Investigation of Microbunching Instabilities in Modern Recirculating Accelerators
Particle accelerators are machines to accelerate and store charged particles, such as electrons or protons, to the energy levels for various scientific applications. A collection of charged particles usually forms a particle beam. There are three basic types of particle accelerators: linear accelerators (linac), storage-ring (or circular) accelerators, and recirculating accelerators. In a linac, particles are accelerated and pass through once along a linear or straight beamline. Storage-ring accelerators propel particles around a circular track and repetitively append the energy to the stored beam. The third type, also the most recent one in chronology, the recirculating accelerator, is designed to accelerate the particle beam in a short section of linac, circulate the beam, and then either continue to accelerate for energy boost or decelerate it for energy recovery. The beam properties of a linac machine are set at best by the initial particle sources. For storage rings, the beam equilibria are instead determined by the overall machine design. The modern recirculating machines share with linacs the advantages to both accelerate and preserve the beam with high beam quality, as well as efficiently reuse the accelerating components. The beamline design in such a machine configuration can however be much more complicated than that of linacs. As modern accelerators push toward the high-brightness or high-intensity frontier by demanding particles in a highly charged bunch (about nano-Coulomb per bunch) to concentrate in an ever-decreasing beam phase space (transverse normalized emittance about 1 μm and relative energy spread of the order of 10^-5 in GeV beam energy), the interaction amongst particles via their self-generated electromagnetic fields can potentially lead to coherent instabilities of the beam and thus pose significant challenges to the machine design and operation. In the past decade and a half, microbunching instability (MBI) has been one of the most challenging issues for such high-brightness or high-intensity beam transport, as it would degrade lasing performance in the fourth-generation light sources, reduce cooling efficiency in electron cooling facilities, and compromise the luminosity of colliding beams in lepton or lepton-hadron colliders. The dissertation work will focus on the MBI in modern recirculating electron accelerators. It has been known that the collective interactions, the coherent synchrotron radiation (CSR) and the longitudinal space charge (LSC) forces, can drive MBI. The CSR effect is a collective phenomenon in which the electrons in a curved motion, e.g. a bending dipole, emit radiation at a scale comparable to the micro-bunched structure of the bunch distribution. The LSC effect stems from non-uniformity of the charge distribution, acts as plasma oscillation, and can eventually accumulate an amount of energy modulation when the beam traverses a long section of a beamline. MBI can be seeded by non-uniformity or shot noise of the beam, which originates from granularity of the elementary charge. Through the aforementioned collective effects, the modulation of the bunch sub-structure can be amplified and, once the beam-wave interaction formed a positive feedback, can result in MBI. The problem of MBI has been intensively studied for linac-based facilities and for storage-ring accelerators. However, systematic studies for recirculation machines are still very limited and form a knowledge gap. Because of the much more complicated machine configuration of the recirculating accelerators than that of linacs, the existing MBI analysis needs to be extended to accommodate the high-brightness particle beam transport in modern recirculating accelerators. This dissertation is focused on theoretical investigation of MBI in such machine configuration in the following seven themes: (1) Development and generalization of MBI theory The theoretical formulation has been extended so as to be applicable to a general linear beamline lattice including horizontal and vertical transport bending elements, and beam acceleration or deceleration. These featured generalizations are required for MBI analysis in recirculation accelerators. (2) Construction of CSR impedance models In addition to the steady-state CSR interaction, it has been found that the exit transient effect (or CSR drift) can even result in more serious MBI in high-brightness recirculation arcs. The onedimensional free-space CSR impedances, especially the exit transients, are derived. The steady-state CSR impedance is also extended to non-ultrarelativistic beam energy for MBI analysis of low-energy merger sections in recirculating accelerators. (3) Numerical implementation of the derived semi-analytical formulation This includes the development of a semi-analytical Vlasov solver for MBI analysis, and also benchmarking of the solver against massive particle tracking simulations. (4) Exploration of multistage amplification behavior of CSR microbunching development The CSR-induced MBI acts as an amplifier, which amplifies the sub-bunch modulation of a beam. The amplification is commonly quantified by the amplification gain. A beam transport system can be considered as a cascaded amplifier. Unlike the two-stage amplification of four-dipole bunch compressor chicanes employed in linacs, the recirculation arcs, which are usually constituted by several tens of bending magnets, show a distinguishing feature of up to six-stage microbunching amplification for our example arc lattices. That is, the maximal CSR amplification gain can be proportional to the peak bunch current up to sixth power. A method to compare lattice performance has been developed in terms of gain coefficients, which nearly depend on the lattice properties only. This method has also proven to be an effective way to quantify the current dependence of the maximal (5) Control of CSR MBI in multibend transport or recirculation arcs The existing mitigation schemes of MBI mostly aim to linac-based accelerators and may not be practical to the recirculating accelerator facilities. Thus a set of conditions for suppression of CSR MBI was proposed and examined for example lattices from low (~100 MeV) to high (~1 GeV) energies. (6) Study of more aspects of microbunched structures in beam phase spaces For a cascaded amplifier in circuit electronics, the total amplification gain can be estimated as the product of individual gains. In a beam transport line of an accelerator, the (scalar) gain multiplication was examined and found to under-estimate the overall microbunching amplification. The concept of gain matrix was developed, which includes the density, energy and transverse-longitudinal modulations in a beam phase space, and used to analyze MBI for a proposed recirculating machine. Throughout the gain matrix approach, it reasonably gives the upper limit of spectral MBI gain curves. This extended analysis can be employed to study multi-pass recirculation. (7) Study of MBI for magnetized beams Driven by a recent energy-recovery-linac based cooler design for electron cooling at Jefferson Lab Electron-Ion Collider Project, the generalized theoretical formulation for MBI to a transversely coupled beam has been developed and applied to this study. A magnetized beam in general features non-zero canonical angular momentum, thus considered to be a transversely coupled beam. A novel idea of utilizing magnetized beam transport was proposed for improvement of cooling efficiency and possible mitigation of collective effects. A concern of MBI regarding this design was studied and excluded. The large transverse beam size associated with the beam magnetization is found to help suppress MBI via the transverse-longitudinal correlation.