WO2013043833A1

WO2013043833A1 - Method and apparatus for multi-pass return arc for recirculating linear accelerators

Info

Publication number: WO2013043833A1
Application number: PCT/US2012/056274
Authority: WO
Inventors: Kevin BEARD; Alex BOGACZ; Vasiliy MOROZOV; Yves ROBLIN
Original assignee: Muons, Inc.
Priority date: 2011-09-20
Filing date: 2012-09-20
Publication date: 2013-03-28

Abstract

In a particular embodiment, a device is disclosed that includes means for allowing a single multi-pass return arc for a recirculating linear accelerator (RLA) to return more than a single energy pass of a charged particle beam. The device also includes means for simplifying a design of the RLA and means for reducing a cost of the RLA. In another particular embodiment, a method is disclosed that includes steps for allowing a single multi-pass return arc for a recirculating linear accelerator (RLA) to return more than a single energy pass of a charged particle beam. The method also includes steps for simplifying a design of the RLA and means for reducing a cost of the RLA.

Description

Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators

METHOD AND APPARATUS FOR MULTI-PASS RETURN ARC FOR

RECIRCULATING LINEAR ACCELERATORS

INVENTORS:

Kevin Beard, Ph.D.

Alex Bogacz, Ph.D.

Vasiliy Morozov, Ph.D.

and

Yves Roblin, Ph.D.

J. Cross-Reference to Related Application

[0001] This application claims the benefit of U.S. Provisional Patent Application No.

61/536,587, filed September 20, 2011, which is hereby incorporated by reference in its entirety, as if set out below.

//. Field of the Disclosure

[0002] The present disclosure is generally related to providing a single multi-pass return arc for a recirculating linear accelerator (RLA) to return more than a single energy pass of a charged particle beam and, in particular, to demonstrating that various proposed cooling subsystems for an energy-frontier muon collider may be consolidated into an integrated end-to-end design.

///. Summary

[0003] In a particular embodiment, a device is disclosed that includes means for allowing a single multi-pass return arc for a recirculating linear accelerator (RLA) to return more than a single energy pass of a charged particle beam. The device also includes means for simplifying a design of the RLA and means for reducing a cost of the RLA.

[0004] In another particular embodiment, a method is disclosed that includes steps for allowing a single multi-pass return arc for a recirculating linear accelerator (RLA) to return more Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators

than a single energy pass of a charged particle beam. The method also includes steps for simplifying a design of the RLA and means for reducing a cost of the RLA.

IV. Brief Description of the Drawings

[0005] The following figures form part of the present specification and are included to further demonstrate certain aspects of the present invention. The present invention may be better understood by reference to one or more of these drawings in combination with the description of embodiments presented herein.

[0006] Consequently, a more complete understanding of the present disclosure and advantages thereof may be acquired by referring to the following description taken in conjunction with the accompanying drawings, in which the leftmost significant digit(s) in the reference numerals denote(s) the first figure in which the respective reference numerals appear, wherein:

[0007] Figure 1 is a diagram illustrating an upgraded Continuous Electron Beam Accelerator Facility (CEBAF) 0.06-12 GeV/c e^" Recirculating Linear Accelerator (RLA);

[0008] Figure 2a is a diagram illustrating a proposed 0.9-3.6 GeV RLA with conventional arcs and central injection;

[0009] Figure 2b is a diagram illustrating the same μ* RLA as shown in Figure 2a, except with multi-pass arcs, as disclosed and described herein;

[0010] Figure 3 is a diagram illustrating a 2:1 momentum ratio multi-pass arc with exagerated trajectory;

[0011] Figure 4a is a diagram illustrating an early attempt of a transverse optics match of the linac to the arcs for all 4.5 passes simultaneously. Only the linac is shown; the arcs are shown by a black line representing a transfer matrix;

[0012] Figure 4b is a diagram illustrating better-matched final pass horizontal and vertical beta functions in the linac of a 6.5 pass muon RLA; Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators

[0013] Figure 5 is a diagram illustrating horizontal (on the left, as shown at 500) and vertical (on the right, as shown at 510) maximum- amplitude stable phase-space trajectories for the linear and non- linear NS-FFAG designs;

[0014] Figure 6a is a diagram illustrating 1.2 GeV/c periodic orbit, dispersion (left) and beta functions (right) of the outward bending super cell;

[0015] Figure 6b is a diagram illustrating 2.4 GeV/c periodic orbit, dispersion (left) and beta functions (right) of the outward bending super cell;

