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A superconducting multipole lens for focusing high energy ions
Nuclear Instruments and Methods in Physics Research B 158 (1999) 74±80
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A superconducting multipole lens for focusing high energy ions G. Datzmann *, G. Dollinger, G. Hinderer, H.-J. K orner Physik Department E12, Technische Universit at M unchen, D-85748 Garching, Germany
Abstract At the Munich 15 MV tandem accelerator a new two stage microprobe system Supraleitendes Nanoskop f ur Angewandte Kernphysikalische Experimente (SNAKE) is currently under construction. In contrast to existing facilities, it is projected to focus up to 30 MeV protons as well as heavy ions with maximum energies of 200 MeV q2 /A to a submicron beam spot. In order to achieve this goal, a superconducting lens with inherent multipole corrections and special shaped edges with respect to fringe ®eld calculations was designed. The introduction of superconductivity enables a pole tip ®eld of 1.2 T at 10 mm bore radius and the possibility of auto correction mechanisms. An implemented electrostatic octupole for active ®eld correction will have a maximum ®eld strength in the same order of magnitude as the intrinsic magnetic octupole correction. For an analytical test of the novel concepts of this lens, a multipole detection device on the rotating coil principle has been built. It is capable of measuring small multipole contributions on a strong quadrupole ®eld. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 07.55.G; 41.85.L; 07.79
1. Introduction The new microbeam facility Supraleitendes Nanoskop f ur Angewandte Kernphysikalische Experimente (SNAKE) at the Munich tandem accelerator is currently under construction [1]. Protons with energies up to 30 MeV as well as heavy ions up to 200 MeV q2 /A shall be focused to a submicron beam spot in standard analyses. This facility aims to investigate and modify micro and nano structured materials coming from solid state physics, biology and geology. The small beam di-
* Corresponding author. Tel.: +49-89-289-14350; fax: +4989-289-12297; e-mail: [email protected]
ameter will be achieved in a two stage ion optical system (Fig. 1). The object of the demagni®cation is provided by a special developed microslit system [2], which operates as the analysing slits of the 90° magnet. The ®rst part of demagni®cation is performed by a standard quadrupole doublet lens. Since the imaging system is accomplished as a separated Russian quadruplet (SRQ), the intermediate foci enable using additional scattering slits. The second and main demagni®cation stage consists of a superconducting multipole lens operating as a quadrupole doublet with ferromagnetic pole pieces. This leads to an overall demagni®cation factor of 200 in both transversal directions. Having an object size of 20 lm, the ion optic will produce a beam spot of 100 nm at the
0168-583X/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 3 0 8 - 0
G. Datzmann et al. / Nucl. Instr. and Meth. in Phys. Res. B 158 (1999) 74±80
75
A beam spot size of 100 nm in diameter can only be achieved, if all types of aberrations are suppressed to low values, which means high perfection of the magnetic ®eld. For this purpose superconductivity can be used for auto correction mechanisms. Field distortions due to asymmetric ¯ux through the four poles will be eliminated by superconducting current loops between each pole and its two next neighbours [1]. 2.1. Treatment of the fringe ®eld Fig. 1. Scheme of the two stage ion beam optics.
target. In order to reduce the chromatic aberrations to the same value a relative energy spread of 10ÿ5 is driven at. The beam conditions at the Munich tandem accelerator will result in a proton current of 100 pA even at this small beam diameter. The brightness of Hÿ beam is actually limited by the ion source, e.g., a brightness of 2 ´ 10ÿ6 A/(mm2 mrad2 MeV) for a commercial duoplasmatron source [3]. High quality beam optic components have to be used in order to reduce aberrations to low levels ®nally achieving the desired diameters for the high energy protons and heavy ion beams. In Section 2 the requirements for such a high resolution system and the realisation concepts are presented. The third section deals with a rotating ®eld probe, which will be used to measure the magnetic multipole components of the superconducting lens.
2. Design of the new superconducting multipole lens First of all, a magnetic ®eld gradient of more than 1 T/cm is necessary in order to focus ions with energies up to 200 MeV q2 /A within a focal length of about 300 mm. A new design, utilising CoFe (ratio 1:1) pole pieces surrounded by small superconducting coils, leads to a calculated poletip ®eld of 1.2 T at a bore radius of 10 mm [1]. This is about three times larger than provided by commercially available quadrupole lenses for microprobe applications [4].
