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Magnetic field control and orbit studies for H− acceleration in a 65 MeV cyclotron
Nuclear Instruments and Methods in Physics Research A285 (1989) 395-402 North-Holland, Amsterdam
395
MAGNETIC FIELD CONTROL AND ORBIT STUDIES FOR H - ACCELERATION IN A 65 MeV CYCLOTRON
P. MANDRILLON Laboratoire du Cyclotron, Centre Antoine Lacassagne, 36 Voie Romaine, 06054 Nice Cedex, France
R. OSTOJIC Boris Kidric Institute of Nuclear Sciences, POB 522, 11001 Belgrado, Yugoslavia
Received 19 June 1989 The results of the mapping of the isochronous magnetic field for the Medicyc cyclotron are presented. The validity of the developed nonlinear methods for the magnetic field control is established, and certain results of detailed orbit studies for H acceleration up to 65 MeV in this machine are given. 1. Introduction As is well known to cyclotron builders, extensive magnetic field measurements are an important step in cyclotron construction . In effect, magnetic field data serve initially as the basis of the cyclotron magnet shirrtrning, a process involving magnetic field measurement and data reduction, computation of the necessary field corrections and appropriate mechanical modifications, with the final goal of accommodating the magnetic field behaviour to the desired operating range of the machine. Furthermore, any beam development work during machine operation needs to rely on the experimental field data, or on field synthesis routines that involve a reduced set of measurements . Hence, the ability to predict with high accuracy the magnetic field distribution in a cyclotron can both simplify the initial design and shorten the construction period, and contribute to the ease of operation of the machine and to the stability and quality of the accelerated beam parameters. The magnetic field of the Medicyc cyclotron [1] has been extensively mapped for the purposes of magnet shimming, as has previously been reported in detail [2]. Following these measurements, it was decided that the proton beam energy should be increased from the design goal of 60 MeV to 65 MeV, as suggested by the analysis of magnetic field data . Furthermore, several machine components (the axial injection line and the central region, and the rf and extraction systems, in particular), were redesigned or modified in accordance with a decision to accelerate an H - beam . With the machine fully assembled and ready for commissioning, a final series of magnetic field measurements, including 0168-9002/89/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
360' maps of the isochronous fields, were performed. Besides giving a full range of data on the average field, field harmonics of all orders, and the harmonic and trimming coil form factors, these measurements also served to verify the validity of our improved algorithms for magnetic field control [3]. Finally, in preparation for regular machine operation, the H - beam acceleration in experimentally determined isochronous fields was studied in considerable detail . In this report, we present several results pertaining to the magnetic field measurements, the control of the isochronous field, and the dynamics of the 65 MeV Hbeam in the Medicyc cyclotron. In particular, we draw attention to an often neglected but common source of the first Fourier harmonic of the magnetic field, establish the general validity of the magnetic field control algorithms, and determine their usefulness for orbit studies in limiting regions of the operating diagram of the cyclotron where high accuracy in synthesizing the magnetic field is needed.
2. Mapping of the magnetic field The magnetic field of the Medicyc cyclotron was extensively studied in previous measurement campaigns. The purpose of these measurements was essentially to determine the final geometry of the pole tips that minimizes the trimming coil power, and to optimize the choice of the operating rf frequency of this machine. For the sake of completeness, we recall that Medicyc is a four-sector isochronous cyclotron with a pole diameter of 160 cm and an extraction radius of 68 cm . The
396
P. Mandrdlon, R. Ostojic / Magnetic field control and orbit studies
average width and spiral angle of the pole tips are 42 .5 ° and 60'/m, respectively . The pole tips, with hill and valley gaps of 13 and 28 cm, respectively, extend to 75 cm where they loin the annular segment of the vacuum chamber . In the region from 66 to 76 cm, the angular width of the pole tips is increased by adding a pole "shoe" which is 13 ° wide . As explained in detail in ref . [21, the modifications introduced following the orbit studies based on experimental magnetic field maps, concerned the change of the exit spiral in order to slightly decrease the angular width of the pole tip, and an introduction of an axial shim 2 mm high and 40 mm wide running across the pole tip width at a radius of 71 cm . As described previously [21, the magnetic field measurement apparatus consisted of 51 thermally stabilized Hall probes mounted in 2 cm steps on a carbon fibre , upport that spans 360' in 1 ° steps, with an overall positioning accuracy better than 2/10 mm . The same arrangement was used for the present measurements, except that the measuring process was fully automated via our VAX 8350 computer with on-line data reduction, so that an azimuthal step, including arm positioning, takes about 3 min of real time to process . We should also point out that during the initial magnet measurements only 90 ° maps were taken, reflecting the basic period of the machine . This was considered to be adequate for the purposes of magnet shimming. However, with all pole tips and other machine components ready, we have decided in the final measurement campaign to stress the mapping of the 360 ° fields, which furnish a complete set of Fourier harmonics . As will be seen later, this has shown to be rather instructive .
lao 17.0
A m
V
150
140
R (C M)
Fig. 1 . The average magnetic field as a function of radius for the main coil currents from 950 to 1200 A in 50 A steps . variation of the most sensitive 8th harmonic amplitude is shown throughout the magnet operating range . This, of course, means that the magnetic field flutter F falls as (B) -2, implying a nearly constant focusing limit of the machine . 2 .2. Trimming coil and harmonic coil data In order to achieve an isochronous magnetic field profile and to better control the beam behaviour, a total
2.1 . 90' magnetic field data In order to verify our previous measurements, a series of 90 ° maps were taken . In fig. 1, the average magnetic field as a function of machine radius is shown for various main coil currents . These field profiles are in good agreement with previously taken data, exhibiting, as before, a noticeable nonlinear behaviour in spite of relatively low central field values . Consequently, in order to take full advantage of our nonlinear magnetic field control codes [31 for achieving optimal conditions for z/A = 0.5 beam acceleration in Medicyc, the maps for 950 and 1000 A were also included in the measurement programme. A plot of the principal Fourier amplitudes for the magnetic field map corresponding to the main coil current of 1150 A is shown in fig . 2, giving a better insight into the details of the pole tip geometry. A prominent feature of the magnetic field Fourier components is the low sensitivity of the harmonic amplitudes on the average field level, illustrated in fig . 3, where the
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R (CM)
60.