[0016] Figure 7a is a diagram illustrating pure dipoles as a spreader/ recombiner for 2:1

momenta trajectories for a single multi-pass arc;

[0017] Figure 7b is a diagram illustrating pure dipoles as a spreader/ recombiner at the

beginning of two multi-pass arcs with momentum ratios of 2: 1 and 4:3;

[0018] Figure 8 is a diagram illustrating vertical bypass of the 2^nd of two multi-pass arcs;

[0019] Figure 9 is a diagram illustrating a double achromatic injection model in OptiM;

[0020] Figure 10 is a diagram illustrating an embodiment of an apparatus including means for allowing a single multi-pass return arc for a recirculating linear accelerator (RLA) to return more than a single energy pass of a charged particle beam and means for simplifying a design of the RLA and means for reducing a cost of the RLA; and

[0021] Figure 11 is a flow diagram of an illustrative embodiment of a method including steps for allowing a single multi-pass return arc for a recirculating linear accelerator (RLA) to return more than a single energy pass of a charged particle beam and steps for simplifying a design of the RLA and steps for reducing a cost of the RLA.

V. Detailed Description

[0022] Illustrative embodiments of the present invention are described in detail below. In the interest of clarity, not all features of an actual implementation are described in this specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators

constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of the present disclosure.

[0023] Particular embodiments of the present disclosure are described with reference to the drawings. In the description, common features are designated by common reference numbers.

[0024] Referring to Figure 1 , a diagram illustrating an upgraded Continuous Electron Beam

Accelerator Facility (CEBAF) 0.06-12 GeV/c e^" Recirculating Linear Accelerator (RLA is depicted and indicated generally, for example, at 100.

[0025] Referring to Figure 2a, a diagram illustrating a proposed 0.9-3.6 GeV RLA with conventional arcs and central injection is depicted and indicated generally, for example, at 200.

[0026] Referring to Figure 2b, a diagram illustrating the same μ* RLA as shown in Figure 2a, except with multi-pass arcs, as disclosed and described herein, is depicted and indicated generally, for example, at 210.

[0027] Referring to Figure 3, a diagram illustrating a 2:1 momentum ratio multi-pass arc with exagerated trajectory is depicted and indicated generally, for example, at 300.

[0028] Referring to Figure 4a, a diagram illustrating an early attempt of a transverse optics match of the linac to the arcs for all 4.5 passes simultaneously is depicted and indicated generally, for example, at 400.

[0029] Referring to Figure 4b, a diagram illustrating better-matched final pass horizontal and vertical beta functions in the linac of a 6.5 pass muon RLA is depicted and indicated generally, for example, at 410.

[0030] Referring to Figure 5, a diagram illustrating horizontal (on the left, as shown at 500) and vertical (on the right, as shown at 510) maximum- amplitude stable phase-space trajectories for the linear and non-linear NS-FFAG designs is depicted and indicated generally, for example, at 500 and 510. Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators

[0031] Referring to Figure 6a, a diagram illustrating 1.2 GeV/c periodic orbit, dispersion (on the left, at 600) and beta functions (on the right, at 610) of the outward bending super cell is depicted and indicated generally, for example, at 600 and 610.

[0032] Referring to Figure 6b, a diagram illustrating 2.4 GeV/c periodic orbit, dispersion (on the left, at 620) and beta functions (on the right, at 630) of the outward bending super cell is depicted and indicated generally, for example, at 620 and 630.

[0033] Referring to Figure 7a, a diagram illustrating pure dipoles as a spreader/ recombiner for 2:1 momenta trajectories for a single multi-pass arc is depicted and indicated generally, for example, at 700.

[0034] Referring to Figure 7b, a diagram illustrating pure dipoles as a spreader/ recombiner at the beginning of two multi-pass arcs with momentum ratios of 2:1 and 4:3 is depicted and indicated generally, for example, at 710.

[0035] Referring to Figure 8, a diagram illustrating vertical bypass of the 2^nd of two multi-pass arcs is depicted and indicated generally, for example, at 800.

[0036] Referring to Figure 9, a diagram illustrating a double achromatic injection model in OptiM is depicted and indicated generally, for example, at 900.

[0037] Referring to Figure 10, a flow diagram of an illustrative embodiment of a method is depicted and indicated generally, for example, at 1000. The apparatus 1000 includes means for allowing, at 1010, a single multi-pass return arc for a recirculating linear accelerator (RLA) to return more than a single energy pass of a charged particle beam and means for simplifying a design of the RLA, at 1020, and means for reducing a cost of the RLA, at 1030.

