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Design study of the KINRIS isotope separator with a 270° wide aperture magnet
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NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 266 (2008) 4188–4191 www.elsevier.com/locate/nimb
Design study of the KINRIS isotope separator with a 270° wide aperture magnet A. Dolinskii b,*, A. Demyanov a, M. Dolinska a, A. Kolosov a, A. Valkov a a
Institut for Nuclear Research, Prospect Nauki 46, 02038 Kiev, Ukraine b GSI, Planckstrasse 1, 64291 Darmstadt, Germany Available online 3 June 2008
Abstract A new isotope separator KINRIS (Kiev Institute for Nuclear Research Isotope Separator) is being constructed at the Institute for Nuclear Research in Kiev (Ukraine). This paper reviews main features of the electromagnetic separator for stable isotopes production using an analyzing magnet with an inhomogeneous magnetic field. Beam-optical principles of the KINRIS separator and results of beamoptical calculations are discussed. In this paper we consider the influence of a beam emittance, momentum spread and aberrations on the mass resolving power of the KINRIS separator. Results show that this separator can be used for isotopes production with an excellent efficiency for any ion mass. Ó 2008 Elsevier B.V. All rights reserved. PACS: 28.60.+s; 41.85.p; 41.75.i Keywords: KINRIS; Isotope separator; Mass resolving power; Ion optic
1. Introduction For the KINRIS separator [1] the goal is to achieve a high mass resolving power at a large acceptance. For design of the separator we are following the requirements: usable with any ion source having either circular or slit geometry and having a high current capability up to 10 mA; a transmission not less than 90%; not more than 1% disruption of original isotopic ratios; a double-directional focusing; a variable dispersion; a focal plane mass spread of 10% [(Mmax Mmin)/Mmin]; a total magnet contribution to aberrations less than 1 mm. The particles with low charge states (+1) are not strongly affected by space charge forces with currents up to 0.1 mA. But for a higher ion current one has to apply a high beam neutralization rate resulting in a lower emittance growth and a higher transmission as it is discussed in [1]. In the following simu-
*
Corresponding author. Tel.: +49 6159 711511. E-mail address: [email protected] (A. Dolinskii).
0168-583X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2008.05.025
lations we assume that the separator at the design intensity of 10 mA is space charge forces free.
2. First order design The general appearance of the KINRIS separator system is shown in Fig. 1, which shows also schematically the various beam-optical elements. The main component of the separator is the CP17 large aperture analyzing magnet [2] (Fig. 2) with an inhomogeneous field, a bending radius q of 2 m and a deflection angle U = 270°. This analyzing magnet determines most of the beam optics of the separator and is placed in a symmetrical arrangement with respect to an ion source and the focal plane. The magnet has an adjustable quadrupole component that provides an adjustable first field index n in the range of from zero up to one. This last adjustment can be easily obtained by use of so-called a-coils (Fig. 2). The dispersion function of such type of magnets is defined by means of the formula
A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4188–4191
4189
lyzing magnet. The ‘‘ordinary” einzel lens is placed close to the extraction region of the ion source. Using the quadrupole magnet in combination with the ‘‘ordinary” einzel lens, the beam emittance pattern can be varied to match to the acceptance of the magnet, thereby increasing the resolving power of the system. Fig. 3 shows the beam envelopes throughout the whole system in the horizontal and vertical directions with a typical set of initial parameters given in Table 1. The mass resolving power of a separator with an inhomogeneous magnet field in case of symmetrical positioning of the source and the image with respect to the magnet is defined by P¼
hxjdm i 2q 1 ¼ ; 2xf 1 n 2xf
ð2Þ
Fig. 1. General layout of the KINRIS isotope separator.
" # 2q0 1 pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi ; 1 Dm ¼ ð1 nÞ cosðU 1 nÞ 1 n Rl10 sinðU 1 nÞ ð1Þ where q0 is a mean radius of the magnet, l1 is a distance from source to the magnet entrance, U is a deflection angle. The mass dispersion Dm is variable depending on the field index n. If n close to 0.7 the ion optics of the system is doubly focusing and the mass dispersion Dm is 12 m. For such Dm two beams with the mass A = 100 and A = 101 are separated by 11 cm. Due to simultaneous focusing in both the horizontal and vertical directions, the exit slit of the ion source is imaged in the focal plane. In this system a mass-separated beam with ion energies in the range of 30–90 keV can be focused. Since the CP17 magnet is installed in one of the U-240 isochronous cyclotron transport branches, the ion source and focal plane are not at the optimal position, where the maximal mass resolving power can be achieved without any additional ion-optical elements. For this reason the beam optics are modified by including additional beam-optical elements in front of the CP17 ana-
Fig. 3. Calculated horizontal and vertical beam envelopes (upper and lower curves respectively) for the horizontal emittance ex = 30p mm mrad and the vertical emittance ey = 200p mm mrad.