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Fig . 2 . The amplitudes of the 4n, n =1, . . .,4, Founer harmonics for the I. =1150 A magnetic field map .
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1 .2
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Q 00 T0-
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0 .6 00
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Fig. 3 . Variation of the amplitude of the 8th harmonic of the magnetic field with the main coil current, I. = 950-1200 A in 50 A steps . of ten trimming coils were fabricated and mounted on pole tip surfaces . Trimming coils 1-9 were wound from a 8 by 1 mm full copper conductor which is cooled indirectly by water circulation in hollow copper tubes located on the outside of the coils . After impregnation, the coils measure 10 mm high and can support a current of 100 A . Trimming coil no. 10, with an interior radius of 66 .8 cm, was made of a 5 by 5 mm and 3 mm diameter hollow copper conductor wound in two layers with an intermediate lead, so that it can be excited as a two-independent-section coil. The form factors of this set of trimming coils are shown in fig . 4, indicating that typically a magnetic field correction of 250 G and a field gradient as high as 30 G/cm could be obtained for an 100 A excitation current of a trimming coil . When compared to our initial trimming coil data, which were obtained using a Poisson model of the magnet, a difference of 15% in the field correction and gradient is found, which may be considered, having in mind the small field differences involved in form factor calculations, as a very good computational result . For most purposes therefore, orbit analysis based on the design data for the trimming coils should be quite satisfactory, since only a slight change in trimming currents is sufficient for adjustment with measured data . However, it should be pointed out that if the beam is to be accelerated to the limits of the focusing power of the magnet, even a small difference between the design and final data for trimming coil form factors may lead to poor beam dynamics in certain regions of the acceleration space. It is therefore advisable to check the beam dynamics, especially if limiting
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R (C M)
Fig . 4 . Experimental form factors of the ten trimming coils at I~ =1150 A magnet excitation . acceleration regimes are important, as soon as the data for the magnet control system are available. Conversely, it seems advantageous to have the trimming coils ready in the early stages of machine construction . Four pairs of harmonic coils, each located in a free valley, are also integrated in the magnetic field control system of the Medicyc cyclotron . These coils, 3 .5 cm high, are fabricated from a 5 by 5 mm copper wire, and span 20 ° between 55 and 75 cm radius . An illustration of their form factors is given in fig. 5 . As customary,
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R (C M)
Fig . 5 . The form factors of the harmonic coil between 22° (1) and 32 ° (2) m 2 ° steps at I. =1150 A magnet excitation.
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P. Mandrrllon, R. Ostojic / Magnetic field control and orbit studies
they are wired to give an average field of zero value . With a current of 100 A in these coils, a harmonic-one amplitude of the order of 35 G at 62 cm can be compensated for any phase angle . 2.3. First Fourier harmonic of the magnetic field As mentioned above, the most important technical difference between the present and the previous series of magnetic field measurements arises from the fact that 360' maps in a completed machine could be obtained. Thus, the field errors giving rise to Fourier components other than those which are a multiple of the machine symmetry could be determined, their sources identified, and means for their compensation investigated .
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Fig . 7 . The amplitude of the first Founer harmonic of the 24 .8 MHz isochronous magnetic field prior (1) and after (2) correction with the harmonic coils.
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w 0
w m a rL
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10 . 20 . 30 .
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R (C M)
Fig. 6 . The amplitude (a) and the phase (b) of the first Founer harmonic of the magnetic field for the Ic =1178 A (1), 1142 A (2) and 1108 A (3) magnetic field maps .
In the course of our measurements, three complete 360* maps were measured, corresponding to main coil currents of 1178, 1142 and 1108 A . The latter two maps correspond to isochronous fields for 25 .0 and 24.8 MHz orbital proton frequency, respectively . In fig. 6, the first Fourier harmonic amplitude and phase of these maps are shown in their respective radial intervals . Unexpectedly, the first harmonic amplitude rises steadily, reaching, for all three maps, a rather high maximum of 40 G around 98 cm, where the corresponding phases approach 330' . The source of this behaviour was sought in pole tip machining, and certain imperfections in the axial shim and pole tip "shoe" were found and corrected between these measurements, resulting in a rather small improvement. Noticing that the maxima of harmonic-one amplitudes occur at the internal edge of the main coil, and that they are proportional to the main coil current, the source of this field imperfection was finally traced to the rather sudden transitions in the winding of the double pancakes that occur near the machine azimuth of 330' . Since this is a common technique of coil winding, similar field imperfections, unmasked in our case by a large main coil current, may be expected in other magnets . Care should therefore be taken to reduce this "naturally" occurring source of the first field harmonic by making the transitions between the two layers sufficiently long and, if possible, at the exterior radius of the pancake . Near extraction, of course, the first field harmonic should be reduced as much as possible, or otherwise suitably modified . Adjusting the currents of the harmonic coils, the harmonic-one imperfection can be
P. Mandrillon, R. Ostojic / Magnetic field control and orbit studies
corrected in the accelerating region of the machine to be lower than 4 G, as is shown in fig . 7 . However, in the transition region from the extraction elements to the beam line, the harmonic coils are ineffective, and a large first harmonic amplitude persists . Its effects on beam extraction are discussed below .
