A design study of the main magnet for a 13 MeV cyclotron has been carried out in a joint collaboration between the Korea Cancer Center Hospital (KCCH) and POSTECH. A maximum energy of 13 MeV has been chosen to produce radioisotopes such as /sup 18/F. There are four magnet sectors, each with radial-ridged shape. Maximum magnetic fields are 1.85 T and 0.48 T at hill and valley centers, respectively. The total size of the cyclotron is less than 2 m in diameter. The program TOSCA has been utilized for the field calculation and optimization. In this paper, we describe design parameters of the 13 MeV PET cyclotron, with emphasis on the magnetic field shape and the beam optics calculation. (3 refs)

Chai, J S

Ha, J H

Oh, S

Yang, W Y

Yoon, M

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MAGNETIC FIELD CALCULATION FOR A 13 MEV PET CYCLOTRONW.Y. Yang, M. Yoon , S. Oh, Dept. of Physics, POSTECH, Korea,J.S.Chai, J.H. Ha, KCCH, KoreaAbstractA design study of the main magnet for a 13 MeV cyclotronhas been carried out in a joint collaboration between theKorea Cancer Center Hospital(KCCH) and POSTECH. Amaximum energy of 13 MeV has been chosen to produceradio-isotopes such as 18F. There are four magnet sectors,each with radial-ridged shape. Maximum magnetic fieldsare 1.85T and 0.48T at hill and valley centers, respectively.The total size of the cyclotron is less than 2 m in diameter.The program TOSCA has been utilized for the field calcu-lation and optimization. In this paper, we describe designparameters of the 13 MeV PET cyclotron, with emphasis onthe magnetic field shape and the beam optics calculation.1 INTRODUCTIONAt the Korea Cancer Center Hospital (KCCH), design studyof a 13 MeV cyclotron for Positron Emission Tomography(PET) has been in progress since 1997. The study hasbeen carried out in a joint collaboration between KCCHand the Pohang University of Science and Technology(POSTECH).The KCCH has played a leading role in Korea in radiationmedicine as well as in the treatment and research of cancer,since it was established as the Radiological Research Insti-tute in 1963 to promote the medical application of atomicenergy in Korea. For neutron therapy and radiation treat-ment, a 50 MeV medical cyclotron, built by Scanditronix,was installed at the hospital in 1986. The cyclotron has pro-vided an in-house source of radio-isotopes such as 201Tl,123I, 67Ga, etc, and in particular, the shorter-lived radio-isotopes for diagnostic or clinical use. In addition to servingin-house duties, this cyclotron has also produced and sup-plied 15% of all cyclotron based radio-isotopes in Korea.This service has greatly contributed towards awareness ofthe potential benefits of nuclear medicine afforded by parti-cle accelerators and evoked calls for similar services in otherhospitals in Korea. So far only two hospitals have installeddedicated cyclotrons for PET (Positron Emission Tomog-raphy) applications, where the isotopes of interest are thefour clinically significant positron emitters 15O, 13N, 11C,and 18F in particular.At the KCCH, increasing desire for an uninterrupted, re-liable and timely supply of the isotopes to customers hasprompted obtaining a dedicated 5-13 MeV cyclotron forPET applications and pursuing the purchase of another 30MeV medical cyclotron in the very near future. A decisionhas been made to design the PET cyclotron in Korea. ThisThis work is supported by Ministry of Science and Technology ofKorean governmentEmail: moohyun@postech.ac.krwill not only ease the problems associated with maintenanceduring operation but also keeps the door open for contin-uous upgrading of the machine in the future. The projectis supported by the Ministry of Science and Technology(MOST) of the government, as a part of the 2nd phase ofthe mid- and long-term nuclear energy research plan. Thecyclotron construction project was officially started in April1999 and is to be completed in three years.In this paper, we introduce the major parameters of this13 MeV PET cyclotron with particular emphasis on themagnetic field design and the equilibrium orbit calculation.2 PARAMETERSTable I shows major design parameters for the 13 MeVPET cyclotron. Maximum beam energy was chosen to be13 MeV which is above the threshold energy for 18F pro-duction. A four-sector magnet structure is employed withradial-ridged shape. Hill angle is chosen to be 46 degree, butthe effective hill angle seen by the beam increases slightlyin radius because the vertex of the hill is not at the center ofthe cyclotron, as will be described later. For ion source, in-ternal PIG source will be used. Though this will deterioratethe vacuum in the central region, it is more economical andsimpler than adopting an external ion source. In order toprovide an efficient vacuum conducting path in the centralregion of the cyclotron, there are four holes in the valleyregion.Negatively charged hydrogen ions will be used for accel-eration because extraction is much easier than for positivelycharged ions. Accelerating negative ions has also an advan-tage in that the maximum extracted energy can be variedeasily by simply repositioning the stripping foil.Magnetic fields at 13 MeV are 1.85 T and 0.48 T at thehill and valley centers, respectively. Maximum averagemagnetic field is about 1.2 T. Harmonic number is four, andtherefore the radio frequency is about 72 MHz. Dee voltageis 