REVIEW OF SCIENTIFIC INSTRUMENTS 85, 085113 (2014)
Measurement of axial injection displacement with trim coil current unbalance Michel Kireeff Covoa) Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
(Received 18 May 2014; accepted 26 July 2014; published online 14 August 2014) The Dee probe used for measuring internal radial beam intensity shows large losses inside the radius of 20 cm of the 88 in. cyclotron. The current of the top and bottom innermost trim coil 1 is unbalanced to study effects of the axial injection displacement. A beam profile monitor images the ion beam bunches, turn by turn. The experimental bunch center of mass position is compared with calculations of the magnetic mirror effect displacement and shows good agreement. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4892463] I. INTRODUCTION
The ions produced by the electron cyclotron resonance ion sources are injected inside the 88 in. cyclotron by a mirror inflector. The inflector assembly is a grounded grid mounted with standoffs on a biased plate that is tilted 45◦ above the cyclotron horizontal midplane. The ions entering the grid inflector experience an electrostatic force that directs them to the cyclotron middle plane. After the ions enter the cyclotron, they are accelerated by a radio frequency (RF) electric field and held to a spiral trajectory by a static magnetic field. The RF field causes the ions to bunch up into packets. The cyclotron has a set of 17 adjustable concentric trim coils located on the pole pieces inside the magnet gap. They are used to modify the distribution of vertical magnetic fields and compensate for the relativistic mass increase to keep an isochronous motion as the ions gain velocity and the orbit increases with radius. The ions that are not synchronized with the RF are lost. The Dee probe is mounted at the end of a shaft that moves radially inward. The probe measures the beam current inside the cyclotron and exhibits the radial beam losses. Low cross section experiments that produce super-heavy elements have increased the demand for high intensity heavy ion beams at energies of about 5 MeV/nucleon; nevertheless initial measurements with the Dee probe show large losses inside 20 cm radius of the cyclotron. The poor transmission suggests a problem in the ion beam injection caused by off-centered initial orbits with bunches partially hitting the lips of the Dee inserts that is consequence of iron being removed in the upper half of the magnet for lenses and the beam transport line itself.1 The magnetic field produced by any trim coil is the superposition of the magnetic fields produced by the top and bottom coils. Trim coil 1 coils are axially spaced by 17 cm and have 3 turns each with an average radius of 16 cm, which makes them suitable to study the beam losses observed inside 20 cm radius. a) Electronic mail: [email protected].
0034-6748/2014/85(8)/085113/3/$30.00
Sections II–IV show the axial displacement modeling and measurements of the beam center of mass position to correct the initial off-center orbits and improve the transmission through the cyclotron. This work is in continuation of the High-Voltage Upgrade Project1 and aims to increase the intensity of the ion beam. II. AXIAL DISPLACEMENT
A sketch of the magnetic field resulting from the trim coil 1 unbalance is represented in Fig. 1 using the cylindrical coordinate system. The magnetic field strength changes and produces a radial magnetic field component, which combined with the azimuthal beam bunch velocity, produces a force in the axial direction downwards.2 This tendency for charged particles to bounce back from the high field region is known in the literature as magnetic mirror effect.3 The axial force Fz towards the low field strength is obtained from the Lorentz law and is shown in Eq. (1), where q is the charge of the ion, Vϕ is the azimuthal velocity of the ion, and Bρ is the radial component of the magnetic field, obtained using a 3D simulation that includes the effects of the main magnet iron core on the trim coil magnetic field with current unbalance of 210 A: Fz = q Vϕ Bρ .
(1)
Similarly, the radial Lorentz force Fρ is shown in Eq. (2), where Bz is the axial component of the magnetic field with the same current unbalance: Fρ = −q Vϕ Bz .
