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Design approach for a 325 MHz, 3 MeV, 70–100 mA proton radio-frequency quadrupole accelerator with low emittance transfer
Nuclear Inst. and Methods in Physics Research, A 947 (2019) 162756
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Design approach for a 325 MHz, 3 MeV, 70–100 mA proton radio-frequency quadrupole accelerator with low emittance transfer Chuan Zhang a ,∗, Holger Podlech b a b
GSI Helmholtz Center for Heavy Ion Research, Planckstr. 1, Darmstadt, Germany Institute for Applied Physics, Goethe University, Frankfurt a. M., Germany
ARTICLE
INFO
Keywords: Radio Frequency Quadrupole accelerator Beam dynamics High current Space charge effects Emittance transfer
ABSTRACT Radio Frequency Quadrupole (RFQ) accelerators often need to face the challenges of space charge effects from high beam currents. This study investigated how to reach an efficient beam dynamics design for a 325 MHz, 3 MeV, 70–100 mA proton RFQ with not only high beam transmission and short structure length but also high 𝜀 beam quality simultaneously. To avoid emittance transfer which can lead to beam instabilities, a so-called 𝜀𝑙 𝑡 (ratio of the longitudinal and transverse emittances) = 1.0 design guideline is being proposed. In this paper, the application of this design guideline integrated with the ‘‘New Four-Section Procedure’’ and the corresponding design results are presented.
1. Introduction The R & D of a new generation of High Power Proton Accelerators (HPPA) with beam energies up to several GeV and power levels up to several MW has become a common interest for the particle accelerator community. Modern HPPA machines are of significant importance for promoting not only basic research but also advanced civil applications, because they can serve as spallation neutron sources, radioactive beam facilities, factories for other interesting secondary particles e.g. antiprotons and neutrinos, or accelerator-driven systems [1,2]. As the typical injector to modern HPPA machines, the Radio Frequency Quadrupole (RFQ) accelerator often needs to face the challenges of space charge effects from high beam currents. The purpose of this study is to develop a new design approach towards an efficient beam dynamics design for a 325 MHz, 3 MeV, 70–100 mA proton RFQ with high beam transmission, short structure length, and high beam quality. The design requirements of the RFQ that will work at a duty cycle of 10% are summarized in Table 1. The RFQ will be optimized for the design beam current 𝐼in = 70 mA and should be able to work at higher currents up to 100 mA. To relax the strong space charge effects at such currents, a relatively high input energy, 𝑊in = 95 keV, has been adopted. Meanwhile, a relatively large input emittance, 𝜀in,trans.,n.,rms = 0.3𝜋 mm mrad, has been chosen, based on the state of the art ion source technology [3,4]. The design goals of this 70–100 mA RFQ are as follows: • The beam transmission should be ≥95% for the design current 70 mA and ≥90% for the required higher current 100 mA, respectively.
• For easy construction and tuning, the maximum structure length of the accelerator is limited to be ∼3 m. It is known that for an adiabatic bunching section, the cell length is proportional to 𝛽 3 , where 𝛽 is the ratio of the beam velocity to the speed of light in vacuum [5]. Therefore, this goal is quite demanding at 95 keV such a high injection energy. • High beam quality with not only small emittance growth but also as few as possible ‘‘unstable particles’’ should be reached. Here ‘‘unstable particles’’ mean the not-well-accelerated particles due to inadequate beam bunching and acceleration. In the acceleration stages behind the RFQ, such particles will see wrong RF fields and can very likely be lost, so they are not favorable to meet the demands for modern linacs e.g. easy maintenance and high reliability especially when superconducting cavities are employed directly after or close to the RFQ exit. 2. Collective instabilities and Hofmann Charts To reach high beam transmission as well as high beam quality for a high current RFQ accelerator, one crucial issue is how to avoid emittance transfer during the beam bunching and acceleration process [6,7]. For beams with sufficient anisotropy of emittance and oscillation energy between different degrees of freedom, exchangerelated resonances can occur and consequently cause beam instabilities, reduction of beam quality, and even beam losses [6,7]. Systematic studies on collective instabilities for anisotropic beams have been done by I. Hofmann since several decades [6]. By imposing
∗ Corresponding author. E-mail address: [email protected] (C. Zhang).
https://doi.org/10.1016/j.nima.2019.162756 Received 10 August 2019; Received in revised form 11 September 2019; Accepted 12 September 2019 Available online 14 September 2019 0168-9002/© 2019 Elsevier B.V. All rights reserved.
C. Zhang and H. Podlech
Nuclear Inst. and Methods in Physics Research, A 947 (2019) 162756 Table 1 Design requirements for the RFQ. Parameters
Values
Frequency f [MHz] Input beam energy 𝑊in [keV] Output beam energy 𝑊out [MeV] Design beam current 𝐼in [mA] Inter-vane voltage U [kV] Normalized rms transverse input emittance 𝜀in,trans.,n.,rms [𝜋 mm mrad] Total structure length L [m] Beam transmission efficiency T [%] Duty cycle [%]
325 95 3.0 70 80 0.30 ∼3.0 ≥95 10
3. Design approach for low emittance transfer
perturbations on an anisotropic Kapchinsky–Vladimirsky distribution in a constant focusing system with arbitrary focusing ratios and emittance ratios, calculations of the Vlasov equation in the two transverse dimensions were performed. I. Hofmann suggested that the same mechanisms of instability and similar thresholds could be applied for the longitudinal–transverse coupling resonances as well [7]. For different emittance ratios, the growth rates and thresholds of the resonances can be identified and visualized in the so-called ‘‘Hofmann Instability Charts’’ by two dimensionless parameters namely the tune ratio 𝜎𝑙 ∕𝜎𝑡 and the tune depression 𝜎∕𝜎0 .
Fig. 1 shows a series of Hofmann Charts for the emittance ratio range from 0.2 to 2.0, where the dashed lines mark the EP positions and the color values indicate the growth rates of the resonances [7]. Generally speaking, after a beam is injected, the RFQ needs firstly to adapt the beam to a time-dependent focusing system by a short radial matching (RM) section, then to bunch it, and finally to accelerate it to the design energy. RFQ input beams have typically very small energy spread but very large phase spread, so for RFQ beam dynamics design studies it is usually assumed that the input energy spread and phase spread are 0 and ±180◦ , respectively, which is corresponding to a zero longitudinal emittance 𝜀𝑙 at the RFQ entrance. Along with the bunching and acceleration, 𝜀𝑙 will be gradually increased to the final value. Besides high beam transmission and short structure length, another typical design goal for RFQs is to hold the transverse emittance 𝜀𝑡 constant throughout the accelerating channel and have as small as possible 𝜀𝑙 at the exit. This is because a development tendency for modern large linacs is to start applying the superconducting RF technologies already in the very low energy part e.g. directly after or close to the RFQ exit. Therefore, this study is 𝜀 focusing on the Hofmann Charts for the emittance ratio 𝜀𝑙 up to 2.0.
