For the development of future synchrotron light sources new operation modes often have to be considered. One such mode is the operation with a negative momentum compaction factor to provide the possibility of increased dynamic aperture. For successful application in future light sources, the influence of this mode has to be investigated. At the KIT storage ring KARA (Karlsruhe Research Accelerator), operation with negative momentum compaction has been implemented and the dynamics can now be investigated. Using a variety of high-performance beam diagnostics devices it is possible to observe the beam dynamics under negative momentum compaction conditions. This contribution presents different aspects of the results of these investigations in the longitudinal and transversal plane

Brosi, M.

Härer, B.

Mochihashi, A.

Müller, A-S.

Papash, A. I.

Ruprecht, R.

Schreiber, P.

Schuh, M.

English

KITopen

BEAM DYNAMICS OBSERVATIONS AT NEGATIVE MOMENTUMCOMPACTION FACTORS AT KARAP. Schreiber∗, M. Brosi, B. Haerer, A. Mochihashi, A. I. Papash,R. Ruprecht, M. Schuh, A.-S. Müller,Karlsruhe Institute of Technology, Karlsruhe, GermanyAbstractFor the development of future synchrotron light sourcesnew operation modes often have to be considered. Onesuch mode is the operation with a negative momentum com-paction factor to provide the possibility of increased dynamicaperture. For successful application in future light sources,the influence of this mode has to be investigated. At theKIT storage ring KARA (Karlsruhe Research Accelerator),operation with negative momentum compaction has been im-plemented and the dynamics can now be investigated. Usinga variety of high-performance beam diagnostics devices it ispossible to observe the beam dynamics under negative mo-mentum compaction conditions. This contribution presentsdifferent aspects of the results of these investigations in thelongitudinal and transversal plane.INTRODUCTIONAt the accelerator test facility KARA (Karlsruhe ResearchAccelerator) a new optics with negative momentum com-paction factors 𝛼c has been implemented in recent years.The aim is to investigate the effects of the negative sign of𝛼c on beam dynamics as well as to confirm the feasibility ofusing negative 𝛼c optics in order to allow reduced sextupoleswithout incurring instabilities such as the head-tail instabil-ity. Previous publications showed effects of the switch insign of 𝛼c such as a shorter bunch length at negative 𝛼c [1].In this contribution the effect of changes to the sextupolemagnet currents, and therefore the chromaticity, on the firstand second order of 𝛼c for the currently implemented opticsat positive and negative 𝛼c are explored. Furthermore, thetransverse stability in regard to head-tail effects at negative𝛼c is investigated.SECOND ORDER OF 𝛼cThe negative 𝛼c optics are operated with negative chro-maticities and therefore reduced sextupoles. This reductionin sextupole magnets strengths affects higher order terms ofthe momentum compaction factor. When including higherorders 𝛼c is a function of momentum𝛼(𝛿) = 𝛼0 + 𝛼1𝛿 + 𝛼2𝛿2 + … . (1)As an analysis of this the second order (first non-linear or-der) has been investigated by means of measurements ofthe synchrotron frequency 𝑓s as function of accelerating fre-quency 𝑓RF used as tuning knob for the energy offset. The∗ patrick.schreiber@kit.edu(a) positive 𝛼c(b) negative 𝛼cFigure 1: Synchrotron frequency as function of the fre-quency of the RF system at positive and negative 𝛼c forvarious sextupole magnet strengths.synchrotron frequency in this case considering the first twoorders of 𝛼c is given as [2]𝑓s = 𝑓rev√ℎ𝑒𝑉RF cos 𝜓s2𝜋𝛽20𝐸⋅√√√⎷𝛼02+ √𝛼204− 𝛼1Δ𝑓RF𝑓RF, (2)where 𝑓rev is the revolution frequency, ℎ the harmonic num-ber, 𝑉RF the accelerating voltage, 𝜓s the synchronous phase,𝛽0 =𝑣𝑐 and 𝐸 is the particle energy. From this equation thefirst and second order of 𝛼c (𝛼0 and 𝛼1) can be identified byfitting the equation to the mentioned measurements.The synchrotron frequency has been measured at positiveand negative 𝛼c in order to allow comparison. In both casesthe beam energy was set to 1.3 GeV. The measurementswere done by using the RF system to vary 𝑓RF and by us-ing the BBB feedback system [3, 4] which calculates thebeam spectrum from BPM data via a Fourier transformation.In this data the synchrotron frequency is then given as a13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-THPOPT006THPOPT006ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI2570MC2: Photon Sources and Electron AcceleratorsA24: Accelerators and Storage Rings, OtherFigure 2: First two orders of 𝛼c extracted as fit of Eq. (2) onthe data shown in Fig. 1 for positive 𝛼c as a function of thesextupole current.Figure 3: First two orders of 𝛼c extracted as fit of Eq. (2) onthe data shown in Fig. 1 for negative 𝛼c as a function of thesextupole current.peak. These measurements have been repeated for differ-ent currents powering the sextupole magnets to explore thedependency. In Fig. 1 the