(2)
As the centripetal force equals to the radial Lorentz force, the velocity Vϕ is given by Eq. (3), where ρ is the radial distance and m is the mass of the ion: ρqBz . (3) Vϕ = m The axial magnetic field Bz of Eq. (4) is obtained by substituting the azimuthal velocity Vϕ from Eq. (3) in the kinetic
85, 085113-1
© 2014 AIP Publishing LLC
085113-2
Michel Kireeff Covo
Rev. Sci. Instrum. 85, 085113 (2014) TABLE I. Total axial displacement z. Turn 0 0.5 1 1.5 2 2.5 3
E (MeV)
Vϕ (m/s)
ρ (cm)
Bρ (G)
Fz (N)
z (mm)
0.20 1.08 1.97 2.86 3.75 4.63 5.52
8.5 × 105 2.0 × 106 2.6 × 106 3.2 × 106 3.7 × 106 4.1 × 106 4.5 × 106
2.7 6.3 8.5 10.3 11.7 13.0 14.2
2.7 6.3 8.5 10.3 11.7 13.2 14.7
5.1 × 10−16 2.8 × 10−15 5.3 × 10−15 7.3 × 10−15 9.8 × 10−15 1.2 × 10−14 1.5 × 10−14
0.0 0.5 1.8 4.0 7.4 12.4 16.4
ulation of Eqs. (2)–(4), assuming an energy gain of 0.89 MeV after each RF kick. The bunch needs 3 turns to reach the radial position of 14.2 cm with a corresponding time of flight of 0.61 μs. The bunch total axial motion of 16.4 mm is obtained by assuming no initial axial velocity Vzo before the first RF kick. FIG. 1. Sketch of the magnetic field resulting from the trim coil unbalance.
III. EXPERIMENTAL SETUP
energy formula of classical mechanics, where E is the beam energy: √ 2 Em . (4) Bz = qρ The main field Bz = 1.23 T is obtained from Eq. (4) by substituting data from the 266 MeV 52 Cr+14 ion beam development run, i.e., E = 266 MeV, m = 8.27 × 10−26 kg, q = 2.24 × 10−18 C, and the cyclotron radial distance ρ = 0.99 m. The azimuthal velocity Vϕ = 4.51 × 106 m/s at ρ = 14.2 cm is obtained from Eq. (3). It corresponds to a change in energy from 196 keV at the injection to 5.52 MeV at ρ = 14.2 cm. The cyclotron frequency n is given by Eq. (5): n=
qBz . 2π m
(5)
The cyclotron frequency n = 5.03 MHz is obtained by substituting data for the development run. The RF frequency is 15.1 MHz, consequently the cyclotron operates in the third harmonic mode. The Dee voltage is 63.38 kV, therefore the 52 Cr+14 ions may gain 63.38 × 14 keV ≈ 0.89 MeV at every half cycle. Equation (6) of uniformly accelerated linear motion is used to find the axial displacement z after each RF kick, where Vz0 is the initial axial velocity, t is the time of flight, and az is the axial acceleration obtained from the Newton’s second law and Eq. (1): 1 z = Vz0 t + az t 2 . 2
(6)
Table I summarizes the results using Bρ obtained from a 3D simulation that includes the effects of the main magnet iron core on the magnetic field. The azimuthal velocity Vϕ , radial distance ρ, and axial force Fz are calculated by manip-
The innermost trim coil 1 system has a 750 A power supply with a reversing switch. The switch can invert the electrical current orientation of the coils and consequently the orientation of the magnetic field. The coils are arranged in series, so all the current of the top coil goes to the bottom coil. Two insulated-gate bipolar transistors are connected in parallel to the coils in order to shunt the current around the top or bottom coils and perform the current unbalance.4 The losses measured with the Dee probe in the center region increase with the top coil unbalance, which weakens the magnetic field above the cyclotron horizontal midplane, however the losses decrease with the bottom coil unbalance, which weakens the field below the horizontal midplane. The insert lips axial height peaks closer to the center, decreasing azimuthally to the edges. The trim coil 1 unbalance moves the bunch axially down, avoiding the lips during the initial turns. In order to image the ion beam bunches and its position, turn by turn, the former 3-finger probe of the cyclotron has been modified into a beam profile monitor.5 A 2 cm × 1.5 cm KBr scintillator replaces the 3-finger probe at the tip of the moveable shaft. It is located on the cyclotron horizontal midplane at 120◦ from south, following the beam orientation.
IV. RESULTS
The scintillator is placed at r = 13 cm and a sequence of frames is taken at the nominal trim coil 1 current of 500 A with different bottom coil current unbalances. Fig. 2 shows the position of the beam center of mass represented in blue diamonds for current unbalance from 0 A to −150 A with decrements of 10 A, −182 A, and −210 A. The abscissa represents the radial position and the ordinate represents the axial position. The top left side diamond shows the center of mass position with no unbalance (0 A) and the bottom right side diamond with −210 A unbalance. The current unbalance is
085113-3
Michel Kireeff Covo
Rev. Sci. Instrum. 85, 085113 (2014)
lips of the Dee inserts during the initial turns. After the unbalance is applied, the other trim coils are tuned again to provide maximum beam current transport to a Faraday cup located after the cyclotron deflectors, improving the beam transmission from 12% to 28%. V. CONCLUSIONS
FIG. 2. Center of mass position.
