Orbit Error Correction on the High Energy Beam Transport Line at the KHIMA Accelerator System
OOrbit Error Correction on the High Energy Beam Transport Line at the KHIMAAccelerator System
Chawon Park, ∗ Heejoong Yim, Garam Hahn, and Dong Hyun An † Division of Heavy Ion Accelerator, Korea Institute of Radiological & Medical Sciences, Seoul 139-706
For the purpose of treatment of various cancer and medical research, the synchrotron based medical machine under the KoreaHeavy Ion Medical Accelerator (KHIMA) project have been conducted and is going to treat the patient at the beginning of2018. The KHIMA synchrotron is designed to accelerate and extract the carbon ion (proton) beam with various energy range,110 up to 430 MeV/u (60 up to 230 MeV). A lattice design and beam optics studies for the High Energy Beam Transport(HEBT) line at the KHIMA accelerator system have been carried out with WinAgile and the MAD-X codes. Because themagnetic field errors and the mis-alignments introduce to the deviations from the design parameters, these error sources shouldbe treated explicitly and the sensitivity of the machine’s lattice to different individual error sources is considered. Varioustypes of errors which are static and dynamic one have been taken into account and have been consequentially corrected witha dedicated correction algorithm by using the MAD-X program. As a result, the tolerances for the diverse error contributionshave been specified for the dedicated lattice components in the whole HEBT lines.
PACS numbers: 29.27.Bd, 29.27.FhKeywords: KIRAMS, KHIMA, HEBT, orbit, error, correction
I. INTRODUCTION
The Korea Heavy Ion Medical Accelerator (KHIMA)project at the Korean Institute of Radiological And Med-ical Sciences (KIRAMS) has carried out the developmentof an accelerator based on synchrotron with multi-ionsources for various cancer treatement. The designed syn-chrotron accelerates the proton beam (the carbon ion, C , beam) from 60 MeV (110 MeV/ u ) to 230 MeV(430 MeV/ u ). Those energy ranges correspond to thepenetration depth of 3.0 cm to 31.0 cm in water. Aschematic layout of the accelerator center is shown inFig. 1. At the Electron Cyclotron Resounce Ion Source FIG. 1: (Color online) Schematic layout of KHIMA syn-chrotron system including each treatment and research rooms. (ECRIS), ions with a charge to mass ratio q/m = 1/3, ei-ther H +3 or C , are generated up to 8.0 keV/ u . Theseions are accelerated up to 7 MeV/ u through Radio Fre-quency Quadrupole (RFQ) linac and Interdigital H-mode ∗ E-mail: [email protected] † E-mail: [email protected]
Drift Tube Linac (IH-DTL). At the beginning of MediumEnergy Beam Transport (MEBT) two corresponding ionsare stripped and fully ionized to either proton or C ,then are transported to the synchrotron being acceler-ated up to designed energies. Each ion is injected intothe synchrotron through a multi-turn injection mecha-nism, accelerated by switching the RF system and thenextracted into High Energy Beam Transport (HEBT) lineby slow resonance extraction scheme [1, 2]. II. BEAM CHARACTERISTIC ON THE HEBT
In each HEBT line, the beam is defined by the medicalspecifications and thus there is a definite range of verticalTwiss functions, 2 . < β y <
27 m , α y = 0. For adjustingthe beam size in the vertical plane, the straightforwardmethod is to be used. The beam size is determined by thetraditional geometrical emittance of the beam originatedfrom synchrotron and the beta function at the iso-center.The vertical beam size is calculated as y = (cid:112) (cid:15) y × β y [3].On the other hand the peculiar distribution in the hori-zontal plane is appeared so called ’bar of charge’ in phasespace, because the extracted beam is the segment of theextraction separatrix that could be represented as the di-ameter of an unfilled ellipse. Thus by varying the phaseadvance (∆ µ x ), namely by changing the orientation ofthe charge bar and consequently its projection to the x-axis determines the horizontal beam size [3–5]. III. BEAM OPTICS SIMULATION
The design concept of KHIMA extraction, HEBT,lines is based on the Proton-Ion Medical Machine Study(PIMMS) [3]. Three medical treatment rooms and oneresearch oriented irradiation room are prepared for thecenter. The HEBT lines compose the 6 different trans-1 a r X i v : . [ phy s i c s . acc - ph ] J un ort branches with 4 horizontal- and 2 vertical-lines asshown in Fig 1. A slowly extracting beam through elec-trostatic septum (ES) in the synchrotron ring is to beselectively transported into each treatment room. An in-tegrated system is designed with telescope modules withinteger π phase advances (∆ µ ). The HEBT lines arealso based on a modular design taking into account thestrong asymmetry between two transverse beams. Thetrapezoidal distribution of the horizontal beam is con-sidered. For horizontal beam in phase space, the bar ofcharge is applied to create an independent control of thehorizontal beam size by rotating the bar in an unfilled el-lipse [6]. On the other hand, the Gaussian shaped beamdistribution is taken into account the vertical beam. A. Electrostatic Septum to Matching Section
