Instabilities driven by the transverse impedance are proven to be one of the limitations for the high intensity reach of the CERN PS. Since several years, fast single bunch vertical instability at transition energy has been observed with the high intensity bunch serving the neutron Time-of-Flight facility (n-ToF). In order to better understand the instability mechanism, a dedicated measurement campaign took place. The results were compared with macro-particle simulations with PyHEADTAIL based on the new impedance model developed for the PS. Instability threshold and growth rate for different longitudinal emittances and beam intensities were studied

Aumon, S.

Biancacci, N.

MIGLIORATI, Mauro

Persichelli, S.

Sterbini, G.

Wang, N.

English

Instabilities driven by the transverse impedance are proven to be one of the limitations for the high intensity reach of the CERN PS. Since several years, fast single bunch vertical instability at transition energy has been observed with the high intensity bunch serving the neu-tron Time-of-Flight facility (n-ToF). In order to better understand the instability mechanism, a dedicated meas-urement campaign took place. The results were compared with macro-particle simulations with PyHEADTAIL based on the new impedance model developed for the PS. Instability threshold and growth rate for different longitu-dinal emittances and beam intensities were studied

Wang, Na

Aumon, Sandra

Biancacci, Nicolo

Migliorati, Mauro

Persichelli, Serena

Sterbini, Guido

CERN Document Server

Simulation of Instability at Transition Energy with a New Impedance Model for CERN PS

