Smoothing of the slowly extracted coasting beam from a synchrotron
SSmoothing of the slowly extracted coasting beam from asynchrotron
R. Singh, ∗ P. Forck, and S. Sorge
GSI Helmholtz Centre for Heavy Ion Research, Darmstadt, Germany
Abstract
Slow extraction of beam from synchrotrons or storage rings as required by many fixed targetexperiments is performed by controlled excitation and feeding of a structural lattice resonance.Due to the sensitive nature of this resonant extraction process, temporal structure of the extractedbeam is modulated by the minuscule current fluctuations present on the quadrupole magnet powersupplies. Such a modulation lead to pile-ups in detectors and significant reduction in accumulatedevent statistics. This contribution proposes and experimentally demonstrates that by introductionof further modulation on quadrupole currents with a specific amplitude and frequency, the inherentpower supply fluctuations are mitigated leading to a smoothening of the beam temporal structure.The slow extraction beam dynamics associated with this method are explained along with theoperational results. a r X i v : . [ phy s i c s . acc - ph ] J u l ontrolled slow extraction of beam from synchrotrons and storage rings is required bya host of “fixed target experiments” as well as hadron cancer therapy based on chargedparticle deposition on tumours [1]. The extracted beam is also referred to as “spill”. Theextraction procedure is performed in two steps: a) exciting a lattice resonance and b) feedingthe driven resonance by moving the betatron tunes of individual particle towards it. Whilemost synchrotron facilities drive the horizontal third order resonance for slow extraction us-ing sextupolar fields [2], there exist a few variants of resonance feeding mechanisms (underoperation) such as quadrupole driven [2], betatron-core driven [2], or RF knock-out [3, 4].During the design phase, the choice of resonance feeding mechanisms is determined by ex-traction parameters such as beam energy, instantaneous momentum spread, total spill periodand macro-shape of spill as requested by experiments as well as the ability to swiftly inter-rupt the extraction process [2, 4]. The accelerator users typically assume that particle arrivaltimes to the detectors is solely governed by Poisson statistics. However, with experience,most facilities and users have realized that the minuscule ripples and noise ( < ∆ I/I ≈ − )on currents supplied to focusing magnets i.e. quadrupoles lead to significant temporal mod-ulation of the extracted spills. These modulated spills are detrimental to statistics obtainedby the experiments, where as much as 2/3rd of the delivered beam has been reported byexperiments to be unusable [5]. Any improvements on the power supply side are eithertechnologically unfeasible or would lead to long disruption in the operation of the facility.Similarly, the hadron cancer therapy synchrotrons are also designed with an assumptionof uniform spill delivery and reliability of the dose delivery is limited by non-uniformityof the spill and efforts are undergoing to improve the spill [6]. In order to deal with spillnon-uniformities, the primary resonance feeding mechanisms in most facilities have beenaugmented by other techniques. One of first such techniques found in literature was pro-posed at CERN [7], where the resonance feeding mechanism is assisted by a longitudinalstochastic noise, such that the particles are fed at a speed faster than the separatrix modula-tion induced by power supply noise. This ”stochastic extraction” method reduced the effectof power supply ripples and is shown to work well for very long (in range of several minutes tohours) extraction times [8, 9]. Other ideas also involved some sort of longitudinal gymnasticssuch as ”rf phase displacement” [10], ”rf channelling” [2] and bunched beam extraction [11]which all reduce the effect of power supply ripples at the cost of rf frequency modulationof the spill. Although these techniques reduce low frequency modulations on the spill, they2ctually hinder experiments which rely on smooth structure at time scales smaller than therevolution times. Spill smoothing based on feedback systems [12] is non-trivial to operategiven that the slow extraction transfer function consists of a large (dynamic) delay in theorder of ms between particle extraction and its measurement in the spill. Feedback/servosystems have thus shown improvement only in low frequency or macro-spill regime ( < >
