Serpentine acceleration in zero-chromatic FFAG accelerators

doi:10.1016/j.nima.2013.03.061

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment

Volume 716, 11 July 2013, Pages 46-53

https://doi.org/10.1016/j.nima.2013.03.061 Get rights and content

Abstract

A fixed rf frequency acceleration scheme is required for rapid-acceleration and producing high-intensity beam in non-relativistic energy region. For these requirements, new-type of fixed rf frequency acceleration scheme called serpentine acceleration is applied in scaling FFAG. To examine a longitudinal motion with serpentine acceleration, longitudinal hamiltonian in scaling FFAG with fixed rf frequency is derived analytically. Then details of serpentine acceleration scheme in scaling FFAG are presented. To demonstrate serpentine acceleration in scaling FFAG, beam experiment has been done with electron scaling FFAG ring. Results are analyzed and confirm the serpentine acceleration in scaling FFAG. Finally, longitudinal design for ADS proton driver with this scheme is presented.

Introduction

A rapid-acceleration scheme is required in order to accelerate short-lived particles within their life time. Furthermore, high-power beam accelerator to produce intense secondary particles is also desired for Accelerator Driven System (ADS) [1].

In order to realize a rapid beam acceleration, it is not suitable to vary field of bending magnets. For classical synchrotrons, magnetic field varies in time with beam energy to keep the orbit. In typical case in synchrotrons, frequency of magnetic field variation is 1 Hz. In the 3 GeV rapid-cycle proton synchrotron (RCS) in Japan Proton Accelerator Research Complex (J-PARC), bending magnets are driven by the rapid-cycle system with 25 Hz. However, even with rapid-cycle system, repetition time is larger than the muon decay period. Furthermore magnetic fields with rapid-cycles ( $> 25 Hz$ ) create eddy current which flows along the metallic elements of the magnet including beam chamber, causing beam loss. From these considerations, bending magnet with static field is suitable for rapid beam acceleration.

Another issue is the production of high average current beams. For this requirement, two approaches are considered. One way is to increase the amount of injection particles per bunch. In this case, however, the number of injected particles is limited by the space charge effect. The other method is continuous wave (c.w.) operation and possibly lower charge per bunch; in this case, an rf cavity with fixed frequency is employed [2]. When c.w. mode is carried out, high average current particle beams can be generated free from space charge effect. True c.w. operation requires fixed rf frequency acceleration; such scheme is adopted in linear accelerators and cyclotrons in general.

Furthermore, to accelerate secondary particles such as muons, large dynamic aperture is secured for large emittance beams acceleration stably. For this requirement, strong focusing theory [3] need to be applied in the machine.

In consequence, to obtain high-intensity beams and realize stable rapid-acceleration, accelerators have to satisfy the following conditions: (i) static guide field, (ii) fixed rf frequency and (iii) strong focusing.

Linear accelerators have been considered as a proper candidate so far. However, their costs make practical realization difficult. Concerning circular accelerators, neither classical cyclotrons nor synchrotrons can be used, since they do not satisfy all the requirements, but spiral-sector ring cyclotrons are not excluded. An alternative candidate is a fixed-field alternating gradient (FFAG) accelerator [4], [5], [6], satisfying all conditions above. FFAG accelerators are categorized by the type of focusing variation: the non-scaling type and the scaling type. The scaling FFAG ring is composed of non-linear magnetic fields so that the chromaticity is null. Therefore, betatron tune is constant for every particle momentum, contrary to the non-scaling FFAG accelerator which uses linear magnetic field.

Recently, fixed rf frequency acceleration has been proposed in FFAG accelerators. In scaling FFAG, stationary bucket acceleration [7], [8] with fixed rf frequency has been considered. In this case, however, the total acceleration energy gain is limited by the bucket height. In order to make a large bucket height, the acceleration in the relativistic energy region is preferable. On the other hand, in non-scaling FFAG, to minimize orbit shifts during acceleration, the parabolic variation in orbit length with energy is created by the appropriate selection of parameters. At the bottom of the parabola, the momentum compaction approaches zero. Furthermore, for relativistic particles with the parabolic variation in orbit length, time of flight is also approximately parabolic. Therefore, the decreased variation in orbital period allows to operate a fixed rf frequency acceleration scheme with an appropriate selection of rf frequency and a high enough rf voltage. This new type of fixed rf frequency acceleration scheme is called serpentine acceleration [9], [10], [11], [12].