One of the main limits in high precision focusing are the geometric aberrations arising from non-ideal ®eld components within a magnetic lens and in the fringing ®eld region. Whereas errors introduced by large apertures inside the magnet can be simulated easily, fringe ®eld eects are hard to handle. It has been reported [5] that multipole components generated by the fringe ®eld can aect the spot size in the same order of magnitude as the aberrations from inside the quadrupole. Both aberrations are inevitable and need to be corrected to meet the projected beam diameter as stated above. Therefore higher order multipole components such as magnetic octupole etc. are added to the focusing system. The magnitude of components, necessary to eliminate the geometrical aberrations of a given lens system, can be eectively calculated only if fringing ®elds of the magnet sections are known. The total multipole series of the magnetic ®eld was ®xed by a new method which is summarized in the following. In principal, the static magnetic potential u may be expressed in polar coordinates r, u, z [6] 1 X 1 X A m; k r2km Um 2k z cos ma u r; a; z m0 k0
Wm 2k z sin ma ; 1 where k
A m; k
ÿ 1 m! : 4k k! m k !
Thereby m is the order of multipole ®eld and the superscript (2k) on Wm and Um denotes the 2k-th
76
G. Datzmann et al. / Nucl. Instr. and Meth. in Phys. Res. B 158 (1999) 74±80
derivative with respect to z. All Um components are zero if skewed 1 multipole components are disregarded. In the central region of a magnet Wm (z) is nearly constant, and therefore all derivatives of W are negligible. This leads to a rather simple equation for the magnetic potential u. Reaching the pole edges the quadrupole strength W2 (z) begins to decline, producing non-zero values for the derivatives and the creation of functions Wm (z) with m ¹ n. However, due to the 4-fold symmetry only functions with m 2l 1n;
l 1; 2; . . . ;
2
are involved [7]. Calculating the three dimensional magnetic ®eld from a given boundary condition introduced by the pole and the superconducting surfaces with sucient accuracy seems to be unpromisingly. Therefore a novel approach to overcome the fringe ®eld problem was chosen for the multipole lens which is exactly vice versa. The pole surface being a constant magnetic potential is calculated from a desired ®eld distribution. Thereby the superconducting surfaces are ®xed in the fringe ®eld region as they are between the poles. For the calculation it has been assumed that the magnetic ®eld vector is always tangential to the foil surface because of self-induced superconducting currents [1]. Finally, an analytical function W2 (z) for the longitudinal quadrupole ®eld pro®le suggested for lenses where the bore radius is smaller then their length [8] is assumed W2 z
1 eP z0 ; 1 eP z
where P z A1 A2 z A3 z2 A4 z3 A5 z4 :
3
Choosing a set of parameters Ai for P(z) and satisfying the given boundary conditions the pole surface at the edge can be calculated as an equipotential surface where u(r,u,z) is constant. Some care should be taken on the choice of the polynomial P(z) to reach a rather smooth behaviour of the resulting pole surface. Fig. 2 shows the selected
1
Symmetry axis of the 2m multipole rotated around 90°/m.
Fig. 2. Calculated magnetic ®eld at the edges of a magnet section for the chosen polynomial P(z). The upper plot shows the curvature of one pole piece in a cross sectional view.
parameters, the decreasing quadrupole ®eld and the corresponding sectional view of the longitudinal pole contour. With these input parameters the magnetic ®eld in the whole lens can be analytically derived from Eq. (1). A home made raytracing code QTRACE was used to optimize the geometric aberrations by adding higher order multipole ®elds. The ®nal result of the procedure is given in Table 1. Although the lens is operated as a quadrupole doublet, the second singlet is divided into two separate sections in order to get three parameters necessary for a complete octupole correction.
Table 1 Relative strength of the higher order multipole correction ®elds for the three magnetic sections. All values are normalized to the quadrupole strength at the bore radius of 10 mm
quadrupole octupole 12-pole 16-pole
Section 1
Section 2
Section 3
100 % ÿ0.397 % +0.069 % +0.005 %
100 % ÿ2.312 % ÿ0.047 % +0.080 %
100 % +2.855 % +0.518 % ÿ1.051 %
G. Datzmann et al. / Nucl. Instr. and Meth. in Phys. Res. B 158 (1999) 74±80
2.2. Realisation A lot of eorts have been made to minimize parasitic aberrations due to mechanical imperfections and misalignment of the lens elements. Instead of positioning separate high order multipole magnets, the hyperbolic surface of a quadrupole magnet has been specially shaped containing the correction ®elds from Table 1 inherently. All 12 pole pieces of the three quadrupole sections are pressed on a common central ceramic tube (Al2 O3 ) to adjust the pole pieces to each other (see Fig. 3). In order to avoid parasitic multipole components the pole contours have to be de®ned up to a high degree. An acceptable change of the octupole strength of 0.05 % (de®nition as in Table 1) results in a contour modi®cation of at most 5 lm within the sector. By surface pro®lometry it was con®rmed that the grinding tolerances of the CoFe pole surface is <2 lm. The outer surface of this tube has also been successfully grinded according to the pole contour with tolerances lower than 5 lm. The symmetry of the four contours in each magnetic section of the ceramic deviates only about 2 lm. Hence, the relative position of all poles to each other will be within the same accuracy as the grinding tolerance. Contour modi®cations due to thermal contraction of the pole pieces amount maximal 1 lm and are therefore negligible.