[0038] Referring to Figure 11, a flow diagram of an illustrative embodiment of a method is depicted and indicated generally, for example, at 1100. The method 1100 includes steps for allowing, at 1110, a single multi-pass return arc for a recirculating linear accelerator (RLA) to return more than a single energy pass of a charged particle beam and steps for simplifying a design of the RLA, at 1120, and steps for reducing a cost of the RLA, at 1130. Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators

[0039] Attached herewith as an Appendix to the Specification are portions of an SBIR/STTR grant application entitled "MULTI-PASS RETURN ARCS FOR RECIRCULATING LINEAR ACCELERATORS," by Dr. Kevin Beard, Dr. Alex Bogacz, Dr. Vasiliy Morozov, and Dr. Yves Roblin, which is incorporated by reference as if set forth below. More details about various illustrative embodiments may be found by referring to the Appendix.

[0040] The present invention is well adapted to carry out the objects and attain the ends and advantages mentioned, as well as those that are inherent therein. While the present invention has been depicted, described and is defined by reference to exemplary embodiments of the present invention, such a reference does not imply a limitation of the present invention, and no such limitation is to be inferred. The present invention is capable of considerable modification, alteration, and equivalency in form and function as will occur to those of ordinary skill in the pertinent arts having the benefit of this disclosure. The depicted and described embodiments of the present invention are exemplary only and are not exhaustive of the scope of the present invention.

Consequently, the present invention is intended to be limited only by the spirit and scope of the appended claims, giving full cognizance to equivalents in all respects.

[0041] The particular embodiments disclosed above are illustrative only, as the present

invention may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Furthermore, no limitations are intended to the details of composition or design herein shown, other than as described in the claims below. It is therefore evident that the particular embodiments disclosed above may be altered or modified and all such variations are considered within the scope and intent of the present invention. In particular, every range of values (of the form, "from about a to about b," or, equivalently, "from approximately a to b," or, equivalently, "from approximately a-b") disclosed herein is to be understood as referring to the power set (the set of all subsets) of the respective range of values, in the sense of Georg Cantor. Accordingly, the protection sought herein is as set forth in the claims below.

[0042] The particular embodiments of the present invention described herein are merely

exemplary and are not intended to limit the scope of this present invention. Many Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators

variations and modifications may be made without departing from the intent and scope of the present invention. Applicants intend that all such modifications and variations are to be included within the scope of the present invention as defined in the appended claims and their equivalents. 3] While the present invention has been illustrated by a description of various

embodiments and while these embodiments have been described in considerable detail, it is not the intention of the Applicants to restrict, or any way limit the scope of the appended claims to such detail. The present invention in its broader aspects is therefore not limited to the specific details, representative apparatus, methods, and illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the scope of Applicants' general inventive concept.

sr Multi-Pass Return Arc for Recirculating Linear Accelerators

Topic 28b ass Return MuPlus Inc.

Phase I-SBIR/STTR Fiscal Year 2012 (Release 1)

NAME of PRINCIPAL INVESTIGATOR: K.B.Beard PHONE NUMBER: (248) 569-5678

TOPIC: 28b

PROJECT TITLE: Multi-pass Return Arcs for Recirculating Linear Accelerators

TECHNICAL ABSTRACT

STATEMENT OF THE PROBLEM OR SITUATION THAT IS BEING ADDRESSED.

Recirculating Linear Accelerators (RLAs) are an efficient way of accelerating lepton and possibly ion beams to medium and high energies by reusing the same linac for multiple passes, or to recycle the energy of the beam. In the conventional scheme, different energy beams coming out of the linac are separated and directed into appropriate arcs for recirculation; each pass through the linac requires a separate fixed-energy arc. This new invention allows a single arc to return more than a single energy pass, greatly simplifying the design and reducing the cost.

GENERAL STATEMENT OF HOW THIS PROBLEM OR SITUATION IS BEING ADDRESSED.

For a first implementation, a multi-pass return arc for a muon RLA for a neutrino factory[2] is being developed in Phase I. Such a design provides a greater compactness than, for instance, a conventional FFAG lattice with its regular alternating bends, and is expected to possess a large dynamic aperture characteristic of linear-field lattices. By adjusting the bending angles and quadrupole components of the combined-function magnets, the arc is designed to be achromatic and to have zero initial and final periodic orbit offsets for the discrete set of the transported momenta. In Phase II, a much more complete model will be optimized on a large farm and used to determine the required tolerances, and later to investigate the radiation deposition due to muon decay. We anticipate that Phase III would involve a contract for a detailed design.