40 kV. The energy gain per turn is given byE = 4qVdeesinhdee2; (1)where Vdeeis the dee voltage, h is the harmonic number anddeeis the dee angle. With Vdee=40 kV, h=4, dee=43.6,the energy gain per turn is E=159 kV. The total numberof turns to reach 13 MeV is therefore approximately 82.0-7803-5573-3/99/$10.00@1999 IEEE. 2265Proceedings of the 1999 Particle Accelerator Conference, New York, 1999Table I : Main parameters of the 13 MeV PET cyclotronParameter Unit ValueMaximum energy MeV 13Beam species NegativehydrogenNumber of sectors 4Ion source Internalnegative PIGHill angle degrees 46.0Valley angle degrees 44.0Maximum averagemagnetic field T 1.2Harmonic number 4Radio-frequency MHz 72Maximum average radiusof a beam cm 43Maximum orbit distancefrom the cyclotron center cm 45Maximum magnetic fieldat the hill center T 1.85Maximum magnetic fieldat the valley center T 0.48Beam current A 203 MAGNET SYSTEMIn the initial stage of the cyclotron design, major cyclotronparameters have been calculated by employing a simplefirst-order theory [1, 2] in beam optics, from which orbitradius, average magnetic field, fields at the hill and valley,focusing frequencies are determined as a function of beamenergy. Fig. 1 shows the side view of the 13 MeV cyclotron.It shows that the height is approximately 93 cm and thediameter is 187 cm. For magnetic field calculation in theFigure 1: Side view of the 13 MeV cyclotronyoke and valley region, a two-dimensional program suchas POISSON [3] has been utilized. Fig. 2 shows the two-dimensional plot of the magnetic field line in the yoke andvalley region, which is obtained with the help of POISSONprogram. Total current per each coil is 44,000 ampere-turnsand the current density is about 3 A/mm2.Figure 2: Magnetic field lines computed by POISSONThe OPERA-3D program was used to calculate the three-dimensional magnetic field. Fig. 3 shows the geometry ofthe cyclotron modeled by the OPERA-3D program. Thisfigure shows four holes at the valley center. Presence ofthese holes distorts the field greatly. A step by step opti-mization of the magnet geometry is thus needed.Figure 3: Cyclotron geometry modeled by OPERA-3DIn order to maintain the isochronous field, we have em-2266Proceedings of the 1999 Particle Accelerator Conference, New York, 1999ployed a variable vertical gap along the radius in the hill re-gion, rather than using conventional trim coils. This makesthe cyclotron operation much simpler, avoiding compli-cated optimization procedure with trim coils. Simplicityin operation is very important for hospital-based cyclotronwhere resources for technical support are limited. Whenthe vertical hill gap decreases in steps along the radius, theaverage magnetic field seen by an accelerating beam is in-creased in radius. We have been able to obtain a reasonableisochronism by adjusting the hill gaps. Difference in gapheight at the minimum and maximum radius is about 6 mm.Fig. 4 shows the average magnetic field as a function ofaverage beam radius. In this figure the average magneticfields are the averaged fields along the equilibrium orbits.For given magnetic fields, equilibrium orbits are found bysolving linearized equations of motion whose details willnot be described here.0 10 20 30 40 5011.011.512.012.513.0  Average field (kG)Average radius (cm)Figure 4: Average magnetic field for the 13 MeV cyclotron as afunction of radiusFig. 5 shows the frequency error due to the magneticfield given in Fig. 4. The vertical axis of this figure in-dicates !0=!   1, where !0is a fixed frequency which isbasically the radio frequency and! is the angular revolutionfrequency of a particle. From this figure, one can obtain thephase error of the particle usingsin(E) = sini+2hqVZ(!0!  1)dE; (2)where the integral extends from the initial energy Eiwhere = ito the given energy E. With the above equationapplied to Fig. 5, we obtain the total phase excursion iswithin 15.Horizontal and vertical focusing frequencies (rand z)are also obtained from the equilibrium orbit calculation.Fig. 6 describes the excursion of rand zfrom injection toextraction radius. The lines in this figure represent 2y= 1,x= 3y, x= 1, 3x+ y= 4, 3x= 4, 3x  y=  4resonances. Therefore these are the structure(or perfect)resonances arising from the 4-fold symmetry of the magnet.It is seen that focusing frequencies are sufficiently awayfrom the resonances.5 10 15 20 25 30 35 40 45-0.10-0.050.000.050.10  Frrequency error Average radius (cm)Figure 5: Frequency error as a function of radius for the 13 MeVcyclotronFigure 6: Tune diagram for the 13 MeV cyclotron4 SUMMARYIn Korea, design studies for a 13 MeV PET cyclotron havebeen in progress. Currently, design of main magnets andthe rf system are being carried out. When completed in2002, this cyclotron will serve to produce short-lived radio-isotopes like 18F.5 REFERENCES[1] M. Yoon, J.S.Chai, J.W.Kim, W.Y.Yang and S.Oh, Pro-ceedings of the International Cyclotron Conference, Caen,France,1998[2] S. Oh, W.Y. Yang, M. Yoon, J.S.Chai, J.H. Ha, J.W. Kim,Proceedings of the European Particle Accelerator Conference,Stockholm, Sweden, 1998[3] User’s Guide for the POISSON/SUPERFISH Group of Codes,LA-UR-87-115, Los Alamos Accelerator Code Group2267Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

Magnetic field calculation for a 13 MeV PET cyclotron

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