Kelliher DJ

Machida S

Peach K

Sheehy SL

Witte H

Yokoi T

English

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PAMELA: LATTICE SOLUTION FOR A MEDICAL C6+ THERAPYFACILITY∗S.L. Sheehy† , K. Peach, H. Witte, T. Yokoi, JAI, Oxford, UKD. J. Kelliher, S. Machida, STFC/RAL/ASTeC, UKAbstractPAMELA (Particle Accelerator for MEdicaL Applica-tions) employs novel non-scaling Fixed Field AlternatingGradient (ns-FFAG) technology in the development of aproton and C6+ particle therapy facility. One of the chal-lenges of this design is the acceleration of high energy C6+in a lattice which enables high flexibility and reliability fortreatments, yet remains minimal in size and complexity.Discussed here is the carbon 6+ lattice solution in termsof both design and performance.INTRODUCTIONThe aim of the PAMELA project is to design a ChargedParticle Therapy (CPT) facility using the features of ns-FFAG technology to improve performance over existingfacilities [1, 2]. A unique feature of the ns-FFAG is theability to provide variable energy beams at repetition ratesof around 1 kHz. In a treatment scenario, the fast beamscanning can be optimised depending on the target volumenot only in the usual transverse plane, but also longitudi-nally. It is this added flexibility which can only be realisedwith an FFAG accelerator.Clinical considerations require that a proton/carbon CPTfacility provides protons from 70 to 250 MeV and Carbon(C6+) from 68 to 400 MeV/u. To achieve this, two acceler-ating rings are required. The first will accelerate protons to250 MeV and carbon ions to 68 MeV/u and the second willaccelerate carbon to 400 MeV/u. The design of the secondring is particularly challenging due to the high rigidity ofthe ions - a factor of more than 2.5 higher than that of fulltreatment-energy protons, as seen in Table 1. The design ofthe second ring is discussed in this paper.In addition to providing variable energy beams with ahigh repetition rate, the lattice design for PAMELA is re-quired to minimise the overall footprint of the acceleratorwhile ensuring that sufficient drift space is available for RFcavities, injection and extraction systems, corrector mag-nets and diagnostics [3]. Another important requirement isfor the total betatron tune variation throughout accelerationto be minimised to within half an integer. This avoids dete-rioration due to resonance crossing, which has been shownto be a problem for proton/ion non-scaling FFAGs [4, 5, 6].∗Supported by EPSRC grant EP/E032869/1† s.sheehy1@physics.ox.ac.ukLATTICE DESIGNDesign StrategyThe design strategies for both PAMELA rings start witha scaling FFAG with a FDF triplet focusing structure, withthe field index k resulting in a horizontal phase advance ofgreater than 180◦ per cell, which is possible in the secondstable region of Hills equation. A number of changes andsimplifications are then made to the lattice. The magneticfield which starts out following Eqn. 1 is approximated by apolynomial fit, the order of which corresponds to magneticmultipoles up to the order of octupole, decapole or dode-capole. The effect of the differing order of polynomial fitis discussed in the optimisation section. The magnets aremade rectangular rather than sector or wedge shaped andaligned parallel to one another along a straight line. Thismakes magnet construction simpler and will improve thealignment accuracy in practise. Each of these simplifica-tions violate the original scaling law, making this accelera-tor a non-scaling FFAG. Details of each simplification andits effect on lattice dynamics for the smaller proton ring canbe found in Ref. [7].Bz = B0( rr0)k(1)Selection of Baseline LatticeA number of parameters can be adjusted to achieve a re-alistic lattice design, including the ring radius, field indexk, lattice packing factor - defined as the ratio of triplet celllength over the circumference - and number of cells. It isimportant to understand the effect that changing each ofthese parameters has on the peak magnetic field, orbit ex-cursion - and therefore magnet bore size - and the length oflong straight sections.A scan of these parameters and their effects was under-taken making the following assumptions:• The field described by the polynomial fit in the latticemagnets is close to the scaling law and the particlesfollow an approximately circular trajectory when in-side the magnets.• Given that the magnets are in an FDF configurationwhere the D provides reverse bending, if the F and Dstrengths are approximately equal it can be assumedthat each F magnet needs to provide the total bendingof, for example, 30◦ in a 12-cell lattice. This results ina total bend of 30◦ from the combination of the threeProceedings of IPAC’10, Kyoto, Japan MOPEA02204 Hadron AcceleratorsA12 FFAG, Cyclotrons 115Table 1: Particle Kinetic Energies and Magnetic Rigidities for 2 Ring ComplexParticle H+Ring 1 inj 1 ref 1 extrKin. En./u [MeV] 30.95 118.38 250Bρ [Tm] 0.811 1.621 2.432Particle C6+Ring 1 inj 1 ref 1 extr/2 inj 2 ref 2 extrKin. En./u [MeV] 7.84 31.0 68.36 208.75 400Bρ [Tm] 0.811 1.621 2.432 4.401 6.370magnets in the FDF triplet. This gives an indication ofthe peak field required.Making these assumptions allows the use of basic ge-ometric equations to describe the changing of parametersin this type of lattice. The number of lattice cells does notgreatly affect the required maximum bending field strength,however factors such as the ring radius and lattice packingfactor have a much greater impact, as expected. The maincontribution to the total magnetic bore size requirement isdetermined by the field index, k. As a result of this, it ispossible to solve for feasible