- Email: [email protected]
Heavy ion beam acceleration in the KEK digital accelerator: Induction acceleration from 200 keV to a few tens of MeV
Nuclear Instruments and Methods in Physics Research A 733 (2014) 141–146
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Heavy ion beam acceleration in the KEK digital accelerator: Induction acceleration from 200 keV to a few tens of MeV T. Yoshimoto a,b,n, M. Barata b,c, T. Iwashita d, S. Harada b,c, D. Arakawa b, T. Arai b, X. Liu a,b, T. Adachi b,e, H. Asao f, E. Kadokura b, T. Kawakubo b, T. Kubo b, K.W. Leo b,e, H. Nakanishi b, Y. Okada f, K. Okamura b,e, K. Okazaki d, H. Someya b, K. Takayama a,b,e, M. Wake b a
Tokyo Institute of Technology, Nagatsuta, Kanagawa, Japan High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan c Tokyo City University, Todoroki, Tokyo, Japan d Nippon Advanced Technology Co. Ltd. (NAT), Tokaimura, Ibaraki, Japan e Graduate University of Advanced Studies, Hayama, Kanagawa, Japan f NEC Network-Sensor, Futyu, Tokyo, Japan b
art ic l e i nf o
a b s t r a c t
Available online 13 June 2013
The procedure for induction acceleration of a heavy ion beam of A/Q ¼4 in the KEK digital accelerator is reported. This paper discusses essential issues associated with induction acceleration of ion beams from low energies, including injection error, relatively large closed orbit distortion, and a fully predictive control method for the acceleration. & 2013 Elsevier B.V. All rights reserved.
Keywords: Induction synchrotron Digital accelerator All-ion accelerator Induction accelerator
1. Introduction The digital accelerator (DA) is an induction synchrotron that is expected to accelerate all species of ions with their possible charge states in a wide energy range, from a few hundred keV to a few hundred MeV [1,2]. This novel circular accelerator has the cost per unit energy substantially better than that of existing circular accelerator. DAs are expected to promote various new applications in a wide range of scientific fields including materials science, space science, cancer therapy, ion-driven high energy density physics studies and heavy-ion inertial confinement fusion [3]. The workshop naturally focuses its discussion on the heavy-ion inertial fusion, which requires high intensity beams at the last stage. To realize such a high intensity beam, so far several accelerator schemes have been seriously considered and proposed. Most of presentations here should be related to those accelerator schemes. In this sense, the DA is not the case. However, the induction synchrotron concept allows us to accommodate a much larger beam current than that in RF synchrotrons due to its inherent characteristics of functionally-separated operation of acceleration and confinement in the longitudinal direction. A wide range of freedom in beam handling by using barrier buckets has been already discussed in literature [4]. This feature should be attractive to the heavy ion fusion accelerator system too. n Corresponding author at: Tokyo Institute of Technology, Nagatsuta, Kanagawa, Japan. E-mail address: [email protected] (T. Yoshimoto).
0168-9002/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2013.05.082
The present DA will provide information and experiences crucial to consider the barrier bucket acceleration in the future heavy ion fusion driver. The KEK digital accelerator (KEK-DA) is a renovation of the former KEK 500 MeV Booster, the former injector to the KEK 12 GeV proton synchrotron. KEK-DA consists of an X-band electron cyclotron resonance ion source (ECRIS) embedded in a 200 kV high-voltage platform [5], a newly developed Einzel lens longitudinal chopper [6], a low-energy beam transport line (LEBT), an electrostatic injection kicker (ES-Kicker), induction acceleration devices, extraction kicker/septum magnets, and a high-energy beam transport line (HEBT), as well as beam diagnostic systems such as a bunch monitor and beam position monitors. Fig. 1 shows an outline of KEK-DA. Ring parameters are listed in Table 1. Beam commissioning has been carried out since summer 2011 [7]. Through preliminary beam commissioning, we have realized that there are crucial issues related to accelerating ions from very low energies in KEK-DA. They are summarized as follows. (1) Low-current beam detection system The current is a few hundred microamperes with the relativistic velocity οf 0.01 at the injection. Therefore raw signals (around 1 mV) observed by the bunch monitor must be amplified to volt levels. In addition, signal amplification in a wide frequency range spanning a few hundred kilohertz is required because of the broad revolution frequency range. It is still difficult to eliminate or reduce noise in the frequency region of current interest.
