Non-scaling Fixed Field Alternating Gradient Research Articles

Experience with online modeling tools during the CBETA fractional arc test and single pass commissioning

The Cornell-Brookhaven CBETA machine is a four-pass Energy Recovery Linac (ERL) with a Non-scaling Fixed-Field Alternating gradient (NS-FFA) arc. For online modeling of single particle dynamics in CBETA, a customized version of the Tao program, which is based upon the Bmad toolkit, has been developed. This online program, called CBETA-V, is interfaced to CBETA’s EPICS control system. This work describes the online modeling system and initial experience during machine running, as well as subsequent developments since its first implementation.

Magnetic-Field Analysis of the Asymmetric Quadrupole for the FFAG Accelerator

We proposed a quadrupole magnet with an asymmetric coil for a nonscaling fixed-field alternatinggradient (NS-FFAG) accelerator. The proposed magnet has a nonlinear magnetic field with the same geometric characteristics as a conventional quadrupole. This nonlinear magnetic field was confirmed to afford beam stability in a ring-type accelerator. In this paper, a magnetic-field analysis using POISSON SUPERFISH to evaluate the generation of the desired nonlinear magnetic field in the 2D geometry of the asymmetric quadrupole magnet for an electron ring is reported. In addition, the magnetic field of the asymmetric quadrupole is compared with that of a conventional quadrupole in an NS-FFAG accelerator.

Evaluation of asymmetric quadrupoles for a non-scaling fixed field alternating gradient accelerator

A non-scaling fixed field alternating gradient (NS-FFAG) accelerator was constructed, which employs conventional quadrupoles. The possible demerit is the beam instability caused by the variable focusing strength when the orbit radius of the beam changes. To overcome this instability, it was suggested that the asymmetric quadrupole has different current flows in each coil. The magnetic field of the asymmetric quadrupole was found to be more similar to the magnetic field required for the FFAG accelerator than the constructed NS-FFAG accelerator. In this study, a simulation of the beam dynamics was carried out to evaluate the improvement to the beam stability for the NS-FFAG accelerator using the SIMION program. The beam dynamics simulation was conducted with the ‘hard edge’ model; it ignored the fringe field at the end of the magnet. The magnetic field map of the suggested magnet was created using the SIMION program. The lattices for the simulation combined the suggested magnets. The magnets were evaluated for beam stability in the lattices through the SIMION program.

EMMA

EMMA stands for Electron Model for Many Applications and is expected to demonstrate the novel concept of a non-scaling Fixed Field Alternating Gradient (FFAG) accelerator. A non-scaling FFAG accelerator was originally invented to accelerate muons up to a few tens of GeV energy range although it is now hoped to have a wider variety of applications such as a proton driver for Accelerator Driven Sub-critical Reactor (ADSR). We will report the recent developments of the EMMA experiment, with more emphasis on acceleration of a muon beam.

Acceleration in the linear non-scaling fixed-field alternating-gradient accelerator EMMA

In a fixed-field alternating-gradient (FFAG) accelerator, eliminating pulsed magnet operation permits rapid acceleration to synchrotron energies, but with a much higher beam-pulse repetition rate. Conceived in the 1950s, FFAGs are enjoying renewed interest, fuelled by the need to rapidly accelerate unstable muons for future high-energy physics colliders. Until now a ‘scaling’ principle has been applied to avoid beam blow-up and loss. Removing this restriction produces a new breed of FFAG, a non-scaling variant, allowing powerful advances in machine characteristics. We report on the first non-scaling FFAG, in which orbits are compacted to within 10 mm in radius over an electron momentum range of 12–18 MeV/c. In this strictly linear-gradient FFAG, unstable beam regions are crossed, but acceleration via a novel serpentine channel is so rapid that no significant beam disruption is observed. This result has significant implications for future particle accelerators, particularly muon and high-intensity proton accelerators.

STATUS OF PAMELA: AN UK PARTICLE THERAPY FACILITY PROJECT USING NS-FFAG

PAMELA(Particle Accelerator for Medical Application) aims to design a particle therapy facility using NS-FFAG(Non-Scaling Fixed Field Alternating Gradient) accelerator. A newly proposed lattice design and the new type of combined function magnet provide the accelerator flexible tuneability of operating point and variability in operation modes. A remarkable features for a fixed field accelerator are its high repetition rate, about 1 kHz, and energy variable beam extraction. These features make the machine a promising candidate of versatile accelerator not restricted to medical applications.