Table 1 Basic parameters of the KINRIS separator Deflection angle of dipole magnet, U (deg) Mean radius of dipole magnet, q (m) Source to magnet distance, L0 (m) First field index, n Magnet to focus distance, Lim (m) Horizontal Acceptance, ex (p mm mrad) Vertical Acceptance, ey (p mm mrad) Mass resolving power, P
270 2 1 0.7 1 30 200 2 103
Fig. 2. A cross section view of the inhomogeneous dipole magnet CP17. Details of the main (1), alfa (2) and stabilized (3) coils are shown.
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A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4188–4191
where hx|dmi is the first order mass dispersion matrix element, dm is the relative mass deviation and 2xf is the final beam spot at the mass slit in the dispersive plane. With the assumption that the width 2xf is 6 mm in a linear separator approximation the resulting linear mass resolving power is 2 103. 3. Nonlinear ion-optical calculations of the separator lattice Constructive inaccuracies in a configuration of magnet poles and errors in a current installation cause aberrations, which have the effect of increasing image sizes on the focal plane. As consequence the achievable resolving power of the separator is limited. This effect is called the ‘‘emittance blow-up”. Uncorrected aberrations may increase the image size by a factor of five or so, with a proportional reduction in the mass resolving power. In a linear approximation the maximum attainable resolving power is determined by the emittance of an ion beam coming out an ion source and the dispersion of the isotope separator on the focal plane. The formula (2) is obtained only in a linear approximation, since for higher order calculations the dispersion matrix element must be replaced by a combination of higher order matrix elements. Considering the aberrations, the width will be the value Dxx0 y0 instead of 2xf, which has as an upper bound Dxx0 y 0 ¼ 2jhxjxix0 j þ jhxjx2 ijx20 þ jhxjxx0 ix0 x00 j þ jhxjx0 dij þ . . . ;
Fig. 4. Beam spots in the phase spaces at the end of the extraction system of the ion source.
ð3Þ
where x0 is the half-width of the angular spread, terms (x|xmx0 n) are the transfer matrix elements, d is a relative momentum deviation (Dp/p). Since the entrance slit x0 is usually small and the solid angle large, only the angle and dispersion aberrations are important. Both map calculations and geometric considerations show that all the terms (x|xmx0 n) (m + n even) vanish. Since (x|y0 2) is usually small, only the second-order term (x|x0 d) has a strong impact and can be as large as 10 mm for the momentum spread of d = 0.2%. In fact, this is the most important factor that causes the decrease of the resolving power. This becomes apparent when the resolving power considering is calculated by P¼
2q 1 2q 1 xd ¼ ¼ : 0 0 ð1 nÞ ð2hxjxix0 þ hxjx dixi dÞ ð1 nÞ xab xab ð4Þ
With the seventh order approximation the particle tracking through the separator has been calculated numerically using the Monte Carlo method. The initial coordinates of particles are taken at the end of the extraction system of the ion source and shown in Fig. 4. The total spot width of xab formed on the focal plane is analyzed. The main contribution in blow up of the beam spots occurs due to dm dependent aberrations. Another result of simulations was that the resolving power of the mass separator depends strongly on the ion beam emittance coming out of the
Fig. 5. Dependence of the achievable maximal horizontal emittance on the momentum spread at the different mass resolving power P.
ion source. In Fig. 5 the dependence of the resolving power on the emittance can be seen. We see that nonlinear field errors have very strong effect if the beam emittance is larger than 10p mm mrad. The resolving power is catastrophically dropped down to several units for a relatively large emittance if its value is in the range of 20–100p mm mrad. However the situation can essentially be improved by means of a sextupolar correction using a sextupole magnet, which position is shown in Fig. 1. For the spot width we assume a statistical rms values with 4r standard deviations. This criterion is necessary to ensure that an overlap between isotopes and a residual gas will be only 0.01% at the mass slit, since the 4r rms value contains 99.99% of the particles. The resolving power of 150 could be ensured for the horizontal emittance up to 40p mm mrad and the momentum spread of 0.5%. To study the achievable parameters of the ion beam, which can be supplied at obtaining of a designed resolving power, series of calculations have been carried out. In Fig. 6 one can see how the resolving power depends on both the beam emittance and the momentum spread. The given results in Fig. 6 have been obtained at the fixed value of the momentum spread d = 0.2%.