Archivio della ricerca- Università di Roma La Sapienza

SIMULATION OF INSTABILITY AT TRANSITION ENERGY WITH A NEW IMPEDANCE MODEL FOR CERN PS N. Wang†, CERN, Geneva, Switzerland and Institute of High Energy Physics, Beijing, China  S. Aumon, N. Biancacci, G. Sterbini, CERN, Geneva, Switzerland M. Migliorati, CERN, Geneva, Switzerland and INFN-ROMA1, Rome, Italy S. Persichelli, University of Rome La Sapienza, Rome, Italy Abstract Instabilities driven by the transverse impedance are proven to be one of the limitations for the high intensity reach of the CERN PS. Since several years, fast single bunch vertical instability at transition energy has been observed with the high intensity bunch serving the neu-tron Time-of-Flight facility (n-ToF). In order to better understand the instability mechanism, a dedicated meas-urement campaign took place. The results were compared with macro-particle simulations with PyHEADTAIL based on the new impedance model developed for the PS. Instability threshold and growth rate for different longitu-dinal emittances and beam intensities were studied. INTRODUCTION  In the CERN Proton Synchrotron (PS) the operational beams have to cross the transition energy. During the transition crossing the synchrotron motion is frozen and the beam is particularly sensitive to the force of the wake fields produced by the beam itself [1, 2]. With increased beam intensity, a fast vertical single bunch instability was observed around transition energy [3-5]. This instability can induce beam emittance blow-up and beam losses. Many studies have been performed on this subject. In reference [6] an extensive measurements campaign has been presented and compared with HEADTAIL code [7] simulations using a simple broadband impedance model (fr=1 GHz, Q=1), as there was no detailed impedance model available [6, 8-9]. A complete impedance model was recently developed for the PS both for longitudinal [10] and transverse plane [11, 12], which makes it possi-ble for us to do the simulations with a more realistic model of the excited wake field. The goal of this work is, therefore, first to measure the characteristics of the insta-bility with the n-ToF beam [13], such as the intensity threshold and its growth rate, and then to benchmark the measurements with simulations based on the available PS impedance model. This study further benchmarks the impedance model and the assumptions of the simulation framework, which are crucial for the PS LIU upgrade studies [14].  INSTABILITY MEASUREMENTS A dedicated single bunch n-ToF beam was set up for the instability measurements. The beam parameters are presented in Table 1. In order to simplify the beam dy-namics, a zero chromaticity plateau is programmed around transition in the vertical plane, and the measure-ments are performed without the gamma jump [6].  Table 1: Beam Parameters Parameter Value Circumference, C 628 m Transition gamma, γt 6.08 RF voltage, Vrf 200 kV Harmonic number, h 8 Number of protons/bunch, Nb 90E10 – 200E10 Longitudinal emittance, εL Transition time  1.9 – 2.9 eV⋅s         312 ms Both the longitudinal bunch profile, and the vertical po-sition are measured with a wall current monitor during transition. Figure 1 shows a measurement example. The particles close to the peak intensity become unstable and oscillate at high frequency in the vertical plane. The am-plitudes of these particles increase rapidly until they are lost on the vacuum chamber.  Figure 1: Bunch profile measured with the wall current monitor. Red curve: longitudinal bunch profile. Blue curve: vertical difference signal. A Fast Fourier Transform analysis of the vertical signal gives a characteristic frequency of the instability in the range 600~700 MHz, as shown in Fig. 2. 30 40 50 60 70 80 90 100 110−4000−2000020004000600080001000012000t [ns]WCM signal [a.u.]  YSUM ____________________________________________   † wangn@ihep.ac.cn    TUPOR010 Proceedings of IPAC2016, Busan, KoreaISBN 978-3-95450-147-21674Copyright©2016CC-BY-3.0andbytherespectiveauthors05 Beam Dynamics and Electromagnetic FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code Developments Figure 2: Amplitude spectrum of the vertical signal.   Instability Growth Time With the multi-turn acquisition system, we can acquire the vertical beam signal for several thousands of consecu-tive turns. By a spectral analysis of all the consecutive traces, we can get the spectrum evolution with respect to time, as presented in Fig. 3.   Figure 3: Evolution of the vertical bunch position in fre-quency.  Figure 4: Computed integral, I, of the bunch frequency spectrum with time. Blue points: measured data. Red curve: fitting of the growth time. The integral, I, over the vertical signal spectrum of each trace is our observable to measure the instability rise time. Figure 4 presents an example of the computed integral as function of time in log scale. The growth time of the in-stability is obtained by fitting the linear part of the curve. At a beam intensity of 140E10 p/b and with a longitudinal emittance of 2.26 eV⋅s, the measured instability growth time is 0.12 ms, which indicates that the instability devel-ops in ~60 turns. Intensity Scans for Different Longitudinal Emit-tances We also measured the dependence of the instability on beam intensity and longitudinal emittance. Beam intensity was varied in the range from 90E10 to 200E10 p/b, whilst the longitudinal emittance was adjusted from 1.9 to 2.9 eV⋅s. Figure 5 shows the dependence of the instability growth rate on bunch intensity and longitudinal emittance.  