1.The Key Laboratory of Radiation Physics and Technology of Ministry of Education, Institute of Nuclear Science and Technology, Sichuan University, Chengdu 610065, China
Scan for full text
Xin-Miao Wan, Xue-Jiang Pu, Zhi-Qiang Ren, et al. Discussion of 90° stopband in low-energy superconducting linear accelerators. [J]. Nuclear Science and Techniques 33(9):121(2022)
Xin-Miao Wan, Xue-Jiang Pu, Zhi-Qiang Ren, et al. Discussion of 90° stopband in low-energy superconducting linear accelerators. [J]. Nuclear Science and Techniques 33(9):121(2022) DOI： 10.1007/s41365-022-01104-z.
Superconducting linear accelerators (SCL) have a high acceleration gradient and are capable of operating in a high-duty factor mode. For high-power and high-intensity SCL, the design of beam dynamics generally follows the principle that the zero-current periodic phase advance (σ,0,) of each degree of freedom is less than 90° to avoid envelope instability caused by space charge. However, this principle is obtained under the condition of a completely periodic focusing channel, and it is ambiguous for pseudo-periodic structures, such as linear accelerators. Although transverse beam dynamics without acceleration have been studied by other researchers, it appears that there are some connections between pure 2D and 3D beam dynamics. Based on these two points, five focusing schemes for the solenoid and quadrupole doublet channels were designed to simulate the beam behavior with non-constant σ,0,. Among them, the four schemes follow the characteristics of variation in the zero-current longitudinal phase advance (σ,0l,) under a constant acceleration gradient and synchronous phase. The zero-current transverse phase advance (σ,0t,) is consistent with σ,0l, based on the equipartition requirement. The initial σ,0t, was set to 120°, 110°, 100°, and 90°, and was then gradually decreased to approximately 40° at the end of the channel. The last scheme maintains the maximum σ,0t, of 88° by reducing the acceleration gradient of the corresponding cavities, until the point at which σ,0t, equals 88° with a normal gradient. Using the stopbands obtained from the linearized envelope equations and multiparticle particle-in-cell (PIC) simulations, the transport properties of both continuous and 3D-bunched beams with the acceleration of the five focusing schemes were studied. It was found that for a CW beam, when tune depression ,>, 0.7, σ,0t, can break through 90° when the beams were transported in both solenoid and quadrupole doublet periodic focusing channels. When tune depression ,<, 0.7, the conclusions were different. For the solenoid focusing system, σ,0t, can partially break through 90°, and the beam quality is not significantly affected. For the quadrupole doublet focusing system, a partial breakthrough of 90° has a greater impact on the beam quality. The same conclusions were obtained for a bunched beam with acceleration.
Proton beamSuperconducting linear acceleratorsEnvelope instabilityPeriodic focusing structureResonance.
J.Y. Liu, J.R. Shi, H. Zha et al., Analytic RF design of a linear accelerator with a SLED-I type RF pulse compressor. Nucl. Sci. Tech. 31, 107 (2020). doi: 10.1007/s41365-020-00815-5http://doi.org/10.1007/s41365-020-00815-5
X.L. Lu, Y. Zhang, J.R. Wang et al., Transport characteristics of space charge-dominated multi-species deuterium beam in electrostatic low-energy beam line. Nucl. Sci. Tech. 29, 51 (2018). doi: 10.1007/s41365-018-0384http://doi.org/10.1007/s41365-018-0384
J. Qiang, Bunched Beam Envelope Instability in a Periodic Focusing Channel. J. Phys: Conf. Ser, 1067, 062015 (2018). doi: 10.1088/1742-6596/1067/6/062015http://doi.org/10.1088/1742-6596/1067/6/062015.
H.Y. Li, X.M. Wan, W. Chen et al. Optimization of the S-band side-coupled cavities for proton acceleration. Nucl. Sci. Tech. 31, 23 (2020). doi: 10.1007/s41365-020-0735-7http://doi.org/10.1007/s41365-020-0735-7
I. Hofmann, L. Laslett, L. Smith et al., Stability of the kapchinskij-vladimirskij (k-v) distribution in long periodic transport systems. Part. Accel, 13. 145-178 (1982).
T. Wangler, F. Merrill, L. Rybarcyk et al., Space charge in proton linacs. AIP Conf. Pro, 448, 3-14 (1998). doi: 10.1063/1.56764http://doi.org/10.1063/1.56764.
Z.H. Li, P. Cheng, H.P. Geng et al., Physics design of an accelerator for an accelerator-driven subcritical system. Phys. Rev. ST Accel. Beams, 16. 080101 (2013). doi: 10.1103/PhysRevSTAB.16.080101http://doi.org/10.1103/PhysRevSTAB.16.080101.
