The PAMELA project to design an accelerator for

hadron therapy using non-scaling Fixed Field Alternating

Gradient (NS-FFAG) magnets requires a transport line

and gantry to take the beam to the patient. The NS-FFAG

principle offers the possibility of a gantry much smaller,

lighter and cheaper than conventional designs, with the

added ability to accept a wide range of fast changing

energies. This paper will build on previous work to

investigate a transport line which could be used for the

PAMELA project. The design is presented along with a

study and optimisation of its acceptance

Edgecock, R.

Fenning, R.J.L.

Kelliher, D.J.

Khan, A

Machida, S.

Peach, K. J.

Yokoi, T.

English

University of Huddersfield Repository

University of Huddersfield RepositoryFenning, R.J.L., Edgecock, R., Kelliher, D.J., Khan, A, Machida, S., Peach, K. J. and Yokoi, T.An FFAG Transport Line for the PAMELA ProjectOriginal CitationFenning, R.J.L., Edgecock, R., Kelliher, D.J., Khan, A, Machida, S., Peach, K. J. and Yokoi, T. (2009) An FFAG Transport Line for the PAMELA Project. In: Proceedings of the 23rd Particle Accelerator Conference. PAC09 . JACoW, Vancouver, British Columbia, Canada, pp. 3741-3743. This version is available at http://eprints.hud.ac.uk/21164/The University Repository is a digital collection of the research output of theUniversity, available on Open Access. Copyright and Moral Rights for the itemson this site are retained by the individual author and/or other copyright owners.Users may access full items free of charge; copies of full text items generallycan be reproduced, displayed or performed and given to third parties in anyformat or medium for personal research or study, educational or not-for-profitpurposes without prior permission or charge, provided:• The authors, title and full bibliographic details is credited in any copy;• A hyperlink and/or URL is included for the original metadata page; and• The content is not changed in any way.For more information, including our policy and submission procedure, pleasecontact the Repository Team at: E.mailbox@hud.ac.uk.http://eprints.hud.ac.uk/ AN FFAG TRANSPORT LINE FOR THE PAMELA PROJECTR. Fenning*, A. Khan, Brunel University, Middlesex, UKK. Peach, T. Yokoi, JAI, Oxford, UKD.Kelliher, S. Machida, STFC/RAL/ASTeC, Didcot, UKT. R.Edgecock, STFC/RAL/PPD, Didcot, UKAbstractThe  PAMELA  project  to  design an  accelerator  forhadron therapy using non-scaling Fixed Field AlternatingGradient  (NS-FFAG)  magnets  requires  a  transport  lineand gantry to take the beam to the patient. The NS-FFAGprinciple offers the possibility of a gantry much smaller,lighter  and cheaper than conventional  designs,  with theadded  ability  to  accept  a  wide  range  of  fast  changingenergies.  This  paper  will  build  on  previous  work  toinvestigate a transport line which could be used for thePAMELA project. The design is presented along with astudy and optimisation of its acceptance. INTRODUCTIONThe  PAMELA  (Particle  Accelerator  for  MEdicaLApplications)  project  [1]  aims  to  design  a  ChargedParticle  Therapy  machine  that  will  be  compact  andaffordable  enough to be used in hospitals to treat someforms of cancer. In order to treat patients, the beam must be transportedto the treatment room without distortion. Figure 1 shows apossible lay-out of such a transport line. Using double 45°bends rather than a single bend into the treatment roomhelps to remove dispersion caused by bending the beam. Figure1: Proposed layout of the transport line.Like the main PAMELA accelerator, the transport linemust accept a large range of energies and cope with veryfast switching between them.  The optics of  FFAG typemagnets offer this possibility, so this paper will build onexisting work on FFAG transport lines [2] and look intothe possibility of using one for the PAMELA project.FFAG magnets can have highly non-linear fields, so theacceptance  must  be  tested  very  carefully  to make surebeam blow-up is kept in check. This paper will describe atest  of  the  acceptance  of  a  simple  transport  line,  thenoptimise its acceptance by altering the field index 'k'  Eq.(3) and the ratio of the focusing magnet strength to thedefocusing magnet strength (FD ratio).ACCEPTANCE DEFINITIONThe  definition  of  acceptance  that  has  been  chosenmakes use of the 'smear'. This is defined as:smear  iav 2av                (1)Where: i Y 'i2	2YiY 'i	Yi2         (2)Y and Y' are the horizontal phase space coordinates andare  measured  from  the  closed  orbit  in  this  equation.Vertical  phase  space (Z,  Z')  smear is calculated in thesame way.Figure 2: Phase space ellipses with smears of (fromcentre) 0.1, 0.25, 0.5 and 1. The acceptance is defined as the initial emittance givento particles which results in a smear of 0.1 after passing______________________________________________*Work supported by STFC CASE studentship PPA/S/C/2006/4528 PamelaTreatment rooms45° bends~10mProceedings of PAC09, Vancouver, BC, Canada TH6PFP022Beam Dynamics and Electromagnetic FieldsD01 - Beam Optics - Lattices, Correction Schemes, Transport 3741through the lattice being studied. So the average deviationfrom  the  average  particle  emittance  is  10%  when  theparticles reach the end. The initial emittance is equal inboth planes and the acceptance is found when the smearreaches the limit in either plane.Figures 2 and 3 give an illustration of why a smear limitof 0.1 was chosen. In figure 2 