Mitigation of the Hose Instability in Plasma-Wakefield Accelerators

Abstract

Current models predict the hose instability to crucially limit the applicability of plasma-wakefield accelerators. By developing an analytical model which incorporates the evolution of the hose instability over long propagation distances, this work demonstrates that the inherent drive-beam energy loss, along with an initial beam-energy spread, detunes the betatron oscillations of beam electrons and thereby mitigates the instability. It is also shown that tapered plasma profiles can strongly reduce initial hosing seeds. Hence, we demonstrate that the propagation of a drive beam can be stabilized over long propagation distances, paving the way for the acceleration of high-quality electron beams in plasma-wakefield accelerators. We find excellent agreement between our models and particle-in-cell simulations. DOI: 10.1103/PhysRevLett.118.174801 Plasma-based accelerators can provide accelerating fields in excess of 10 GV=m [1,2]. As a result, these devices can potentially contribute to a future generation of more compact particle accelerators and radiation sources. Plasma-wakefield accelerators (PWFAs) [3,4] employ charged particle beams as drivers of large-amplitude plasma waves. Significant experimental results [2,5] were obtained in the blowout regime, in which a particle beam with a charge density greater than the ambient plasma density expels all plasma electrons within its vicinity, thereby generating a copropagating ion channel with linear electron focusing and extreme accelerating fields [6].Identified by Whittum et al. in the early 1990s [7], the hose instability (HI) remains a long-standing challenge for PWFAs. Hosing is seeded by initial transverse asymmetries of the beam or plasma phase-space distributions. According to current models, the beam-centroid displacement is amplified exponentially during propagation in the plasma [7][8][9][10][11], ultimately leading to a beam breakup. The most recent description for the coupled evolution of the ionchannel centroid X c ðξ; tÞ and the beam centroid X b ðξ; tÞ in the blowout regime is given by [11]with the time t and the comoving coordinate ξ ¼ ct − z, where z is the longitudinal coordinate and c is the speed of light. The plasma wave number is denoted by k p ¼ ω p =c, and the betatron frequency by ω β ¼ ω p = ffiffiffiffiffi 2γ p , with the Lorentz factor γ, where ω p ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4πn 0 e 2 =m p is the plasma frequency with the ambient plasma density n 0 , the elementary charge e, and the electron rest mass m. The coefficients c ψ ðξÞ and c r ðξÞ account for the relativistic motion of electrons in the blowout sheath and for a ξ dependence of the blowout radius and the beam current [11]. According to Eq. (1), a beam-centroid displacement X b leads to a displacement of the ion-channel centroid X c along the beam. The displacement X c couples back to the temporal evolution of X b according to Eq. (2). The case where c ψ ¼ c r ¼ 1 recovers the seminal hosing model [7]. This limit, which accounts for a linear resp...

Saturation of the Hosing Instability in Quasilinear Plasma Accelerators

“…We note that the qualitative behavior for ∂ ξ k β < 0, whereby the amplitude of the oscillations initially increases but later decreases, is consistent with the behavior shown in [11], where the authors observed, in numerical simulations, that the deceleration of the tail of driver bunch (which induces ∂ ξ k β < 0) in the blow-out regime could cause a similar decrease in amplitude.…”

Efficiency versus instability in plasma accelerators

“…A remedy for mitigation of the hose instability for the drive bunch was suggested in Ref. [15]. It is based on tapering of plasma density at the input and the output of a plasma channel.…”

“…We would like to stress that until ways to overcome this limit are found, plasma-based collider schemes remain impractical from the perspective of acceleration efficiency. The BBU (also known as the hose) instability in PWFA concepts has been considered previously only for drive bunches [14,15]. Although these considerations are important, the quality of the drive ♦ E-mail: val@fnal.gov bunch (i.e.…”

Plasma wakefield linear colliders—opportunities and challenges

“…A number of methods have been suggested for mitigating the PWFA transverse instabilities. As discussed in [26,27] they may be grouped into three; reduction of instability seed [31]; disruption of the coherence and reduction of the beam-plasma coupling. Disruption of the coherence can be done in a variety of ways.…”