Shinji Machida

In this article, we will review beam dynamics of a Fixed Field Alternating Gradient Accelerator (FFA). Difference between scaling and nonscaling design, some novel concepts studied recently are explained. Longitudinal dynamics specific to an FFA is introduced. Techniques for modeling of linear and nonlinear dynamics are discussed.

Beam stacking allows a fixed field alternating gradient accelerator (FFA) to increase the extracted beam current while also enabling a flexible time structure, making FFAs a promising candidate for future spallation neutron sources and other high intensity beam applications. For successful beam stacking, beam loss caused by rf knockout must be prevented. rf knockout can occur during beam stacking because of the finite dispersion function at the rf cavity location, which is unavoidable in a scaling FFA. In this work, the rf knockout resonance is characterized and through a series of experiments at the ISIS Neutron and Muon Source, we show that it is possible to suppress losses due to rf knockout.

A key challenge in particle accelerators is to achieve high peak intensity. Space charge is particularly strong at lower energy such as during injection and typically limits achievable peak intensity. The beam stacking technique can overcome this limitation by accumulating a beam at high energy where space charge is weaker. In beam stacking, a bunch of particles is injected and accelerated to high energy. This bunch continues to circulate, while a second and subsequent bunches are accelerated to merge into the first. It also allows the user cycle and acceleration cycles to be separated which is often valuable. Beam stacking is not possible in a time varying magnetic field, but a fixed field machine such as an fixed field alternating gradient accelerator (FFA) does not sweep the magnetic field. In this paper, we describe experimental demonstration of beam stacking of two beams at KURNS FFA in Kyoto University. The momentum spread and intensity of the beam was analyzed by study of the Schottky signal, demonstrating stacking with only a slight increase of momentum spread of the combined beams. The intensity of the first beam was, however, significantly reduced. rf knockout is the suspected source of the beam loss.

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

The intensity frontier has called for new initiatives in hadron accelerator design in order to accommodate space charge dominated beams. Octupoles are often used to damp beam instabilities caused by space charge, however the insertion of octupole magnets leads to a nonintegrable lattice which reduces the area of stable particle motion. One proposed solution is Quasi-Integrable optics (QIO), where the octupoles are inserted between sections of a specific lattice insertion called a T-insert. An octupole with a strength that scales as 1/β ³(s) is applied in the drift region, where the horizontal and vertical beta functions are equal, to create a time independent octupole field. This leads to a lattice with a time-independent Hamiltonian which is robust to small perturbations. IBEX is a Paul trap which allows the transverse dynamics of a collection of trapped particles to be studied, mimicking the propagation through multiple quadrupole lattice periods, whilst remaining stationary in the laboratory frame. In order to test QIO at the IBEX experiment, it has recently undergone an upgrade to allow for the creation of octupole fields. We present our design of the IBEX experiment upgrade along with simulation results of our proposed experiment to test QIO with space charge.

Circular accelerator lattices are usually confined in the horizontal plane. Optics design does not rely on the orbit in the vertical direction. Here we propose a circular accelerator lattice in which the orbit moves in both horizontal and vertical directions. Having another degree of freedom, flexibility of the optics increases with less constraints of the orbit, e.g. a zero momentum compaction factor lattice without reverse bending magnets or a negative dispersion function. As a possible application of the concept, a collider ring arc of a muon collider facility is illustrated.

Vertical excursion fixed-field alternating gradient accelerators can be designed with tunes that are invariant with respect to momentum and trajectories that are scaled images of each other displaced only in the vertical direction. This is possible using guiding fields that have a vertical exponential increase, with a skew quadrupole component in the magnet body and a solenoid component at the magnet ends. Numerical analysis was used in optimization due to the coupling effects on orbits and optics. In this paper, idealized magnetic fields are calculated from first principles, taking into account end fields. The parameter dependence of the optics and the dynamic aperture of the ring are calculated for the example of a ring with an approximately 25 m circumference that accelerates proton beams from 3 MeV to 12 MeV. The paper reports for the first time the design of such an accelerator lattice using tools specifically devised to analyze transverse coupled optics without the need for approximations.

Vertical excursion fixed-field alternating gradient accelerators can be designed with tunes that are invariant with respect to momentum and trajectories that are scaled images of each other displaced only in the vertical direction. This is possible using guiding fields that have a vertical exponential increase, with a skew quadrupole component in the magnet body and a solenoid component at the magnet ends. Because of the coupling this introduces, orbit and optics calculations and optimisation of parameters need to be performed numerically. In this paper, idealised magnetic fields are calculated from first principles, taking into account end fields. The parameter dependence of the optics and the dynamic aperture of the ring are calculated for the example of a ring with an approximately 25 m circumference that accelerates proton beams from 3 MeV to 12 MeV. The paper reports for the first time the design of such an accelerator lattice using tools specifically devised to analyse transverse coupled optics without the need for approximations.

In this paper we present the first quantitative measurement of the change in frequency (tune) with intensity of four transverse resonances in a high intensity Gaussian beam. Due to the nonlinear space charge forces present in high intensity beams, particle motion cannot be analytically described. Instead we use the simulator of particle orbit dynamics and the intense beam experiment, two linear Paul traps (LPTs), to replicate the system experimentally. In high intensity beams a coherent resonant response to both space charge and external field driven perturbations is possible, these coherent resonances are excited at a tune that differs by a factor C _m from that of the incoherent resonance. By increasing the number of ions stored in the LPT and studying the location of four different resonances we extract provisional values describing the change in tune of the resonance with intensity. These values are then compared to the C _m factors for coherent resonances. We find that the C _m factors do not accurately predict the location of resonances in high intensity Gaussian beams. Further insight into the experiment was gained through simulation using Warp, a particle-in-cell code.