399
20 .0 15.0 100 50
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3. Isochronous magnetic field maps
w -5 .0
0
Medicyc is a fixed-frequency cyclotron designed to operate at 24.8 MHz rf frequency, which corresponds to a proton beam energy of 65 MeV. Hence, in order to experimentally verify the isochronous magnetic field profile for this orbital frequency, a 360 ° map has been measured. An isochronous field corresponding to a slightly higher frequency of 25 .0 MHz, which is within the range of the rf frequency adjustment system, was also mapped in view of possible increase of proton beam energy, which could bring an improvement to the proton therapy program of this facility . In both cases several main coil and trimming coil current settings were studied using a method which exploits the nonlinear behaviour of the average magnetic field profile and of the trimming coil form factors [3] . An example of the resulting isochronous field error 8B and of the central phase variation 80 for the 24 .8 MHz field is given in fig . 8 . As may be seen, SB is conveniently small in the whole accelerating region, being within ± 5 G between 20 cm and the extraction radius of 68 cm . In this particular case, the trimming
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Fig. 8 . The isochronous field error SB as a result of nonlinear control of the magnetic field, and the central phase S¢ for h =1 acceleration in the resulting 24.8 MHz isochronous magnetic field.
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-100 -15 .0 -20 .0
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(C M)
Fig. 9. Comparison of the calculated (full lines) and measured (symbols) isochronous field errors for the 25 .0 MHz isochronous magnetic field.
m ô M 0
coil currents are all smaller than 40 A, and their total power is about 1 kW . Also, trim coil no . 10 (with a flat form factor up to 66 cm), and trim coil no. l, which was designed to control the magnetic bump in the central region, were turned off, which explains the rise in the isochronous field error for r < 20 cm . In fig. 9, the experimental isochronous field error is compared with the calculated values for the 25 .0 MHz cyclotron operation. As can be observed, the difference between these 8B profiles is systematically of the order of 1 G, which is estimated to be the absolute error of the measurements, except near extraction, where it reaches 5 G . The excellent agreement of the predicted and experimentally observed values indicates that the principles employed in the control algorithms fully account for the nonlinearities of the magnetic field . Furthermore, since the methods of determining the main and trimming coil currents are independent of the design and operating range of the magnetic field of the cyclotron, one may also conclude that these measurements serve to establish their general validity. Hence, with a large margin of confidence, the resulting magnetic field maps may be employed for detailed orbit studies. We should also mention that the results of fig . 9 indicate that the power supplies of Medicyc are very stable, conform with design specifications . 4 . Orbit studies for H - acceleration In preparation for the commissioning of the cyclotron, extensive orbit studies of H - acceleration in
P. Mandrillon, R. Ostojic / Magnetic field control and orbit studies
Medicyc were performed with a complete set of experimental magnetic field maps . These studies entail essentially three different regimes of beam dynamics . First, in the low energy region, the transport of the beam along the axial injection line was analyzed, the bunching ratio and beam losses were determined, and the injection through a spiral inflector and the beam motion in the central region of the cyclotron were studied . An especially important step in these studies, which is a subject of another report [41, was an analysis of the transverse and longitudinal beam coupling in the inflector located in the axially variable magnetic field, and of the centering and focusing of the beam in the central region, that were accomplished with an improved Agora code. In the acceleration region proper, the focusing properties, and more generally the principal trajectories of the beam were determined, and the acceleration of the known beam emittance simulated . Finally, in the extraction region, the optics of the ejected beam was obtained . In the following, we present certain results pertaining to the studies of the acceleration and extraction of the H - beam in Medicyc, stressing those that are related to precise control of the isochronous field .
4.1 . Equilibrium and accelerated orbits A typical plot of the radial and axial focusing frequencies v, and P., obtained by integrating the equations of motion in the 25 .0 MHz magnetic field map, is shown in fig . 10 . Quite ordinarily, the v, focusing frequency rises steadily to reach a maximum value of 1 .067 at r = 63 cm, from where on it drops to 0.94 at 20 .
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tt
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60.
70.
(C M)
Fig. 11 . The isochronous field error 6B (a) and the focusing frequency v (b) as a function of radius for the optimal trimming coil setting for the 25 .0 MHz isochronous field (symbols), and a setting differing by less than 15% in currents of coils nos . 5, 6 and 7 .
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Z 0.3
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Fig . 10. The radial and axial focusing frequencies v, and v of the equilibrium orbits in the 25 .0 MHz isochronous magnetic field.