In these years, low energy muon beam less than 100 MeV is desired for particle physics [13], [14]. In this case, muon particles cannot be accelerated within lifetime without a rapid-acceleration scheme in non-relativistic energy region. In other fields, around 1 GeV proton beam with c.w. modes is required for ADS in nuclear engineering. For these applications, a fixed rf frequency acceleration scheme is useful in non-relativistic energy region. Only relativistic energy particles are suitable for fixed rf frequency acceleration in both types of FFAG so far. However if serpentine acceleration is applied to scaling FFAG, a fixed rf frequency acceleration scheme can be done not only in relativistic energy region but also in non-relativistic energy region.

In this paper, the longitudinal hamiltonian in scaling FFAG with fixed rf frequency is derived analytically first. Then the features of serpentine acceleration in longitudinal phase space are studied. Experiment for demonstration of serpentine acceleration is carried out, and features of serpentine acceleration are measured. Design of proton driver for ADS is finally presented. We use the convention of the light velocity c=1 in this paper.

Section snippets

Longitudinal beam dynamics in scaling FFAG with fixed rf frequency acceleration

In cylindrical coordinates, the magnetic field in scaling FFAG has the form $B_{z} (r, z = 0) = B_{0} {(\frac{r}{r_{0}})}^{k},$ where r is the radial coordinate with respect to the center of the ring, B₀ is the magnetic field at r₀, k is the geometrical field index, and z is the vertical coordinate. The closed orbits for different momenta P in scaling FFAG are given by $r = r_{0} {(\frac{P}{P_{0}})}^{1 / k + 1},$ where r₀ is the radius of the closed orbit at the momentum P₀.

In longitudinal particle dynamics with constant rf frequency acceleration, the phase

Longitudinal phase space in non-relativistic energy region

When the rf frequency is fixed near the transition energy, serpentine channel appears between two stationary buckets. With appropriate selection of the transition energy and rf frequency, serpentine acceleration can be achieved in non-relativistic energy region as shown in Fig. 1.

Minimum rf voltage to connect fixed points

The lower limit of rf voltage V_min to connect fixed points, called minimum rf voltage, is derived from Eq. (11). The limiting serpentine channel goes through two unstable fixed points where $H (E_{s 1}, π)$ equals $H (E_{s 2}, 0)$ .

Beam experiment

Serpentine acceleration in scaling FFAG had not been demonstrated yet. Thus the demonstration of serpentine acceleration was carried out in electron scaling FFAG accelerator. First we measure the electron beam accelerated in serpentine channel. Then phase acceptance of serpentine channel with different rf voltage is measured to clarify the features of serpentine acceleration.

Longitudinal design of proton driver for ADS

High-power beam accelerator to produce intense secondary particles is desired for ADS. Linear accelerators have been considered as a proper candidate so far, however, it is expensive to construct and operate systems. An alternative candidate is FFAG accelerator. In order to obtain a high-intensity beam in non-relativistic energy region, the acceleration scheme with serpentine acceleration is proposed in scaling FFAG. Maximum beam energy over 1 GeV is desired for ADS.

From the study of serpentine

Conclusion

We have confirmed that serpentine acceleration in scaling FFAG can work not only in relativistic energy region but also in non-relativistic energy region. The longitudinal hamiltonian with fixed rf frequency scheme has been derived analytically, and minimum rf voltage to open an infinitesimal serpentine channel has been obtained. Total energy gain and phase acceptance of serpentine channel have also been evaluated. The world's first experiment on serpentine acceleration in scaling FFAG has been

Acknowledgments

We would like to thank Dr. T. Baba and Dr. Y. Yuasa for their supports on the experiment.

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