50 Hz) [14].In this report, we take a new view of the problem of uneven spill structure by primarilyinfluencing the particle transit time, i.e. the time required by the particle to reach the elec-trostatic septum after it first becomes unstable. Consequently, the instantaneous variationof transit times for particles with different initial phase space co-ordinates and momenta be-ing extracted at that same time instant referred to as ”transit time spread” is also modified.It led us into developing a new method based on controlled tune modulation in correla-tion with the transit time referred to as ”transit time dependent tune modulation”. Thismethod while smoothing the spill structure against power supply ripples, does not introduceany significant additional longitudinal structure at higher frequencies. The first applicationof this method is with the quadrupole driven resonance feeding mechanism, where the effectof power supply fluctuations on spill are expected to be the strongest [2]. The recentlyconcluded High Acceptance Di-Electron Spectrometer (HADES) experiment [15] reported50% increase in recorded events compared to previous campaigns [5] as a direct result ofthese investigations.Proton Ion Medical Machine Study (PIMMS) [2] provides a comprehensive account ofthe slow extraction process. Here we discuss only the aspects relevant for this paper andtry to utilize the PIMMS notations wherever possible. Figure 1(a) shows the stable phasespace area for the considered one dimensional third order slow extraction mechanism. Thetriangular shape is a characteristic of third order resonance described by Kobayashi theory[16]. (cid:126)X ≡ ( X, X (cid:48) ) is a phase space vector with the normalized coordinates with X = x √ β x and X (cid:48) = √ β x x (cid:48) + α x √ β x x . where α x , β x are the Twiss parameters. The size of phase spacearea is defined by unstable fixed points of betatron motion and is given as A stable = 4 √ π (cid:18) ε Q S v (cid:19) , (1)where ε Q = 6 π ( Q m − Q r ) is the difference between machine and resonance tunes. S v isthe strength of a virtual sextupole created by an arrangement of N sextupoles governed3 hase space area fluctuations T r a n s i t t i m e } E l. S e p t u m A BSpiral step X X Stable phase-spacearea fluctuationsTransit time spread } El. SeptumAB (cid:12)(cid:12)(cid:12) ~ X (cid:12)(cid:12)(cid:12) ∆ pp UnstableStable
FIG. 1: (a) Schematic showing stable phase space area modulation due to power supplyripples for any specific tune and the particle transit towards the septum.(b) Steinbachdiagram showing the spread in transit times due to amplitude and momentum distributionof fed particles.by the relation, S v · e ψ v = (cid:80) n S n e ψ n with the normalised sextupole strength of the n th sextupole S n = β / x,n ( k L ) n and the phase advance ψ n between the considered locationwhich is usually that of the electrostatic septum and the location of the n th sextupole,where ψ n corresponds to the third integer tune of the resonance Q r and ψ v determinesthe orientation of the stable phase space. The Steinbach diagram in Fig. 1(b) shows the4eparation of stable and unstable area as a function of particle momentum ∆ p . The slopeof separating line is, (cid:12)(cid:12)(cid:12) (cid:126)X (cid:12)(cid:12)(cid:12) / ∆ p ∝ ( Q r ξ ) / ( p S v ) where ξ is the chromaticity in the plane ofextraction and p is the momentum of zero amplitude particle at resonance tune Q r . Inquadrupole driven extraction, the stable phase area is slowly shrunk with time by movingthe machine tune Q m towards resonance Q r such that the particles (starting from largeramplitudes/action) leave the stable area and traverse towards the extraction septum. Uponcrossing the electrostatic septum, particles obtain a kick such that the particle trajectorypasses through another magnetic kicker, thus spilling it out of the synchrotron. For a particlewith a certain amplitude (cid:12)(cid:12)(cid:12) (cid:126)X (cid:12)(cid:12)(cid:12) , the transit time is primarily determined by the distance toresonance ε Q at which the particle becomes unstable, which in turn is directly proportionalto the strength of resonance ( S v ) as shown by Eq. 4.17 in [2] T tr ∝ ε Q (2)For a particle beam with a given emittance and finite momentum spread, there is corre-sponding spread in transit times. This is also schematically shown in Fig. 1(b). The transittime spread scales with the ”mean” transit time T tr , T tr ∝ ε Q (3)∆ T tr = dT tr dε Q ∆ ε Q ∝ ε Q ∆ ε Q (4)as discussed in [17]. The spiral step growth at any time step is given as a function ofsextupole field strength and coordinates in the previous time step ( X , X (cid:48) ) as ∆ X ∝ S v X (cid:48) (3 / √ A stable / . X ) .The fluctuations of A stable shown in Fig. 1 are dominated by the field ripples of quadrupoleand sextupole magnets. The modulations in size of the stable phase space area for indepen-dent quadrupole and sextupole ripples is estimated as, δA stable = 2 A stable (cid:18) π (cid:12)(cid:12)(cid:12)(cid:12) δQ m ε Q (cid:12)(cid:12)(cid:12)(cid:12) + (cid:12)(cid:12)(cid:12)(cid:12) δS v S v (cid:12)(cid:12)(cid:12)(cid:12)(cid:19) (5) δε Q = 6 πδQ m because Q r = const. If we assume that quadrupole and sextupole fluctua-tions are of the same order, i.e. | δQ m /Q m | ∼ | δS v /S v | , the contribution of the quadrupoleripples has a larger influence since | ε Q | (cid:28) Q m so that | δQ m /ε Q | (cid:29) | δQ m /Q m | resulting in | δQ m /ε Q | (cid:29) | δS v /S v | as also observed at GSI SIS-18 and CERN SPS [19].5 o excitationExternal excitation T tr AB A U F P C o un t s C o un t s Time