77
Between the pole pieces of each section multilayers of thin superconducting NbTi-foil are positioned on the ceramic tube along the desired ®eld lines. As mentioned above, the induced superconducting currents shall eliminate the magnetic ®eld normal to the foil surface. The NbTi-foils are ®xed to the ceramic surface by a thin adhesive ®lm. A thickness of only 4 1 lm was achieved rolling ¯uid epoxy on the ceramic. Thereby, the original shape of the ceramic surface is preserved within the required tolerances. The whole multipole lens is operated in a specially designed helium bath cryostat. The design of the multipole lens oers a possibility to add a variable electric octupole correction ®eld. Choosing ceramic as central support the NbTi-foils are electrically isolated from the pole pieces. Therefore high voltage can be applied to all foils of one magnetic section. The breakthrough voltage between a foil and a pole piece at a distance of 1 mm in liquid helium has been experimentally determined to be 4 kV. This allows a rather high degree of correction potential. Table 2 gives a comparison of the forces exerted to dierent ions and energies by the maximum electrical and built in magnetic octupole. Since the high voltage can be adjusted in each magnetic section separately, there are three independent parameters at our disposal.
Fig. 3. Photo of major components of the superconducting multipole lens. The white grinded ceramic tube in the middle, the aluminium cage for the 12 pole pieces and the octagonal iron yoke. One the left side one pole piece can been seen.
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G. Datzmann et al. / Nucl. Instr. and Meth. in Phys. Res. B 158 (1999) 74±80
Table 2 List of planned projectile types and energies. The last column contains the degree to which the implemented maximum magnetic octupole component can be altered by applying the maximum voltage of 4 kV to the foils as an electrical octupole correction Ion
Energy (MeV)
AE/q2 (MeV)
p p
30 20 30 60 60 170 170
30 20 30 26.7 189.6 149.9 198.2
16
O4 O6 79 Br5 127 12 I 197 Au13 16
Magnetic quadrupole ®eld (T) 0.454 0.370 0.454 0.428 1.140 1.014 1.166
3. Multipole detection device It has been reported [9], that an axial analysis of the magnetic ®eld in lenses used for microprobe applications has advantages compared to grid shadow methods. Especially, due to the novel design of the superconducting lens, miscellaneous questions arise concerning their multipole components. Hall probes suggested in Ref. [7] are not suitable, because of an enormous temperature gradient from 300 (outside the lens) to 4 K (inside) due to the ``cold'' superconducting lens. Additionally, this means that the whole apparatus has to work under vacuum condition. Therefore, a multipole detection device based on a rotating coil system has been developed that faces these special requirements. Small induction coils with dierent geometries are mounted on a long glass tube,
Max. electrical octupole vs. intrinsic magnetic octupole (%) 42 62 163 122 102 86 93
which is rotated by a DC motor with variable speed (Fig. 4). The whole equipment is placed in a vacuum chamber mounted in front of the superconducting lens. It is ®xed on a linear transporter to scan along the complete axis of the magnetic lens. The voltage signals of the coil can be variably ampli®ed up to a factor of 105 . The sinusoidal signals are converted into a modulated frequency signal. Both electronic circuits rotate on the axis to enable a wireless data transmission. The generated frequency is sent by infra red-diodes located in the center of the rotating glass tube to photo-diodes outside the rotating system. A standard personal computer equipped with a frequency counter card provides the data acquisition system. The incrementer of the rotation motor gates the data collection in exactly 100 angular equidistant steps per
Fig. 4. Multipole detection device in front of a standard quadrupole magnet. The small induction coil on the left at the end of the glass tube is utilised to scan the magnetic ®eld of the multipole lens inside the ceramic tube.