WHAT WILL BE DONE IN PHASE I.

Linear optics of a prototype multi-pass arc will be developed and evaluated; practical limits on the magnet parameters, transported momentum ratios, and number of passes will be identified. Simulations to evaluate the dynamic aperture, momentum acceptance and error sensitity will be initiated. A preview of the topics to be explored in Phase II will be carried out.

COMMERCIAL APPLICATIONS AND OTHER BENEFITS

RLAs are used for nuclear physics, high energy physics, and light sources, and have been proposed for use in nuclear interdiction, nuclear power generation and waste recycling, and for volcano tomography. In addition, a multi-pass arc may find an application for the transport of ions for use in cancer treatment. [1]

KEY WORDS: muon, neutrino, recirculating, linear, accelerators, linac, RLA, FEL, lattice, optics

SUMMARY FOR MEMBERS OF CONGRESS:

A multi-pass arc is a new type of magnetic channel capable of simultaneously transporting two or more particle beams of very different energies, where normally a separate string of magnets would be required for each individual energy. It has wide application in nuclear physics, high energy physics, and Free Electron Lasers (FELs). Method and Apparatus for Multi-Pass Return Arc tor Recirculating Linear Accelerators Topic 28b Multipass Return Arcs for RLAs MuPlus Inc.

Multi-pass Return Arcs

for Recirculating Linear Accelerators

Table of Contents a. Cover Page 1 b. Proprietary Data Legend - Not Applicable 2

Project Overview 3 c. Identification and Significance of the Problem or Opportunity, and Technical Approach 5

Identification and Significance of the Problem or Opportunity 5

Technical Approach 5

Droplet Arc Geometry and Optics Requirements 5

Tools 6

Muon Recirculating Linear Accelerator 6

Linear Arc Optics 7

Ancillary Considerations 10 d. Anticipated Public Benefits 1 e. Technical Objectives 13 f Phase I Work Plan 13

Responsibilities 1 g. Phase I Performance Schedule 14 h. Related Research or R&D 14 i. Principal Investigator and other Key Personnel 14 j. Facilities/Equipment 15 k. Consultants and Subcontractors 15

Appendix 1. Letter of Support from MAP 17

Appendix 2. Letter of Support from CERN 18

Appendix 3. Letter of Support from BNL 19 b. Proprietary Data Legend - Not Applicable Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators Topic 28b Multipass Return Arcs for RLAs MuPlus Inc.

Project Overview

Recirculating Linear Accelerators (RLAs) are powerful, but expensive devices that, unlike synchrotrons, can produce a continuous beam. RLAs are used for nuclear physics, high energy physics, and light sources, and have been proposed for use in nuclear interdiction, volcano tomography, and even possibly for accelerator-driven nuclear reactors. They are often used in Free Electron Lasers (FELs), with many applications from basic research on biological systems, nanotechnology fabrication, to directed energy weapons. Reducing RLAs size and cost and simplifying their construction makes them more attractive and cost effective.

Figure 1. Upgraded CEBAF 0.06-12 GeV/c e^" RLA.

RLAs are most commonly used for electron beams, but also are an efficient way of accelerating short-lived muons to the multi-GeV energies required for neutrino factories and TeV energies required for muon colliders. Conventional RLAs use a different arc for each momentum beam; for each pass, the beam must be spread and redirected into its own arc, then recombined upon the exit of the arcs into a single beam to put back into the linac (Fig. 1 and Fig. 2a). Fig. 1 is the upgraded CEBAF 5.5 pass accelerator at Jefferson Lab, and Fig. 2 is a 4.5 pass muon RLA proposed for a Neutrino Factory. [2]

This new invention, a multi-pass RLA return arc, is based on linear combined function magnets, in which two charge particle beams with momenta differing by a factor of two or less are transported through the same string of magnets at the same time (Fig. 2b and Fig. 3). Unlike a conventional Fixed Field Alternating Gradient (FFAG) arc which can transport a range of momenta, the multi-pass arc fields do not alternate so the multi-pass arc has a much smaller size. Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators Topic 28b Multipass Return Arcs for RLAs MuPlus Inc.

The multi-pass arc is composed of 60°-bending symmetric super cells allowing for a simple geometric closing. By adjusting the dipole and quadrupole components of the combined-function magnets, each super cell is designed to be achromatic and to have zero initial and final periodic orbit offsets for both momenta.