142
T. Yoshimoto et al. / Nuclear Instruments and Methods in Physics Research A 733 (2014) 141–146
Fig. 1. Outline of the KEK digital accelerator. Table 1 Lattice/beam parameters. Circumference Bending radius Maximum B Bet. tune in x/y Transition energy Energy (inj.)/nucleon Rev. frequency
C0 ρ Bmax Qx/Qy γT Einj f
37.7 m 3.3 m 0.84 T 2.17/2.30 2.25 200 keV (Q/A) ∼80 kHz–3 MHz
(2) Advanced data acquisition system To efficiently optimize various parameters required for fully predictive acceleration control, which is described in detail below, as well as to collect basic information about the beam orbit, rapid simultaneous data acquisition of beam and equipment parameters and fast analysis are crucial. (3) Injection error/closed orbit distortion (COD) correction In acceleration from low energy, COD correction becomes more important because residual fields affect the injection fields. (4) Self-consistent programmed gate control for the Switching Power supplies (SPSs) A key consideration is how the beam is controlled from the low injection energy region through the entire energy region, where the velocity changes rapidly. At the present stage, the beam feedback method for triggering the induction acceleration system, which was demonstrated in a proof-of-principle experiment of the induction synchrotron [8], is not employed because the beam signal level is insufficient. Instead, a fully predictive control method has been developed, where a fieldprogrammable gate array (FPGA) generates the gate signals necessary to drive SPSs according to an acceleration scenario programmed in advance. An ideal particle guided in the magnetic fields to mimic the real bending magnet fields is always assumed in the program and circulates in a virtual ring in synchrony with the so-called B-clock.
Fig. 2. Electrostatic position monitor installed in the KEK-DA ring.
Fig. 3. Outline of the data acquisition system.
2. Beam diagnostic and data acquisition systems 2.1. Monitors and detected signal In the former booster, electrostatic position monitors were placed immediately after each main magnet to monitor the beam position in both directions. This did not work, however, because the electrode surface was too small to induce a sufficient signal level due to the relatively low intensity of the beam in KEK-DA. Recently four position monitors with large pickup heads (Fig. 2)
have been installed, and signals from them are amplified to a few volts by newly developed specific amplifiers. In addition, the existing bunch monitor is used to detect the bunch profile in time. The detected signal is amplified by a three-stage amplifier. 2.2. Data acquisition system A new data acquisition system has been developed to semiautomatically collect real-time beam and equipment information and to perform rapid analysis for beam/equipment diagnostics. As shown in Fig. 3, the system consists of transmission lines
T. Yoshimoto et al. / Nuclear Instruments and Methods in Physics Research A 733 (2014) 141–146
connected to individual monitors, a multiplexer, an oscilloscope, and a computer for handling acquired data. The system can automatically select a necessary signal with the multiplexer. In addition to data from the above-mentioned beam pulse profile and beam center position, data about the pulse voltages for acceleration and confinement, which are detected as continuous-time signals of the matching resistances inserted in parallel to the induction acceleration cells, is transferred to the system. Analysis integrating these data is indispensable, because the synchronization between beam circulation and the timing of acceleration/ confinement pulse voltages is crucial for acceleration in KEK-DA, where the fully predictive control method based on the B-clock is employed for acceleration control. The FPGA code calculates reference signals corresponding to the B-clock, which is uniquely determined once Bmin and Bmax are given. Using the data acquisition system, we can determine the turn-byturn x and y positions, beam loss, betatron tune (Qx and Qy), and injection timing error. Synchronization error and over- and underacceleration can be immediately identified. Consequently, a judgment can be made as to whether the FPGA code is performing satisfactorily.
3. Beam correction 3.1. Injection error correction Two steering magnets positioned immediately before the injection point are used to correct injection error. In general, the beam center position is expressed by pffiffiffiffiffiffiffiffiffiffi xðsÞ ¼ εβðsÞ cos ð2πQ x s þ δÞ þ xcod ðsÞ; where β(s) is the beta-function at s, (εβ(s))1/2 is the betatron amplitude of the beam center with injection error, δ is the initial betatron phase, and xcod(s) is the residual closed orbit. Using this formula and the beam position data, we find the injection error (x(0)−xcod(0), x′(0)−xcod′(0)). Then, excitation currents of two steering magnets are supplied to correct this injection error. A typical result after correction is shown in Fig. 4, where the oscillation amplitude of the beam center is drastically reduced from 12 mm to 2.6 mm. Note that the oscillation center after correction, seen as an offset of the betatron oscillation, corresponds to xcod(s) at observing point s.