G. Datzmann et al. / Nucl. Instr. and Meth. in Phys. Res. B 158 (1999) 74±80
turn of the coil. Using this signal the measured voltages are corrected for the actual rotation speed. A harmonic Fourier analysis of the signal provides the amplitudes and phases of the multipole components. Since one gets a complete multipole expansion around the rotation center of the coil, the multipole contribution in any point of this plane can be calculated by transformation of coordinates. As described above it is planned to measure several magnetic properties of the multipole lens. The ®rst question to answer is the actual strength of the implemented correction multipole components in the central region of each section (see Table 1). Therefrom the octupole is the largest and most important contribution, but it is intended to accurately measure the 12- and 16-pole as well. Test measurements in a conventional quadrupole magnet revealed that the quadrupole signal to background ratio is better than 1 ´ 10ÿ4 (see Fig. 5). The detection limit for higher order compo-
79
nents depend strongly on the geometry of the used induction coil. A special program code was developed to optimize and to calibrate the induced voltage in the coil for a desired multipole. Taking this into account the detection limit for octupole ®elds in the will be 0.03% for the 12-pole 0.05% and for the 16-pole 0.35% compared to the quadrupole strength at the bore radius of 10 mm. The triangles in Fig. 5 represent the expected signal height for the multipole contributions in the third section of the superconducting lens if optimized coils for each component are taken. The sextupole component was found to be the most commonly generated parasitic aberration and has also the largest eect on microprobe resolution [9]. Since this is an odd harmonic ®eld (m 3) it is possible to measure it without the dominant quadrupole ®eld improving the resolution. Basically, there are two geometries to do so: Rotation of two symmetric coils [9]; or even simpler a large coil rotating around its center.
Fig. 5. Fourier spectrum of a measurement in a standard quadrupole magnet. Besides the dominant quadrupole peak (m 2) small contributions of higher order ®eld components can be observed. The triangles represent the expected values for the correction multipole components for a measurement in the third section of the superconducting multipole lens.
80
G. Datzmann et al. / Nucl. Instr. and Meth. in Phys. Res. B 158 (1999) 74±80
However, mechanical vibrations of the coil which could be suppressed for the even components appear in this signals, deteriorating the resolution. This limits the sextupole detection in a quadrupole magnet to 0.2% of the quadrupole amplitude. Measuring the sextupole component along the three sections of the lens, local misalignments can be spotted. Analysing the multipole components of the fringe ®elds will be a major interest if the special shaped pole edges generate the desired analytical magnetic quadrupole ®eld. The investigations will also be focused to the duodecapole component which is the largest aberration component in the fringe ®eld. Therefore a special induction coil with a small extension in the direction of the beam axis will be chosen to get a good resolution in this direction. 4. Conclusion All parts of the superconducting multipole lens are ®nished and show the desired mechanical precision. A complete cooling cycle of the whole lens down to 4 K has been carried out successfully and revealed no mechanical problems due to thermal contraction of the dierent materials. After their assembly, a ®rst test of the magnetic ®eld with the multipole detection device is planned. Measurements of a standard quadrupole singlet revealed a good performance of the magnetic ®eld probe with sucient accuracy.
Acknowledgements This work has been supported by the Beschleunigerlaboratorium of the Technische Universitat and Ludwig-Maximilians-Universitat M unchen and the Bundesministerium f ur Forschung und Technologie (Kont. Nr. 06TM8739). References [1] G. Hinderer, G. Dollinger, G. Datzmann, H.-J. K orner, Nucl. Instr. and Meth. B 130 (1997) 51. [2] O. Schmelmer, G. Dollinger, G. Datzmann, C. Goeden, H.-J. K orner, these proceedings (ICNMTA-6), Nucl. Instr. and Meth. B 158 (1999) 107. [3] Air cooled direct extraction duoplasmatron 1995, Fa. NEC Middleton, Wisconsin, USA. [4] U.A.S Tapper, W.R. McMurray, G.F. Ackermann, C. Churms, G. De Villiers, D. Fourie, P.J. Groenewald, J. Kritzinger, C.A. Pineda, J. Pilcher, H. Schmitt, K. Springhorn, T. Swart, Nucl. Instr. and Meth. B 77 (1993) 17. [5] G.R. Moloney, D.N. Jamieson, G.J.F. Legge, Nucl. Instr. and Meth. B 77 (1993) 35. [6] M. Szilagyi, Electron and Ion Optics, Plenum, New York, 1988. [7] G.R. Moloney, D.N. Jamieson, G.J.F. Legge, Nucl. Instr. and Meth. B 54 (1991) 24. [8] G.W. Grime, F. Watt, Beam Optics of Quadrupole Probe Forming Systems, Adam Hilger, Bristol, 1984, p. 41. [9] M.B.H. Breese, D.N. Jamieson, J.A. Cookson, Nucl. Instr. and Meth. B 54 (1991) 28.