0 10 20 30 40 50

x (m)

Figure 3. A 2: 1 momentum ratio multi-pass arc with exagerated trajectory.

As the initial and most challenging case, we'll begin by seeking a solution for a 2: 1 momentum ratio in a muon RLA proposed for a neutrino factory. [2] Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators Topic 28b Multipass Return Arcs for RLAs MuPlus Inc.

A successful multi-pass arc design could be used for other applications, perhaps for applications where ions in two or more charge states need to be transported, such as facilities for the production of exotic isotopes or cancer treatment.[l] c. Identification and Significance of the Problem or Opportunity, and

Technical Approach

Identification and Significance of the Problem or Opportunity

The motivation behind a RLA is to use the expensive ($40-50M/GeV) RF more than once. All current RLAs use a single arc for each beam momentum; for example, the CEBAF accelerator uses 5 arcs at one end and 4 at the other is currently being upgraded to accelerate electrons to 12 GeV (Fig. 1). Upon exiting the North linac, the CEBAF beam is split into 5 beams, each beam is sent through its own arc, then subsequently recombined into one for injection into the South linac. If two (or perhaps more) passes could be sent through a single arc, this would greatly simplify the design and perhaps reduce the cost.

By design in the multi-pass arc, the beam is centered inside the dispersion-free linac on each pass. The isochronicity of the arc ensures proper RF synchronization. The design requires only conventional linear combined function magnets with large apertures, thereby alleviating any stringent requirements for magnetic field profiles and manufacturing tolerances. While a conventional Fixed Field Alternating Gradient (FFAG) arc could be used, it has a much longer path (due to the alternating bending inward and outward); what is needed is an arc lattice in which little or no bending is required in the "wrong" direction.

Accelerating muons of both signs with a single accelerator is especially challenging; the short muon lifetime means that no time may be wasted during acceleration or too many muons will decay away. In addition, the muons are created as a tertiary beam and have a very large phase space volume.

Technical Approach

Droplet Arc Geometry and Optics Requirements

We illustrate our scheme with the present baseline muon RLA for a neutrino factory [2], in which a 0.9 GeV/c muon beam is injected in the middle of a 0.6 GeV/pass linac. The linac is then traversed by the beam four and one half times. Therefore, one of the return arcs must

accommodate 1.2 and 2.4 GeV/c muon momenta, while the other arc must accommodate 1.8 and 3.0 GeV/c momenta. Since the two arcs are designed using the same approach, here we focus our discussion on the 1.2/2.4 GeV/c arc whose design is somewhat more complicated than that of the 1.8/3.0 GeV/c arc due to the greater fractional momentum difference of the two passes.

Each droplet arc consists of a 60° outward bend, a 300° inward bend and another 60° outward bend so that the net bend is 180°. This arc geometry has the advantage that if the outward and inward bends are composed of similar cells, the geometry automatically closes without the need for any additional straight sections, making it simpler and more compact. tethod and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators

Topic 28b Multipass Return Arcs for RLAs MuPlus Inc.

To transport different energy muons of both charges through the same arc structure, the arc must possess the following properties:

• For each transported momentum, both the offset and slope of the periodic orbit at the arc's entrance and exit must be zero to ensure that the beam goes through the center of the linac.

• The arc must be achromatic for each momentum to keep the linac dispersion free.

• The arc must be mirror symmetric, so that μ⁺ and μ^" can pass through the same lattice in opposite directions. If such a symmetric arc is designed with a periodic solution for the optics, the periodic beta functions are equal at the arc's ends while the periodic alpha functions and the dispersion slope are zero at both ends.

• The times of flight of the two momenta must provide proper synchronization with the linac.

• The dynamic aperture and momentum acceptance must be adequate for a large-emittance muon beam.

• The orbit offsets as well as beta functions and dispersion for both energies should be small enough to keep the aperture size acceptable.

Below we discuss a design satisfying all these requirements.

Tools

Different steps of this work require different tools; the OptiM[3] program has been used for the linac and ancillary components, while the Polymorphic Tracking Code (PTC) module of MAD- X[4] has been used for the multi-pass arcs. The designs for the injection and linac were done using OptiM. The overall tracking will be done using ELEGANT[5] and G4beamline[6]; the former is excellent for tolerance studies, while latter is especially useful for estimating the radiation loads from muon decay.