The Hofmann Charts have been obtained without including the effects of beam acceleration. A recent study [8] shows that the resonance instability can be mitigated with a sufficiently high accelerating gradient e.g. 2–8 MV/m mentioned in Ref. [8]. The RFQ accelerators for which the accelerating gradients are typically ≤1 MV/m often need to face the challenges of beam instabilities, especially at high currents. On the Hofmann Charts, the shaded areas mark the dangerous positions for emittance transfer, and the color values indicate the developing speed of these parametric resonances (the darker the color is, the higher the developing speed is). Usually, the resonance peaks appear 𝜎 when 𝜎𝑙 = 𝑚𝑛 (m and n are integers), e.g. at the positions: 1/1, 1/2, 𝑡 2/3, etc. Actually, such resonances also exist at zero current because of the RF defocusing effect caused by the negative synchronous phase. However, the stop bands are significantly widened in the presence of strong space charge effects. On the charts, the maximum spread of the safe tune depression (not shaded areas) always appears at a location 𝜎 𝜀 where 𝜎𝑡 = 𝜀𝑙 is satisfied and a resonance peak expected to be present 𝑙 𝑡 is ‘‘killed’’. Because this condition can reach an energy-balanced beam and provide no free energy for driving the resonances, it is known as the equipartitioning (EP) condition [9].
𝑡
𝜀
Fig. 1 shows that the 𝜀𝑙 = 1.0 Hofmann Chart i.e. Graph (e) can be 𝑡 used to minimize the emittance transfer due to the following reasons: • It allows safe evolutions of the beam parameters in a quasi𝜎 rectangular area with very wide ranges of tune ratio ( 𝜎𝑙 = 𝑡 𝜎 0.5–2.0) and tune depression ( 𝜎 = ∼0.2–1.0), respectively. This 0 ‘‘safe rectangle’’ is ideal to cover the most critical part for space charge effects during the RFQ bunching to the greatest extent. • Its overall growth rate is relatively low. This is indicated by the upper limit of its colorbar range (limited by the code, different graphs have slightly different colorbar ranges in Fig. 1), which is one of the lowest among all those shown. • As the RFQ uses the same RF field for both bunching and acceleration, the longitudinal focusing force as well as the longitudinal phase advance will become smaller after the real acceleration 𝜎 starts. This usually moves the tune footprints into the 𝜎𝑙 ≤ 0.5 𝑡 region and lets them enter the resonance peaks there. As the quickly increased beam velocity weakens the transverse space charge effects naturally, the caused emittance transfer will lead 𝜀 𝜎 to an increased 𝜀𝑙 . Fig. 1 shows that all 𝜎𝑙 ≤ 0.5 resonance peaks
Following this idea, a so-called ‘‘Equipartitioning Procedure’’ was developed and applied to the beam dynamics design of a 140 mA, Continuous Wave (CW) deuteron RFQ [10]. It has been shown that the EP design is successful and robust against very strong space charge effects by very carefully varying the beam parameters to focus the tune footprints of the main RFQ always on the EP line. In order to accelerate such a high current, CW D+ beam to 5 MeV safely, a very strict constraint on particle losses, especially those at over 1 MeV, was imposed on the design, so it was worthwhile seeking the best beam quality at the expense of a ∼12.3 m long RFQ (for the CDR Version; the RFQ was later shortened to ∼8 m in the Post-CDR phase) [10].
in the
𝜀𝑙 𝜀𝑡
𝑡
𝑡
> 1.0 Hofmann Charts have much lower growth rates
𝜀𝑙 < 1.0 Hofmann Charts. Therefore, it is a good 𝜀 𝜀𝑙 𝑡 choice to have 𝜀 = 1.0 before the real acceleration starts. 𝑡 𝜀 In a real machine, it is difficult to always hold 𝜀𝑙 = 1.0 perfectly 𝑡
than those in the
For RFQ designs, there is always a trade-off between beam quality, manufacturing complexity, investment, and other practical considerations. In most cases, a strict EP design is not necessary. There are three ways to minimize beam quality loss: (1) to put the tune footprints in the ‘‘clean’’ area on the Hofmann Charts; (2) to let the tune footprints traverse the resonance peaks quickly enough e.g. the design presented in [11]; (3) to choose the working area with as low as possible growth rates of the resonances. This study is aiming to achieve high beam transmission, short structure length, and high beam quality simultaneously for an RFQ design by integrating these three ways.
•
due to different reasons e.g. errors. In Fig. 1, it can be seen that the 1/1 resonance peak will appear when a deviation from 𝜀𝑙 = 1.0 starts. Fortunately, this peak is not significant and its 𝜀 𝑡
𝜀
growth rates are low in the range 𝜀𝑙 = 0.8–1.4. Moreover, the 𝑡 boundary of the ‘‘safe rectangle’’ can be also roughly kept even 𝜀𝑙 up to 𝜀 = 2.0. It means that there are sufficient safety margins for a 2
𝜀𝑙 𝑡 = 𝜀𝑡
1.0 design.
C. Zhang and H. Podlech
Fig. 1. Hofmann Charts for emittance ratios
Nuclear Inst. and Methods in Physics Research, A 947 (2019) 162756
𝜀𝑙 𝜀𝑡
= 0.2 to 2.0, where the dashed lines are marking the EP positions (the graphs have been generated using the TraceWin Code [12]) 𝜀
To conclude, it can be a useful guideline to choose 𝜀𝑙 = 1.0 for 𝑡 designing RFQs with low emittance transfer. For the RFQ beam dynamics design, the ‘‘Four-Section Procedure’’ (FSP) [13] developed by LANL is a classic technique. If the short RM section (typically only 4–6 cells long) at the entrance is ignored, it divides the main RFQ into three sequential sections: a ‘‘Shaper’’ (SH) section for prebunching, a ‘‘Gentle Buncher’’ (GB) section for main bunching, and finally an ‘‘Accelerator’’ (ACC) section for main acceleration. The GB section holding the longitudinal small oscillation frequency of the particles and the geometric length of the separatrix constant is the key of this method for adiabatic bunching [5]. In practice, all of the bunching cannot be done adiabatically in order to avoid a too long RFQ, so the SH section which ramps the phase and the acceleration efficiency
linearly with axial distance for a fast prebunching is introduced. This can be a potential source for unstable particles. Another characteristic of the FSP method is that the mid-cell electrode aperture 𝑟0 as well as the transverse focusing strength B are held constant along the main RFQ. When the method was originally developed in 1978–1980, it was helpful for easing manufacturing and tuning (limited by the technologies at that time), but it is not reasonable from today’s point of view, as the space charge forces are changing along an RFQ. To improve the FSP-style bunching process by adapting the transverse focusing strength to the changing space charge situation along the RFQ, a so-called ‘‘New Four-Section Procedure’’ (NFSP) [14], has been developed. The NFSP method has enabled several efficient RFQ designs e.g. [15,16] with both high beam transmission and short structure 3
C. Zhang and H. Podlech
Nuclear Inst. and Methods in Physics Research, A 947 (2019) 162756
length, even at very high beam intensities e.g. 200 mA [14]. To further improve the beam quality especially to minimize the unstable particles, 𝜀 a new design approach implementing the 𝜀𝑙 = 1.0 design guideline into 𝑡 the NFSP method is being proposed. The new approach divides the main RFQ into also three sections: a main bunching (MB) section, a mixed-bunching-acceleration (MBA) section, and a main acceleration (MA) section in the following way: • In the MB section, the beam goes through a so-called ‘‘𝜀𝑙 formation phase’’ in which the longitudinal emittance will be gradually 𝜀 increased from 0 to a value that satisfies 𝜀𝑙 ≅ 1.0. In this phase, 𝑡
𝜎
the tune ratio 𝜎𝑙 should be brought from 0 to a value between 𝑡 0.5 and 2.0 as fast as possible, because there are some remarkable 𝜎 𝜀 resonance peaks in the 𝜎𝑙 ≤ 0.5 region on the way to 𝜀𝑙 = 1.0 (see 𝑡 𝑡 Graphs (a)–(d) in Fig. 1). The phase advances 𝜎𝑙 and 𝜎𝑡 represent the longitudinal and transverse focusing strength, respectively. The FSP method holds the transverse focusing strength B constant for the main RFQ, so usually 𝜎𝑡 is already relatively large at the beginning of the bunching where 𝜎𝑙 is still close to zero. This is 𝜎 not favorable to enter the safe 𝜎𝑙 range quickly. This problem 𝑡 can be overcome by the NFSP method, which applies a different strategy for this phase: (1) B starts with a relatively small value because of the relatively weak transverse space charge effects before the bunching starts; (2) B will be gradually increased to balance the increased longitudinal focusing during the bunching process; (3) longitudinally the synchronous phase 𝜑s will be kept at ∼-90◦ to provide a strong bunching and to increase 𝜎𝑙 rapidly. In this way, a quick arrival of the tune footprints at the ‘‘safe 𝜀 rectangle’’ provided by the 𝜀𝑙 = 1.0 Hofmann Chart is possible.