Leaving particles
FIG. 2: Bottom: Stable phase space area modulation due to inherent power supply ripples(black solid lines) and when external ripples are introduced on quadrupoles (red dottedlines). Middle: Spill just after crossing the separatrix, Point A in Fig. 1. Top: Spill at themeasurement location, Point B in Fig. 1 after convolution with transit time distribution.The effect of fluctuations on the measured spill structure is illustrated in Fig. 2. Thedashed line in Fig. 2 (bottom) show the controlled shrinkage of stable phase space areaas it is performed with time, while the solid black line depicts the undesired modulation δA stable due to quadrupole field fluctuations for particles with a specific momentum. Thenature of fluctuations is similar irrespective of particle momentum although the absolutestable phase space area is different for different momenta as indicated in Fig. 1(b). As the6table area shrinks, particles are ”released” and their relative counts are shown in Figure 2(middle) shortly after crossing their respective momentum dependent separatrices denotedby point A (also shown in Figure 1). Following that, the released particle are convolved withthe instantaneous transit time distribution ∆ T tr while traversing from point A to the Point B (top) which can be seen as the point of ”spill measurement or user experiment”.Theconvolution has the effect of low pass filtering and higher frequency components above acertain cut-off frequency f cut ∝ ∆ T tr are suppressed.The transit time distribution parameters i.e. T tr and ∆ T tr primarily depend on the slowextraction settings which in turn are determined by the beam parameters, beam emittance,beam energy and its spread, as well as length of spill discussed as elaborated in [17]. Animprint of the transit time spread ∆ T tr can be seen on the spill spectrum by means of the cut-off frequency f cut , while T tr is expected to scale with ∆ T tr in accordance to Eq. 3. Figure 3shows the evaluated transit time distributions from particle tracking simulations during atypical spill for SIS-18 synchrotron. The simulated beam energy is 300 MeV/u C beamwith mean extraction rate of 2 × /s in 0.5 s. The virtual sextupole setting S v = 5 . m − / and the tune Q x is driven from 4.327 into the third order resonance 4 .
33. The revolutionfrequency is 1 . µ s and momentum spread ∆ p/p = 5 · − (2 σ ) and natural chromaticity ξ = − .
94. The distribution mean T tr and spread ∆ T tr evolve and are correlated T tr ∝ ∆ T tr at all instances during the spill (blue and red curves in Fig. 3). From hereon, we will utilizefor the ”total” transit time distribution for the discussion (black curve in Fig. 3) unlessotherwise specified. The mean transit time T tr is 488 µ s. The filtering effect of transittime spread is shown in Fig. 3 (bottom), where the Fourier transform of the transit timedistribution is compared with the respective spill spectrum. Since the ”total” transit timedistribution resembles a decaying exponential, the ∆ T tr , can be recovered from the frequencycorresponding to half maximum in its Fourier transform i.e. ∆ T tr = 1 / (2 πf cut ) = 138 µs .Our first approach towards spill smoothening looked at influencing the transit timespread. As evident from Eq. 2 and Fig. 1(b), the transit time spread ∆ T tr can be increasedby reducing the initial ε Q which in turn is performed either by reducing the sextupole fields S v [17, 18] or reducing the beam emittance. This is demonstrated by comparing three sce-narios with a 300 MeV/u C beam with mean rate of 2 × /s. Case (1) is that of a”typical” working point in terms of sextupole strength S v = 11 . m − / optimized for min-imizing beam losses and nominal beam emittance of 15 mm-mrad , second (case 2) is that7
500 1000 1500 2000050100150200250300 T tr ∆ T tr Transit time ( µs ) C o un t s ( a r b . un i t s ) Start of spillEnd of spillTotal Spill . . f c u t Frequency (kHz) FF T ( a r b . un i t s ) FFT of complete spillFFT of total transit time