Muon Recirculating Linear Accelerator

The CEBAF machine in Fig. 1 is a "racetrack" RLA; the electrons travel clockwise through the arcs. In contrast, a muon RLA needs to accelerate both μ⁺ and μ^" simultaneously; the "dogbone" layout with "teardrop" 420° arcs use the same magnets for both charges as they travel in opposite directions around the arc (Fig. 2a and 2b). With each pass' increasing energy as it travels down the linac, the focusing gets weaker, and so we employ a beta function-beating technique in which the quadrupole focusing strengths increase symmetrically with distance from the center of the linac. [7] An early match using OptiM is shown in Fig 5. [8] This necessitates that the beam be injected at the middle of the linac and extracted from an end.

Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators Topic 28b Multipass Return Arcs for RLAs MuPlus Inc.

Figure 5a: An early attempt of a transverse optics match of the linac to the arcs for all 4.5 passes simultaneously. Only the linac is shown; the arcs are shown by a black line representing a transfer matrix.

Figure 5b. Better matched final pass horizontal and vertical beta functions in the linac of a 6.5 pass muon RLA.

Multiple RLAs are planned for the muon collider; we anticipate that all the solutions will just be appropriately scaled from the lowest energy one.

Linear Arc Optics

We earlier considered [9] a non-linear NS-FFAG design for the RLA return arcs. Here we present a new design based on a linear lattice, which has a number of advantages over the nonlinear solution:

• much greater dynamic aperture and momentum acceptance,

• no need for a complicated compensation of non-linear effects,

• simpler adjustment of the path length and the time of flight at each energy,

• easier control of the beta-function and dispersion values, which simplifies matching to the linac,

• simpler combined-function magnet design with only dipole and quadrupole field components.

The relative stable phase space areas of the nonlinear and our first linear solution are illustrated in Fig. 6.

We earlier developed a linear optics solution for a multi-pass arc [7,8,10] based on the

conventional linear Non-Scaling Fixed Field Alternating Gradient (NS-FFAG) lattice [11]. The disadvantage of such a conventional FFAG approach is an inefficient usage of the channel's length due to the alternating outward-inward-outward bends in the underlying triplet structure. In other words, bending the beam by a certain net angle requires a total bend of three times that angle. That made the multi-pass arc very long and difficult for it to compete with the separate arc solution. In this new design, we deviate from the conventional FFAG scheme by not using regular alternating bends.

A solution satisfying the requirements discussed in the section above can be obtained using only same-direction bends, which can shorten the arc by almost a factor of 3. However, in our parameter range of relatively low energies and large momentum ratio such a solution would still Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators

Topic 28b Multipass Return Arcs for RLAs MuPlus Inc. not be optimal in terms of the channel length and magnet parameters. The number of magnets required to meet all of the requirements would make the channel unnecessarily long.

2.4 GeV/c 2.4 GeV/c

-300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300

Y (mm) Y (mm)

Figure 6: Horizontal (left) and vertical (right) maximum-amplitude stable phase-space trajectories for the linear and non-linear NS-FFAG designs.

Therefore, we introduce another innovation to increase the number of available parameters without increasing the number of magnets. We make the bending angle of each combined function magnet variable with a constraint that the bending angles of all magnets in a super cell must add up to the required fixed total bend. Such a solution combines compactness of the design with all the advantages of our earlier linear NS-FFAG solution [9], namely, large dynamic aperture and momentum acceptance essential for large-emittance muon beams, no need for a complicated compensation of non-linear effects, simpler combined-function magnet design with only dipole and quadrupole field components, etc.

To study the optics for large momentum offsets, we used the Polymorphic Tracking Code (PTC) module of MAD-X. While perturbative method codes are not suitable for such a study, PTC allows symplectic integration through all elements with user control over the precision with full or expanded Hamiltonian.

We assume that the arc is composed of identical super cells. In our energy range, we use the maximum possible bend of 60° per super cell to have the largest possible number of magnets in the super cell and therefore the largest number of free parameters for optics tuning. The super cell consists of 24 combined function magnets with dipole and quadrupole field components. The magnets are 0.5 m long and are separated by 0.2 m gaps. The total arc length is 117.6 m.

The super cell is symmetric with respect to its center. Therefore, out of the 24 magnets constituting the super cell, 12 are independent. As discussed below in the next section, 2 of these magnets are pure dipoles with a fixed bending angle of 6° each. The remaining 10 magnets each have variable dipole and quadrupole field components with a constraint that the bending angles of all super cell's magnets add up to a net bend of 60°. This gives a total of 19 independent parameters. tethod and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators

Topic 28b Multipass Return Arcs for RLAs MuPlus Inc.