configurations of the latticedesign. The possible configurations are shown in Fig. 1 forvarying machine radius and lattice packing factor, assum-ing straight sections > 1.2 m with a peak magnetic field <4.0 T and a magnetic bore less than 0.35m. The parametersof the chosen baseline lattice are given in Table 2.8.0 8.5 9.0 9.5 10.00.500.550.600.650.70Radius mPackingfactorFigure 1: Possible configurations of carbon lattice obtainedby varying radius and packing factor.OptimisationThe optimisation procedure begins by calculating the po-sitions of particle orbits throughout acceleration in a per-fectly scaling version of the FFAG. The non-scaling versionthen takes the middle point of the orbit excursion withineach magnet as the central point of the polynomial fit, inorder to achieve the best possible fit of the multipole coeffi-cients to Eqn. 1 in the region of magnetic field that the beamTable 2: Lattice Parameters of the Baseline Lattice (alllengths are quoted in metres)Parameter ValueRadius 9.3Lattice packing factor 0.65Circumference 58.4Approx. k value 42Long straight 1.1979Short straight 0.1266Magnet length 1.1395Orbit shift 0.217Bore size ≈0.35experiences. Outside the region that the beam traverses, themagnetic field is allowed to be different to Eqn. 1. In carte-sian co-ordinates the expansion of the field takes the formof Eqn. 2, where x0 is used instead of r0 of Eqn. 1, thedistance from the centre of the machine to the centre of themagnet.BzBz,0= 1 +∑n=11n!k(k − 1) · · · (k − n+ 1)xn0xn (2)PERFORMANCEOrbit ExcursionThe total orbit excursion throughout acceleration isshown in Fig. 2. The total change in orbit position betweenthe lowest and highest energy orbits is 0.217 m for the en-ergy range required. A larger energy range is achievablewith the same lattice design, for example an energy rangeof 50 to 430 MeV/u is possible with a total orbit excursionof 0.237 m. The final choice of energy range will dependon magnet and RF designs, as the aperture of these compo-nents will determine the allowed orbit excursion.Tune VariationThe variation of the betatron cell tunes throughout ac-celeration are shown in Fig. 3 for varying orders of poly-nomial fit to Eqn. 1, corresponding to different orders ofmultipole. The total machine tune variation for each caseMOPEA022 Proceedings of IPAC’10, Kyoto, Japan11604 Hadron AcceleratorsA12 FFAG, CyclotronsKin. Energy [MeV/u]Horizontalposition[cm]Figure 2: Variation of orbit position in the horizontal direc-tion during acceleration.is given in Table 3. In each case, including the simplestcase of multipoles only up to the octupole, the tune varia-tion is less than half an integer, the upper limit imposed bythe lattice requirements to avoid resonance crossing. Theoperating point can be shifted to completely avoid the half-integer resonance currently crossed at high momentum inthe octupole case.HorizontalcelltuneKin. Energy [MeV/u].....VerticalcelltuneOctupoleDecapoleDodecapoleFigure 3: Variation of horizontal cell tune (upper) and verti-cal cell tune (lower) for different orders of multipoles. Dot-ted lines correspond to integer and half integer resonancesof the total machine tune.Table 3: Total machine tune variation for different ordersof polynomial fit to the scaling law.ΔQx ΔQyOctupole 0.4056 0.3574Decapole 0.1297 0.1165Dodecapole 0.1727 0.0805Dynamic ApertureThe dynamic aperture is determined at the injection en-ergy (68.36 MeV/u) for a range of horizontal and verticaltunes, determined by changing the k value and ratio be-tween the F and D strengths. The lattice does not have anyalignment errors, and the case of polynomial fit up to de-capole is used. Single particles are tracked over 1000 turns,starting with the same normalised amplitude in both hori-zontal and vertical planes. The amplitude is then increaseduntil the particle is lost, and the dynamic aperture plottednext to each point in Fig. 4 is the highest amplitude surviv-ing particle in units of π mm mrad.Horizontal cell tuneVerticalcelltune62.061.067.080.083.088.0Figure 4: Calculated dynamic aperture at injection energyfor varying horizontal and vertical tunes, dynamic aper-tures are listed next to each point in π mm mrad (nor-malised).CONCLUSIONSA non-scaling FFAG lattice has been designed whichmeets the requirements for accelerating carbon 6+ ions forparticle therapy, with variable energy extraction at a repeti-tion rate of up to 1 kHz. The achievable repetition rate maybe limited by the RF and extraction kicker requirements,but it is expected that a repetition rate of at least 200 Hzis achievable, which is far in excess of any present system.The betatron tunes are very well constrained to within halfan integer in order to avoid the crossing of resonances. Thedesign has sufficient dynamic aperture for this application.REFERENCES[1] K. Peach et al., in Proceedings of PAC ‘07, p. 2880 (2007).[2] R. Barlow et al., in Proceedings of PAC ‘07, p. 2886 (2007).[3] K. Peach et al., in Proceedings of PAC ‘09 (2009).[4] S. Machida, Phys. Rev. ST Accel. Beams 11, 094003 (2008).[5] T. Yokoi, J. Cobb, K. Peach, and S. L. Sheehy, in Proceedingsof EPAC ‘08, p. 3398 (2008).[6] S. L. Sheehy, D. J. Kelliher, in preparation for Proceedings ofFFAG ‘09, Int. J. Mod. Phys. A (2010).[7] S. L. Sheehy, K. Peach, H. Witte, D. J. Kelliher, S. Machida,Phys. Rev. ST Accel. Beams 13, 040101 (2010).Proceedings of IPAC’10, Kyoto, Japan MOPEA02204 Hadron AcceleratorsA12 FFAG, Cyclotrons 117

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PAMELA : lattice solution for a medical C6+ therapy facility

PAMELA : lattice solution for a medical C6+ therapy facility

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