Fig. 2. Main beam dynamics design parameters of the RFQ.
𝑡
• The MBA section is the most critical part for beam bunching, because the space charge effects are getting stronger and stronger with the decreasing bunch size and become most significant at the end of this section. To keep the emittance transfer as low as possible, this section should be well localized in the ‘‘safe 𝜀 rectangle’’ provided by the 𝜀𝑙 = 1.0 Hofmann Chart in order to 𝑡 allow safe and fast changes of the beam parameters. • In the MA section, the longitudinal focusing force and the longitudinal phase advance will become smaller. If the transverse 𝜎 focusing strength is held as strong as with the FSP method, 𝜎𝑙 𝑡 will be decreased quickly. In the NFSP method, B is decreased such as to slow down the leaving speed of the tune trajectories from the ‘‘safe rectangle’’.
Fig. 3. Ratios of emittances
𝜀𝑙 𝜀𝑡
, phase advances
𝜎𝑙 𝜎𝑡
, and beam sizes
𝑏 𝑎
along the RFQ.
4. Design & simulation results of the 70–100 mA RFQ The beam dynamics design of the 70–100 mA RFQ has been achieved using the new design approach based on the combination of 𝜀 the 𝜀𝑙 = 1.0 design guideline and the NFSP method. The evolutions 𝑡 of the main beam dynamics parameters along the RFQ are shown in Fig. 2, where 𝑎min is the minimum electrode aperture, m is the electrode modulation, B is the transverse focusing strength, 𝑊s is the synchronous energy, and 𝜑s is the synchronous phase, respectively. The beam dynamics simulation has been performed using the PARMTEQM code [17] with a 4D-Waterbag input distribution. Fig. 3 plots several key ratios between the longitudinal and transverse planes, where b and a are the longitudinal and transverse rms beam sizes in mm, respectively. The partitions of the RFQ can also be distinguished in the figure: (1) MB: Cell 0 to Cell 90; (2) MBA: Cell 91 to Cell 145; (3) 𝜀 MA: Cell 146 to the exit. At the end of the MB section, 𝜀𝑙 reaches ∼1.0 𝑡 and the beam starts to enter the ‘‘safe rectangle’’. In the remainder of the RFQ, the emittance ratio is kept close to 1.0. 𝜀 The tune footprints of the RFQ at 70 mA are plotted on the 𝜀𝑙 = 1.0 𝑡 Hofmann Chart in Fig. 4. The different sections are marked in different colors: red for MB, green for MBA, and blue for MA. The solid and dashed curves represent the tune depressions in the transverse and
Fig. 4. Tune footprints of the RFQ at 70 mA on the
𝜀𝑙 𝜀𝑡
= 1.0 Hofmann Chart.
longitudinal directions, respectively. It can be seen that the main part of the tune trajectories with big oscillations is located in the safe place on the chart so that this kind of bunching process can be performed much faster than the GB section in the FSP method, which can shorten the structure length. In the MA section, the tune trajectories step into the instability 𝜎 region. On one side, the transverse tune depression 𝜎 𝑡 rises from ∼0.65 0𝑡 to 0.8 as a result of weakened transverse space charge effects, and the corresponding tune trajectory travels still mostly in the resonance-free area, so the transverse emittance can stay essentially constant. On the other side, the longitudinal tune trajectory enters the resonance peaks 𝜎 and 𝜎 𝑙 drops from 0.5 to 0.3, which will cause a certain longitudinal 0𝑙 emittance growth. But the tune trajectory has no big oscillation any𝜀 more and the growth rates in this area are low enough, so 𝜀𝑙 can be 𝑡 still held close to ∼1.0. 4
C. Zhang and H. Podlech
Nuclear Inst. and Methods in Physics Research, A 947 (2019) 162756
Fig. 5. Tune footprints of the RFQ at 100 mA on the
𝜀𝑙 𝜀𝑡
‘‘clean’’ space below the beam trajectories, which gives a hint that this RFQ can work at even higher currents. Furthermore, the ratios of the longitudinal and transverse emittances as well as phase advances along the RFQ for both 70 mA and 100 mA are compared in Fig. 6. The evolutions of these parameters are fairly close to each other. The emittance ratio of the 100 mA beam has 𝜀 a few ‘‘jumps’’ in the MA section due to the deviation from 𝜀𝑙 = 1.0 𝑡 at the MB end. From the curve of the emittance ratio calculated with the longitudinal emittance for 99% instead of 100% of the beam, it can be deducted that this difference has been caused by only ≤1% of halo particles. Fig. 7 shows the output particle distributions in the three phase spaces. Again, it shows the similarity between the 70 mA and 100 mA cases. The 100 mA beam has slightly bigger beam sizes due to stronger space charge effects. But in both cases, the beam is still well concentrated. More detailed design and simulation results of the RFQ are given in Table 2. The design goals with respect to the beam transmission, ≥95% for 70 mA and ≥90% for 100 mA, are met. At both currents, there is almost no transverse emittance growth with very moderate values for the output longitudinal emittances.
= 1.0 Hofmann Chart.