143
Fig. 5. COD correction system with four figure-8 back-leg coils excited by independent power sources.
flux density in the magnets varies within 710 G, depending on the individual magnet [1]. Thus, residual fields become a major source of COD. KEK-DA has eight bending magnets and four position monitors (Fig. 5). Obviously, the number of observation points is insufficient to ascertain the entire COD profile along the ring. The lower-harmonics COD correction method is effective in a ring with a small betatron tune. Here, only the first and second harmonic components of the COD have been corrected by four pairs of 8 figure back leg coils [9]. The result is shown in Fig. 6.
4. FPGA code and gate trigger for confinement and acceleration 4.1. Gate control of the SPSs using FPGA Production of confinement and accelerating voltage pulses is controlled by FPGA gate signals for SPSs. The SPS of a full-bridge circuit always generates a set of positive and negative pulses (called set/reset voltage) to prevent the saturation of cell magnetic cores. Thus the FPGA generates two different set/reset signals (Fig. 7).
3.2. COD correction The injection magnetic flux density is quite low, 390 G for a 200 keV heavy beam of A/Q¼4. Furthermore, the residual magnetic
4.2. Adjustment of beam control parameters in the FPGA code In the present fully predictive control method for acceleration, the B-clock is the most essential parameter. In the FPGA control device, the B-clock is based on the ideal magnetic field Bideal(t), which must be precisely adjusted to the actual bending magnetic field Bactual(t), which is described by Bmax þ Bmin Bactual ðtÞ ¼ 2 Bmax −Bmin cos ½ωðt þ δÞ; − 2
Fig. 4. Typical injection error and its correction in the horizontal direction, before (red) and after correction (blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
where ω is the angular frequency of the driving resonant circuit and ωδ is the initial phase seen by the injected beam. Every aspect of equipment operation, including ideal or resonant particles that remain in the ideal/design orbit through the entire acceleration period, is determined from this guiding field profile. It is essential to adjust three injection timing parameters: δ, Bmin, and Bmax. The following describes how these three parameters are obtained directly from beam information.
144
T. Yoshimoto et al. / Nuclear Instruments and Methods in Physics Research A 733 (2014) 141–146
The horizontal position of the beam center observed at a specific position monitor x(t) is expressed by D(s)ΔB(t)/Bmin, where D(s) is the dispersion function at the specific position. In the time region near B(t) ¼Bmin, the deviation from Bmin is approximated as follows: Bmax −Bmin f1− cos ½ωðt þ δÞg ΔBðtÞ ¼ BðtÞ−Bmin ¼ 2 " ( )# Bmax −Bmin ½ωðt þ δÞ2 ≈ 1− 1− þ ⋯ ∝ðt þ δÞ2 : 2 2! An integrated change in the revolution period and the deviation of the beam center from the ideal orbit are represented as follows: Rt 3 0 ΔT∝ðt þ δÞ Fig. 6. COD before correction: observed COD at the position monitors (red point) and its harmonic fitting (solid blue line), after correction: observed ones (blue point) and predicted one (solid green line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
xðtÞ∝ðt þ δÞ2 From these properties, we can directly derive δ by observing the beam motion in two ways. Fig. 9 shows a projection of the bunch profile signal on the time-turn plane, where a beam circulates in the ring without application of accelerating or confinement voltage; the horizontal axis shows the inner time clocked with Bmin, and the vertical axis shows the time after injection. The beam center is calculated and shown in Fig. 10. We can obtain the actual injection timing directly by cubic fitting; δ is −1141.7 μs.
Fig. 7. Schematic view of the induction acceleration system with the gate control system.
Fig. 8. Field ramping pattern and injection timing.
Fig. 9. Projection of the bunch monitor signal on the time-turn plane triggered by the constant clock determined by Bmin.
4.3. Determination of injection timing δ First, δ must be specified. For this purpose, a beam is injected at an earlier timing than the timing of Bactual_min (Fig. 8). After injection, the actual beam motion in the time domain is observed during the constant period Tmin, which is the revolution period of the ideal particle at B ¼ Bmin. The revolution period T of the bunch center depends on the guiding field strength. The temporal fluctuation in the revolution period is given by ΔTðtÞ ΔC Δv − ¼ T min C v Δp ΔBðtÞ 1 Δp ¼α − − 2 pmin Bmin γ pmin ΔBðtÞ ¼ −α ð∵Δp ¼ 0Þ; Bmin where C is the ideal circumference of the ring, pmin is the injection momentum uniquely determined from Bmin, and α(¼ 1/γ2T−1/γ2) is the momentum compaction factor.