On the base of the PIMMS report, the dispersion vec-tor at the ES is determined by appearance of the chargebar for different momenta of the particle beam. In Ta-ble I, the data for lowest extraction energy are summa-rized and the dispersion ( Dx ) and its derivative ( Dx (cid:48) )values are listed. At higher energies, the correspondingvalues are not so different and not significantly gottenout.Furthermore, the Dx and Dx (cid:48) from the synchrotronare not representative ones as for the betatron amplitudefunction. The Dx and Dx (cid:48) were calculated as listed inTable I, thus it could be utilized universally up to match-ing section. In principle any values can be selected as aninitial values at the ES, but the useful one should beselected depending on the dedicated machine. Becausethe dispersion function represents the displacement of theoff-momentum particles, it is natural to be selected as aninitial value corresponding to the distance between thecenter of gravity of the on-momentum particles and thecenter of gravity of the off-momentum ones divided bythe relative momentum difference as described and cal-culated in Table I. According to the determined values inTable I, the boundary conditions at the ES are selected.Fig. 2 shows the distribution of Twiss parameters at thematching module. B. Horizontal Beam Lines
The common module downstream matching section inthe horizontal common line (HC) is interleaved for con-trolling beam size at the iso-center. This module has animportant advantage for commissioning and operation.As described in previous section, the vertical beam size atthe iso-center is controlled by the vertical β function. Inorder to fulfil the requirements, the module can be tunedto provide the values among 2 < β y <
27 m with α y = 0.A minimum of five components are needed to control thefive Twiss variables, i.e., the horizontal, vertical β ’s andthe α ’s at the exit and the horizontal phase advance. As FIG. 2: (Color online) Betatron amplitude and dispersionfunction at the matching section for the horizontal and ver-tical plane, where half height rectangular box corresponds tothe quadrupole magnet having their polarity while the fullheight one for the dipole magnet.FIG. 3: (Color online) Betatron amplitude and the dispersionfunctions for the 3rd Horizontal (H3) line, where ∆ µ x = 6 . π and β y = 27 m at the iso-center are set. the variable component, each quadrupole magnet in thecommon line is used. At least six quadrupoles are neededto facilitate the matching and to have some redundancy.This composition of consecutive six quadrupole magnets,which functions as the phase shifter on the horizontalplane and also as the stepper on the vertical plane, isnamed simply as the stepper.As one of the horizontal lines, Fig. 3 shows the Twissfunction distributions up to 3rd treatment room throughthe horizontal H3 line.2 ABLE I: Dispersion of the extracted beam at the entry to the ES.On resonance particles Off resonace particles∆ p/p = 0 ∆ p/p = 0 . Dx (m) 0.7407Derivative of dispersion, Dx (cid:48) (m) 0.1272 IV. ERROR ANALYSIS
Because various distortion making elements in thetransport line are exist, the closed orbit control is a ba-sic constituent for the efficient performance in the beamline. A large closed orbit distortion minimizes the avail-able aperture and also affect the dynamics of the beamvia non-linear elements. Various error sources contributeto the closed orbit distortion. Most of errors are randomin nature, while others are systematic and some may betime or field dependent [7].The results have been calculated by using the accel-erator codes, which are the WinAGile [8] or the MAD-X [9, 10]. Both codes base the correction process on aleast square method. A series of test runs showed that theresults obtained from two program codes are consistentwithin their statistical uncertainty. Thus it is determinedto use the MAD-X code representatively in this analysis.One of the simulations is performed with a statistics for1000 randomly generated machines in the vertical trans-port line (V2).