5. Conclusions
Fig. 6. Comparison of emittance ratios
𝜀𝑙 𝜀𝑡
and phase advance ratios
𝜎𝑙 𝜎𝑡
How to efficiently avoid emittance transfer which can lead to beam instabilities has been investigated for a 325 MHz, 3 MeV, 70–100 mA 𝜀 proton RFQ accelerator. A so-called 𝜀𝑙 = 1.0 design guideline is being 𝑡 proposed. 𝜀𝑙 As a combination of the 𝜀 = 1.0 design guideline and the NFSP 𝑡 method, the new approach integrates the three ways of minimizing beam quality loss for designing different sections of an RFQ as follows:
between the
70 mA and 100 mA cases.
• In the MB section, it allows the tune footprints a fast traversal through the resonance peaks and a quick arrival at the ‘‘safe 𝜀 rectangle’’ provided by the 𝜀𝑙 = 1.0 Hofmann Chart.
It is also required that this RFQ should work at currents up to 100 mA. Fig. 5 checks the tune footprints at 100 mA. Generally speaking, the behavior is similar to that in the 70 mA case. Of course, from 70 mA to 100 mA, the space charge effects are getting stronger, so the ‘‘center of gravity’’ of the beam trajectories has been lowered from ∼0.65 to ∼0.55 in the 𝜎𝜎 direction and the final longitudinal tune 0 depression has fallen down from 0.3 to 0.2. But there is still sufficient
𝑡
• In the MBA section i.e. the most critical part for space charge effects during the bunching, it puts the tune footprints inside the ‘‘safe rectangle’’. • In the MA section, after the real acceleration starts, it lets the tune footprints only enter the resonance peaks with low growth rates.
Fig. 7. Output particle distributions of the RFQ (top: 70 mA; bottom: 100 mA). (color online).
5
C. Zhang and H. Podlech
Nuclear Inst. and Methods in Physics Research, A 947 (2019) 162756 Table 2 Main design results of the RFQ. Parameters
At 70 mA At 100 mA
Normalized rms transverse input emittance 𝜀in,trans.,n.,rms [𝜋 mm mrad] Normalized rms output emittance in the x-plane 𝜀out,x,n.,rms [𝜋 mm mrad] Normalized rms output emittance in the y-plane 𝜀out,y,n.,rms [𝜋 mm mrad] rms longitudinal output emittance 𝜀out,z,rms [keV-ns] Total structure length L [m] Beam transmission efficiency T [%]
0.30
0.300
0.301
0.299
0.297
0.299
1.0
1.2
3.0 96.0
3.0 90.1
The beam dynamics simulation results of the 70–100 mA RFQ chosen for this study have demonstrated that the new design approach can lead to not only high beam transmission and short structure length but also high beam quality simultaneously.
[6] I. Hofmann, Emittance growth of beams close to the space charge limit, IEEE Trans. Nucl. Sci. 28 (3) (1981) 2399–2401. [7] I. Hofmann, Stability of anisotropic beams with space charge, Phys. Rev. E 57 (4) (1998) 4713–4724. [8] J. Qiang, Mitigation of envelope instability through fast acceleration in linear accelerators, Phys. Rev. Accel. Beams 21 (114201) (2018) 1–10. [9] R.A. Jameson, Equipartitioning in linear accelerators, in: Proceedings of the 1981 Linac Accelerator Conference in Santa Fe, New Mexico, USA, September 19–23, 1981, pp. 125–129. [10] R.A. Jameson, RFQ Designs and Beam-Loss Distributions for IFMIF, Oak Ridge National Laboratory Tech. Rep. ORNL/TM-2007/001, 2007. [11] C. Zhang, Z.Y. Guo, A. Schempp, R.A. Jameson, J.E. Chen, J.X. Fang, Low-beamloss design of a compact, high-current deuteron radio frequency quadrupole accelerator, Phys. Rev. ST Accel. Beams 7 (100101) (2004) 1–6. [12] http://irfu.cea.fr/Sacm/logiciels/. [13] R.H. Stokes, K.R. Crandall, J.E. Stovall, D.A. Swenson, RF quadrupole beam dynamics, in: Proceedings of the 8th Particle Accelerator Conference, San Francisco, USA, March 12–14, 1979, pp. 3469–3471. [14] C. Zhang, A. Schempp, Beam dynamics studies on a 200 mA proton radio frequency quadrupole accelerator, Nuclear Instrum. Methods Phys. Res. A 586 (2008) 153–159. [15] M. Okamura, J. Alessi, E. Beebe, K. Kondo, R. Lambiase, R. Lockey, V. LoDestro, M. Mapes, A. McNerney, D. Phillips, A.I. Pikin, D. Raparia, J. Ritter, L. Smart, L. Snydstrup, A. Zaltsman, J. Tamura, A. Schempp, C. Zhang, J.S. Schmidt, M. Vossberg, T. Kanesue, Beam commissioning results for the RFQ and MEBT of the EBIS based preinjector for RHIC, in: Proceedings of the 25th International Linear Accelerator Conference, Tsukuba, Japan, September 12–17, 2010, pp. 473–475. [16] Chuan Zhang, Marco Busch, Horst Klein, Holger Podlech, Ulrich Ratzinger, Rudolf Tiede, Jean-Luc Biarrotte, Biarrotte Reliability and current-adaptability studies of a 352 MHz, 17 MeV, continuous-wave injector for an acceleratordriven system, Phys. Rev. ST Accel. Beams 13 (080101) (2010) 1–11. [17] Manual of the LANL RFQ Design Codes, LANL Report No. LA-UR-96-1836 (revised June3, 2005).
Acknowledgment The author CZ would like to thank Eugene Tanke very much for his friendly and patient help which enabled a deep look inside the design and convenient data analyses as well as his valuable suggestions for the improvement of the manuscript. References [1] https://www.oecd-nea.org/science/pubs/2001/3051-HPPA-France%201999.pdf. [2] O. Kester, W. Barth, O. Dolinskyy, F. Hagenbuck, K. Knie, H. Reich-Sprenger, H. Simon, P.J. Spiller, U. Weinrich, M. Winkler, R. Maier, Status of the FAIR accelerator facility, in: Proceedings of the 5th International Particle Accelerator Conference, Dresden, Germany, June 15–20, 2014, pp. 2084–2087. [3] R. Gobin, P.-Y. Beauvais, D. Bogard, G. Charruau, O. Delferrière, D. De Menezes, A. France, R. Ferdinand, Y. Gauthier, F. Harrault, P. Mattéi, K. Benmeziane, P. Leherissier, J.-Y. Paquet, P. Ausset, S. Bousson, D. Gardes, A. Olivier, L. Celona, J. Sherman, Status of the light ion source developments at CEA/Saclay, Rev. Sci. Instrum. 75 (2004) 1414–1416. [4] R. Berezov, R. Brodhage, N. Chauvin, O. Delferriere, J. Fils, R. Hollinger, V. Ivanova, O. Tuske, C. Ullmann, High intensity proton injector for facility of antiproton and ion research, Rev. Sci. Instrum. 87 (02A705) (2016) 1–3. [5] R.F. Thomas, Linear Accelerators, Second Completely Revised and Enlarged ed., Wiley, New York, ISBN: 978-3-527-40680-7, 2008.