limited to −210 A to not truncate the beam image at the edge of the scintillator. The figure shows the beam center of mass axial position moving down with the current unbalance. The current unbalance produces a magnetic mirror effect that results in a tendency for charged particles to move towards the lower field region. At the same time the beam center of mass radial position augments with the unbalance, which is consequence of the overall center field decreasing with the current unbalance. The green dashed line displays the position of the cyclotron horizontal midplane. The unbalance of −145 A moves the center of mass of the beam to the cyclotron midplane, however better transmission through the cyclotron is obtained with unbalance of −210 A. The predicted total displacement z of 16.4 mm obtained with the current unbalance of −210 A shows reasonable agreement with the 11.4 mm axial displacement from Fig. 2, uncertainties in the radial component of the magnetic field contribute to the difference observed. The calculated radial position ρ of the ions also has excellent agreement with the radial position of Fig. 2. It shows that the geometry of the Dee inserts, which narrows the RF gap from 4.8 to 0.6 cm at the center region, assures that ions gain full energy during the first turns to clear the inflector, so the transit time effect can be neglected. The transit time effect can be important when the ion velocity is low enough that there is large change in the phase of the applied voltage during the time the bunch is in the accelerating RF gap. As a result, the ions perceive the average electric field, so the energy gained per gap crossing can be greatly reduced. The best transmission is obtained with an unbalance of −210 A in the bottom coil. The unbalance overshoots the cyclotron midplane by 5 mm, Fig. 2, however it quickly moves the beam center of mass down and decreases the losses to the
The Dee probe shows large losses inside the 20 cm radius of the 88 in. cyclotron. The innermost trim coil 1 is modified to provide a current unbalance and alter the center region magnetic field strength, producing a magnetic mirror effect. A beam profile monitor images the ion beam bunch profile turn by turn. The center of mass at the radius of 13.4 cm is located 7 mm above the cyclotron horizontal midplane when trim coil 1 is balanced, therefore the trim coil 1 unbalance is used to move the position of the beam center of mass and study the beam transmission effects. The −210 A current unbalance of trim coil 1 shows that the center of mass position of the 266 MeV 52 Cr+14 ions from the development run moves 11.4 mm axially down and is in reasonable agreement with the 16.4 mm from the calculated predictions, concurrently the radial position increases due to a change of the overall magnetic field. The measurement of the beam profile monitor shows the dynamic correction of the beam axial position in the center region of the cyclotron. The axial displacement reduces the losses from the beam partially hitting the lips of the Dee inserts during the initial turns. The beam transmission through the cyclotron of high efficiency runs using the trim coil unbalance reaches ∼28% in experiments with different ion species, charge states, and energies. ACKNOWLEDGMENTS
The author would like to thank Damon Todd and Markus Strohmeier for fruitful comments. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award Number DEAC02-05CH11231. 1 D.
S. Todd, J. Y. Benitez, K. Y. Franzen, M. K. Covo, C. M. Lyneis, L. Phair, P. Pipersky, and M. M. Strohmeier, in Proceedings of the 20th International Conference on Cyclotrons and their Applications, Vancouver, Canada, 16–20 September 2013. 2 L. Root, “Review of the TRIUMF trim coil data,” TRIUMF Design Note, File number TRI-DN-08-26 (December, 2008). 3 R. T. McIver, Int. J. Mass Spectrom. Ion Proc. 98, 35 (1990). 4 M. Kireeff Covo, B. Bingham, C. M. Lyneis, B. Ninemire, L. Phair, P. Pipersky, A. Ratti, M. M. Strohmeier, D. S. Todd, K. Y. Franzen, in Proceedings of the 20th International Conference on Cyclotrons and their Applications, Vancouver, Canada, 16–20 September 2013. 5 M. M. Strohmeier, J. Y. Benitez, M. Kireeff Covo, C. M. Lyneis, B. Ninemire, L. Phair, P. Pipersky, and D. S. Todd, in Proceedings of the 20th International Conference on Cyclotrons and their Applications, Vancouver, Canada, 16–20 September 2013.