CROSSING RESONANCES IN A NON-SCALING FFAG

There are many possible applications for the non-scaling Fixed Field Alternating Gradient (NS-FFAG): accelerating non-relativistic ions, ion cancer therapy, proton drivers, accelerator driven subcritical reactors, heavy radioactive ions, recirculating linacs, and etc. They are confronted with two significant challenges: first is crossing integer resonances as the tunes vary with energy, and that the required fast acceleration has not yet been achieved in practice. An example of a small 30–250 MeV NS-FFAG proton accelerator is used to study both problems. After an introduction, the second chapter shows theoretical predictions for the emittance blow up from crossing the integer resonances. In the third part, the lattice of the ring is briefly described. The fourth chapter describes the "phase jump" a method for fast proton acceleration, while in the chapter five a six dimensional simulations of acceleration is described, ending with conclusions.

FFAGs as Accelerators and Beam Delivery Devices for Ion Cancer Therapy

First, a review is given of fixed field alternating gradient (FFAG) accelerators, presenting a bit of their history and basic concepts. Special attention is paid to the concept of scaling (S-FFAG) and nonscaling (NS-FFAG) FFAGs. This notation is used only in the NS-FFAG part of the article. A discussion is then provided on operating FFAGs. A presentation is made of the designs being considered for S-FFAGs. A bit more is said about the concept of the NS-FFAG and a resonance crossing problem resulting from designs of the NS-FFAGs. A beam delivery system (gantry) employing the NS-FFAG concept is presented after that and, finally, future plans and R&D requirements are put forward.

Resonance crossing and dynamic aperture in nonscaling fixed field alternating gradient accelerators

Operation with natural chromaticity in a linear nonscaling fixed field alternating gradient (FFAG) accelerator causes crossing of the low order resonances such as integer and half-integer. Although those resonances are not systematic ones, small errors, such as a typical misalignment of $10\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ rms, significantly increase particle amplitude when the accelerator is operated with a slow acceleration rate. For example, there is practically no dynamic aperture if it takes 1000 turns to finish the whole acceleration cycle. Chromaticity correction with sextupole and octupole reduces the maximum available dynamic aperture in a lattice without errors. On the other hand, the accelerator becomes less sensitive to errors. To use a nonscaling FFAG for applications where, unlike a muon accelerator, the large acceptance is not a high priority demand (such as a proton driver or a particle therapy accelerator), chromaticity correction seems to be an essential ingredient.

Orbit and optics distortion in fixed field alternating gradient muon accelerators

In a linear nonscaling fixed field alternating gradient (FFAG) accelerator, betatron tunes vary over a wide range and a beam has to cross integer and half-integer tunes several times. Although it is plausible to say that integer and half-integer resonances are not harmful if the crossing speed is fast, no quantitative argument exists. With tracking simulation, we studied orbit and optics distortion due to alignment and magnet errors. It was found that the concept of integer and half-integer resonance crossing is irrelevant to explain beam behavior in a nonscaling FFAG when acceleration is fast and betatron tunes change quickly. In a muon FFAG accelerator, it takes 17 turns for acceleration and the betatron tunes change more than 10, for example. Instead, the orbit and optics distortion is excited by random dipole and quadrupole kicks. The latter causes beam size growth because the beam starts tumbling in phase space, but not necessarily with emittance growth.

Carbon/proton therapy: A novel gantry design

A major expense and design challenge in carbon/proton cancer therapy machines are the isocentric gantries. The transport elements of the carbon/proton gantry are presently made of standard conducting dipoles. Because of their large weight, of the order of $\ensuremath{\sim}100\text{ }\mathrm{\text{tons}}$, the total weight of the gantry with support structure is $\ensuremath{\sim}600\text{ }\mathrm{\text{tons}}$. The novel gantry design that is described here is made of fixed field superconducting magnets, thus dramatically reducing magnet size and weight compared to conventional magnets. In addition, the magnetic field is constant throughout the whole energy region required for tumor treatment. Particles make very small orbit offsets, passing through the beam line. The beam line is built of combined-function dipoles such as a nonscaling fixed field alternating gradient (NS-FFAG) structure. The very large momentum acceptance NS-FFAG comes from very strong focusing and very small dispersion. The NS-FFAG small magnets almost completely filled the beam line. They first make a quarter (or close to a quarter) of an arc bending upward and an additional half of a circle beam line finishing so that the beam is pointed towards the patient. At the end of the gantry, additional magnets with a fast response are required to allow radial scanning and to provide the required position and spot size. The fixed field combined-function magnets for the carbon gantry could be made of superconducting magnets by using low temperature superconducting cable or by using high temperature superconductors.