A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4188–4191
Fig. 6. Calculated mass resolving power versus horizontal emittance at the fixed momentum spread of 0.2%.
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the separator, which consists of the CP17 high aperture analyzing magnet. This magnet has an inhomogeneous magnetic field that provides double focusing of the ion beam. In combination with additional focusing magnets the value of 12 m of the dispersion function on the focal plane can be reached that leads to the high mass resolving power in this separator. The influence of aberrations resulting from different types of focusing systems (such as an extraction system of the ion source, the nonlinearity of the magnet field in the CP17 dipole) puts an upper limit on the resolving power, which was obtained. The introduction of several optical elements (the quadrupole magnet, the einzel lens and the sextupole magnet) into the KINRIS separator has improved the mass resolving power of the system considerably. The result of simulations shows that the resolving power of the mass separator depends strongly on both the emittance and the momentum spread of the ion beam coming out of the ion source. The resolving power of 150 could be ensured for the horizontal emittance up to 40p mm mrad and for a momentum not larger then 0.2%.
4. Conclusion References The electromagnetic isotope separator at the Kiev Institute for Nuclear Research, Ukrainian National Academy, has been developed. This isotope separator is under construction and will be used for research on the separation of stable isotopes, the development of technological equipments and the production of highly enriched stable isotopes. Ion-optical calculations have been performed for
[1] A. Valkov, A. Demyanov, A. Dolinskii, M. Dolinska, Yu. Kamishnikov, Utilization of the magnet monochromator of the isochronous cyclotron U-240 for the stable ions separations, Scientific papers of the INR, Kiev No.1 (14), 2005 (in Ukrainian). [2] Yu. Basargin, N. Doynikov, A. Popov, B. Rozhdestvenskiy, G. Samsonov, A. Simakov, J Tech Phys XXXIX (N8) (1969) 147, (in Russian).
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 266 (2008) 4188–4191 www.elsevier.com/locate/nimb
Design study of the KINRIS isotope separator with a 270° wide aperture magnet A. Dolinskii b,*, A. Demyanov a, M. Dolinska a, A. Kolosov a, A. Valkov a a
Institut for Nuclear Research, Prospect Nauki 46, 02038 Kiev, Ukraine b GSI, Planckstrasse 1, 64291 Darmstadt, Germany Available online 3 June 2008
Abstract A new isotope separator KINRIS (Kiev Institute for Nuclear Research Isotope Separator) is being constructed at the Institute for Nuclear Research in Kiev (Ukraine). This paper reviews main features of the electromagnetic separator for stable isotopes production using an analyzing magnet with an inhomogeneous magnetic field. Beam-optical principles of the KINRIS separator and results of beamoptical calculations are discussed. In this paper we consider the influence of a beam emittance, momentum spread and aberrations on the mass resolving power of the KINRIS separator. Results show that this separator can be used for isotopes production with an excellent efficiency for any ion mass. Ó 2008 Elsevier B.V. All rights reserved. PACS: 28.60.+s; 41.85.p; 41.75.i Keywords: KINRIS; Isotope separator; Mass resolving power; Ion optic
1. Introduction For the KINRIS separator [1] the goal is to achieve a high mass resolving power at a large acceptance. For design of the separator we are following the requirements: usable with any ion source having either circular or slit geometry and having a high current capability up to 10 mA; a transmission not less than 90%; not more than 1% disruption of original isotopic ratios; a double-directional focusing; a variable dispersion; a focal plane mass spread of 10% [(Mmax Mmin)/Mmin]; a total magnet contribution to aberrations less than 1 mm. The particles with low charge states (+1) are not strongly affected by space charge forces with currents up to 0.1 mA. But for a higher ion current one has to apply a high beam neutralization rate resulting in a lower emittance growth and a higher transmission as it is discussed in [1]. In the following simu-
*
Corresponding author. Tel.: +49 6159 711511. E-mail address: [email protected] (A. Dolinskii).
0168-583X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2008.05.025
lations we assume that the separator at the design intensity of 10 mA is space charge forces free.