D.O. Jeon, Classification of space-charge resonances and instabilities in high-intensity linear accelerators. J. Korean Phys. Soc, 72. 1523-1530 (2018). doi: 10.3938/jkps.72.1523http://doi.org/10.3938/jkps.72.1523.
R.A. Jameson, Beam-intensity limitations in linear accelerators. IEEE T. Nucl. Sci, 28. 2408-2412 (1981). doi: 10.1109/TNS.1981.4331708http://doi.org/10.1109/TNS.1981.4331708
C. Li, Q. Qin, R.A. Jameson et al., Space Charge Induced Collective Modes and Beam Halo in Periodic Channels. Paper Presented at the 7th Int. Particle Accelerator Conf.(IPAC'16), Busan, Korea, 8-13May, 2016.
J. Struckmeier, M. Reiser, Theoretical studies of envelope oscillations and instabilities of mismatched intense charged particle beams in periodic focusing channels. Part. Accel, 14. 227-260 (1983).
M. Chung, Y.L. Cheon, H. Qin, Linear beam stability in periodic focusing systems: Krein signature and band structure. Nucl. Instrum. Meth. A, 962. 163708 (2020). doi: 10.1016/j.nima.2020.163708http://doi.org/10.1016/j.nima.2020.163708.
X.Q. Yan, R.A. Jameson, Y. Lu et al., Matched and equipartitioned design method for modern high-intensity radio frequency quadrupole accelerators. Nucl. Instrum. Meth. A, 577. 402-408 (2007). doi: 10.1016/j.nima.2007.03.031http://doi.org/10.1016/j.nima.2007.03.031.
R.A. Jameson, An approach to fundamental study of beam loss minimization. Paper Presented at the AIP Conference Proceedings. American Institute of Physics, 480, 21-30 (1999). doi: 10.1063/1.59501http://doi.org/10.1063/1.59501
P. Paul, G. Sprouse, Superconducting linear accelerators for heavy ions. Comments on Nuclear and Particle Physics, 11. 217-229 (1983).
G. Geschonke, Superconducting structures for high intensity linac applications Proceedings of the XVIII International Linear Accelerator Conference, 8 October 1996. pp. 910-914. doi: 10.5170/CERN-1996-007.910http://doi.org/10.5170/CERN-1996-007.910.
M. Weiss, Radio-frequency quadrupole. 5th Advanced Accelerator Physics Course. 959-991 (1995). doi: 10.5170/CERN-1995-006.959http://doi.org/10.5170/CERN-1995-006.959
D.O. Jeon, J. Jang, H. Jin, Interplay of space-charge fourth order resonance and envelope instability. Nucl. Instrum. Meth. A, 832. 43-50 (2016). doi: 10.1016/j.nima.2016.06.036http://doi.org/10.1016/j.nima.2016.06.036.
F. J. Sacherer, Rms envelope equations with space charge. IEEE T. Nucl. Sci, 18. 1105-1107 (1971). doi: 10.1109/TNS.1971.4326293http://doi.org/10.1109/TNS.1971.4326293
D. Chernin, Evolution of rms beam envelopes in transport systems with linear x-y coupling. Part. Accel, 24, 29-44 (1988).
C. Li, R.A. Jameson, Structure resonances due to space charge in periodic focusing channels. Phys. Rev. Accel. Beams, 21, 024204 (2018). doi: 10.1103/PhysRevAccelBeams.21.024204http://doi.org/10.1103/PhysRevAccelBeams.21.024204.
Wolfram mathematica, URL http://www.wolfram.com/mathematica/http://www.wolfram.com/mathematica/. Accessed 9 Jul 2022.
TraceWin, URL http://irfu.cea.fr/dacm/en/logicielshttp://irfu.cea.fr/dacm/en/logiciels. Accessed 9 Jul 2022.
T. Wangler, K. Crandall, R. Ryne et al., Particle-core model for transverse dynamics of beam halo. Physical review special topics-accelerators and beams, 1, 084201 (1998). doi: 10.1103/PhysRevSTAB.1.084201http://doi.org/10.1103/PhysRevSTAB.1.084201.
Y.S. Yuan, O. Boine-Frankenheim, I. Hofmann, Modeling of second order space charge driven coherent sum and difference instabilities. Physical Review Accelerators and Beams, 20, 104201 (2017). doi: 10.1103/PhysRevAccelBeams.20.104201http://doi.org/10.1103/PhysRevAccelBeams.20.104201.
Y. Cheon, S. Moon, M. Chung et al., Analysis on the stop band of fourth-order resonance in high-intensity linear accelerators. Physics of Plasmas. 27, 063105 (2020). doi: 10.1063/5.0004651http://doi.org/10.1063/5.0004651.
R.A. Jameson, Equipartitioning in linear accelerators. Los Alamos National Laboratory (Report) LA, Santa Fe, NM, USA, 19 October 1981.