www.elsevier.nl/locate/nimb
A superconducting multipole lens for focusing high energy ions G. Datzmann *, G. Dollinger, G. Hinderer, H.-J. K orner Physik Department E12, Technische Universit at M unchen, D-85748 Garching, Germany
Abstract At the Munich 15 MV tandem accelerator a new two stage microprobe system Supraleitendes Nanoskop f ur Angewandte Kernphysikalische Experimente (SNAKE) is currently under construction. In contrast to existing facilities, it is projected to focus up to 30 MeV protons as well as heavy ions with maximum energies of 200 MeV q2 /A to a submicron beam spot. In order to achieve this goal, a superconducting lens with inherent multipole corrections and special shaped edges with respect to fringe ®eld calculations was designed. The introduction of superconductivity enables a pole tip ®eld of 1.2 T at 10 mm bore radius and the possibility of auto correction mechanisms. An implemented electrostatic octupole for active ®eld correction will have a maximum ®eld strength in the same order of magnitude as the intrinsic magnetic octupole correction. For an analytical test of the novel concepts of this lens, a multipole detection device on the rotating coil principle has been built. It is capable of measuring small multipole contributions on a strong quadrupole ®eld. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 07.55.G; 41.85.L; 07.79
1. Introduction The new microbeam facility Supraleitendes Nanoskop f ur Angewandte Kernphysikalische Experimente (SNAKE) at the Munich tandem accelerator is currently under construction [1]. Protons with energies up to 30 MeV as well as heavy ions up to 200 MeV q2 /A shall be focused to a submicron beam spot in standard analyses. This facility aims to investigate and modify micro and nano structured materials coming from solid state physics, biology and geology. The small beam di-
* Corresponding author. Tel.: +49-89-289-14350; fax: +4989-289-12297; e-mail: [email protected]
ameter will be achieved in a two stage ion optical system (Fig. 1). The object of the demagni®cation is provided by a special developed microslit system [2], which operates as the analysing slits of the 90° magnet. The ®rst part of demagni®cation is performed by a standard quadrupole doublet lens. Since the imaging system is accomplished as a separated Russian quadruplet (SRQ), the intermediate foci enable using additional scattering slits. The second and main demagni®cation stage consists of a superconducting multipole lens operating as a quadrupole doublet with ferromagnetic pole pieces. This leads to an overall demagni®cation factor of 200 in both transversal directions. Having an object size of 20 lm, the ion optic will produce a beam spot of 100 nm at the
0168-583X/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 3 0 8 - 0
G. Datzmann et al. / Nucl. Instr. and Meth. in Phys. Res. B 158 (1999) 74±80
75
A beam spot size of 100 nm in diameter can only be achieved, if all types of aberrations are suppressed to low values, which means high perfection of the magnetic ®eld. For this purpose superconductivity can be used for auto correction mechanisms. Field distortions due to asymmetric ¯ux through the four poles will be eliminated by superconducting current loops between each pole and its two next neighbours [1]. 2.1. Treatment of the fringe ®eld Fig. 1. Scheme of the two stage ion beam optics.
target. In order to reduce the chromatic aberrations to the same value a relative energy spread of 10ÿ5 is driven at. The beam conditions at the Munich tandem accelerator will result in a proton current of 100 pA even at this small beam diameter. The brightness of Hÿ beam is actually limited by the ion source, e.g., a brightness of 2 ´ 10ÿ6 A/(mm2 mrad2 MeV) for a commercial duoplasmatron source [3]. High quality beam optic components have to be used in order to reduce aberrations to low levels ®nally achieving the desired diameters for the high energy protons and heavy ion beams. In Section 2 the requirements for such a high resolution system and the realisation concepts are presented. The third section deals with a rotating ®eld probe, which will be used to measure the magnetic multipole components of the superconducting lens.
2. Design of the new superconducting multipole lens First of all, a magnetic ®eld gradient of more than 1 T/cm is necessary in order to focus ions with energies up to 200 MeV q2 /A within a focal length of about 300 mm. A new design, utilising CoFe (ratio 1:1) pole pieces surrounded by small superconducting coils, leads to a calculated poletip ®eld of 1.2 T at a bore radius of 10 mm [1]. This is about three times larger than provided by commercially available quadrupole lenses for microprobe applications [4].