Review of Scientific Instruments is copyrighted by the American Institute of Physics (AIP). Redistribution of journal material is subject to the AIP online journal license and/or AIP copyright. For more information, see http://ojps.aip.org/rsio/rsicr.jsp
Measurement of axial injection displacement with trim coil current unbalance Michel Kireeff Covoa) Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
(Received 18 May 2014; accepted 26 July 2014; published online 14 August 2014) The Dee probe used for measuring internal radial beam intensity shows large losses inside the radius of 20 cm of the 88 in. cyclotron. The current of the top and bottom innermost trim coil 1 is unbalanced to study effects of the axial injection displacement. A beam profile monitor images the ion beam bunches, turn by turn. The experimental bunch center of mass position is compared with calculations of the magnetic mirror effect displacement and shows good agreement. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4892463] I. INTRODUCTION
The ions produced by the electron cyclotron resonance ion sources are injected inside the 88 in. cyclotron by a mirror inflector. The inflector assembly is a grounded grid mounted with standoffs on a biased plate that is tilted 45◦ above the cyclotron horizontal midplane. The ions entering the grid inflector experience an electrostatic force that directs them to the cyclotron middle plane. After the ions enter the cyclotron, they are accelerated by a radio frequency (RF) electric field and held to a spiral trajectory by a static magnetic field. The RF field causes the ions to bunch up into packets. The cyclotron has a set of 17 adjustable concentric trim coils located on the pole pieces inside the magnet gap. They are used to modify the distribution of vertical magnetic fields and compensate for the relativistic mass increase to keep an isochronous motion as the ions gain velocity and the orbit increases with radius. The ions that are not synchronized with the RF are lost. The Dee probe is mounted at the end of a shaft that moves radially inward. The probe measures the beam current inside the cyclotron and exhibits the radial beam losses. Low cross section experiments that produce super-heavy elements have increased the demand for high intensity heavy ion beams at energies of about 5 MeV/nucleon; nevertheless initial measurements with the Dee probe show large losses inside 20 cm radius of the cyclotron. The poor transmission suggests a problem in the ion beam injection caused by off-centered initial orbits with bunches partially hitting the lips of the Dee inserts that is consequence of iron being removed in the upper half of the magnet for lenses and the beam transport line itself.1 The magnetic field produced by any trim coil is the superposition of the magnetic fields produced by the top and bottom coils. Trim coil 1 coils are axially spaced by 17 cm and have 3 turns each with an average radius of 16 cm, which makes them suitable to study the beam losses observed inside 20 cm radius. a) Electronic mail: [email protected].
0034-6748/2014/85(8)/085113/3/$30.00
Sections II–IV show the axial displacement modeling and measurements of the beam center of mass position to correct the initial off-center orbits and improve the transmission through the cyclotron. This work is in continuation of the High-Voltage Upgrade Project1 and aims to increase the intensity of the ion beam. II. AXIAL DISPLACEMENT
A sketch of the magnetic field resulting from the trim coil 1 unbalance is represented in Fig. 1 using the cylindrical coordinate system. The magnetic field strength changes and produces a radial magnetic field component, which combined with the azimuthal beam bunch velocity, produces a force in the axial direction downwards.2 This tendency for charged particles to bounce back from the high field region is known in the literature as magnetic mirror effect.3 The axial force Fz towards the low field strength is obtained from the Lorentz law and is shown in Eq. (1), where q is the charge of the ion, Vϕ is the azimuthal velocity of the ion, and Bρ is the radial component of the magnetic field, obtained using a 3D simulation that includes the effects of the main magnet iron core on the trim coil magnetic field with current unbalance of 210 A: Fz = q Vϕ Bρ .
(1)
Similarly, the radial Lorentz force Fρ is shown in Eq. (2), where Bz is the axial component of the magnetic field with the same current unbalance: Fρ = −q Vϕ Bz .