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Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Design approach for a 325 MHz, 3 MeV, 70–100 mA proton radio-frequency quadrupole accelerator with low emittance transfer Chuan Zhang a ,∗, Holger Podlech b a b
GSI Helmholtz Center for Heavy Ion Research, Planckstr. 1, Darmstadt, Germany Institute for Applied Physics, Goethe University, Frankfurt a. M., Germany
ARTICLE
INFO
Keywords: Radio Frequency Quadrupole accelerator Beam dynamics High current Space charge effects Emittance transfer
ABSTRACT Radio Frequency Quadrupole (RFQ) accelerators often need to face the challenges of space charge effects from high beam currents. This study investigated how to reach an efficient beam dynamics design for a 325 MHz, 3 MeV, 70–100 mA proton RFQ with not only high beam transmission and short structure length but also high 𝜀 beam quality simultaneously. To avoid emittance transfer which can lead to beam instabilities, a so-called 𝜀𝑙 𝑡 (ratio of the longitudinal and transverse emittances) = 1.0 design guideline is being proposed. In this paper, the application of this design guideline integrated with the ‘‘New Four-Section Procedure’’ and the corresponding design results are presented.
1. Introduction The R & D of a new generation of High Power Proton Accelerators (HPPA) with beam energies up to several GeV and power levels up to several MW has become a common interest for the particle accelerator community. Modern HPPA machines are of significant importance for promoting not only basic research but also advanced civil applications, because they can serve as spallation neutron sources, radioactive beam facilities, factories for other interesting secondary particles e.g. antiprotons and neutrinos, or accelerator-driven systems [1,2]. As the typical injector to modern HPPA machines, the Radio Frequency Quadrupole (RFQ) accelerator often needs to face the challenges of space charge effects from high beam currents. The purpose of this study is to develop a new design approach towards an efficient beam dynamics design for a 325 MHz, 3 MeV, 70–100 mA proton RFQ with high beam transmission, short structure length, and high beam quality. The design requirements of the RFQ that will work at a duty cycle of 10% are summarized in Table 1. The RFQ will be optimized for the design beam current 𝐼in = 70 mA and should be able to work at higher currents up to 100 mA. To relax the strong space charge effects at such currents, a relatively high input energy, 𝑊in = 95 keV, has been adopted. Meanwhile, a relatively large input emittance, 𝜀in,trans.,n.,rms = 0.3𝜋 mm mrad, has been chosen, based on the state of the art ion source technology [3,4]. The design goals of this 70–100 mA RFQ are as follows: • The beam transmission should be ≥95% for the design current 70 mA and ≥90% for the required higher current 100 mA, respectively.
• For easy construction and tuning, the maximum structure length of the accelerator is limited to be ∼3 m. It is known that for an adiabatic bunching section, the cell length is proportional to 𝛽 3 , where 𝛽 is the ratio of the beam velocity to the speed of light in vacuum [5]. Therefore, this goal is quite demanding at 95 keV such a high injection energy. • High beam quality with not only small emittance growth but also as few as possible ‘‘unstable particles’’ should be reached. Here ‘‘unstable particles’’ mean the not-well-accelerated particles due to inadequate beam bunching and acceleration. In the acceleration stages behind the RFQ, such particles will see wrong RF fields and can very likely be lost, so they are not favorable to meet the demands for modern linacs e.g. easy maintenance and high reliability especially when superconducting cavities are employed directly after or close to the RFQ exit. 2. Collective instabilities and Hofmann Charts To reach high beam transmission as well as high beam quality for a high current RFQ accelerator, one crucial issue is how to avoid emittance transfer during the beam bunching and acceleration process [6,7]. For beams with sufficient anisotropy of emittance and oscillation energy between different degrees of freedom, exchangerelated resonances can occur and consequently cause beam instabilities, reduction of beam quality, and even beam losses [6,7]. Systematic studies on collective instabilities for anisotropic beams have been done by I. Hofmann since several decades [6]. By imposing
∗ Corresponding author. E-mail address: [email protected] (C. Zhang).
https://doi.org/10.1016/j.nima.2019.162756 Received 10 August 2019; Received in revised form 11 September 2019; Accepted 12 September 2019 Available online 14 September 2019 0168-9002/© 2019 Elsevier B.V. All rights reserved.
C. Zhang and H. Podlech
Nuclear Inst. and Methods in Physics Research, A 947 (2019) 162756 Table 1 Design requirements for the RFQ. Parameters
Values
Frequency f [MHz] Input beam energy 𝑊in [keV] Output beam energy 𝑊out [MeV] Design beam current 𝐼in [mA] Inter-vane voltage U [kV] Normalized rms transverse input emittance 𝜀in,trans.,n.,rms [𝜋 mm mrad] Total structure length L [m] Beam transmission efficiency T [%] Duty cycle [%]
325 95 3.0 70 80 0.30 ∼3.0 ≥95 10
3. Design approach for low emittance transfer
perturbations on an anisotropic Kapchinsky–Vladimirsky distribution in a constant focusing system with arbitrary focusing ratios and emittance ratios, calculations of the Vlasov equation in the two transverse dimensions were performed. I. Hofmann suggested that the same mechanisms of instability and similar thresholds could be applied for the longitudinal–transverse coupling resonances as well [7]. For different emittance ratios, the growth rates and thresholds of the resonances can be identified and visualized in the so-called ‘‘Hofmann Instability Charts’’ by two dimensionless parameters namely the tune ratio 𝜎𝑙 ∕𝜎𝑡 and the tune depression 𝜎∕𝜎0 .
Fig. 1 shows a series of Hofmann Charts for the emittance ratio range from 0.2 to 2.0, where the dashed lines mark the EP positions and the color values indicate the growth rates of the resonances [7]. Generally speaking, after a beam is injected, the RFQ needs firstly to adapt the beam to a time-dependent focusing system by a short radial matching (RM) section, then to bunch it, and finally to accelerate it to the design energy. RFQ input beams have typically very small energy spread but very large phase spread, so for RFQ beam dynamics design studies it is usually assumed that the input energy spread and phase spread are 0 and ±180◦ , respectively, which is corresponding to a zero longitudinal emittance 𝜀𝑙 at the RFQ entrance. Along with the bunching and acceleration, 𝜀𝑙 will be gradually increased to the final value. Besides high beam transmission and short structure length, another typical design goal for RFQs is to hold the transverse emittance 𝜀𝑡 constant throughout the accelerating channel and have as small as possible 𝜀𝑙 at the exit. This is because a development tendency for modern large linacs is to start applying the superconducting RF technologies already in the very low energy part e.g. directly after or close to the RFQ exit. Therefore, this study is 𝜀 focusing on the Hofmann Charts for the emittance ratio 𝜀𝑙 up to 2.0.