Fig. 10. Beam center tracking in time on the time-turn plane.
T. Yoshimoto et al. / Nuclear Instruments and Methods in Physics Research A 733 (2014) 141–146
Fig. 11. Time varying position of the horizontal beam center. The fine structure in the oscillation is the betatron oscillation. The noisy signal beyond 250 turns makes no sense because the beam without acceleration is lost due to the ramping B(t).
145
Fig. 14. Time-turn plane view of Vbb where set pulse (yellow) and reset pulse (blue) (experiment). The beam bucket with 2 μs length consists of two confinement voltages. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. Confinement voltage Vbb, acceleration voltages Vac, and the beam on the time axis.
Fig. 15. Time-turn plane view of Vac (experiment) where set pulse (yellow) and reset pulse (blue). The pulse-generation density is weaker in the injection and final stage than the medium stage. This corresponds to the needed acceleration voltage (see Fig. 13). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 13. Bideal(t) (top), required acceleration voltage per turn (bottom, solid red line), and Vac trigger pulse timing. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The horizontal position is observed by the position monitor (Fig. 11). In a straightforward manner, quadratic fitting gives δ¼ −1122.2 μs. The difference between the two δs is 19.5 μs and this magnitude may be the resolution of this method. 4.4. Acceleration scheme and typical example Accelerating voltage Vac and confinement voltage Vbb are generated separately on individual induction cells (Fig. 12). The confinement voltage is generated every turn, whereas the accelerating voltage is intermittently generated because of the limited capabilities of the induction acceleration system, as described in a previous report [1]. This feature is illustrated in Fig. 13. In the
Fig. 16. Time-turn plane view of a trapped and accelerated beam signal (white and succeeding blue region) (experiment). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
present experiment (Bmax ¼ 2.5 kG), two induction cells produce two sets of set/reset voltage pulses, where pulse height and length are fixed to be 1 kV and 150 ns, respectively, and the time duration between the two sets is changed in proportion to the revolution
146
T. Yoshimoto et al. / Nuclear Instruments and Methods in Physics Research A 733 (2014) 141–146
period. The pulse width of Vac, which is generated on a single induction cell, is set so as to fully cover the region occupied by the beam pulse. Experimentally demonstrated temporal changes in Vbb and Vac over one acceleration cycle are shown in Figs. 14 and 15. Actual beam motion is shown in Fig. 16. It is emphasized that the above operation is realized as a result of triggering the participating SPSs following the gate trigger program in the FPGA.
5. Summary We have successfully demonstrated induction acceleration of a heavy beam of A/Q¼ 4. Basic but essential equipment conditioning such as injection error correction and COD correction has been carried out. We have established a method for setting control parameters for induction acceleration by analyzing the motion of an injected beam. In addition, the acceleration scheme and typical experimental results have been introduced.