When solving for the periodic orbit and the periodic Twiss functions of the super cell, the initial values of the orbit offset, dispersion, their slopes and the alpha functions were all set to zero at both momenta. The initial values of the horizontal and vertical beta functions were set to 2 m at both momenta to provide easy matching to the linac and to keep the peak values of the beta functions inside the super cell at an acceptable level. The 19 independent parameters discussed above were then adjusted to give zero slopes of the orbit offset, dispersion and beta functions at the center of the super cell at the two momenta. The super cell's symmetry then ensures the appropriate properties at the super cell's exit. Since the 2.4 GeV/c beam goes through the magnet centers, its periodic orbit by definition has zero offset everywhere. This results in a total of 7 constraints. The extra free parameters were used to control the maximum values of the orbit deviation, beta functions and dispersion. In terms of magnetic field requirements, the maximum needed dipole field is about 1.7 T while the maximum quadrupole gradient is about 28 T/m. Figures 7a and 7b show solutions for the periodic orbit, dispersion, and beta functions of the outward-bending super cell at 1.2 and 2.4 GeV/c, respectively. An inward-bending super cell is identical to the outward-bending cell except that its bends are reversed.

Figure 7a: 1.2 GeV/c periodic orbit, dispersion (left) and beta functions (right) of the outward bending super cell.

Figure 7b: 2.4 GeV/c periodic orbit, dispersion (left) and beta functions (right) of the outward bending super cell.

Figure 3 shows geometric layouts of the 1.2 and 2.4 GeV/c closed periodic orbits. The displacement of the 1.2 GeV/c orbit was enhanced by a factor of 10. Note that because of the varying bending angles, the arc is not perfectly circular. The largest orbit separation occurs only in a small number of magnets and is caused by the necessity to spread/recombine the different Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators Topic 28b Multipass Return Arcs for RLAs MuPlus Inc. momenta orbits at the beginning of the arc. The maximum orbit deviation is reduced for smaller momentum ratios such as that of the 1.8/3.0 GeV/c arc.

At few-GeV energies muons are not ultra-relativistic; there is a non-negligible difference in the speeds of 1.2 and 2.4 GeV/c muons. Because of the short arc circumference it was not possible to compensate the time of flight difference by adjusting the path lengths. One can attain an appropriate synchronization with the linac by placing a path-length chicane in front of the arc. Such a chicane would have a cumulative effect on the opposite-direction passes.

We would study the dynamic aperture and momentum acceptance of the arc. Earlier studies with a similar linear lattice yielded promising results [7,9]. We will investigate chromatic effects and if necessary, implement their control and compensation. Another important aspect that requires investigation is the design sensitivity to magnet misalignments and magnetic field errors.

Establishing tolerance levels on these errors is crucial for the costing of large aperture magnets.

Ancillary Considerations

One must still get the muons in to and out of each multi-pass arc. Due to the arc's geometric closing, the first and the last few magnets of the arc overlap. These magnets cannot contain quadrupole field components because the symmetry would otherwise lead to the quadrupole fields having opposite slopes in the overlapping magnets. Therefore, we keep the first two magnets of each super cell as pure dipoles. Their bending angles are fixed and are chosen to provide a sufficient separation of the incoming and outgoing higher-momentum beam while keeping the separation of the lower and higher-momentum beams within acceptable limits. Also based on these considerations, we choose the higher 2.4 GeV/c momentum as the reference momentum going through the magnet centers. The beam trajectories at the beginning of the arc are shown in Fig. 8a. A layout appropriate for two multi-pass arcs is shown in Fig. 8b.

0 0.5 1 1.5 2 2.5

x (m)

Figure 8a: Pure dipoles as a spreader/ recombiner for 2: 1 momenta trajectories for a single multipass arc. Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators Topic 28b Multipass Return Arcs for RLAs MuPlus Inc.

Figure 8b: Pure dipoles as a spreader/ recombiner at the beginning of two multi-pass arcs with momentum ratios of 2: 1 and 4:3.

If an application calls for a "racetrack" rather than a "dogbone" RLA, the same multi-pass concept may be applied with an additional degree of freedom in that quadrupole components may be used in the end magnets, reducing the maximum orbit excursion.

If more than a single multi-pass arc is used, for clearance it is necessary to insert a vertical bypass that preserves the optics. The current solution is shown in Fig. 9.

Figure 9. Vertical bypass of the 2ⁿ of two multi-pass arcs. Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators Topic 28b Multipass Return Arcs for RLAs MuPlus Inc.