The Hofmann Charts have been obtained without including the effects of beam acceleration. A recent study [8] shows that the resonance instability can be mitigated with a sufficiently high accelerating gradient e.g. 2–8 MV/m mentioned in Ref. [8]. The RFQ accelerators for which the accelerating gradients are typically ≤1 MV/m often need to face the challenges of beam instabilities, especially at high currents. On the Hofmann Charts, the shaded areas mark the dangerous positions for emittance transfer, and the color values indicate the developing speed of these parametric resonances (the darker the color is, the higher the developing speed is). Usually, the resonance peaks appear 𝜎 when 𝜎𝑙 = 𝑚𝑛 (m and n are integers), e.g. at the positions: 1/1, 1/2, 𝑡 2/3, etc. Actually, such resonances also exist at zero current because of the RF defocusing effect caused by the negative synchronous phase. However, the stop bands are significantly widened in the presence of strong space charge effects. On the charts, the maximum spread of the safe tune depression (not shaded areas) always appears at a location 𝜎 𝜀 where 𝜎𝑡 = 𝜀𝑙 is satisfied and a resonance peak expected to be present 𝑙 𝑡 is ‘‘killed’’. Because this condition can reach an energy-balanced beam and provide no free energy for driving the resonances, it is known as the equipartitioning (EP) condition [9].
𝑡
𝜀
Fig. 1 shows that the 𝜀𝑙 = 1.0 Hofmann Chart i.e. Graph (e) can be 𝑡 used to minimize the emittance transfer due to the following reasons: • It allows safe evolutions of the beam parameters in a quasi𝜎 rectangular area with very wide ranges of tune ratio ( 𝜎𝑙 = 𝑡 𝜎 0.5–2.0) and tune depression ( 𝜎 = ∼0.2–1.0), respectively. This 0 ‘‘safe rectangle’’ is ideal to cover the most critical part for space charge effects during the RFQ bunching to the greatest extent. • Its overall growth rate is relatively low. This is indicated by the upper limit of its colorbar range (limited by the code, different graphs have slightly different colorbar ranges in Fig. 1), which is one of the lowest among all those shown. • As the RFQ uses the same RF field for both bunching and acceleration, the longitudinal focusing force as well as the longitudinal phase advance will become smaller after the real acceleration 𝜎 starts. This usually moves the tune footprints into the 𝜎𝑙 ≤ 0.5 𝑡 region and lets them enter the resonance peaks there. As the quickly increased beam velocity weakens the transverse space charge effects naturally, the caused emittance transfer will lead 𝜀 𝜎 to an increased 𝜀𝑙 . Fig. 1 shows that all 𝜎𝑙 ≤ 0.5 resonance peaks
Following this idea, a so-called ‘‘Equipartitioning Procedure’’ was developed and applied to the beam dynamics design of a 140 mA, Continuous Wave (CW) deuteron RFQ [10]. It has been shown that the EP design is successful and robust against very strong space charge effects by very carefully varying the beam parameters to focus the tune footprints of the main RFQ always on the EP line. In order to accelerate such a high current, CW D+ beam to 5 MeV safely, a very strict constraint on particle losses, especially those at over 1 MeV, was imposed on the design, so it was worthwhile seeking the best beam quality at the expense of a ∼12.3 m long RFQ (for the CDR Version; the RFQ was later shortened to ∼8 m in the Post-CDR phase) [10].
in the
𝜀𝑙 𝜀𝑡
𝑡
𝑡
> 1.0 Hofmann Charts have much lower growth rates
𝜀𝑙 < 1.0 Hofmann Charts. Therefore, it is a good 𝜀 𝜀𝑙 𝑡 choice to have 𝜀 = 1.0 before the real acceleration starts. 𝑡 𝜀 In a real machine, it is difficult to always hold 𝜀𝑙 = 1.0 perfectly 𝑡
than those in the
For RFQ designs, there is always a trade-off between beam quality, manufacturing complexity, investment, and other practical considerations. In most cases, a strict EP design is not necessary. There are three ways to minimize beam quality loss: (1) to put the tune footprints in the ‘‘clean’’ area on the Hofmann Charts; (2) to let the tune footprints traverse the resonance peaks quickly enough e.g. the design presented in [11]; (3) to choose the working area with as low as possible growth rates of the resonances. This study is aiming to achieve high beam transmission, short structure length, and high beam quality simultaneously for an RFQ design by integrating these three ways.
•
due to different reasons e.g. errors. In Fig. 1, it can be seen that the 1/1 resonance peak will appear when a deviation from 𝜀𝑙 = 1.0 starts. Fortunately, this peak is not significant and its 𝜀 𝑡
𝜀
growth rates are low in the range 𝜀𝑙 = 0.8–1.4. Moreover, the 𝑡 boundary of the ‘‘safe rectangle’’ can be also roughly kept even 𝜀𝑙 up to 𝜀 = 2.0. It means that there are sufficient safety margins for a 2
𝜀𝑙 𝑡 = 𝜀𝑡
1.0 design.
C. Zhang and H. Podlech
Fig. 1. Hofmann Charts for emittance ratios
Nuclear Inst. and Methods in Physics Research, A 947 (2019) 162756
𝜀𝑙 𝜀𝑡
= 0.2 to 2.0, where the dashed lines are marking the EP positions (the graphs have been generated using the TraceWin Code [12]) 𝜀
To conclude, it can be a useful guideline to choose 𝜀𝑙 = 1.0 for 𝑡 designing RFQs with low emittance transfer. For the RFQ beam dynamics design, the ‘‘Four-Section Procedure’’ (FSP) [13] developed by LANL is a classic technique. If the short RM section (typically only 4–6 cells long) at the entrance is ignored, it divides the main RFQ into three sequential sections: a ‘‘Shaper’’ (SH) section for prebunching, a ‘‘Gentle Buncher’’ (GB) section for main bunching, and finally an ‘‘Accelerator’’ (ACC) section for main acceleration. The GB section holding the longitudinal small oscillation frequency of the particles and the geometric length of the separatrix constant is the key of this method for adiabatic bunching [5]. In practice, all of the bunching cannot be done adiabatically in order to avoid a too long RFQ, so the SH section which ramps the phase and the acceleration efficiency
linearly with axial distance for a fast prebunching is introduced. This can be a potential source for unstable particles. Another characteristic of the FSP method is that the mid-cell electrode aperture 𝑟0 as well as the transverse focusing strength B are held constant along the main RFQ. When the method was originally developed in 1978–1980, it was helpful for easing manufacturing and tuning (limited by the technologies at that time), but it is not reasonable from today’s point of view, as the space charge forces are changing along an RFQ. To improve the FSP-style bunching process by adapting the transverse focusing strength to the changing space charge situation along the RFQ, a so-called ‘‘New Four-Section Procedure’’ (NFSP) [14], has been developed. The NFSP method has enabled several efficient RFQ designs e.g. [15,16] with both high beam transmission and short structure 3
C. Zhang and H. Podlech
Nuclear Inst. and Methods in Physics Research, A 947 (2019) 162756
length, even at very high beam intensities e.g. 200 mA [14]. To further improve the beam quality especially to minimize the unstable particles, 𝜀 a new design approach implementing the 𝜀𝑙 = 1.0 design guideline into 𝑡 the NFSP method is being proposed. The new approach divides the main RFQ into also three sections: a main bunching (MB) section, a mixed-bunching-acceleration (MBA) section, and a main acceleration (MA) section in the following way: • In the MB section, the beam goes through a so-called ‘‘𝜀𝑙 formation phase’’ in which the longitudinal emittance will be gradually 𝜀 increased from 0 to a value that satisfies 𝜀𝑙 ≅ 1.0. In this phase, 𝑡
𝜎
the tune ratio 𝜎𝑙 should be brought from 0 to a value between 𝑡 0.5 and 2.0 as fast as possible, because there are some remarkable 𝜎 𝜀 resonance peaks in the 𝜎𝑙 ≤ 0.5 region on the way to 𝜀𝑙 = 1.0 (see 𝑡 𝑡 Graphs (a)–(d) in Fig. 1). The phase advances 𝜎𝑙 and 𝜎𝑡 represent the longitudinal and transverse focusing strength, respectively. The FSP method holds the transverse focusing strength B constant for the main RFQ, so usually 𝜎𝑡 is already relatively large at the beginning of the bunching where 𝜎𝑙 is still close to zero. This is 𝜎 not favorable to enter the safe 𝜎𝑙 range quickly. This problem 𝑡 can be overcome by the NFSP method, which applies a different strategy for this phase: (1) B starts with a relatively small value because of the relatively weak transverse space charge effects before the bunching starts; (2) B will be gradually increased to balance the increased longitudinal focusing during the bunching process; (3) longitudinally the synchronous phase 𝜑s will be kept at ∼-90◦ to provide a strong bunching and to increase 𝜎𝑙 rapidly. In this way, a quick arrival of the tune footprints at the ‘‘safe 𝜀 rectangle’’ provided by the 𝜀𝑙 = 1.0 Hofmann Chart is possible.