phase space ellipses withsmears of 0.25 upwards show noticeable distortion, so asignificant change to the properties to the beam over thefull range of the transport line is likely to occur; whereasthe ellipse with a 0.1 smear is much less effected. The 10 (mm  mrad)  emittance  shown  in  figure  3  appears  onlyslightly affected through a lattice with an acceptance of54  (mm mrad) and has a smear of just 0.004. Figure 3: A 10  (mm mrad) emittance in a lattice with a54  (mm mrad) acceptance defined using a smear of 0.1. LATTICE DESCRIPTIONThe FFAGs used in this study is described in [2]. Theyobey the scaling law:BzBz0  y0	yy0k                        (3)Where y0  is the radius of curvature of the magnet, y isthe horizontal distance from it, Bz0  is the vertical field aty0 and Bz is the vertical field at y. k is the field indexwhich controls how quickly Bz rises with y.To transport the beam in a straight line, y0 was set verylarge (1km) compared to the cell length (1.6m). Howeverto create  similar behaviour as a beam with a y0 of 1m, thefield index, k, is increased by the same proportion, so a kof 5 becomes k = 5000. For convenience this paper willrefer to k/y0  simply as k. Each  cell  consists  of  equal  length  focusing  anddefocusing magnets in an FDDF configuration with theBz0 of F = 2.0T and D = -3.0T. k= 5. ACCEPTANCE CALCULATIONIt was decided to test a transport line with a length of9.6m because this is close to the proposed length of thestraight  sections  (figure  1)  and exactly the  length of  6cells.  The transport considered will be straight as this isthe simplest case.The  energy  range  of  this  study  is  taken  from  theplanned  extraction  energy  of  PAMELA:  protons  from60MeV  to  240MeV  and  carbon  from  110MeV/u  to450MeV/u  [1].  This  study  will  consider  protons  withmomentum ranging from 0.25GeV/c to 0.75GeV/c. Laterstudies will consider carbon.Closed orbits were found for the highest, lowest and anintermediate  momentum  by  finding  the  centre  of  thephase  space  ellipse  drawn  by a  single  particle  movingthrough a single cell multiple times.The Twiss functions required for Eq. (2) were found bycalculating  the  transfer  matrices  at  the  required  pointsusing a modified version of the Zgoubi [3] tracking code. Groups  of  particles  were  then  tracked  through  thelattice with larger  and larger  initial emittances until  thesmear exceeded the 0.1 limit. The acceptance was foundby approaching the limit in smaller and smaller emittancesteps until the smear = 0.1 to an adequate precision.There  was  little  variation  of  acceptance  withmomentum, but a large variation with tune, so a range ofk and FD ratios with a fixed momentum of 0.5GeV/c waschosen.  An initial working point  study indicated that  kshould range from 5 to 10 and FD ratio from 1.3 to 1.8.The FD ratio was changed by holding the F strength andaltering the D. RESULTSAs is shown in figures 4 and 5, the optimal k seems tobe 4.75 and the FD ratio 1.4. This is close to the initialworking point, however the acceptance is increased by anorder of magnitude. Figure 4: Acceptance/  (mm mrad) in numbers and dotsproportional to the square root.This dramatic variation in acceptance could be due tothe  resonance structure of the cell,  however,  the  pointsfrom figure 5 were mapped onto the tune diagram (figureTH6PFP022 Proceedings of PAC09, Vancouver, BC, Canada3742Beam Dynamics and Electromagnetic FieldsD01 - Beam Optics - Lattices, Correction Schemes, Transport6)  and  it  is  not  obvious  that  this  is  the  case.  Furtherstudies will test the resonance structure more fully in thisand longer transport lines. Figure 5: Acceptance/  (mm mrad) zoomed in aroundlikely working point.Figure 6: Tune diagram showing the square root of theacceptance in dot size. The diagonal resonance lines are:(from left) qy-qz=0,  3qy-2qz=0 and 2qy-qz=0.Optimal ConfigurationThe  closed  orbits  and   functions  were  found  for  theoptimal configuration (figures 7, 8) and a 10  (mm mrad)ellipse  was  tracked  at  each  momentum  to  check  thedistortion (figure 9). Figure 7: Closed orbits for the three different momenta(GeV/c) in one cell of the optimised lattice.Figure 8:  functions for the optimised lattice.Figure 9: The initial and final states of 10  (mm mrad) ellipses in the centre of ellipses corresponding to the 828(mm mrad) acceptance.CONCLUSIONSA transport line with an acceptance far in excess of theexpected PAMELA beam has been designed and there aremany other working points with an adequate acceptance.Further studies will track through a much longer transportline, look at the resonance structure and investigate how tointroduce  45°  bends  without  creating  additionaldispersion. The field profile Eq. (3) will also be relaxed tomake a transport line with NS-FFAG magnets similar tothose used in the PAMELA ring.REFERENCES[1] K. Peach et. al.,   “PAMELA Overview: Design Goals andPrinciples”, This conference, TH4GAC03.[2] S. Machida, "Beam transport  line with scaling fixed field  alternating gradient type magnets", submitted to Phys. Rev. ST Accel. Beams.[3] F. Meot, Nucl. Instr. Meth. A, 427, p. 353 (1999).Proceedings of PAC09, Vancouver, BC, Canada TH6PFP022Beam Dynamics and Electromagnetic FieldsD01 - Beam Optics - Lattices, Correction Schemes, Transport 3743

An FFAG Transport Line for the PAMELA Project

An FFAG Transport Line for the PAMELA Project

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