2. First order design The general appearance of the KINRIS separator system is shown in Fig. 1, which shows also schematically the various beam-optical elements. The main component of the separator is the CP17 large aperture analyzing magnet [2] (Fig. 2) with an inhomogeneous field, a bending radius q of 2 m and a deflection angle U = 270°. This analyzing magnet determines most of the beam optics of the separator and is placed in a symmetrical arrangement with respect to an ion source and the focal plane. The magnet has an adjustable quadrupole component that provides an adjustable first field index n in the range of from zero up to one. This last adjustment can be easily obtained by use of so-called a-coils (Fig. 2). The dispersion function of such type of magnets is defined by means of the formula
A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4188–4191
4189
lyzing magnet. The ‘‘ordinary” einzel lens is placed close to the extraction region of the ion source. Using the quadrupole magnet in combination with the ‘‘ordinary” einzel lens, the beam emittance pattern can be varied to match to the acceptance of the magnet, thereby increasing the resolving power of the system. Fig. 3 shows the beam envelopes throughout the whole system in the horizontal and vertical directions with a typical set of initial parameters given in Table 1. The mass resolving power of a separator with an inhomogeneous magnet field in case of symmetrical positioning of the source and the image with respect to the magnet is defined by P¼
hxjdm i 2q 1 ¼ ; 2xf 1 n 2xf
ð2Þ
Fig. 1. General layout of the KINRIS isotope separator.
" # 2q0 1 pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi ; 1 Dm ¼ ð1 nÞ cosðU 1 nÞ 1 n Rl10 sinðU 1 nÞ ð1Þ where q0 is a mean radius of the magnet, l1 is a distance from source to the magnet entrance, U is a deflection angle. The mass dispersion Dm is variable depending on the field index n. If n close to 0.7 the ion optics of the system is doubly focusing and the mass dispersion Dm is 12 m. For such Dm two beams with the mass A = 100 and A = 101 are separated by 11 cm. Due to simultaneous focusing in both the horizontal and vertical directions, the exit slit of the ion source is imaged in the focal plane. In this system a mass-separated beam with ion energies in the range of 30–90 keV can be focused. Since the CP17 magnet is installed in one of the U-240 isochronous cyclotron transport branches, the ion source and focal plane are not at the optimal position, where the maximal mass resolving power can be achieved without any additional ion-optical elements. For this reason the beam optics are modified by including additional beam-optical elements in front of the CP17 ana-
Fig. 3. Calculated horizontal and vertical beam envelopes (upper and lower curves respectively) for the horizontal emittance ex = 30p mm mrad and the vertical emittance ey = 200p mm mrad.
Table 1 Basic parameters of the KINRIS separator Deflection angle of dipole magnet, U (deg) Mean radius of dipole magnet, q (m) Source to magnet distance, L0 (m) First field index, n Magnet to focus distance, Lim (m) Horizontal Acceptance, ex (p mm mrad) Vertical Acceptance, ey (p mm mrad) Mass resolving power, P
270 2 1 0.7 1 30 200 2 103
Fig. 2. A cross section view of the inhomogeneous dipole magnet CP17. Details of the main (1), alfa (2) and stabilized (3) coils are shown.
4190
A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4188–4191
where hx|dmi is the first order mass dispersion matrix element, dm is the relative mass deviation and 2xf is the final beam spot at the mass slit in the dispersive plane. With the assumption that the width 2xf is 6 mm in a linear separator approximation the resulting linear mass resolving power is 2 103. 3. Nonlinear ion-optical calculations of the separator lattice Constructive inaccuracies in a configuration of magnet poles and errors in a current installation cause aberrations, which have the effect of increasing image sizes on the focal plane. As consequence the achievable resolving power of the separator is limited. This effect is called the ‘‘emittance blow-up”. Uncorrected aberrations may increase the image size by a factor of five or so, with a proportional reduction in the mass resolving power. In a linear approximation the maximum attainable resolving power is determined by the emittance of an ion beam coming out an ion source and the dispersion of the isotope separator on the focal plane. The formula (2) is obtained only in a linear approximation, since for higher order calculations the dispersion matrix element must be replaced by a combination of higher order matrix elements. Considering the aberrations, the width will be the value Dxx0 y0 instead of 2xf, which has as an upper bound Dxx0 y 0 ¼ 2jhxjxix0 j þ jhxjx2 ijx20 þ jhxjxx0 ix0 x00 j þ jhxjx0 dij þ . . . ;
Fig. 4. Beam spots in the phase spaces at the end of the extraction system of the ion source.