Acknowledgment This work was supported by a Grant-In-Aid for Scientific Research (A) (KAKENHI no. 23240082). References [1] T. Iwashita, et al., Physical Review Special Topics—Accelerators and Beams 14 (2011) 071301. [2] K. Takayama, et al., Journal of Applied Physics 101 (2007) 063304. (with Erratum). [3] S. Kawata, et al., Nuclear Instruments and Methods A 577 (2007) 21. [4] Ken Takayama, Richard J. Briggs, Induction Accelerator, Springer, Van Godewijckstraat 30, 3311 GX Dordrecht, Netherlands, 2011. [5] Leo Kwee Wah, et al., Permanent magnet ECRIS for the KEK digital accelerator, in: Proceedings of the 19th International Workshop on ECRIS, August 23–26, Grenoble, France, TUPOT15, 2010. [6] T. Adachi, et al., Review of Scientific Instruments 82 (2011) 083305. [7] K. Takayama, et al., KEK digital accelerator and its beam commissioning, in: Proceedings of IPAC2011, WEOBA02, San Sebastián, Spain, September 4–9, 2011. [8] K. Takayama, et al., Physical Review Letters 98 (2007) 054801. [9] K. Takayama, et al., KEK Digital Accelerator and Latest Switching Device R&D, in this conference, The 19th International Symposium on Heavy Ion Inertial Fusion, August 12–17, 2012, Berkeley, California, USA.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Heavy ion beam acceleration in the KEK digital accelerator: Induction acceleration from 200 keV to a few tens of MeV T. Yoshimoto a,b,n, M. Barata b,c, T. Iwashita d, S. Harada b,c, D. Arakawa b, T. Arai b, X. Liu a,b, T. Adachi b,e, H. Asao f, E. Kadokura b, T. Kawakubo b, T. Kubo b, K.W. Leo b,e, H. Nakanishi b, Y. Okada f, K. Okamura b,e, K. Okazaki d, H. Someya b, K. Takayama a,b,e, M. Wake b a
Tokyo Institute of Technology, Nagatsuta, Kanagawa, Japan High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan c Tokyo City University, Todoroki, Tokyo, Japan d Nippon Advanced Technology Co. Ltd. (NAT), Tokaimura, Ibaraki, Japan e Graduate University of Advanced Studies, Hayama, Kanagawa, Japan f NEC Network-Sensor, Futyu, Tokyo, Japan b
art ic l e i nf o
a b s t r a c t
Available online 13 June 2013
The procedure for induction acceleration of a heavy ion beam of A/Q ¼4 in the KEK digital accelerator is reported. This paper discusses essential issues associated with induction acceleration of ion beams from low energies, including injection error, relatively large closed orbit distortion, and a fully predictive control method for the acceleration. & 2013 Elsevier B.V. All rights reserved.
Keywords: Induction synchrotron Digital accelerator All-ion accelerator Induction accelerator
1. Introduction The digital accelerator (DA) is an induction synchrotron that is expected to accelerate all species of ions with their possible charge states in a wide energy range, from a few hundred keV to a few hundred MeV [1,2]. This novel circular accelerator has the cost per unit energy substantially better than that of existing circular accelerator. DAs are expected to promote various new applications in a wide range of scientific fields including materials science, space science, cancer therapy, ion-driven high energy density physics studies and heavy-ion inertial confinement fusion [3]. The workshop naturally focuses its discussion on the heavy-ion inertial fusion, which requires high intensity beams at the last stage. To realize such a high intensity beam, so far several accelerator schemes have been seriously considered and proposed. Most of presentations here should be related to those accelerator schemes. In this sense, the DA is not the case. However, the induction synchrotron concept allows us to accommodate a much larger beam current than that in RF synchrotrons due to its inherent characteristics of functionally-separated operation of acceleration and confinement in the longitudinal direction. A wide range of freedom in beam handling by using barrier buckets has been already discussed in literature [4]. This feature should be attractive to the heavy ion fusion accelerator system too. n Corresponding author at: Tokyo Institute of Technology, Nagatsuta, Kanagawa, Japan. E-mail address: [email protected] (T. Yoshimoto).
0168-9002/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2013.05.082
The present DA will provide information and experiences crucial to consider the barrier bucket acceleration in the future heavy ion fusion driver. The KEK digital accelerator (KEK-DA) is a renovation of the former KEK 500 MeV Booster, the former injector to the KEK 12 GeV proton synchrotron. KEK-DA consists of an X-band electron cyclotron resonance ion source (ECRIS) embedded in a 200 kV high-voltage platform [5], a newly developed Einzel lens longitudinal chopper [6], a low-energy beam transport line (LEBT), an electrostatic injection kicker (ES-Kicker), induction acceleration devices, extraction kicker/septum magnets, and a high-energy beam transport line (HEBT), as well as beam diagnostic systems such as a bunch monitor and beam position monitors. Fig. 1 shows an outline of KEK-DA. Ring parameters are listed in Table 1. Beam commissioning has been carried out since summer 2011 [7]. Through preliminary beam commissioning, we have realized that there are crucial issues related to accelerating ions from very low energies in KEK-DA. They are summarized as follows. (1) Low-current beam detection system The current is a few hundred microamperes with the relativistic velocity οf 0.01 at the injection. Therefore raw signals (around 1 mV) observed by the bunch monitor must be amplified to volt levels. In addition, signal amplification in a wide frequency range spanning a few hundred kilohertz is required because of the broad revolution frequency range. It is still difficult to eliminate or reduce noise in the frequency region of current interest.