the extraction radius of 68 cm . The axial focusing frequency has an almost constant value of 0 .12 for all radii, except beyond 60 cm, when it begins to rise due to the flattening of the average field, and for a narrow radial interval around 56 cm, where for this particular trimming coil setting it drops below 0.1 . This interval has already been identified during the shimming of the magnetic field as a region where the drop of the field flutter is not sufficiently compensated by the spiral action, so that even a small error in the current setting of trimming coil no . 6 can shift the axial frequency out of the desired range . The sensitivity of the axial beam focusing on the trimming coil currents is illustrated in
40 1
P. Mandrillon, R. Ostojic / Magnetic field control and orbit studies
fig . 11, where the optimal magnet control system setting is compared, in terms of the isochronous field error 8B and focusing frequency vZ , with a similar trimming current setting which differs in that the current of trimming coil no . 6 is changed by 15%, and those of trimming coils 5 and 7 by less than 10% . Clearly, even such a small change, corresponding to a field gradient difference of 3 G/cm, may yield an improvement in the axial focusing properties of the beam in the region around 56 cm . This is an example of the situation when properly adjusted main and trimming coil currents can act to widen the operating region of the cyclotron beyond the natural focusing power of the magnet. An analysis of the accelerated orbits was performed by multiparticle simulation of the accelerated motion of the injected beam in the 360' experimental magnetic field maps. Due to the small emittance of our H multicusp source of E = 0 .141r mm mrad, which is much smaller than the estimated admittance of the accelerating region of the machine of about 2 .hr mm mrad, the resulting beam distributions in both the axial and radial phase spaces show no distortions, indicating that linear motion is prevailing for these acceleration conditions . Using the Triumf experimental data for the probability of H - dissociation in electromagnetic fields [5], the total loss of the beam due to this effect was estimated to be at a level of 5% . This is slightly higher than is customary for application-dedicated cyclotrons [6], due to the relatively higher orbital frequency of the proton beam in Medicyc. Nevertheless, having in mind that we require beam intensities of the order of 10 pA at the exit, and that an efficient extraction scheme is employed, this level of beam losses seems to be acceptable . 4.2. H - extraction trajectories
To extract the negatively charged H - beam from Medicyc, a 100 Wg/cm2 carbon stripper foil, mounted on a positioning mechanism described in ref . [1], is introduced at a convenient azimuth . After passing through the foil, the beam crosses the fringing field and travels about 1 m in the axially defocusing gradients before arriving at the first beam line quadrupole . Furthermore, this is the region where the harmonic-one field imperfection achieves its maximum . Hence, in order to determine the effects of the fringing magnetic field on beam extraction, the beam ejection in experimental field maps was studied in detail. In fig . 12, a comparison is given of the axial phase spaces of the extracted beam at the exit of the machine vacuum chamber, 0 .7 m downstream from the stripper foil, in cases of a perfectly fourfold-symmetric magnetic field, and of the measured field with a harmonic-one imperfection compensated as shown in fig. 7 . In passing through the stray field, the beam is of course slightly axially defocused even in a perfectly symmetric field,
80 6.0 40 20 00
â
-2 0 -40 -60 -8.0
a)
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ô
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Z (M M)
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Fig . 12. The axial phase space of the extracted beam in case of a perfectly fourfold-symmetric magnetic field (a), and the measured field with the compensated harmonic-one imperfection (b).
the beam spot increasing from 1 .1 to 1 .7 mm between the stripper and the vacuum chamber exit port . The presence of the first field harmonic, as evidenced by fig. 12b, contributes substantially to further axial defocusing of the beam, as the axial beam size in this case reaches 5 .8 mm at the beam exit . However, it should be noted that the radial positions of the exiting beam differ between the two cases by only 4 mm, indicating that the first harmonic field imperfection has a small influence on particle trajectories beyond the stripping point. The growth of the axial beam size during extraction is in fact generated by the relatively slow crossing of the coupling resonances 2 vs = v, and 2 vz + v, = 2, which occur at radii of 67 .43 cm and 68 .41 cm, respectively,
40 2
P. Mandrillon, R. Ostojtc / Magnetic field control and orbitstudies
following the radial displacement of the beam in the v, = 1 resonance at 66.55 cm . Although the harmonic-one amplitude is only about 5 G in this region, the beam spot increases by a factor of 2 during the thirty turns that follow this resonance prior to extraction . Even so, the achieved beam emittance at machine exit of 0.16m mm mrad radially and 0.55 -TT mm mrad axially is quite satisfactory for efficient beam transport beyond the cyclotron. 5. Conclusions Negatively charged light ion H- and D- beams have recently gained, after a brief period of hesitation awaiting ion source and axial injection developments, an important role in cyclotrons designed for medical applications and radioisotope production . Since these machines often operate at the limits of their operating regions a tight control of the accelerating conditions must be achieved if beam losses are to be kept low. In this report we have shown that in the case of the Medicyc cyclotron a very efficient control of the iso-
chronous magnetic field has been achieved . The precision and validity of the magnetic field control algorithms have been established, and it has been demonstrated that by adequate setting of the magnetic field control system the limits of the magnetic focusing power may be extended . Finally, as an illustration of the generality of developed methods for beam development work, the results of orbit studies for H- beam acceleration to 65 MeV in this cyclotron have been presented.
References [1] P. Mandrillon et al., Proc. 12th Int. Conf . on Cyclotrons and their Applications, Berlin (1989) . [2] P. Mandrillon and R. Ostojic, Nucl . Instr. and Meth . A243 (1986) 237. [3] R. Ostojic, Nucl . Instr. and Meth . A243 (1986) 231. [4] P. Mandrillon, to be published. [5] G.M . Stinson, W.C . Olsen, W.J . McDonald and P. Ford, TRIUMF, TRI-69-i. [6] Y. Jongen, Proc. 12th Int. Conf. on Cyclotrons and their Applications, Berlin (1989) .