A. Requirements for Closed Orbit Correction
The basic guidelines for the closed orbit correction forthe HEBT in the KHIMA accelerator are that the globalclosed orbit correction must be within 7.5 mm for bothhorizontal and vertical planes. For error analysis in thestudy, only the static errors are described, while the dy-namic errors originated from the stability of magnets aresmall enough to be ignored compared to static ones.
B. Alignment and Field Tolerances
The impact of each error source, so called sensitivitystudy, was evaluated using the MAD-X simulation code.The accepted tolerances for various errors resulting in anorbit distortion are listed in Table II. The dipole fielderror is originated from the packing factor tolerance and the its length error. The correctors and position monitorsare considered to be affected by several errors. The po-sition monitors also include both alignment and readingerrors. Alignment- and field-errors are applied to all theelements according to Gaussian distribution by cutting3 standard deviations, while the monitor reading errorsare given with a uniform distribution as described in Ta-ble II.
C. Monitor and Corrector System
The monitor system is correlated with the dual cor-rector which is the steering activated as a pair in thehorizontal and vertical plane. The precision and reliabil-ity of the measurement system are extremely important,because they determine the quality of the corrector to-gether with the precision of the corrector and their max-imum magnetic strength. The layout through V2 line foroptimizing the orbit correction is shown in Fig. 4.
FIG. 4: (Color online) Beam line layout through V2 with thebeam position monitor and corrector.
D. Closed Orbit Estimation and Correction
The orbits have been calculated with MAD-X code onthe HEBT line through V2. The mechanism of the trans-formation is provided by the technique of singular valuedecomposition (SVD) [11] of matrices. For testing whatvarious sources of errors have a sensitivity, the execursedquantity with respect to the sequential beam line is eval-uated before and after correction as shown in Fig. 5. In3
ABLE II: Accepted tolearances for the magnet elements and position monitors.Error type Tolerance DistributionQaudrupole alignment (x, y, z) 0.3 mm Truncated GaussianQaudrupole tilt 0.3 mrad Truncated GaussianDipole alignment (x, y, z) 0.3 mm Truncated GaussianDipole tilt 0.3 mrad Truncated GaussianIntegrated dipole field error (∆
BL/BL ) 0.001 Truncated GaussianIntegrated quadrupole field error 0.001 Truncated GaussianMonitor reading error ± . the beginning, the total number of monitors used is 15,while 9 for correctors. One thousand of machines with FIG. 5: (Color online) Excursion distributions through theV2 line before and after correction. random errors have been analysed before and after thecorrection on the vertical line through V2. At iso-center,the beam position is accurate dramatically after correc-tion as shown in Fig. 6.
FIG. 6: (Color online) Excursion distributions of closed orbitat iso-center before and after correction.