(2)
As the centripetal force equals to the radial Lorentz force, the velocity Vϕ is given by Eq. (3), where ρ is the radial distance and m is the mass of the ion: ρqBz . (3) Vϕ = m The axial magnetic field Bz of Eq. (4) is obtained by substituting the azimuthal velocity Vϕ from Eq. (3) in the kinetic
85, 085113-1
© 2014 AIP Publishing LLC
085113-2
Michel Kireeff Covo
Rev. Sci. Instrum. 85, 085113 (2014) TABLE I. Total axial displacement z. Turn 0 0.5 1 1.5 2 2.5 3
E (MeV)
Vϕ (m/s)
ρ (cm)
Bρ (G)
Fz (N)
z (mm)
0.20 1.08 1.97 2.86 3.75 4.63 5.52
8.5 × 105 2.0 × 106 2.6 × 106 3.2 × 106 3.7 × 106 4.1 × 106 4.5 × 106
2.7 6.3 8.5 10.3 11.7 13.0 14.2
2.7 6.3 8.5 10.3 11.7 13.2 14.7
5.1 × 10−16 2.8 × 10−15 5.3 × 10−15 7.3 × 10−15 9.8 × 10−15 1.2 × 10−14 1.5 × 10−14
0.0 0.5 1.8 4.0 7.4 12.4 16.4
ulation of Eqs. (2)–(4), assuming an energy gain of 0.89 MeV after each RF kick. The bunch needs 3 turns to reach the radial position of 14.2 cm with a corresponding time of flight of 0.61 μs. The bunch total axial motion of 16.4 mm is obtained by assuming no initial axial velocity Vzo before the first RF kick. FIG. 1. Sketch of the magnetic field resulting from the trim coil unbalance.
III. EXPERIMENTAL SETUP
energy formula of classical mechanics, where E is the beam energy: √ 2 Em . (4) Bz = qρ The main field Bz = 1.23 T is obtained from Eq. (4) by substituting data from the 266 MeV 52 Cr+14 ion beam development run, i.e., E = 266 MeV, m = 8.27 × 10−26 kg, q = 2.24 × 10−18 C, and the cyclotron radial distance ρ = 0.99 m. The azimuthal velocity Vϕ = 4.51 × 106 m/s at ρ = 14.2 cm is obtained from Eq. (3). It corresponds to a change in energy from 196 keV at the injection to 5.52 MeV at ρ = 14.2 cm. The cyclotron frequency n is given by Eq. (5): n=
qBz . 2π m
(5)
The cyclotron frequency n = 5.03 MHz is obtained by substituting data for the development run. The RF frequency is 15.1 MHz, consequently the cyclotron operates in the third harmonic mode. The Dee voltage is 63.38 kV, therefore the 52 Cr+14 ions may gain 63.38 × 14 keV ≈ 0.89 MeV at every half cycle. Equation (6) of uniformly accelerated linear motion is used to find the axial displacement z after each RF kick, where Vz0 is the initial axial velocity, t is the time of flight, and az is the axial acceleration obtained from the Newton’s second law and Eq. (1): 1 z = Vz0 t + az t 2 . 2
(6)
Table I summarizes the results using Bρ obtained from a 3D simulation that includes the effects of the main magnet iron core on the magnetic field. The azimuthal velocity Vϕ , radial distance ρ, and axial force Fz are calculated by manip-
The innermost trim coil 1 system has a 750 A power supply with a reversing switch. The switch can invert the electrical current orientation of the coils and consequently the orientation of the magnetic field. The coils are arranged in series, so all the current of the top coil goes to the bottom coil. Two insulated-gate bipolar transistors are connected in parallel to the coils in order to shunt the current around the top or bottom coils and perform the current unbalance.4 The losses measured with the Dee probe in the center region increase with the top coil unbalance, which weakens the magnetic field above the cyclotron horizontal midplane, however the losses decrease with the bottom coil unbalance, which weakens the field below the horizontal midplane. The insert lips axial height peaks closer to the center, decreasing azimuthally to the edges. The trim coil 1 unbalance moves the bunch axially down, avoiding the lips during the initial turns. In order to image the ion beam bunches and its position, turn by turn, the former 3-finger probe of the cyclotron has been modified into a beam profile monitor.5 A 2 cm × 1.5 cm KBr scintillator replaces the 3-finger probe at the tip of the moveable shaft. It is located on the cyclotron horizontal midplane at 120◦ from south, following the beam orientation.
IV. RESULTS
The scintillator is placed at r = 13 cm and a sequence of frames is taken at the nominal trim coil 1 current of 500 A with different bottom coil current unbalances. Fig. 2 shows the position of the beam center of mass represented in blue diamonds for current unbalance from 0 A to −150 A with decrements of 10 A, −182 A, and −210 A. The abscissa represents the radial position and the ordinate represents the axial position. The top left side diamond shows the center of mass position with no unbalance (0 A) and the bottom right side diamond with −210 A unbalance. The current unbalance is
085113-3
Michel Kireeff Covo
Rev. Sci. Instrum. 85, 085113 (2014)
lips of the Dee inserts during the initial turns. After the unbalance is applied, the other trim coils are tuned again to provide maximum beam current transport to a Faraday cup located after the cyclotron deflectors, improving the beam transmission from 12% to 28%. V. CONCLUSIONS
FIG. 2. Center of mass position.