142
T. Yoshimoto et al. / Nuclear Instruments and Methods in Physics Research A 733 (2014) 141–146
Fig. 1. Outline of the KEK digital accelerator. Table 1 Lattice/beam parameters. Circumference Bending radius Maximum B Bet. tune in x/y Transition energy Energy (inj.)/nucleon Rev. frequency
C0 ρ Bmax Qx/Qy γT Einj f
37.7 m 3.3 m 0.84 T 2.17/2.30 2.25 200 keV (Q/A) ∼80 kHz–3 MHz
(2) Advanced data acquisition system To efficiently optimize various parameters required for fully predictive acceleration control, which is described in detail below, as well as to collect basic information about the beam orbit, rapid simultaneous data acquisition of beam and equipment parameters and fast analysis are crucial. (3) Injection error/closed orbit distortion (COD) correction In acceleration from low energy, COD correction becomes more important because residual fields affect the injection fields. (4) Self-consistent programmed gate control for the Switching Power supplies (SPSs) A key consideration is how the beam is controlled from the low injection energy region through the entire energy region, where the velocity changes rapidly. At the present stage, the beam feedback method for triggering the induction acceleration system, which was demonstrated in a proof-of-principle experiment of the induction synchrotron [8], is not employed because the beam signal level is insufficient. Instead, a fully predictive control method has been developed, where a fieldprogrammable gate array (FPGA) generates the gate signals necessary to drive SPSs according to an acceleration scenario programmed in advance. An ideal particle guided in the magnetic fields to mimic the real bending magnet fields is always assumed in the program and circulates in a virtual ring in synchrony with the so-called B-clock.
Fig. 2. Electrostatic position monitor installed in the KEK-DA ring.
Fig. 3. Outline of the data acquisition system.
2. Beam diagnostic and data acquisition systems 2.1. Monitors and detected signal In the former booster, electrostatic position monitors were placed immediately after each main magnet to monitor the beam position in both directions. This did not work, however, because the electrode surface was too small to induce a sufficient signal level due to the relatively low intensity of the beam in KEK-DA. Recently four position monitors with large pickup heads (Fig. 2)
have been installed, and signals from them are amplified to a few volts by newly developed specific amplifiers. In addition, the existing bunch monitor is used to detect the bunch profile in time. The detected signal is amplified by a three-stage amplifier. 2.2. Data acquisition system A new data acquisition system has been developed to semiautomatically collect real-time beam and equipment information and to perform rapid analysis for beam/equipment diagnostics. As shown in Fig. 3, the system consists of transmission lines
T. Yoshimoto et al. / Nuclear Instruments and Methods in Physics Research A 733 (2014) 141–146
connected to individual monitors, a multiplexer, an oscilloscope, and a computer for handling acquired data. The system can automatically select a necessary signal with the multiplexer. In addition to data from the above-mentioned beam pulse profile and beam center position, data about the pulse voltages for acceleration and confinement, which are detected as continuous-time signals of the matching resistances inserted in parallel to the induction acceleration cells, is transferred to the system. Analysis integrating these data is indispensable, because the synchronization between beam circulation and the timing of acceleration/ confinement pulse voltages is crucial for acceleration in KEK-DA, where the fully predictive control method based on the B-clock is employed for acceleration control. The FPGA code calculates reference signals corresponding to the B-clock, which is uniquely determined once Bmin and Bmax are given. Using the data acquisition system, we can determine the turn-byturn x and y positions, beam loss, betatron tune (Qx and Qy), and injection timing error. Synchronization error and over- and underacceleration can be immediately identified. Consequently, a judgment can be made as to whether the FPGA code is performing satisfactorily.
3. Beam correction 3.1. Injection error correction Two steering magnets positioned immediately before the injection point are used to correct injection error. In general, the beam center position is expressed by pffiffiffiffiffiffiffiffiffiffi xðsÞ ¼ εβðsÞ cos ð2πQ x s þ δÞ þ xcod ðsÞ; where β(s) is the beta-function at s, (εβ(s))1/2 is the betatron amplitude of the beam center with injection error, δ is the initial betatron phase, and xcod(s) is the residual closed orbit. Using this formula and the beam position data, we find the injection error (x(0)−xcod(0), x′(0)−xcod′(0)). Then, excitation currents of two steering magnets are supplied to correct this injection error. A typical result after correction is shown in Fig. 4, where the oscillation amplitude of the beam center is drastically reduced from 12 mm to 2.6 mm. Note that the oscillation center after correction, seen as an offset of the betatron oscillation, corresponds to xcod(s) at observing point s.
