frequency peaks. Scales are attuned for illustration purpose. The bottom sketch illustrates an unstable ray trajectory in a system of periodic focusing lenses—an analogue of unstable longitudinal oscillations. The waists of the beam serve as “short focusing elements” for the longitudinal plasma oscillations. Beam propagating with velocity vo through the lattice (with period 2l) would experience density modulation in the co-moving frame with period of T \uf03d 2l / \uf067 ovo : f\uf05e \uf03d no t \uf028 \uf029 \uf03d Io e\uf062o\uf067 oc 1 \uf070a \uf067 o\uf062oct \uf028 \uf029 . (1) where Io is the beam current and \uf067 o \uf03d 1\uf02d \uf062o 2 \uf028 \uf029\uf02d1/2 ,\uf062o \uf03d vo / c is the beam’s relativistic factor. It is well known [23] that modulation of oscillator frequency with a period close twice of oscillation period would result in exponential growth of oscillation amplitude: the phenomena known as parametric resonance. The extreme case of δ-function-like modulation is well known: periodic focusing lenses with focal length shorter than a quarter of the separating distances will make rays unstable and the entire half-space F < l/2 is occupied by this parametric resonance.