measurements are displayed. Byfitting Eq. (2) to this data the mentioned two orders of 𝛼ccan be extracted. The results are shown in Fig. 2 and Fig. 3.The measurements at negative 𝛼c were taken at relativelyhigh absolute values of 𝛼c due to the reduction in lifetimeassociated with a drastic reduction of |𝛼c|. Furthermore, thenecessary reduction in 𝑓RF leads to beam loss at lower |𝛼c|for negative 𝛼c. For both signs of 𝛼c the first order 𝛼0 reducesin absolute value with increasing sextupole magnet strengths(indicated in the plots via the sextupole current). However, asthe sign at negative 𝛼c is negative, this means the sextupoleshave a different effect on the dispersion. At positive 𝛼c,where the value of 𝛼0 decreases, it can be concluded thatthe dispersion gets more stretched, while at negative 𝛼c,where the values of 𝛼0 increases, it can be concluded thatthe dispersion gets relaxed. In both cases the change seemslinearly with sextupole current. The change in first order𝛼c at positive 𝛼c is about 4 % for a change with sextupolemagnet current of about 10 %. The equivalent for negative𝛼c is a change of 1.25 % in 𝛼0 for a sextupole magnet currentchange of about 8 %. Therefore, it seems the first order of 𝛼cis less sensitive to changes of the vertical sextupole current atnegative 𝛼c than at positive 𝛼c for the currently implementedoptics at KARA.The second order 𝛼1 seems linearly dependent on thesextupole magnet current for positive 𝛼c. At negative 𝛼c, adependency is visible as well, albeit not as clearly linear asFigure 4: Beam position data after a horizontal kick on aturn-by-turn basis at positive 𝛼c for a positive and a negativehorizontal chromaticity.for positive 𝛼c. For this order the dependency is the samefor both signs of 𝛼c, both increase with increasing sextupolemagnet currents. Furthermore, the sign of the second order𝛼1 flips when flipping the sign of the first order 𝛼0.These observations show the effect of sextupole magnetson the higher orders of 𝛼c and that these effects have to beconsidered when implementing optics with different chro-maticity values. Influence of different orders of higher ordersof 𝛼c on the longitudinal beam dynamics have been studiede.g. in [5]. In general the third order 𝛼2 is of interest as well,for example in regard to alpha-buckets [2], and should bedetermined in the future.TRANSVERSE STABILITYA reduction of sextupole magnet strengths would be idealfor multi-bend achromat lattices as this could increase thedynamic aperture. However, at positive 𝛼c a reduction toofar, resulting in negative chromaticities, brings the risk ofloosing head-tail damping effects and even incurring thehead-tail instability. Therefore, one solution could be the useof negative 𝛼c optics which would in theory allow negativechromaticities without the aforementioned downsides.In order to investigate this with the negative 𝛼c optics atKARA a combination of kicks and BPM measurements wasused. By firing one of the horizontal injection kickers everysecond and measuring the beam position on a turn-by-turnbasis, the stability of the beam was tested at positive as wellas negative 𝛼c. In theory the head-tail damping time 𝜏 formode 𝑛 is given by [6]𝛽𝑛 =1𝜏= 𝑁𝑆𝜋2𝑐𝛾𝑚e𝜁𝛼c𝜎z4𝑛2 − 1, (3)where 𝜏 is the corresponding damping time, 𝑁 is the numberof particles in a bunch, 𝑆 is the strength of the wakefield and𝜎z is the bunch length. The electron mass is denoted with𝑚e, the chromaticity with 𝜁 and 𝛾 is the relativistic Lorentzfactor. From this a larger damping time is expected at lowerenergies which is why the measurements presented herewere performed at injection energy (0.5 GeV).For positive alpha with the usual (positive) chromaticity,an initial damping of the large position offset is visible inFig. 4 in blue. Afterwards over the remaining turns oscilla-tions of a fairly constant amplitude are present. These oscil-lations conform to the synchrotron and betatron frequencies13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-THPOPT006MC2: Photon Sources and Electron AcceleratorsA24: Accelerators and Storage Rings, OtherTHPOPT0062571ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOIFigure 5: Beam position data after a horizontal kick on aturn-by-turn basis at negative 𝛼c for a negative horizontalchromaticity.and are expected. For the kick at a negative chromaticity forpositive 𝛼c the situation is different. This is shown in Fig. 4in orange. After a short initial damping, large non-constantin amplitude oscillations are present. These oscillations arenot linked to synchrotron or betatron oscillation frequenciesand are not expected for a stable beam. From this it can al-ready be guessed that head-tail damping effects are presentat the measurement with a positive chromaticity and absentin the measurement for a negative chromaticity.To test whether this effect can be reversed at negativechromaticities when using negative 𝛼c such measurementswere also performed in these settings. Figure 5 shows sucha measurement. Again an initial