395
MAGNETIC FIELD CONTROL AND ORBIT STUDIES FOR H - ACCELERATION IN A 65 MeV CYCLOTRON
P. MANDRILLON Laboratoire du Cyclotron, Centre Antoine Lacassagne, 36 Voie Romaine, 06054 Nice Cedex, France
R. OSTOJIC Boris Kidric Institute of Nuclear Sciences, POB 522, 11001 Belgrado, Yugoslavia
Received 19 June 1989 The results of the mapping of the isochronous magnetic field for the Medicyc cyclotron are presented. The validity of the developed nonlinear methods for the magnetic field control is established, and certain results of detailed orbit studies for H acceleration up to 65 MeV in this machine are given. 1. Introduction As is well known to cyclotron builders, extensive magnetic field measurements are an important step in cyclotron construction . In effect, magnetic field data serve initially as the basis of the cyclotron magnet shirrtrning, a process involving magnetic field measurement and data reduction, computation of the necessary field corrections and appropriate mechanical modifications, with the final goal of accommodating the magnetic field behaviour to the desired operating range of the machine. Furthermore, any beam development work during machine operation needs to rely on the experimental field data, or on field synthesis routines that involve a reduced set of measurements . Hence, the ability to predict with high accuracy the magnetic field distribution in a cyclotron can both simplify the initial design and shorten the construction period, and contribute to the ease of operation of the machine and to the stability and quality of the accelerated beam parameters. The magnetic field of the Medicyc cyclotron [1] has been extensively mapped for the purposes of magnet shimming, as has previously been reported in detail [2]. Following these measurements, it was decided that the proton beam energy should be increased from the design goal of 60 MeV to 65 MeV, as suggested by the analysis of magnetic field data . Furthermore, several machine components (the axial injection line and the central region, and the rf and extraction systems, in particular), were redesigned or modified in accordance with a decision to accelerate an H - beam . With the machine fully assembled and ready for commissioning, a final series of magnetic field measurements, including 0168-9002/89/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
360' maps of the isochronous fields, were performed. Besides giving a full range of data on the average field, field harmonics of all orders, and the harmonic and trimming coil form factors, these measurements also served to verify the validity of our improved algorithms for magnetic field control [3]. Finally, in preparation for regular machine operation, the H - beam acceleration in experimentally determined isochronous fields was studied in considerable detail . In this report, we present several results pertaining to the magnetic field measurements, the control of the isochronous field, and the dynamics of the 65 MeV Hbeam in the Medicyc cyclotron. In particular, we draw attention to an often neglected but common source of the first Fourier harmonic of the magnetic field, establish the general validity of the magnetic field control algorithms, and determine their usefulness for orbit studies in limiting regions of the operating diagram of the cyclotron where high accuracy in synthesizing the magnetic field is needed.
2. Mapping of the magnetic field The magnetic field of the Medicyc cyclotron was extensively studied in previous measurement campaigns. The purpose of these measurements was essentially to determine the final geometry of the pole tips that minimizes the trimming coil power, and to optimize the choice of the operating rf frequency of this machine. For the sake of completeness, we recall that Medicyc is a four-sector isochronous cyclotron with a pole diameter of 160 cm and an extraction radius of 68 cm . The
396
P. Mandrdlon, R. Ostojic / Magnetic field control and orbit studies
average width and spiral angle of the pole tips are 42 .5 ° and 60'/m, respectively . The pole tips, with hill and valley gaps of 13 and 28 cm, respectively, extend to 75 cm where they loin the annular segment of the vacuum chamber . In the region from 66 to 76 cm, the angular width of the pole tips is increased by adding a pole "shoe" which is 13 ° wide . As explained in detail in ref . [21, the modifications introduced following the orbit studies based on experimental magnetic field maps, concerned the change of the exit spiral in order to slightly decrease the angular width of the pole tip, and an introduction of an axial shim 2 mm high and 40 mm wide running across the pole tip width at a radius of 71 cm . As described previously [21, the magnetic field measurement apparatus consisted of 51 thermally stabilized Hall probes mounted in 2 cm steps on a carbon fibre , upport that spans 360' in 1 ° steps, with an overall positioning accuracy better than 2/10 mm . The same arrangement was used for the present measurements, except that the measuring process was fully automated via our VAX 8350 computer with on-line data reduction, so that an azimuthal step, including arm positioning, takes about 3 min of real time to process . We should also point out that during the initial magnet measurements only 90 ° maps were taken, reflecting the basic period of the machine . This was considered to be adequate for the purposes of magnet shimming. However, with all pole tips and other machine components ready, we have decided in the final measurement campaign to stress the mapping of the 360 ° fields, which furnish a complete set of Fourier harmonics . As will be seen later, this has shown to be rather instructive .
lao 17.0
A m
V
150
140
R (C M)
Fig. 1 . The average magnetic field as a function of radius for the main coil currents from 950 to 1200 A in 50 A steps . variation of the most sensitive 8th harmonic amplitude is shown throughout the magnet operating range . This, of course, means that the magnetic field flutter F falls as (B) -2, implying a nearly constant focusing limit of the machine . 2 .2. Trimming coil and harmonic coil data In order to achieve an isochronous magnetic field profile and to better control the beam behaviour, a total
2.1 . 90' magnetic field data In order to verify our previous measurements, a series of 90 ° maps were taken . In fig. 1, the average magnetic field as a function of machine radius is shown for various main coil currents . These field profiles are in good agreement with previously taken data, exhibiting, as before, a noticeable nonlinear behaviour in spite of relatively low central field values . Consequently, in order to take full advantage of our nonlinear magnetic field control codes [31 for achieving optimal conditions for z/A = 0.5 beam acceleration in Medicyc, the maps for 950 and 1000 A were also included in the measurement programme. A plot of the principal Fourier amplitudes for the magnetic field map corresponding to the main coil current of 1150 A is shown in fig . 2, giving a better insight into the details of the pole tip geometry. A prominent feature of the magnetic field Fourier components is the low sensitivity of the harmonic amplitudes on the average field level, illustrated in fig . 3, where the
40
30
20
10
10
20
30
40
50
R (CM)
60.