limited to −210 A to not truncate the beam image at the edge of the scintillator. The figure shows the beam center of mass axial position moving down with the current unbalance. The current unbalance produces a magnetic mirror effect that results in a tendency for charged particles to move towards the lower field region. At the same time the beam center of mass radial position augments with the unbalance, which is consequence of the overall center field decreasing with the current unbalance. The green dashed line displays the position of the cyclotron horizontal midplane. The unbalance of −145 A moves the center of mass of the beam to the cyclotron midplane, however better transmission through the cyclotron is obtained with unbalance of −210 A. The predicted total displacement z of 16.4 mm obtained with the current unbalance of −210 A shows reasonable agreement with the 11.4 mm axial displacement from Fig. 2, uncertainties in the radial component of the magnetic field contribute to the difference observed. The calculated radial position ρ of the ions also has excellent agreement with the radial position of Fig. 2. It shows that the geometry of the Dee inserts, which narrows the RF gap from 4.8 to 0.6 cm at the center region, assures that ions gain full energy during the first turns to clear the inflector, so the transit time effect can be neglected. The transit time effect can be important when the ion velocity is low enough that there is large change in the phase of the applied voltage during the time the bunch is in the accelerating RF gap. As a result, the ions perceive the average electric field, so the energy gained per gap crossing can be greatly reduced. The best transmission is obtained with an unbalance of −210 A in the bottom coil. The unbalance overshoots the cyclotron midplane by 5 mm, Fig. 2, however it quickly moves the beam center of mass down and decreases the losses to the
The Dee probe shows large losses inside the 20 cm radius of the 88 in. cyclotron. The innermost trim coil 1 is modified to provide a current unbalance and alter the center region magnetic field strength, producing a magnetic mirror effect. A beam profile monitor images the ion beam bunch profile turn by turn. The center of mass at the radius of 13.4 cm is located 7 mm above the cyclotron horizontal midplane when trim coil 1 is balanced, therefore the trim coil 1 unbalance is used to move the position of the beam center of mass and study the beam transmission effects. The −210 A current unbalance of trim coil 1 shows that the center of mass position of the 266 MeV 52 Cr+14 ions from the development run moves 11.4 mm axially down and is in reasonable agreement with the 16.4 mm from the calculated predictions, concurrently the radial position increases due to a change of the overall magnetic field. The measurement of the beam profile monitor shows the dynamic correction of the beam axial position in the center region of the cyclotron. The axial displacement reduces the losses from the beam partially hitting the lips of the Dee inserts during the initial turns. The beam transmission through the cyclotron of high efficiency runs using the trim coil unbalance reaches ∼28% in experiments with different ion species, charge states, and energies. ACKNOWLEDGMENTS
The author would like to thank Damon Todd and Markus Strohmeier for fruitful comments. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award Number DEAC02-05CH11231. 1 D.
S. Todd, J. Y. Benitez, K. Y. Franzen, M. K. Covo, C. M. Lyneis, L. Phair, P. Pipersky, and M. M. Strohmeier, in Proceedings of the 20th International Conference on Cyclotrons and their Applications, Vancouver, Canada, 16–20 September 2013. 2 L. Root, “Review of the TRIUMF trim coil data,” TRIUMF Design Note, File number TRI-DN-08-26 (December, 2008). 3 R. T. McIver, Int. J. Mass Spectrom. Ion Proc. 98, 35 (1990). 4 M. Kireeff Covo, B. Bingham, C. M. Lyneis, B. Ninemire, L. Phair, P. Pipersky, A. Ratti, M. M. Strohmeier, D. S. Todd, K. Y. Franzen, in Proceedings of the 20th International Conference on Cyclotrons and their Applications, Vancouver, Canada, 16–20 September 2013. 5 M. M. Strohmeier, J. Y. Benitez, M. Kireeff Covo, C. M. Lyneis, B. Ninemire, L. Phair, P. Pipersky, and D. S. Todd, in Proceedings of the 20th International Conference on Cyclotrons and their Applications, Vancouver, Canada, 16–20 September 2013.
Review of Scientific Instruments is copyrighted by the American Institute of Physics (AIP). Redistribution of journal material is subject to the AIP online journal license and/or AIP copyright. For more information, see http://ojps.aip.org/rsio/rsicr.jsp