143
Fig. 5. COD correction system with four figure-8 back-leg coils excited by independent power sources.
flux density in the magnets varies within 710 G, depending on the individual magnet [1]. Thus, residual fields become a major source of COD. KEK-DA has eight bending magnets and four position monitors (Fig. 5). Obviously, the number of observation points is insufficient to ascertain the entire COD profile along the ring. The lower-harmonics COD correction method is effective in a ring with a small betatron tune. Here, only the first and second harmonic components of the COD have been corrected by four pairs of 8 figure back leg coils [9]. The result is shown in Fig. 6.
4. FPGA code and gate trigger for confinement and acceleration 4.1. Gate control of the SPSs using FPGA Production of confinement and accelerating voltage pulses is controlled by FPGA gate signals for SPSs. The SPS of a full-bridge circuit always generates a set of positive and negative pulses (called set/reset voltage) to prevent the saturation of cell magnetic cores. Thus the FPGA generates two different set/reset signals (Fig. 7).
3.2. COD correction The injection magnetic flux density is quite low, 390 G for a 200 keV heavy beam of A/Q¼4. Furthermore, the residual magnetic
4.2. Adjustment of beam control parameters in the FPGA code In the present fully predictive control method for acceleration, the B-clock is the most essential parameter. In the FPGA control device, the B-clock is based on the ideal magnetic field Bideal(t), which must be precisely adjusted to the actual bending magnetic field Bactual(t), which is described by Bmax þ Bmin Bactual ðtÞ ¼ 2 Bmax −Bmin cos ½ωðt þ δÞ; − 2
Fig. 4. Typical injection error and its correction in the horizontal direction, before (red) and after correction (blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
where ω is the angular frequency of the driving resonant circuit and ωδ is the initial phase seen by the injected beam. Every aspect of equipment operation, including ideal or resonant particles that remain in the ideal/design orbit through the entire acceleration period, is determined from this guiding field profile. It is essential to adjust three injection timing parameters: δ, Bmin, and Bmax. The following describes how these three parameters are obtained directly from beam information.
144
T. Yoshimoto et al. / Nuclear Instruments and Methods in Physics Research A 733 (2014) 141–146
The horizontal position of the beam center observed at a specific position monitor x(t) is expressed by D(s)ΔB(t)/Bmin, where D(s) is the dispersion function at the specific position. In the time region near B(t) ¼Bmin, the deviation from Bmin is approximated as follows: Bmax −Bmin f1− cos ½ωðt þ δÞg ΔBðtÞ ¼ BðtÞ−Bmin ¼ 2 " ( )# Bmax −Bmin ½ωðt þ δÞ2 ≈ 1− 1− þ ⋯ ∝ðt þ δÞ2 : 2 2! An integrated change in the revolution period and the deviation of the beam center from the ideal orbit are represented as follows: Rt 3 0 ΔT∝ðt þ δÞ Fig. 6. COD before correction: observed COD at the position monitors (red point) and its harmonic fitting (solid blue line), after correction: observed ones (blue point) and predicted one (solid green line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
xðtÞ∝ðt þ δÞ2 From these properties, we can directly derive δ by observing the beam motion in two ways. Fig. 9 shows a projection of the bunch profile signal on the time-turn plane, where a beam circulates in the ring without application of accelerating or confinement voltage; the horizontal axis shows the inner time clocked with Bmin, and the vertical axis shows the time after injection. The beam center is calculated and shown in Fig. 10. We can obtain the actual injection timing directly by cubic fitting; δ is −1141.7 μs.
Fig. 7. Schematic view of the induction acceleration system with the gate control system.
Fig. 8. Field ramping pattern and injection timing.
Fig. 9. Projection of the bunch monitor signal on the time-turn plane triggered by the constant clock determined by Bmin.
4.3. Determination of injection timing δ First, δ must be specified. For this purpose, a beam is injected at an earlier timing than the timing of Bactual_min (Fig. 8). After injection, the actual beam motion in the time domain is observed during the constant period Tmin, which is the revolution period of the ideal particle at B ¼ Bmin. The revolution period T of the bunch center depends on the guiding field strength. The temporal fluctuation in the revolution period is given by ΔTðtÞ ΔC Δv − ¼ T min C v Δp ΔBðtÞ 1 Δp ¼α − − 2 pmin Bmin γ pmin ΔBðtÞ ¼ −α ð∵Δp ¼ 0Þ; Bmin where C is the ideal circumference of the ring, pmin is the injection momentum uniquely determined from Bmin, and α(¼ 1/γ2T−1/γ2) is the momentum compaction factor.