One of the main limits in high precision focusing are the geometric aberrations arising from non-ideal ®eld components within a magnetic lens and in the fringing ®eld region. Whereas errors introduced by large apertures inside the magnet can be simulated easily, fringe ®eld eects are hard to handle. It has been reported [5] that multipole components generated by the fringe ®eld can aect the spot size in the same order of magnitude as the aberrations from inside the quadrupole. Both aberrations are inevitable and need to be corrected to meet the projected beam diameter as stated above. Therefore higher order multipole components such as magnetic octupole etc. are added to the focusing system. The magnitude of components, necessary to eliminate the geometrical aberrations of a given lens system, can be eectively calculated only if fringing ®elds of the magnet sections are known. The total multipole series of the magnetic ®eld was ®xed by a new method which is summarized in the following. In principal, the static magnetic potential u may be expressed in polar coordinates r, u, z [6] 1 X 1 X A m; k r2km Um 2k z cos ma u r; a; z m0 k0
Wm 2k z sin ma ; 1 where k
A m; k
ÿ 1 m! : 4k k! m k !
Thereby m is the order of multipole ®eld and the superscript (2k) on Wm and Um denotes the 2k-th
76
G. Datzmann et al. / Nucl. Instr. and Meth. in Phys. Res. B 158 (1999) 74±80
derivative with respect to z. All Um components are zero if skewed 1 multipole components are disregarded. In the central region of a magnet Wm (z) is nearly constant, and therefore all derivatives of W are negligible. This leads to a rather simple equation for the magnetic potential u. Reaching the pole edges the quadrupole strength W2 (z) begins to decline, producing non-zero values for the derivatives and the creation of functions Wm (z) with m ¹ n. However, due to the 4-fold symmetry only functions with m 2l 1n;
l 1; 2; . . . ;
2
are involved [7]. Calculating the three dimensional magnetic ®eld from a given boundary condition introduced by the pole and the superconducting surfaces with sucient accuracy seems to be unpromisingly. Therefore a novel approach to overcome the fringe ®eld problem was chosen for the multipole lens which is exactly vice versa. The pole surface being a constant magnetic potential is calculated from a desired ®eld distribution. Thereby the superconducting surfaces are ®xed in the fringe ®eld region as they are between the poles. For the calculation it has been assumed that the magnetic ®eld vector is always tangential to the foil surface because of self-induced superconducting currents [1]. Finally, an analytical function W2 (z) for the longitudinal quadrupole ®eld pro®le suggested for lenses where the bore radius is smaller then their length [8] is assumed W2 z
1 eP z0 ; 1 eP z
where P z A1 A2 z A3 z2 A4 z3 A5 z4 :
3
Choosing a set of parameters Ai for P(z) and satisfying the given boundary conditions the pole surface at the edge can be calculated as an equipotential surface where u(r,u,z) is constant. Some care should be taken on the choice of the polynomial P(z) to reach a rather smooth behaviour of the resulting pole surface. Fig. 2 shows the selected
1
Symmetry axis of the 2m multipole rotated around 90°/m.
Fig. 2. Calculated magnetic ®eld at the edges of a magnet section for the chosen polynomial P(z). The upper plot shows the curvature of one pole piece in a cross sectional view.
parameters, the decreasing quadrupole ®eld and the corresponding sectional view of the longitudinal pole contour. With these input parameters the magnetic ®eld in the whole lens can be analytically derived from Eq. (1). A home made raytracing code QTRACE was used to optimize the geometric aberrations by adding higher order multipole ®elds. The ®nal result of the procedure is given in Table 1. Although the lens is operated as a quadrupole doublet, the second singlet is divided into two separate sections in order to get three parameters necessary for a complete octupole correction.
Table 1 Relative strength of the higher order multipole correction ®elds for the three magnetic sections. All values are normalized to the quadrupole strength at the bore radius of 10 mm
quadrupole octupole 12-pole 16-pole
Section 1
Section 2
Section 3
100 % ÿ0.397 % +0.069 % +0.005 %
100 % ÿ2.312 % ÿ0.047 % +0.080 %
100 % +2.855 % +0.518 % ÿ1.051 %
G. Datzmann et al. / Nucl. Instr. and Meth. in Phys. Res. B 158 (1999) 74±80
2.2. Realisation A lot of eorts have been made to minimize parasitic aberrations due to mechanical imperfections and misalignment of the lens elements. Instead of positioning separate high order multipole magnets, the hyperbolic surface of a quadrupole magnet has been specially shaped containing the correction ®elds from Table 1 inherently. All 12 pole pieces of the three quadrupole sections are pressed on a common central ceramic tube (Al2 O3 ) to adjust the pole pieces to each other (see Fig. 3). In order to avoid parasitic multipole components the pole contours have to be de®ned up to a high degree. An acceptable change of the octupole strength of 0.05 % (de®nition as in Table 1) results in a contour modi®cation of at most 5 lm within the sector. By surface pro®lometry it was con®rmed that the grinding tolerances of the CoFe pole surface is <2 lm. The outer surface of this tube has also been successfully grinded according to the pole contour with tolerances lower than 5 lm. The symmetry of the four contours in each magnetic section of the ceramic deviates only about 2 lm. Hence, the relative position of all poles to each other will be within the same accuracy as the grinding tolerance. Contour modi®cations due to thermal contraction of the pole pieces amount maximal 1 lm and are therefore negligible.