damping is visible followedby fairly large but constant in amplitude oscillations. Theseresidual oscillations are in accordance to synchrotron andbetatron frequencies. The larger amplitude can be explainedby the largely increased dispersion necessary for the negativemomentum compaction factor. For comparison, at positive𝛼c the dispersion at the used BPM is about 0.17 m whileat negative 𝛼c it is about 1.25 m. Through this increaseddispersion the usual energy oscillations from the synchrotronoscillation manifest in enlarged horizontal position offsets.Therefore, combined with the rather constant amplitude ofthe oscillations, these measurements hint at the presenceof the head-tail damping effect at negative 𝛼c with negativechromaticity.From the BPM data a damping time can be extracted, atleast in the damped cases of positive 𝛼c with positive chro-maticity and negative 𝛼c with negative chromaticity. Whilethe absolute damping time is a composition of at least radi-ation damping and the head-tail effect, the presence of thehead-tail effect can be assessed by analyzing the bunch cur-rent dependency of the extracted damping time. In order todo this, the previously shown measurements were repeated atmultiple bunch currents and the damping time extracted. Thecurrent dependency for positive 𝛼c with positive chromatici-ties can be seen from the results in Fig. 6. A clear increaseof 1𝜏 with current is visible. The same measurements wereconducted at negative 𝛼c with negative chromaticities whichare shown in Fig. 7. Again a clear increase of 1𝜏 with currentis visible. In both cases the relative sign between 𝛼c and 𝜁x ispositive. Therefore, the observed current dependency of thedamping time is in accordance to the theory in Eq. (3). Thus,it can be concluded that indeed head-tail damping is presentFigure 6: Inverse damping time 1𝜏 after an initial kick asfunction of bunch current for positive 𝛼c ≈ 8.1 ⋅ 10−3 at twodifferent positive chromaticities.Figure 7: Inverse damping time 1𝜏 after an initial kick asfunction of bunch current for negative 𝛼c ≈ −1.5 ⋅ 10−3 attwo different negative chromaticities.in both cases. This means the negative 𝛼c operation mode atKARA successfully circumvented the head-tail instabilitywhen using negative chromaticities.SUMMARYThe negative momentum compaction regime is a possiblesolution to circumvent the need for high sextupole currents inmulti-bend achromat structures. This contribution describedthe effects of possible changes in sextupole current on thefirst and second order of 𝛼c seen at KARA in both, positiveand negative 𝛼c operation.Furthermore, the validity of this mode has been investi-gated by studying the transverse beam stability. Kick mea-surements show a loss of head-tail damping at positive 𝛼cwith negative chromaticity and a regaining of head-tail damp-ing at negative 𝛼c with negative chromaticity.ACKNOWLEDGEMENTThis project has received funding from the EuropeanUnion’s Horizon 2020 Research and Inovation programmeunder Grant Agreement No 730871.P. Schreiber acknowledges the support by the DoctoralSchool ”Karlsruhe School of Elementary and AstroparticlePhysics: Science and Technology”REFERENCES[1] P. Schreiber et al., “Effect of negative momentum compactionoperation on the current-dependent bunch length,” in Proc. of13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-THPOPT006THPOPT006ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI2572MC2: Photon Sources and Electron AcceleratorsA24: Accelerators and Storage Rings, OtherIPAC21, (Campinas, SP, Brazil), JACoW Publishing, Geneva,Switzerland, Aug. 2021, pp. 2786–2789. doi:10.18429/JACoW-IPAC2021-WEPAB083[2] A. Papash et al., “Alpha-buckets in High Energy ElectronStorage Rings (Review of Existing Experiments and FeasibilityStudies for Future Developments),” Advances in Theoretical& Computational Physics, vol. 4, no. 2, Apr. 9, 2021, doi:10.33140/ATCP.04.02.08[3] E. Blomley, “Investigation and Control of Beam Instabilities atthe Karlsruhe Research Accelerator using a 3-D Digital Bynch-By-Bunch Feedback System,” PhD thesis, Karlsruhe Instituteof Technology, 2021. doi:10.5445/IR/1000137621[4] Dimtel, Inc., https://www.dimtel.com/[5] M. Ries, “Nonlinear momentum compaction and coher-ent synchrotron radiation at the Metrology Light Source,”PhD thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2014. doi:10.18452/16979[6] J. M. Paterson, “The ‘Head-Tail’ Instability,” IEEE Transac-tions on Nuclear Science, vol. 20, no. 3, pp. 850–850, 1973.doi:10.1109/TNS.1973.432726213th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-THPOPT006MC2: Photon Sources and Electron AcceleratorsA24: Accelerators and Storage Rings, OtherTHPOPT0062573ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI

Beam Dynamics Observations at Negative Momentum Compaction Factors at KARA

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Beam Dynamics Observations at Negative Momentum Compaction Factors at KARA

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