Fig. 2. Main beam dynamics design parameters of the RFQ.
𝑡
• The MBA section is the most critical part for beam bunching, because the space charge effects are getting stronger and stronger with the decreasing bunch size and become most significant at the end of this section. To keep the emittance transfer as low as possible, this section should be well localized in the ‘‘safe 𝜀 rectangle’’ provided by the 𝜀𝑙 = 1.0 Hofmann Chart in order to 𝑡 allow safe and fast changes of the beam parameters. • In the MA section, the longitudinal focusing force and the longitudinal phase advance will become smaller. If the transverse 𝜎 focusing strength is held as strong as with the FSP method, 𝜎𝑙 𝑡 will be decreased quickly. In the NFSP method, B is decreased such as to slow down the leaving speed of the tune trajectories from the ‘‘safe rectangle’’.
Fig. 3. Ratios of emittances
𝜀𝑙 𝜀𝑡
, phase advances
𝜎𝑙 𝜎𝑡
, and beam sizes
𝑏 𝑎
along the RFQ.
4. Design & simulation results of the 70–100 mA RFQ The beam dynamics design of the 70–100 mA RFQ has been achieved using the new design approach based on the combination of 𝜀 the 𝜀𝑙 = 1.0 design guideline and the NFSP method. The evolutions 𝑡 of the main beam dynamics parameters along the RFQ are shown in Fig. 2, where 𝑎min is the minimum electrode aperture, m is the electrode modulation, B is the transverse focusing strength, 𝑊s is the synchronous energy, and 𝜑s is the synchronous phase, respectively. The beam dynamics simulation has been performed using the PARMTEQM code [17] with a 4D-Waterbag input distribution. Fig. 3 plots several key ratios between the longitudinal and transverse planes, where b and a are the longitudinal and transverse rms beam sizes in mm, respectively. The partitions of the RFQ can also be distinguished in the figure: (1) MB: Cell 0 to Cell 90; (2) MBA: Cell 91 to Cell 145; (3) 𝜀 MA: Cell 146 to the exit. At the end of the MB section, 𝜀𝑙 reaches ∼1.0 𝑡 and the beam starts to enter the ‘‘safe rectangle’’. In the remainder of the RFQ, the emittance ratio is kept close to 1.0. 𝜀 The tune footprints of the RFQ at 70 mA are plotted on the 𝜀𝑙 = 1.0 𝑡 Hofmann Chart in Fig. 4. The different sections are marked in different colors: red for MB, green for MBA, and blue for MA. The solid and dashed curves represent the tune depressions in the transverse and
Fig. 4. Tune footprints of the RFQ at 70 mA on the
𝜀𝑙 𝜀𝑡
= 1.0 Hofmann Chart.
longitudinal directions, respectively. It can be seen that the main part of the tune trajectories with big oscillations is located in the safe place on the chart so that this kind of bunching process can be performed much faster than the GB section in the FSP method, which can shorten the structure length. In the MA section, the tune trajectories step into the instability 𝜎 region. On one side, the transverse tune depression 𝜎 𝑡 rises from ∼0.65 0𝑡 to 0.8 as a result of weakened transverse space charge effects, and the corresponding tune trajectory travels still mostly in the resonance-free area, so the transverse emittance can stay essentially constant. On the other side, the longitudinal tune trajectory enters the resonance peaks 𝜎 and 𝜎 𝑙 drops from 0.5 to 0.3, which will cause a certain longitudinal 0𝑙 emittance growth. But the tune trajectory has no big oscillation any𝜀 more and the growth rates in this area are low enough, so 𝜀𝑙 can be 𝑡 still held close to ∼1.0. 4
C. Zhang and H. Podlech
Nuclear Inst. and Methods in Physics Research, A 947 (2019) 162756
Fig. 5. Tune footprints of the RFQ at 100 mA on the
𝜀𝑙 𝜀𝑡
‘‘clean’’ space below the beam trajectories, which gives a hint that this RFQ can work at even higher currents. Furthermore, the ratios of the longitudinal and transverse emittances as well as phase advances along the RFQ for both 70 mA and 100 mA are compared in Fig. 6. The evolutions of these parameters are fairly close to each other. The emittance ratio of the 100 mA beam has 𝜀 a few ‘‘jumps’’ in the MA section due to the deviation from 𝜀𝑙 = 1.0 𝑡 at the MB end. From the curve of the emittance ratio calculated with the longitudinal emittance for 99% instead of 100% of the beam, it can be deducted that this difference has been caused by only ≤1% of halo particles. Fig. 7 shows the output particle distributions in the three phase spaces. Again, it shows the similarity between the 70 mA and 100 mA cases. The 100 mA beam has slightly bigger beam sizes due to stronger space charge effects. But in both cases, the beam is still well concentrated. More detailed design and simulation results of the RFQ are given in Table 2. The design goals with respect to the beam transmission, ≥95% for 70 mA and ≥90% for 100 mA, are met. At both currents, there is almost no transverse emittance growth with very moderate values for the output longitudinal emittances.
= 1.0 Hofmann Chart.