77
Between the pole pieces of each section multilayers of thin superconducting NbTi-foil are positioned on the ceramic tube along the desired ®eld lines. As mentioned above, the induced superconducting currents shall eliminate the magnetic ®eld normal to the foil surface. The NbTi-foils are ®xed to the ceramic surface by a thin adhesive ®lm. A thickness of only 4 1 lm was achieved rolling ¯uid epoxy on the ceramic. Thereby, the original shape of the ceramic surface is preserved within the required tolerances. The whole multipole lens is operated in a specially designed helium bath cryostat. The design of the multipole lens oers a possibility to add a variable electric octupole correction ®eld. Choosing ceramic as central support the NbTi-foils are electrically isolated from the pole pieces. Therefore high voltage can be applied to all foils of one magnetic section. The breakthrough voltage between a foil and a pole piece at a distance of 1 mm in liquid helium has been experimentally determined to be 4 kV. This allows a rather high degree of correction potential. Table 2 gives a comparison of the forces exerted to dierent ions and energies by the maximum electrical and built in magnetic octupole. Since the high voltage can be adjusted in each magnetic section separately, there are three independent parameters at our disposal.
Fig. 3. Photo of major components of the superconducting multipole lens. The white grinded ceramic tube in the middle, the aluminium cage for the 12 pole pieces and the octagonal iron yoke. One the left side one pole piece can been seen.
78
G. Datzmann et al. / Nucl. Instr. and Meth. in Phys. Res. B 158 (1999) 74±80
Table 2 List of planned projectile types and energies. The last column contains the degree to which the implemented maximum magnetic octupole component can be altered by applying the maximum voltage of 4 kV to the foils as an electrical octupole correction Ion
Energy (MeV)
AE/q2 (MeV)
p p
30 20 30 60 60 170 170
30 20 30 26.7 189.6 149.9 198.2
16
O4 O6 79 Br5 127 12 I 197 Au13 16
Magnetic quadrupole ®eld (T) 0.454 0.370 0.454 0.428 1.140 1.014 1.166
3. Multipole detection device It has been reported [9], that an axial analysis of the magnetic ®eld in lenses used for microprobe applications has advantages compared to grid shadow methods. Especially, due to the novel design of the superconducting lens, miscellaneous questions arise concerning their multipole components. Hall probes suggested in Ref. [7] are not suitable, because of an enormous temperature gradient from 300 (outside the lens) to 4 K (inside) due to the ``cold'' superconducting lens. Additionally, this means that the whole apparatus has to work under vacuum condition. Therefore, a multipole detection device based on a rotating coil system has been developed that faces these special requirements. Small induction coils with dierent geometries are mounted on a long glass tube,
Max. electrical octupole vs. intrinsic magnetic octupole (%) 42 62 163 122 102 86 93
which is rotated by a DC motor with variable speed (Fig. 4). The whole equipment is placed in a vacuum chamber mounted in front of the superconducting lens. It is ®xed on a linear transporter to scan along the complete axis of the magnetic lens. The voltage signals of the coil can be variably ampli®ed up to a factor of 105 . The sinusoidal signals are converted into a modulated frequency signal. Both electronic circuits rotate on the axis to enable a wireless data transmission. The generated frequency is sent by infra red-diodes located in the center of the rotating glass tube to photo-diodes outside the rotating system. A standard personal computer equipped with a frequency counter card provides the data acquisition system. The incrementer of the rotation motor gates the data collection in exactly 100 angular equidistant steps per
Fig. 4. Multipole detection device in front of a standard quadrupole magnet. The small induction coil on the left at the end of the glass tube is utilised to scan the magnetic ®eld of the multipole lens inside the ceramic tube.