The injection chicane into the middle of the linac must handle both μ and μ^" and be dispersion free. Our doubly achromatic solution based on using 4 cells horizontally and 3 cells vertically was done using OptiM as shown in Fig. 10.

Figure 10. A double achromatic injection model in OptiM.

The extraction mechanism has not yet been modeled, but is straightforward, d. Anticipated Public Benefits

Scientific progress has always depended on its tools. Unraveling the mysteries of fundamental particles and their forces will require large and expensive facilities. Muons have advantages over other particles for probing the regime; being a lepton, they don't have the internal structure of protons, and being >200x heavier than electrons, don't emit significant synchrotron radiation at energies of interest. The cost of proposed neutrino factories and muon colliders are in the multi-$B range, and any innovation that could save even a fraction of the total cost is significant. Two colleagues from the neutrino factory and muon collider collaborations, but unaffiliated with this proposal, have written letters in support of this proposal that appear in the Appendix.

Similarly, large RLAs are proposed for the production of ~GeV μ^" beams for the detection and interrogation of nuclear, especially fissionable, materials; since a relatively large number of these devices would be needed to cover every major port and strait around the world, the savings could be huge. [12] Another muon RLA producing ~10s GeV μ has been proposed for volcano tomography to detect impending eruptions. [13]

To date, no non-relativistic RLA has been constructed anywhere in the world, but recent discussions have suggested such a device may be possible and very useful to produce -20MW of Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators Topic 28b Multipass Return Arcs for RLAs MuPlus Inc.

~1 GeV kinetic energy protons for use in Accelerator Driven Systems, a new generation of nuclear reactors for electric power generation and recycling of high level radioactive waste. If ADS became the dominant source of US electrical power, one could expect about -700 RLAs in total, an investment of ~$700B, of which the multi-pass arc would be an integral part.

This same invention could reduce the footprint and cost of smaller RLAs, most notably Free Electron Lasers (FELs). FELs, especially those operating in the ultraviolet on down to the infrared, could be made more compact and less expensive. Many industrial and medical applications of FELs are under consideration, as well as military applications. The size of such a device is of special interest to the U.S. Navy, whose R&D effort is directed toward placing FELs operating near 1 um and >1 MW on warships for protection against enemy missiles.

A multi-pass arc could be used to transport multiple ion beams too. One application would be for a far more efficient collection of exotic isotopes in nuclear physics experiments. Another application would be to improve cancer treatment based on light ion beams.[l]

Perhaps the greatest benefit would be expertise gained by MuPlus, Inc. and Muons, Inc. in the design of multi-pass arcs, making them a more valuable resource to the Muon Acceleration Program and the Neutrino Factory International Design Study collaborations and other potential RLA applications. e. Technical Objectives

Our first objective is to produce a working, multi-pass arc that satisfies all the criteria at the ends, including the time of flight issues, with a reasonable acceptance. A methodology for more than two passes and an algorithm to easily generate the parameters for any given momentum ratio will be explored. Limiting design parameters will be investigated. We will begin simulations to optimize the dynamic aperture and momentum acceptance and determine magnet tolerance requirements. We will prepare a paper describing the technique and reporting the results. f. Phase I Work Plan

In Phase I, the linear optics design of a prototype multipass arc will be developed. Limiting design parameters will be investigated. Simulations of the prototype design will be initiated. The design and simulation work will be done using the PTC/MAD-X, ELEGANT and G4beamline codes.

The goals of the Phase I project are:

1. Development of the linear optics design of a prototype multipass arc.

2. Study of the possibility of a three-pass design.

3. Development of an algorithm for automation of the multipass arc design process.

4. Investigation of the prototype design limitations in terms of magnet parameters, transported momentum ratios and orbit excursions and their optimization.

5. Matching of the arc optics to the linac.

6. Initial numerical simulations for evaluation and optimization of the arc's dynamic aperture and momentum acceptance.

7. Initial estimates of the design sensitivity to magnetic field and magnet positioning errors and of the related error tolerance requirements.

Claims

Method and Apparatus for Multi-Pass Return Arc for Recircu fating Linear Accelerators CLAIMS

1. A device comprising:

means for allowing a single multi-pass return arc for a recirculating linear accelerator (RLA) to return more than a single energy pass of a charged particle beam; and

means for simplifying a design of the RLA and means for reducing a cost of the RLA.

2. A method comprising:

steps for allowing a single multi-pass return arc for a recirculating linear

accelerator (RLA) to return more than a single energy pass of a charged particle beam; and

steps for simplifying a design of the RLA and means for reducing a cost of the RLA.