Fig. 10. Beam center tracking in time on the time-turn plane.
T. Yoshimoto et al. / Nuclear Instruments and Methods in Physics Research A 733 (2014) 141–146
Fig. 11. Time varying position of the horizontal beam center. The fine structure in the oscillation is the betatron oscillation. The noisy signal beyond 250 turns makes no sense because the beam without acceleration is lost due to the ramping B(t).
145
Fig. 14. Time-turn plane view of Vbb where set pulse (yellow) and reset pulse (blue) (experiment). The beam bucket with 2 μs length consists of two confinement voltages. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. Confinement voltage Vbb, acceleration voltages Vac, and the beam on the time axis.
Fig. 15. Time-turn plane view of Vac (experiment) where set pulse (yellow) and reset pulse (blue). The pulse-generation density is weaker in the injection and final stage than the medium stage. This corresponds to the needed acceleration voltage (see Fig. 13). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 13. Bideal(t) (top), required acceleration voltage per turn (bottom, solid red line), and Vac trigger pulse timing. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The horizontal position is observed by the position monitor (Fig. 11). In a straightforward manner, quadratic fitting gives δ¼ −1122.2 μs. The difference between the two δs is 19.5 μs and this magnitude may be the resolution of this method. 4.4. Acceleration scheme and typical example Accelerating voltage Vac and confinement voltage Vbb are generated separately on individual induction cells (Fig. 12). The confinement voltage is generated every turn, whereas the accelerating voltage is intermittently generated because of the limited capabilities of the induction acceleration system, as described in a previous report [1]. This feature is illustrated in Fig. 13. In the
Fig. 16. Time-turn plane view of a trapped and accelerated beam signal (white and succeeding blue region) (experiment). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
present experiment (Bmax ¼ 2.5 kG), two induction cells produce two sets of set/reset voltage pulses, where pulse height and length are fixed to be 1 kV and 150 ns, respectively, and the time duration between the two sets is changed in proportion to the revolution
146
T. Yoshimoto et al. / Nuclear Instruments and Methods in Physics Research A 733 (2014) 141–146
period. The pulse width of Vac, which is generated on a single induction cell, is set so as to fully cover the region occupied by the beam pulse. Experimentally demonstrated temporal changes in Vbb and Vac over one acceleration cycle are shown in Figs. 14 and 15. Actual beam motion is shown in Fig. 16. It is emphasized that the above operation is realized as a result of triggering the participating SPSs following the gate trigger program in the FPGA.
5. Summary We have successfully demonstrated induction acceleration of a heavy beam of A/Q¼ 4. Basic but essential equipment conditioning such as injection error correction and COD correction has been carried out. We have established a method for setting control parameters for induction acceleration by analyzing the motion of an injected beam. In addition, the acceleration scheme and typical experimental results have been introduced.
Acknowledgment This work was supported by a Grant-In-Aid for Scientific Research (A) (KAKENHI no. 23240082). References [1] T. Iwashita, et al., Physical Review Special Topics—Accelerators and Beams 14 (2011) 071301. [2] K. Takayama, et al., Journal of Applied Physics 101 (2007) 063304. (with Erratum). [3] S. Kawata, et al., Nuclear Instruments and Methods A 577 (2007) 21. [4] Ken Takayama, Richard J. Briggs, Induction Accelerator, Springer, Van Godewijckstraat 30, 3311 GX Dordrecht, Netherlands, 2011. [5] Leo Kwee Wah, et al., Permanent magnet ECRIS for the KEK digital accelerator, in: Proceedings of the 19th International Workshop on ECRIS, August 23–26, Grenoble, France, TUPOT15, 2010. [6] T. Adachi, et al., Review of Scientific Instruments 82 (2011) 083305. [7] K. Takayama, et al., KEK digital accelerator and its beam commissioning, in: Proceedings of IPAC2011, WEOBA02, San Sebastián, Spain, September 4–9, 2011. [8] K. Takayama, et al., Physical Review Letters 98 (2007) 054801. [9] K. Takayama, et al., KEK Digital Accelerator and Latest Switching Device R&D, in this conference, The 19th International Symposium on Heavy Ion Inertial Fusion, August 12–17, 2012, Berkeley, California, USA.