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turn of the coil. Using this signal the measured voltages are corrected for the actual rotation speed. A harmonic Fourier analysis of the signal provides the amplitudes and phases of the multipole components. Since one gets a complete multipole expansion around the rotation center of the coil, the multipole contribution in any point of this plane can be calculated by transformation of coordinates. As described above it is planned to measure several magnetic properties of the multipole lens. The ®rst question to answer is the actual strength of the implemented correction multipole components in the central region of each section (see Table 1). Therefrom the octupole is the largest and most important contribution, but it is intended to accurately measure the 12- and 16-pole as well. Test measurements in a conventional quadrupole magnet revealed that the quadrupole signal to background ratio is better than 1 ´ 10ÿ4 (see Fig. 5). The detection limit for higher order compo-
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nents depend strongly on the geometry of the used induction coil. A special program code was developed to optimize and to calibrate the induced voltage in the coil for a desired multipole. Taking this into account the detection limit for octupole ®elds in the will be 0.03% for the 12-pole 0.05% and for the 16-pole 0.35% compared to the quadrupole strength at the bore radius of 10 mm. The triangles in Fig. 5 represent the expected signal height for the multipole contributions in the third section of the superconducting lens if optimized coils for each component are taken. The sextupole component was found to be the most commonly generated parasitic aberration and has also the largest eect on microprobe resolution [9]. Since this is an odd harmonic ®eld (m 3) it is possible to measure it without the dominant quadrupole ®eld improving the resolution. Basically, there are two geometries to do so: Rotation of two symmetric coils [9]; or even simpler a large coil rotating around its center.
Fig. 5. Fourier spectrum of a measurement in a standard quadrupole magnet. Besides the dominant quadrupole peak (m 2) small contributions of higher order ®eld components can be observed. The triangles represent the expected values for the correction multipole components for a measurement in the third section of the superconducting multipole lens.
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However, mechanical vibrations of the coil which could be suppressed for the even components appear in this signals, deteriorating the resolution. This limits the sextupole detection in a quadrupole magnet to 0.2% of the quadrupole amplitude. Measuring the sextupole component along the three sections of the lens, local misalignments can be spotted. Analysing the multipole components of the fringe ®elds will be a major interest if the special shaped pole edges generate the desired analytical magnetic quadrupole ®eld. The investigations will also be focused to the duodecapole component which is the largest aberration component in the fringe ®eld. Therefore a special induction coil with a small extension in the direction of the beam axis will be chosen to get a good resolution in this direction. 4. Conclusion All parts of the superconducting multipole lens are ®nished and show the desired mechanical precision. A complete cooling cycle of the whole lens down to 4 K has been carried out successfully and revealed no mechanical problems due to thermal contraction of the dierent materials. After their assembly, a ®rst test of the magnetic ®eld with the multipole detection device is planned. Measurements of a standard quadrupole singlet revealed a good performance of the magnetic ®eld probe with sucient accuracy.
Acknowledgements This work has been supported by the Beschleunigerlaboratorium of the Technische Universitat and Ludwig-Maximilians-Universitat M unchen and the Bundesministerium f ur Forschung und Technologie (Kont. Nr. 06TM8739). References [1] G. Hinderer, G. Dollinger, G. Datzmann, H.-J. K orner, Nucl. Instr. and Meth. B 130 (1997) 51. [2] O. Schmelmer, G. Dollinger, G. Datzmann, C. Goeden, H.-J. K orner, these proceedings (ICNMTA-6), Nucl. Instr. and Meth. B 158 (1999) 107. [3] Air cooled direct extraction duoplasmatron 1995, Fa. NEC Middleton, Wisconsin, USA. [4] U.A.S Tapper, W.R. McMurray, G.F. Ackermann, C. Churms, G. De Villiers, D. Fourie, P.J. Groenewald, J. Kritzinger, C.A. Pineda, J. Pilcher, H. Schmitt, K. Springhorn, T. Swart, Nucl. Instr. and Meth. B 77 (1993) 17. [5] G.R. Moloney, D.N. Jamieson, G.J.F. Legge, Nucl. Instr. and Meth. B 77 (1993) 35. [6] M. Szilagyi, Electron and Ion Optics, Plenum, New York, 1988. [7] G.R. Moloney, D.N. Jamieson, G.J.F. Legge, Nucl. Instr. and Meth. B 54 (1991) 24. [8] G.W. Grime, F. Watt, Beam Optics of Quadrupole Probe Forming Systems, Adam Hilger, Bristol, 1984, p. 41. [9] M.B.H. Breese, D.N. Jamieson, J.A. Cookson, Nucl. Instr. and Meth. B 54 (1991) 28.