70
80
90
Fig . 2 . The amplitudes of the 4n, n =1, . . .,4, Founer harmonics for the I. =1150 A magnetic field map .
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P. Mandrtllon, R. Ostohr / Magnetic fieldcontrol and orbit studies
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30
R (C M)
Fig. 3 . Variation of the amplitude of the 8th harmonic of the magnetic field with the main coil current, I. = 950-1200 A in 50 A steps . of ten trimming coils were fabricated and mounted on pole tip surfaces . Trimming coils 1-9 were wound from a 8 by 1 mm full copper conductor which is cooled indirectly by water circulation in hollow copper tubes located on the outside of the coils . After impregnation, the coils measure 10 mm high and can support a current of 100 A . Trimming coil no. 10, with an interior radius of 66 .8 cm, was made of a 5 by 5 mm and 3 mm diameter hollow copper conductor wound in two layers with an intermediate lead, so that it can be excited as a two-independent-section coil. The form factors of this set of trimming coils are shown in fig . 4, indicating that typically a magnetic field correction of 250 G and a field gradient as high as 30 G/cm could be obtained for an 100 A excitation current of a trimming coil . When compared to our initial trimming coil data, which were obtained using a Poisson model of the magnet, a difference of 15% in the field correction and gradient is found, which may be considered, having in mind the small field differences involved in form factor calculations, as a very good computational result . For most purposes therefore, orbit analysis based on the design data for the trimming coils should be quite satisfactory, since only a slight change in trimming currents is sufficient for adjustment with measured data . However, it should be pointed out that if the beam is to be accelerated to the limits of the focusing power of the magnet, even a small difference between the design and final data for trimming coil form factors may lead to poor beam dynamics in certain regions of the acceleration space. It is therefore advisable to check the beam dynamics, especially if limiting
40
50
60
70
R (C M)
Fig . 4 . Experimental form factors of the ten trimming coils at I~ =1150 A magnet excitation . acceleration regimes are important, as soon as the data for the magnet control system are available. Conversely, it seems advantageous to have the trimming coils ready in the early stages of machine construction . Four pairs of harmonic coils, each located in a free valley, are also integrated in the magnetic field control system of the Medicyc cyclotron . These coils, 3 .5 cm high, are fabricated from a 5 by 5 mm copper wire, and span 20 ° between 55 and 75 cm radius . An illustration of their form factors is given in fig. 5 . As customary,
2 .0 10
-30 -40
40
50
60
70
80
R (C M)
Fig . 5 . The form factors of the harmonic coil between 22° (1) and 32 ° (2) m 2 ° steps at I. =1150 A magnet excitation.
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P. Mandrrllon, R. Ostojic / Magnetic field control and orbit studies
they are wired to give an average field of zero value . With a current of 100 A in these coils, a harmonic-one amplitude of the order of 35 G at 62 cm can be compensated for any phase angle . 2.3. First Fourier harmonic of the magnetic field As mentioned above, the most important technical difference between the present and the previous series of magnetic field measurements arises from the fact that 360' maps in a completed machine could be obtained. Thus, the field errors giving rise to Fourier components other than those which are a multiple of the machine symmetry could be determined, their sources identified, and means for their compensation investigated .
40 .
30
20
10
20
30
40
50 . 60 . 70 . 80 . 90.100 .110 . R (C M)
Fig . 7 . The amplitude of the first Founer harmonic of the 24 .8 MHz isochronous magnetic field prior (1) and after (2) correction with the harmonic coils.
40
30
20
10
350
320
w 0
w m a rL
290
260
230
10 . 20 . 30 .
40.
50
60.
70
80
90.100 .110 .
R (C M)
Fig. 6 . The amplitude (a) and the phase (b) of the first Founer harmonic of the magnetic field for the Ic =1178 A (1), 1142 A (2) and 1108 A (3) magnetic field maps .
In the course of our measurements, three complete 360* maps were measured, corresponding to main coil currents of 1178, 1142 and 1108 A . The latter two maps correspond to isochronous fields for 25 .0 and 24.8 MHz orbital proton frequency, respectively . In fig. 6, the first Fourier harmonic amplitude and phase of these maps are shown in their respective radial intervals . Unexpectedly, the first harmonic amplitude rises steadily, reaching, for all three maps, a rather high maximum of 40 G around 98 cm, where the corresponding phases approach 330' . The source of this behaviour was sought in pole tip machining, and certain imperfections in the axial shim and pole tip "shoe" were found and corrected between these measurements, resulting in a rather small improvement. Noticing that the maxima of harmonic-one amplitudes occur at the internal edge of the main coil, and that they are proportional to the main coil current, the source of this field imperfection was finally traced to the rather sudden transitions in the winding of the double pancakes that occur near the machine azimuth of 330' . Since this is a common technique of coil winding, similar field imperfections, unmasked in our case by a large main coil current, may be expected in other magnets . Care should therefore be taken to reduce this "naturally" occurring source of the first field harmonic by making the transitions between the two layers sufficiently long and, if possible, at the exterior radius of the pancake . Near extraction, of course, the first field harmonic should be reduced as much as possible, or otherwise suitably modified . Adjusting the currents of the harmonic coils, the harmonic-one imperfection can be
P. Mandrillon, R. Ostojic / Magnetic field control and orbit studies
corrected in the accelerating region of the machine to be lower than 4 G, as is shown in fig . 7 . However, in the transition region from the extraction elements to the beam line, the harmonic coils are ineffective, and a large first harmonic amplitude persists . Its effects on beam extraction are discussed below .