The absolute maximum excursions are quoted, becausethese values are of more direct interest for the aperturethan the peak-to-peak values. The requirement of closedorbit correction was set to be within 7.5 mm for both hor-izontal and vertical planes. With a standard alignment
FIG. 7: (Color online) (Top) Maximum absolute excursionsof the closed orbit before and after correction in both plane.(Bottom) Zoomed distributions of the excursions after correc-tion within the global closed orbit margin, 7.5 mm, in hori-zontal and vertical planes respectively. technique, a 100.0 % of the machines after correction inhorizontal plane and a 99.7 % in the vertical plane couldbe within the allowed global closed orbit margin, 7.5 mm,as shown in Fig. 7. After correction, thus almost all themachines could be well within the stricter tolerances forthe line. Fig. 8 shows the maximum absolute kick anglefor both horizontal and vertical planes at highest carbonbeam energy ( E = 430 MeV/u). As a result, the maxi-mum required kick angle is foreseen to have the value lessthan 3.5 mrad in both plane. An average steering powerfor the orbit correction of all static errors can be esti-mated as one root mean square (rms) and is less than 0.5mrad. Accordingly the specification of correcting magnetis set to 5 mrad including margin as shown in Table III.In order to optimize the alignment of corrector andbeam position monitor, various combinations of correctorand monitor are disposed with respect to the number ofmonitor as shown in Fig. 9. The optimized number ofmonitor in the beam line is determined to use 9 monitors.4
IG. 8: (Color online) Maximum absolute steering angle forthe horizontal and vertical planes at highest carbon beamenergy, E = 430 MeV/u.FIG. 9: (Color online) Ratio of the machines within tolerancewith respect to the number of beam position monitor in theV2 line.
V. CONCLUSION
The extracted transfer lines are based on the modulardesign taking into account the strong asymmetry betweentwo transverse emittances and depend on the trapezoidaldistribution of the beam in horizontal phase space. TheKHIMA HEBT line has been fundamentally designed byusing the WinAgile/Mad-X code for the whole beam linesup to each treatment room. Based on the error analy-sis for every single line, the optimized correction setupis settled and the specifications for the correcting mag-nets of the HEBT lines are determined. A specificationof corrector must fulfil the requirement for highest car-bon beam energy, 430 MeV/u. Table III summarizes thespecification of corrector used in the HEBT beam lines.
TABLE III: Specification for the correcting magnet of theHEBT line.Parameters Values UnitMaximum rigidity (B ρ ) 6.62 TmMax. deflection angle ( θ ) 5 mradEffective length ( L eff ) 0.3 mMax. magnetic field 0.11 T( B = θ/L eff × B ρ )∆BL/BL < × − Field stability 500 ppmNo. of corrector 23 ea.
Acknowledgments
This work was supported by the National Researchand Development Program through the Korea Insti-tute of Radiological and Medical Sciences funded bythe Ministry of Science, ICT & Future Planning (NRF-2015M2C3A1001637). [1] Heejoong Yim et al. , J. Korean Phys. Soc. ,1364(2015).[2] M. Benedikt et al. , Nucl. Instrum. Methods Phys. Res.A , 523 (1999).[3] P. J. Bryant et al. , Proton Ion Medical Machine Study(PIMMS) Part 1 and 2, CERN/PS 1999-01-DI (1999)and CERN/PS 2000-007- DR, Geneva (2000).[4] M. Benedikt and A. Wrulich, “MedAdustron-Projectoverview and status”, Eur. Phys. J. Plus (2011).[5] S. Rossi et al. , “The Status of CNAO”, Eur. Phys. J.Plus (2011).[6] M. Benedikt, “Optics design of the extraction lines forthe MedAustron hadron therapy centre”, Nucl. Instrum.Methods A 539 (2004). [7] L. Badano et al. (2003).[10] W. Herr, “Implemenation of new closed orbit correctionprocedures in the MAD-X program”, CERN/SL 2002-48(2002).[11] K. Baker, Singular Value Decomposition Tutorial, March29, (2005).(2003).[10] W. Herr, “Implemenation of new closed orbit correctionprocedures in the MAD-X program”, CERN/SL 2002-48(2002).[11] K. Baker, Singular Value Decomposition Tutorial, March29, (2005).