ð3Þ
where x0 is the half-width of the angular spread, terms (x|xmx0 n) are the transfer matrix elements, d is a relative momentum deviation (Dp/p). Since the entrance slit x0 is usually small and the solid angle large, only the angle and dispersion aberrations are important. Both map calculations and geometric considerations show that all the terms (x|xmx0 n) (m + n even) vanish. Since (x|y0 2) is usually small, only the second-order term (x|x0 d) has a strong impact and can be as large as 10 mm for the momentum spread of d = 0.2%. In fact, this is the most important factor that causes the decrease of the resolving power. This becomes apparent when the resolving power considering is calculated by P¼
2q 1 2q 1 xd ¼ ¼ : 0 0 ð1 nÞ ð2hxjxix0 þ hxjx dixi dÞ ð1 nÞ xab xab ð4Þ
With the seventh order approximation the particle tracking through the separator has been calculated numerically using the Monte Carlo method. The initial coordinates of particles are taken at the end of the extraction system of the ion source and shown in Fig. 4. The total spot width of xab formed on the focal plane is analyzed. The main contribution in blow up of the beam spots occurs due to dm dependent aberrations. Another result of simulations was that the resolving power of the mass separator depends strongly on the ion beam emittance coming out of the
Fig. 5. Dependence of the achievable maximal horizontal emittance on the momentum spread at the different mass resolving power P.
ion source. In Fig. 5 the dependence of the resolving power on the emittance can be seen. We see that nonlinear field errors have very strong effect if the beam emittance is larger than 10p mm mrad. The resolving power is catastrophically dropped down to several units for a relatively large emittance if its value is in the range of 20–100p mm mrad. However the situation can essentially be improved by means of a sextupolar correction using a sextupole magnet, which position is shown in Fig. 1. For the spot width we assume a statistical rms values with 4r standard deviations. This criterion is necessary to ensure that an overlap between isotopes and a residual gas will be only 0.01% at the mass slit, since the 4r rms value contains 99.99% of the particles. The resolving power of 150 could be ensured for the horizontal emittance up to 40p mm mrad and the momentum spread of 0.5%. To study the achievable parameters of the ion beam, which can be supplied at obtaining of a designed resolving power, series of calculations have been carried out. In Fig. 6 one can see how the resolving power depends on both the beam emittance and the momentum spread. The given results in Fig. 6 have been obtained at the fixed value of the momentum spread d = 0.2%.
A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4188–4191
Fig. 6. Calculated mass resolving power versus horizontal emittance at the fixed momentum spread of 0.2%.
4191
the separator, which consists of the CP17 high aperture analyzing magnet. This magnet has an inhomogeneous magnetic field that provides double focusing of the ion beam. In combination with additional focusing magnets the value of 12 m of the dispersion function on the focal plane can be reached that leads to the high mass resolving power in this separator. The influence of aberrations resulting from different types of focusing systems (such as an extraction system of the ion source, the nonlinearity of the magnet field in the CP17 dipole) puts an upper limit on the resolving power, which was obtained. The introduction of several optical elements (the quadrupole magnet, the einzel lens and the sextupole magnet) into the KINRIS separator has improved the mass resolving power of the system considerably. The result of simulations shows that the resolving power of the mass separator depends strongly on both the emittance and the momentum spread of the ion beam coming out of the ion source. The resolving power of 150 could be ensured for the horizontal emittance up to 40p mm mrad and for a momentum not larger then 0.2%.
4. Conclusion References The electromagnetic isotope separator at the Kiev Institute for Nuclear Research, Ukrainian National Academy, has been developed. This isotope separator is under construction and will be used for research on the separation of stable isotopes, the development of technological equipments and the production of highly enriched stable isotopes. Ion-optical calculations have been performed for
[1] A. Valkov, A. Demyanov, A. Dolinskii, M. Dolinska, Yu. Kamishnikov, Utilization of the magnet monochromator of the isochronous cyclotron U-240 for the stable ions separations, Scientific papers of the INR, Kiev No.1 (14), 2005 (in Ukrainian). [2] Yu. Basargin, N. Doynikov, A. Popov, B. Rozhdestvenskiy, G. Samsonov, A. Simakov, J Tech Phys XXXIX (N8) (1969) 147, (in Russian).