5. Conclusions
Fig. 6. Comparison of emittance ratios
𝜀𝑙 𝜀𝑡
and phase advance ratios
𝜎𝑙 𝜎𝑡
How to efficiently avoid emittance transfer which can lead to beam instabilities has been investigated for a 325 MHz, 3 MeV, 70–100 mA 𝜀 proton RFQ accelerator. A so-called 𝜀𝑙 = 1.0 design guideline is being 𝑡 proposed. 𝜀𝑙 As a combination of the 𝜀 = 1.0 design guideline and the NFSP 𝑡 method, the new approach integrates the three ways of minimizing beam quality loss for designing different sections of an RFQ as follows:
between the
70 mA and 100 mA cases.
• In the MB section, it allows the tune footprints a fast traversal through the resonance peaks and a quick arrival at the ‘‘safe 𝜀 rectangle’’ provided by the 𝜀𝑙 = 1.0 Hofmann Chart.
It is also required that this RFQ should work at currents up to 100 mA. Fig. 5 checks the tune footprints at 100 mA. Generally speaking, the behavior is similar to that in the 70 mA case. Of course, from 70 mA to 100 mA, the space charge effects are getting stronger, so the ‘‘center of gravity’’ of the beam trajectories has been lowered from ∼0.65 to ∼0.55 in the 𝜎𝜎 direction and the final longitudinal tune 0 depression has fallen down from 0.3 to 0.2. But there is still sufficient
𝑡
• In the MBA section i.e. the most critical part for space charge effects during the bunching, it puts the tune footprints inside the ‘‘safe rectangle’’. • In the MA section, after the real acceleration starts, it lets the tune footprints only enter the resonance peaks with low growth rates.
Fig. 7. Output particle distributions of the RFQ (top: 70 mA; bottom: 100 mA). (color online).
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C. Zhang and H. Podlech
Nuclear Inst. and Methods in Physics Research, A 947 (2019) 162756 Table 2 Main design results of the RFQ. Parameters
At 70 mA At 100 mA
Normalized rms transverse input emittance 𝜀in,trans.,n.,rms [𝜋 mm mrad] Normalized rms output emittance in the x-plane 𝜀out,x,n.,rms [𝜋 mm mrad] Normalized rms output emittance in the y-plane 𝜀out,y,n.,rms [𝜋 mm mrad] rms longitudinal output emittance 𝜀out,z,rms [keV-ns] Total structure length L [m] Beam transmission efficiency T [%]
0.30
0.300
0.301
0.299
0.297
0.299
1.0
1.2
3.0 96.0
3.0 90.1
The beam dynamics simulation results of the 70–100 mA RFQ chosen for this study have demonstrated that the new design approach can lead to not only high beam transmission and short structure length but also high beam quality simultaneously.
[6] I. Hofmann, Emittance growth of beams close to the space charge limit, IEEE Trans. Nucl. Sci. 28 (3) (1981) 2399–2401. [7] I. Hofmann, Stability of anisotropic beams with space charge, Phys. Rev. E 57 (4) (1998) 4713–4724. [8] J. Qiang, Mitigation of envelope instability through fast acceleration in linear accelerators, Phys. Rev. Accel. Beams 21 (114201) (2018) 1–10. [9] R.A. Jameson, Equipartitioning in linear accelerators, in: Proceedings of the 1981 Linac Accelerator Conference in Santa Fe, New Mexico, USA, September 19–23, 1981, pp. 125–129. [10] R.A. Jameson, RFQ Designs and Beam-Loss Distributions for IFMIF, Oak Ridge National Laboratory Tech. Rep. ORNL/TM-2007/001, 2007. [11] C. Zhang, Z.Y. Guo, A. Schempp, R.A. Jameson, J.E. Chen, J.X. Fang, Low-beamloss design of a compact, high-current deuteron radio frequency quadrupole accelerator, Phys. Rev. ST Accel. Beams 7 (100101) (2004) 1–6. [12] http://irfu.cea.fr/Sacm/logiciels/. [13] R.H. Stokes, K.R. Crandall, J.E. Stovall, D.A. Swenson, RF quadrupole beam dynamics, in: Proceedings of the 8th Particle Accelerator Conference, San Francisco, USA, March 12–14, 1979, pp. 3469–3471. [14] C. Zhang, A. Schempp, Beam dynamics studies on a 200 mA proton radio frequency quadrupole accelerator, Nuclear Instrum. Methods Phys. Res. A 586 (2008) 153–159. [15] M. Okamura, J. Alessi, E. Beebe, K. Kondo, R. Lambiase, R. Lockey, V. LoDestro, M. Mapes, A. McNerney, D. Phillips, A.I. Pikin, D. Raparia, J. Ritter, L. Smart, L. Snydstrup, A. Zaltsman, J. Tamura, A. Schempp, C. Zhang, J.S. Schmidt, M. Vossberg, T. Kanesue, Beam commissioning results for the RFQ and MEBT of the EBIS based preinjector for RHIC, in: Proceedings of the 25th International Linear Accelerator Conference, Tsukuba, Japan, September 12–17, 2010, pp. 473–475. [16] Chuan Zhang, Marco Busch, Horst Klein, Holger Podlech, Ulrich Ratzinger, Rudolf Tiede, Jean-Luc Biarrotte, Biarrotte Reliability and current-adaptability studies of a 352 MHz, 17 MeV, continuous-wave injector for an acceleratordriven system, Phys. Rev. ST Accel. Beams 13 (080101) (2010) 1–11. [17] Manual of the LANL RFQ Design Codes, LANL Report No. LA-UR-96-1836 (revised June3, 2005).
Acknowledgment The author CZ would like to thank Eugene Tanke very much for his friendly and patient help which enabled a deep look inside the design and convenient data analyses as well as his valuable suggestions for the improvement of the manuscript. References [1] https://www.oecd-nea.org/science/pubs/2001/3051-HPPA-France%201999.pdf. [2] O. Kester, W. Barth, O. Dolinskyy, F. Hagenbuck, K. Knie, H. Reich-Sprenger, H. Simon, P.J. Spiller, U. Weinrich, M. Winkler, R. Maier, Status of the FAIR accelerator facility, in: Proceedings of the 5th International Particle Accelerator Conference, Dresden, Germany, June 15–20, 2014, pp. 2084–2087. [3] R. Gobin, P.-Y. Beauvais, D. Bogard, G. Charruau, O. Delferrière, D. De Menezes, A. France, R. Ferdinand, Y. Gauthier, F. Harrault, P. Mattéi, K. Benmeziane, P. Leherissier, J.-Y. Paquet, P. Ausset, S. Bousson, D. Gardes, A. Olivier, L. Celona, J. Sherman, Status of the light ion source developments at CEA/Saclay, Rev. Sci. Instrum. 75 (2004) 1414–1416. [4] R. Berezov, R. Brodhage, N. Chauvin, O. Delferriere, J. Fils, R. Hollinger, V. Ivanova, O. Tuske, C. Ullmann, High intensity proton injector for facility of antiproton and ion research, Rev. Sci. Instrum. 87 (02A705) (2016) 1–3. [5] R.F. Thomas, Linear Accelerators, Second Completely Revised and Enlarged ed., Wiley, New York, ISBN: 978-3-527-40680-7, 2008.
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