Figure 5: Bunch intensity versus longitudinal emittance color-coded with the instability growth rate. (Dots: meas-urements, Red line: Ith=37 (εL)1.5). For a certain emittance, the instability growth rate in-creases with the bunch intensity as expected. The thresh-old intensity, Ith, is expected to go to zero for zero intensi-ty. The fit shown in Fig. 5 assumes Ith∝ (εL)1.5. Further simulations and measurements are needed to validate the proposed fit in the low emittance region. MACRO-PARTICLE SIMULATIONS WITH PYHEADTAIL In order to better understand the instability mechanism, macro-particle simulations with PyHEADTAIL [15] have been performed based on the new PS impedance model. The initial longitudinal distribution has been obtained by fitting the measured longitudinal profile with a Gaussian function. The bunch dynamics has been simulated during the acceleration without gamma transition jump and tak-ing into account the machine parameters, such as RF voltage, bending magnetic field, transverse tunes and chromaticity setting. Proceedings of IPAC2016, Busan, Korea TUPOR01005 Beam Dynamics and Electromagnetic FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code DevelopmentsISBN 978-3-95450-147-21675 Copyright©2016CC-BY-3.0andbytherespectiveauthorsImpedance Model The transverse impedance model used in the simulation is shown in Fig. 6 and compared with the broadband im-pedance model used in Ref. [6]. Both dipolar and quadru-polar impedances are considered. The impedance shows a low Q resonance around 700 MHz. The resonance is mainly driven by the kickers impedance, which should be the main reason for  the fast vertical single bunch instabil-ity described above.  Figure 6: Transverse impedance model compared with the broadband impedance model used in Ref. [6]. The red curves are the dipolar impedance; the cyan curves are the quadrupolar impedance; the blue curves are the broad-band impedance model (fr=1 GHz, Q=1, Rs=1 MΩ/m). Instability Growth Time By taking into account the PS impedance model, the beam dynamics has been simulated with the PyHEAD-TAIL code. Using the same analysis applied to the meas-urements, a spectrogram of the instability has been com-puted from the simulation results. The spectrum obtained from the simulation (Fig. 7) features the same frequency behaviour of the one observed in the measurement (Fig. 3).   Figure 7: An example of the frequency spectrum evolu-tion obtained in simulation (same machine condition as Fig. 3). With an intensity of 140E10 and a longitudinal emit-tance of 2.26 eV⋅s, the simulated growth time is  ~0.075 ms, in comparison to the measured value of 0.12 ms.  Dependence on Beam Intensity In addition, the instability growth rate as a function of the beam intensity has been simulated. Figure 8 shows the comparison between the simulation and the measurement for similar beam conditions.   Figure 8: Simulated instability growth rate as a function of the beam intensity, and compared with the measure-ment. The results indicate that the simulation gives a lower instability threshold and a stronger growth rate with re-spect to the measurement. The difference between the two increases for low intensity beams. This can be explained by the lack of stabilizing factors in the simulations, which do not take into account space charge tune spread and magnetic non-linearities of the machine. In addition, measuring the chromaticity during transition is challeng-ing due to the vanishing slip factor. Simulations were done with the measured chromaticity and with zero chro-maticity for comparison. The difference in the instability time constant between the two cases was marginal. CONCLUSIONS In this work we presented the results of a measurement campaign on the instability of the n-ToF bunch occurring in the PS during the transition crossing. Instability growth time and intensity threshold versus longitudinal emittance are obtained. Simulations based on the new PS impedance model have been performed and compared to the meas-urements. A fairly good agreement has been reached between simulations and observations. The residual dif-ferences could be explained by taking into account addi-tional stabilizing ingredients such as space charge and nonlinear effects, presently neglected but to be considered in future studies.  ACKNOWLEDGEMENT The authors would like to thank E. Métral, S. Gilardoni, B. Salvant, A. Huschauer, H. Damerau and P. Freyermuth for helpful discussions, and the PS-PSB Operation group for their help and support during the measurements. The authors would also like to thank the support from NSFC (No. 11205171). 0 0.5 1 1.5 2 2.5 3 3.5 4ï0.500.51 f [GHz] Zy [M 1/m]  Re Zy, dipRe Zy, quadIm Zy, dipIm Zy, quadRe ZBBIm ZBBTUPOR010 Proceedings of IPAC2016, Busan, KoreaISBN 978-3-95450-147-21676Copyright©2016CC-BY-3.0andbytherespectiveauthors05 Beam Dynamics and Electromagnetic FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code DevelopmentsREFERENCES [1] E. Métral and D. Möhl, Transition Crossing, CERN-2011-004, June 2011, pp. 59. [2] E. Métral, “Effects near transition”, CERN Topical CAS on High Intensity Limitations, 2015. [3] E. Métral, “Stability criteria for high-intensity single-bunch beams in sychrotrons”, in Proc. EPAC’02, Paris, France, June 2002, pp. 1532-1534. [4] R. Cappi, E. Métral, G. Métral, “Beam breakup instability in the CERN PS near transition”, in Proc. EPAC’00, Vien-na, Austria, June 2000, pp. 1152-1154. [5] S. Hancock and E. Métral, “Ghost bunches and blow-up losses with high-intensity beams”, PS/RF Note 2002-198. [6] S. Aumon, “High Intensity Beam Issues in the CERN PS”, Ph. D. thesis, CERN-THESIS-2012-261. [7] G. Rumolo, F. Zimmermann, “Practical user guide for HEADTAIL”, SL-Note-2002-036-AP, CERN. [8] S. Aumon, et al, “Transverse mode coupling instability measurements at transition crossing in the CERN PS”, in Proc. IPAC’10, Kyoto, Japan, May 2000, pp. 2036-2038. [9] S. Aumon, et al, “Transverse mode coupling instability measurements at transition crossing in the CERN PS”, in Proc. HB’10, Morschach, Switzerland, 2010, pp. 681-685. [10] M. Migliorati et al., Phys,.Rev. STAB 2013, 16, 031001. [11] S. Persichelli et al., “The Proton Synchrotron Transverse Impedance Model”, in Proc. IPAC’14, Dresden, Germany, 2014, pp. 4096-4098. [12] S. Persichelli et al., “Transverse beam coupling impedance of the CERN Proton Synchrotron”, Phys. Rev. STAB 19, 041001, 2016. [13] “n-ToF Technical Design Report on experimental Area”, CERN-INTC-2000-018, CERN, Geneva, November, 2000. [14] R. Garoby et al., “Plans for the upgrade of the LHC injec-tors”, in Proc. IPAC’11, San Sebastian, Spain, pp. 2517-2519. [15] https://github.com/PyCOMPLETE/PyHEADTAIL.  Proceedings of IPAC2016, Busan, Korea TUPOR01005 Beam Dynamics and Electromagnetic FieldsD05 Coherent and Incoherent Instabilities - Theory, Simulations, Code DevelopmentsISBN 978-3-95450-147-21677 Copyright©2016CC-BY-3.0andbytherespectiveauthors

Simulation of instability at transition energy with a new impedance model for CERN PS

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Simulation of instability at transition energy with a new impedance model for CERN PS

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