International Journal of Modern Physics A

The document summarizes the recent papers, presentations and other public information on Radio-Frequency (RF) Linear Accelerators (linacs) and Fixed-Field Alternating-Gradient (FFAG) accelerators for hadron therapy. The main focus is on technical aspects of these accelerators. This report intends to provide a general overview of the state-of-the-art in those accelerators which could be used in short and middle-term for treating cancer.

Accelerators are playing increasingly important roles in basic science, technology, and medicine. Ultra high-intensity and high-energy (GeV) proton drivers are a critical technology for accelerator-driven sub-critical reactors (ADS) and many HEP programs (Muon Collider) but remain particularly challenging, encountering duty cycle and space-charge limits in the synchrotron and machine size concerns in the weaker-focusing cyclotrons; a 10–20 MW proton driver is not presently considered technically achievable with conventional re-circulating accelerators. One, as-yet, unexplored re-circulating accelerator, the Fixed-field Alternating Gradient or FFAG, is an attractive alternative to the other approaches to a high-power beam source. Its strong focusing optics can mitigate space charge effects and achieve higher bunch charges than are possible in a cyclotron, and a recent innovation in design has coupled stable tunes with isochronous orbits, making the FFAG capable of fixed-frequency, CW acceleration, as in the classical cyclotron but beyond their energy reach, well into the relativistic regime. This new concept has been advanced in non-scaling nonlinear FFAGs using powerful new methodologies developed for FFAG accelerator design and simulation. The machine described here has the high average current advantage and duty cycle of the cyclotron (without using broadband RF frequencies) in combination with the strong focusing, smaller losses, and energy variability that are more typical of the synchrotron. The current industrial and medical standard is a cyclotron, but a competing CW FFAG could promote a shift in this baseline. This paper reports on these new advances in FFAG accelerator technology and presents advanced modeling tools for fixed-field accelerators unique to the code COSY INFINITY.¹

Progress in the study of beam optics and acceleration of the scaling FFAG accelerator has been presented in this paper.

Microscopic images of the surfaces of metallic electrodes used in high-pressure gas-filled 805 MHz RF cavity experiments¹ have been used to investigate the mechanism of RF breakdown.² The images show evidence for melting and boiling in small regions of ~10 micron diameter on tungsten, molybdenum, and beryllium electrode surfaces. In these experiments, the dense hydrogen gas in the cavity prevents electrons or ions from being accelerated to high enough energy to participate in the breakdown process so that the only important variables are the fields and the metallic surfaces. The distributions of breakdown remnants on the electrode surfaces are compared to the maximum surface gradient E predicted by an ANSYS model of the cavity. The local surface density of spark remnants, proportional to the probability of breakdown, shows a strong exponential dependence on the maximum gradient, which is reminiscent of Fowler-Nordheim behavior of electron emission from a cold cathode. New simulation results have shown good agreement with the breakdown behavior of the hydrogen gas in the Paschen region and have suggested improved behavior with the addition of trace dopants such as SF₆.³ Present efforts are to extend the computer model to include electrode breakdown phenomena and to use scanning tunneling microscopy to search for work function differences between the conditioned and unconditioned parts of the electrodes.

Novel accelerator technology, including Fixed Field Alternating Gradient Accelerators (FFAG) coupled with medical imaging devices, hold significant promise for enhanced proton therapy. The accuracy and efficiency of proton therapy treatments will see improvements with the implementation of proton computed tomography (pCT), currently under development. Here, we analyze the robustness of the image reconstruction method in pCT with respect to three different error sources and conclude that pCT is inherently resilient with respect to errors in mean ionization potential, discrete sampling of proton trajectories and bias in the limit of large radiation doses.