Hadron cancer therapy complex using nonscaling fixed field alternating gradient accelerator and gantry design

Nonscaling fixed field alternating gradient (FFAG) rings for cancer hadron therapy offer reduced physical aperture and large dynamic aperture as compared to scaling FFAGs. The variation of tune with energy implies the crossing of resonances during acceleration. Our design avoids intrinsic resonances, although imperfection resonances must be crossed. We consider a system of three nonscaling FFAG rings for cancer therapy with 250 MeV protons and $400\text{ }\mathrm{MeV}/u$ carbon ions. Hadrons are accelerated in a common radio frequency quadrupole and linear accelerator, and injected into the FFAG rings at $v/c=0.1294$. ${\mathrm{H}}^{+}/{\mathrm{C}}^{6+}$ ions are accelerated in the two smaller/larger rings to 31 and $250\text{ }\text{ }\mathrm{MeV}/68.8$ and $400\text{ }\mathrm{MeV}/u$ kinetic energy, respectively. The lattices consist of doublet cells with a straight section for rf cavities. The gantry with triplet cells accepts the whole required momentum range at fixed field. This unique design uses either high-temperature superconductors or superconducting magnets reducing gantry magnet size and weight. Elements with a variable field at the beginning and at the end set the extracted beam at the correct position for a range of energies.

Emittance growth mechanisms for space-charge dominated beams in fixed field alternating gradient and proton driver rings

Systematic space-charge resonances are found to cause substantial emittance growth in proton driver rings and non-scaling fixed field alternating gradient (FFAG) accelerators. To avoid systematic nonlinear resonances, the phase advance of each cell must avoid π/2 and π/3. This limits the betatron tune range and the momentum acceptance for non-scaling FFAG accelerators. The emittance growth factor (EGF), defined as the ratio of final emittance to the initial emittance, is found to obey scaling properties in the linear space-charge tune shift parameter, the tune ramping rate, and stop-band widths of random quadrupole and skew-quadrupole errors.

Fundamental Limit of Nonscaling Fixed-Field Alternating-Gradient Accelerators

Systematic nonlinear space-charge resonances may cause substantial emittance growth in the nonscaling fixed-field alternating-gradient (FFAG) accelerators. To avoid systematic nonlinear space-charge resonances, the phase advance of each nonscaling FFAG cell must avoid pi/2 and pi/3. Using multiparticle numerical simulations, we empirically obtain a minimum tune ramp rate vs the systematic 4th order space-charge resonance strength. We also find that the emittance growth obeys a simple scaling property when the betatron tunes cross the linear half-integer and sum resonances.

MUON ACCELERATION USING FIXED FIELD, ALTERNATING GRADIENT (FFAG) RINGS

Given their 2.2 μs lifetime, muons must be accelerated fairly rapidly for a neutrino factory or muon collider. Muon bunches tend to be large. Progress in fixed field, alternating gradient (FFAG) lattices to meet these challenges are reviewed. FFAG magnets are naturally wide; low momentum muons move from the low field side of a gradient magnet to the high field side as they gain energy. This can be exploited to do double duty and allow a large beam admittance without unduly increasing the magnetic field volume. If the amount of RF must be reduced to optimize cost, an FFAG ring can accommodate extra orbits. I describe scaling FFAGs in which the bends in each magnet are energy independent and non-scaling FFAGs in which the bends in each magnet do vary with muon energy. In all FFAG designs the sum of the bends in groups of magnets are constant; otherwise orbits would not close. Ways of keeping the accelerating beam in phase with the RF are described. Finally, a 1 MeV proof of principle scaling FFAG has been built at KEK and began accelerating protons in June 2000 with a 1 kHz repetition rate.

Muon acceleration in FFAG rings

Muon acceleration from 6 or 10 to 20 GeV in fixed-field alternating gradient (FFAG) rings is considered. The novel physics issues associated with non-scaling FFAG machines, namely the very acceleration process and the crossing of transverse imperfection resonances are addressed. These FFAG machines are essentially strong-focusing rings with a dispersion small enough to keep muons over the full momentum range inside the same magnet aperture. We consider two cases: (i) A Modified FODO Ring with about a metre long straight sections, enough to house normal-conducting RF cavities at about 200 MHz and (ii) A Doublet Ring with a few metres long straight sections, enough for super-conducting RF cavities also at about 200 MHz. Parameters are derived for the lattice and RF system of an electron model. It accelerates electrons from about 10–20 MeV and allows one to study the critical issues of non-scaling FFAGs. For both a full machine and a model, lattice parameters such as magnet type and dimension, spacing, and number of cells are presented. The consequences of misaligned magnets are studied by simulation. Practical RF system design issues, e.g. RF power, and the limit on the bunch population due to beam loading are estimated.