Mitigation of space-charge-driven resonance and instability in high-intensity linear accelerators via beam spinning

Abstract

For modern high-intensity linear accelerators, the well-known envelope instability and recently reported fourth-order particle resonance impose a fundamental operational limit (i.e., zero-current phase advance should be less than $90°$). Motivated by the stability of spinning flying objects, we propose a novel approach of using spinning beams to surpass this limit. We discovered that spinning beams have an intrinsic characteristic that can suppress the impact of the fourth-order resonance on emittance growth and the associated envelope instability.

Introduction

Spinning flying objects such as American footballs, spinning rockets, and rifled bullets are stabilized against small disturbances by maintaining a large angular momentum vector in a specific direction [1]. In certain situations, the spin motion counteracts a misaligned thrust to the object [1]. Motivated by this long-known stability principle of mechanical systems [2], we address the following fundamental question, which has not been systematically investigated thus far: Can charged-particle beams under strong space-charge effects [3], [4], [5], [6] in high-intensity linear accelerators (linacs) benefit from spinning? If beam spinning is in fact an effective countermeasure against such effects, it could significantly facilitate the application of intense proton and ion beams to intensity-frontier particle and nuclear physics experiments, fusion material irradiation tests, nuclear waste transmutation, and accelerator-driven subcritical reactors. Here, space-charge effects include both coherent instabilities (also called parametric resonances) [7], [8], [9], [10], [11] and incoherent resonances (also called particle resonances) [12], [13], [14].

Recently, Jeon and coworkers [15] reported $4\sigma =360°$ (or 4:1) fourth-order particle resonance in high-intensity linacs for the first time, and then verified it experimentally [16], [17]. Here, $\sigma$ is the depressed phase advance per cell. Subsequent studies discovered that the fourth-order particle resonance is manifested predominantly over the envelope instability when $\sigma$ is kept constant along the linacs [18], [19], [20]. In particular, Ref. [20] summarizes the difference between coherent instabilities and particle resonances. Further investigations, presented in Ref. [21], established that the general stop band for the $4\sigma =360°$ fourth-order particle resonance is ${\sigma }_0>90°$ and $\sigma <90°$, where ${\sigma }_0$ is the zero-current phase advance. It is worth noting that the fourth-order resonance stop band is wider than the envelope instability stop band, and the envelope instability is induced following the fourth-order resonance only within the envelope instability stop band in the tune-depression space.

Certainly, it is desirable to overcome these operational limitations associated with space-charge-driven resonances and instabilities. It has already been discussed (mainly in the context of high-intensity rings) that active suppression of coherent instabilities can be achieved through Landau damping [22] or nonlinear decoherence [23] using octupoles, feedback dampers, electron lenses, or dedicated nonlinear lattices to provide favorable tune spreads of beam particles. These methods aim at mitigating coherent instabilities originating from collective perturbations or envelope mismatches. However, in high-intensity linacs, even for initially well-matched beams without any external repetitive perturbations, nonlinear space-charge forces can excite particle resonances. In particular, our previous study [18] revealed that for ${\sigma }_0>90°$, the fourth-order resonance is always excited, whereas the appearance of envelope instability depends on the lattice and initial matching conditions. Accordingly, the fourth-order resonance stop band imposes one of the fundamental operational limits: the zero-current phase advance ${\sigma }_0$ should be maintained below $90°$.

Hence, in this paper, we investigate whether we can mitigate the $4\sigma =360°$ fourth-order particle resonance in linacs by introducing the novel concept of beam spinning. A spinning beam has a non-zero average canonical angular momentum and exhibits rigid-rotor rotation around the beam propagation axis. This scheme is based on two notable achievements in beam physics: (i) a rigid-rotor beam equilibrium was obtained for an intense beam propagating through a periodic solenoidal lattice [24], and (ii) a rotating beam was generated by stripping an ion beam inside a solenoid [25]. To take advantage of the beam spinning effect, we consider an axisymmetric system, in which the canonical angular momentum is conserved. We note that many modern low-energy superconducting linacs adopt solenoidal focusing lattices and maintain beam axisymmetry. For beam generation, we propose the stripping of H⁻(or D⁻) beams using a thin foil inside a pair of solenoids installed in a medium energy beam transport (MEBT) line, and injecting the resultant spinning ${\mathrm{H}}^{+}$(or ${\mathrm{D}}^{+}$) beams into the main linac after proper matching.

Here, we observe that the stop band and emittance growth of coherent (or envelope) instability following the fourth-order particle resonance are indeed reduced for spinning beams. This is because the beam mismatch triggered by the fourth-order resonance decreases. We present both analytical and multi-particle simulation results to support this argument. In our analysis, non-KV Gaussian beams are initially rms-matched to a periodic solenoid focusing channel.