399
20 .0 15.0 100 50
m
3. Isochronous magnetic field maps
w -5 .0
0
Medicyc is a fixed-frequency cyclotron designed to operate at 24.8 MHz rf frequency, which corresponds to a proton beam energy of 65 MeV. Hence, in order to experimentally verify the isochronous magnetic field profile for this orbital frequency, a 360 ° map has been measured. An isochronous field corresponding to a slightly higher frequency of 25 .0 MHz, which is within the range of the rf frequency adjustment system, was also mapped in view of possible increase of proton beam energy, which could bring an improvement to the proton therapy program of this facility . In both cases several main coil and trimming coil current settings were studied using a method which exploits the nonlinear behaviour of the average magnetic field profile and of the trimming coil form factors [3] . An example of the resulting isochronous field error 8B and of the central phase variation 80 for the 24 .8 MHz field is given in fig . 8 . As may be seen, SB is conveniently small in the whole accelerating region, being within ± 5 G between 20 cm and the extraction radius of 68 cm . In this particular case, the trimming
20 .0
10 .0
15 .0
7 .5
100
50
50
2.5
0 .0
00
w -5.0
-2 .5
-10 .0
-5 .0
-150
-7 .5
-20 .0
-100
m
0
10
20
30
40
50 .
60.
70 .
R (C M)
Fig. 8 . The isochronous field error SB as a result of nonlinear control of the magnetic field, and the central phase S¢ for h =1 acceleration in the resulting 24.8 MHz isochronous magnetic field.
0 .0
-100 -15 .0 -20 .0
10 .
20 .
30
40 . R
50.
60
70 .
(C M)
Fig. 9. Comparison of the calculated (full lines) and measured (symbols) isochronous field errors for the 25 .0 MHz isochronous magnetic field.
m ô M 0
coil currents are all smaller than 40 A, and their total power is about 1 kW . Also, trim coil no . 10 (with a flat form factor up to 66 cm), and trim coil no. l, which was designed to control the magnetic bump in the central region, were turned off, which explains the rise in the isochronous field error for r < 20 cm . In fig. 9, the experimental isochronous field error is compared with the calculated values for the 25 .0 MHz cyclotron operation. As can be observed, the difference between these 8B profiles is systematically of the order of 1 G, which is estimated to be the absolute error of the measurements, except near extraction, where it reaches 5 G . The excellent agreement of the predicted and experimentally observed values indicates that the principles employed in the control algorithms fully account for the nonlinearities of the magnetic field . Furthermore, since the methods of determining the main and trimming coil currents are independent of the design and operating range of the magnetic field of the cyclotron, one may also conclude that these measurements serve to establish their general validity. Hence, with a large margin of confidence, the resulting magnetic field maps may be employed for detailed orbit studies. We should also mention that the results of fig . 9 indicate that the power supplies of Medicyc are very stable, conform with design specifications . 4 . Orbit studies for H - acceleration In preparation for the commissioning of the cyclotron, extensive orbit studies of H - acceleration in
P. Mandrillon, R. Ostojic / Magnetic field control and orbit studies
Medicyc were performed with a complete set of experimental magnetic field maps . These studies entail essentially three different regimes of beam dynamics . First, in the low energy region, the transport of the beam along the axial injection line was analyzed, the bunching ratio and beam losses were determined, and the injection through a spiral inflector and the beam motion in the central region of the cyclotron were studied . An especially important step in these studies, which is a subject of another report [41, was an analysis of the transverse and longitudinal beam coupling in the inflector located in the axially variable magnetic field, and of the centering and focusing of the beam in the central region, that were accomplished with an improved Agora code. In the acceleration region proper, the focusing properties, and more generally the principal trajectories of the beam were determined, and the acceleration of the known beam emittance simulated . Finally, in the extraction region, the optics of the ejected beam was obtained . In the following, we present certain results pertaining to the studies of the acceleration and extraction of the H - beam in Medicyc, stressing those that are related to precise control of the isochronous field .
4.1 . Equilibrium and accelerated orbits A typical plot of the radial and axial focusing frequencies v, and P., obtained by integrating the equations of motion in the 25 .0 MHz magnetic field map, is shown in fig . 10 . Quite ordinarily, the v, focusing frequency rises steadily to reach a maximum value of 1 .067 at r = 63 cm, from where on it drops to 0.94 at 20 .
40 . R
tt
50 .
60.
70.
(C M)
Fig. 11 . The isochronous field error 6B (a) and the focusing frequency v (b) as a function of radius for the optimal trimming coil setting for the 25 .0 MHz isochronous field (symbols), and a setting differing by less than 15% in currents of coils nos . 5, 6 and 7 .
0.9 0 .7
N Z
30.
0 .5
Z 0.3
01
20.
30
40
50.
R (CM)
60 .
70 .