Non-scaling FFAG (NS-FFAG) rings have been proposed as a solution for muon acceleration in the Neutrino Factory. In order to achieve small orbit excursion and small time of flight variation, lattices with a very compact cell structure and consequent short straight sections are required. The resulting geometry, combined with the large transverse emittance of the muon bunch, places very challenging constraints on the injection/extraction systems. The injection/extraction system requires a set of distributed kickers, a superconducting septum and increased aperture in some of the main ring magnets. A scheme for both injection and extraction for a FFAG with triplet geometry is presented. In addition, a solution for the required kicker magnets is proposed.

Fixed Field Alternating Gradient (FFAG) elements are usually designed in a circular shape, but straight sections can also be imagined. A demonstration using the scaling condition is first shown. Combining different scaling FFAG sections is then discussed and opens new possibilities for scaling FFAGs. As an example, an application with a new lattice proposal for the PRISM project is finally presented in this paper.

The constant field nature of a fixed field alternating gradient (FFAG) accelerator requires a modeling which separates the layout of accelerator elements from the geometry of beam orbits. A new code, named s-code, is made to design an FFAG accelerator and to track a beam in it. We will describe the model of accelerator elements and the way to integrate the equation of motion of a particle.

The precise determination of the dynamics in accelerators with complicated field arrangements such as Fixed Field Alternating Gradient accelerators (FFAG) depends critically on the ability to describe the appearing magnetic fields in full 3D. However, frequently measurements or models of FFAG fields postulate their behavior in the midplane only, and rely on the fact that this midplane field and its derivatives determine the field in all of space. The detailed knowledge of the resulting out-of-plane fields is critical for a careful assessment of the vertical dynamics.

We describe a method based on the differential algebraic (DA) approach to obtain the resulting out-of-plane expansions to any order in an order-independent, straightforward fashion. In particular, the resulting fields satisfy Maxwell's equations to the order of the expansion up to machine precision errors, and without any inaccuracies that can arise from conventional divided difference or finite element schemes for the computation of out-of-plane fields.

The method relies on re-writing the underlying PDE as a fixed point problem involving DA operations, and in particular the differential algebraic integration operator. We illustrate the performance of the method for a variety of practical examples, and obtain estimates for the orders necessary to describe the fields to a prescribed accuracy.

EMMA is an experiment to study beam dynamics in fixed field alternating gradient accelerators (FFAGs). It accelerates the beam in about 10 turns using 1.3 GHz cavities in a mode like that used for muon accelerators. Many applications of FFAGs prefer to have slower acceleration, typically thousands of turns. To do so in EMMA would require the RF system to be replaced with a low-frequency, high-gradient system. This paper describes the motivation for studying slow acceleration in EMMA and the required parameters for an RF system to do that. It then describes the technology needed for the RF system.

The harmonic number jump acceleration in scaling FFAG rings is considered in this paper. Constraints fixed by the acceleration scheme on the lattice design are detailed. An example of a 3.6 to 12.6 GeV muon lattice which satisfy these constraints is presented.

Non-scaling FFAGs have gained interest in the past decade for their potential application to charged particle therapy using proton and ion beams. However, linear ns-FFAGs naturally cross betatron resonances throughout acceleration. With an acceleration cycle of thousands rather than tens of turns, we find that resonance crossing produces severe orbit distortion in a linear proton/ion ns-FFAG in the presence of alignment errors. To overcome this, the PAMELA (Particle Accelerator for MEdicaL Applications) lattice design avoids resonance crossing with a non-linear ns-FFAG design. This design is outlined and a comparative analysis of alignment tolerances presented.

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.

Stationary bucket acceleration in the scaling type of fixed field alternating gradient (FFAG) accelerator is examined in this paper.

The most challenging issue to realize an accelerator for an Accelerator Driven Sub-critical Reactor system (ADSR) is the handling of high intensity beam—more than 1 mA. For such an application, FFAG is one of most promising candidates. To take advantage of the FFAG as a high intensity accelerator, efficient injection/extraction and acceleration schemes are crucially important. One approach to achieve a high intensity FFAG is to eliminate the kicker magnet from the injection and extraction process and also to implement multi-bunch acceleration.

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.