Fig . 10. The radial and axial focusing frequencies v, and v of the equilibrium orbits in the 25 .0 MHz isochronous magnetic field.
the extraction radius of 68 cm . The axial focusing frequency has an almost constant value of 0 .12 for all radii, except beyond 60 cm, when it begins to rise due to the flattening of the average field, and for a narrow radial interval around 56 cm, where for this particular trimming coil setting it drops below 0.1 . This interval has already been identified during the shimming of the magnetic field as a region where the drop of the field flutter is not sufficiently compensated by the spiral action, so that even a small error in the current setting of trimming coil no . 6 can shift the axial frequency out of the desired range . The sensitivity of the axial beam focusing on the trimming coil currents is illustrated in
40 1
P. Mandrillon, R. Ostojic / Magnetic field control and orbit studies
fig . 11, where the optimal magnet control system setting is compared, in terms of the isochronous field error 8B and focusing frequency vZ , with a similar trimming current setting which differs in that the current of trimming coil no . 6 is changed by 15%, and those of trimming coils 5 and 7 by less than 10% . Clearly, even such a small change, corresponding to a field gradient difference of 3 G/cm, may yield an improvement in the axial focusing properties of the beam in the region around 56 cm . This is an example of the situation when properly adjusted main and trimming coil currents can act to widen the operating region of the cyclotron beyond the natural focusing power of the magnet. An analysis of the accelerated orbits was performed by multiparticle simulation of the accelerated motion of the injected beam in the 360' experimental magnetic field maps. Due to the small emittance of our H multicusp source of E = 0 .141r mm mrad, which is much smaller than the estimated admittance of the accelerating region of the machine of about 2 .hr mm mrad, the resulting beam distributions in both the axial and radial phase spaces show no distortions, indicating that linear motion is prevailing for these acceleration conditions . Using the Triumf experimental data for the probability of H - dissociation in electromagnetic fields [5], the total loss of the beam due to this effect was estimated to be at a level of 5% . This is slightly higher than is customary for application-dedicated cyclotrons [6], due to the relatively higher orbital frequency of the proton beam in Medicyc. Nevertheless, having in mind that we require beam intensities of the order of 10 pA at the exit, and that an efficient extraction scheme is employed, this level of beam losses seems to be acceptable . 4.2. H - extraction trajectories
To extract the negatively charged H - beam from Medicyc, a 100 Wg/cm2 carbon stripper foil, mounted on a positioning mechanism described in ref . [1], is introduced at a convenient azimuth . After passing through the foil, the beam crosses the fringing field and travels about 1 m in the axially defocusing gradients before arriving at the first beam line quadrupole . Furthermore, this is the region where the harmonic-one field imperfection achieves its maximum . Hence, in order to determine the effects of the fringing magnetic field on beam extraction, the beam ejection in experimental field maps was studied in detail. In fig . 12, a comparison is given of the axial phase spaces of the extracted beam at the exit of the machine vacuum chamber, 0 .7 m downstream from the stripper foil, in cases of a perfectly fourfold-symmetric magnetic field, and of the measured field with a harmonic-one imperfection compensated as shown in fig. 7 . In passing through the stray field, the beam is of course slightly axially defocused even in a perfectly symmetric field,
80 6.0 40 20 00
â
-2 0 -40 -60 -8.0
a)
8.0 6.0 4 .0
ô
2.0 0.0 -2 .0 -4 .0 -6 .0 -80 -80-6.0-40-2.0
0.0
2.0
Z (M M)
4.0
60
8.0
Fig . 12. The axial phase space of the extracted beam in case of a perfectly fourfold-symmetric magnetic field (a), and the measured field with the compensated harmonic-one imperfection (b).
the beam spot increasing from 1 .1 to 1 .7 mm between the stripper and the vacuum chamber exit port . The presence of the first field harmonic, as evidenced by fig. 12b, contributes substantially to further axial defocusing of the beam, as the axial beam size in this case reaches 5 .8 mm at the beam exit . However, it should be noted that the radial positions of the exiting beam differ between the two cases by only 4 mm, indicating that the first harmonic field imperfection has a small influence on particle trajectories beyond the stripping point. The growth of the axial beam size during extraction is in fact generated by the relatively slow crossing of the coupling resonances 2 vs = v, and 2 vz + v, = 2, which occur at radii of 67 .43 cm and 68 .41 cm, respectively,
40 2
P. Mandrillon, R. Ostojtc / Magnetic field control and orbitstudies
following the radial displacement of the beam in the v, = 1 resonance at 66.55 cm . Although the harmonic-one amplitude is only about 5 G in this region, the beam spot increases by a factor of 2 during the thirty turns that follow this resonance prior to extraction . Even so, the achieved beam emittance at machine exit of 0.16m mm mrad radially and 0.55 -TT mm mrad axially is quite satisfactory for efficient beam transport beyond the cyclotron. 5. Conclusions Negatively charged light ion H- and D- beams have recently gained, after a brief period of hesitation awaiting ion source and axial injection developments, an important role in cyclotrons designed for medical applications and radioisotope production . Since these machines often operate at the limits of their operating regions a tight control of the accelerating conditions must be achieved if beam losses are to be kept low. In this report we have shown that in the case of the Medicyc cyclotron a very efficient control of the iso-
chronous magnetic field has been achieved . The precision and validity of the magnetic field control algorithms have been established, and it has been demonstrated that by adequate setting of the magnetic field control system the limits of the magnetic focusing power may be extended . Finally, as an illustration of the generality of developed methods for beam development work, the results of orbit studies for H- beam acceleration to 65 MeV in this cyclotron have been presented.
References [1] P. Mandrillon et al., Proc. 12th Int. Conf . on Cyclotrons and their Applications, Berlin (1989) . [2] P. Mandrillon and R. Ostojic, Nucl . Instr. and Meth . A243 (1986) 237. [3] R. Ostojic, Nucl . Instr. and Meth . A243 (1986) 231. [4] P. Mandrillon, to be published. [5] G.M . Stinson, W.C . Olsen, W.J . McDonald and P. Ford, TRIUMF, TRI-69-i. [6] Y. Jongen, Proc. 12th Int. Conf. on Cyclotrons and their Applications, Berlin (1989) .