FIG. 3: Transit time distribution and the comparison of the Fourier transform with thespill spectra.of reduced sextupole strength S v = 5 . m − / for nominal injection beam emittance of 15mm-mrad, and the third (case 3) is for a small emittance of 4 mm-mrad at the lower sex-tupole setting S v = 5 . m − / . These are compared against their respective power spectrain Fig. 4. It is clear that, for the last case, the f cut is the lowest as the higher frequencyfluctuations are curbed and results in the best (smooth) micro-spill structure. Another im-portant observation is that the transit time spread increases as ε Q approaches zero towardsthe end of spill, and thus the duty factor or quality of spill is improved. The “duty fac-tor” [2, 18] F is defined as the ratio F = (cid:104) N p (cid:105) / (cid:104) N p (cid:105) where N p is the number of particlecounts per measurement time T m = 10 µ s and (cid:104)·(cid:105) represents the operation ”mean”. Eachduty factor is calculated over 1000 such measurements if the characterization bin is T c = 10ms i.e p = 1 → S v and distance to resonance ε Q for micro-spill improvement [20]. Thelimitation of our first approach is that both the sextupole strength and beam size cannotbe arbitrarily reduced without effective loss is statistics for the experiments. As discussedearlier, lower sextupole strength results in a smaller spiral step ∆ X , which below a certainthreshold leads to losses on the septum wires. Similarly, reducing the beam size at multi-8 − − − − − Frequency (kHz) N o r m a li ze dp o w e r ( a r b . un i t s ) Case 1Case 2Case 3 . . . . . . . . D u t y f a c t o r Case 1Case 2Case 3Poisson Limit P a r t i c l ec o un t s i n µ s b i n s Case 1Case 3
FIG. 4: Comparison of beam spill (bottom), its duty factor (middle) and the powerspectra (top) for case (1) stronger sextupole strength and large emittance, case (2) weakersextupole strength and large emittance and case (3) weaker sextupole strength and smallemittance.turn injection synchrotrons typically results in lower intensities, and thus effective loss inevent rate for experiments. Transverse beam cooling also needs significant time and thusis not a viable option for experiments relying on large cumulative statistics. Therefore, anew method independent of sextupole strength and beam emittance was developed and isdiscussed next. 9he foundation of this method is an application of external current modulation withamplitudes larger than the inherent ripples into the quadrupole power supplies with a schemediscussed in [18]. This leads to a modulation of machine tune Q m and thus the stable spacearea as marked with dotted red lines in Fig. 2 (bottom). The spill smoothing works asfollows; due to relatively large tune modulation at the introduced frequency compared toinherent ripples, particles undergo a forced release from the stable phase space area atthe applied frequency (Fig. 2 (middle)). The introduced modulation prevents the lowerfrequency inherent ripples from ”feeding” on the particles, which is in principle similar to afast separatrix crossing in the rf based methods [10] and thus low frequency inherent ripplesare strongly suppressed in spill. In order to ensure that the spill does not form a significantmodulation at the introduced frequency,i.e. it has to be higher than the cut-off frequency f ext > f cut . The upper limit on the introduced frequency is given by the condition that theparticles are not re-captured in the other half of the cycle. This conditions hint at a certainscaling of introduced modulation frequency with the mean transit time f ext ∝ /T tr andtherefore f cut . . . . f c u t Unperturbed F W W e i g h t e ddu t y f a c t o r I ex /I Hz = 5 I ex /I Hz = 10 I ex /I Hz = 15 . . f c u t Unperturbed F W Excitation Frequency (Hz) W e i g h t e ddu t y f a c t o r . . . . C u t - o ff f r e q u e n c y Unperturbed F W W e i g h t e ddu t y f a c t o r . . . . C u t - o ff f r e q u e n c y Uperturbed F W Excitation Frequency (Hz) W e i g h t e ddu t y f a c t o r FIG. 5: Weighted duty factor in experiment (top) and simulations (bottom) as a functionof excitation frequency and amplitude. The left plots are with S v = 5 . m − / and rightplots are for S v = 11 m − / .Figure 5 show the simulation and experimental results of the dependence of spill quality10n the excitation amplitude and frequency. The legend marks the set amplitude with respectto the inherent 600 Hz ripple amplitude. During experiments, the introduced excitation wasdistorted as a function of frequency for I ex /I Hz = 15 case, and might have resulted inlower effective amplitude. The weighted duty factor F W is the weighted sum of duty factorscalculated along the spill for each k th characterization bin ( T c =10 ms) resulting in a singlenumber per excitation frequency and amplitude setting. F W = N (cid:88) i =1 F k · (cid:104) N (cid:105) k (cid:104) N (cid:105) k (6)The extraction parameters are the same as discussed earlier both for simulations and experi-ments, the only difference is in the extraction rate which is a factor 10 higher in experimentsi.e. 10 /s . There are two clear trends, that the optimal excitation frequency scales with thecut-off frequency i.e. ≈ f ext = (3 − · f cut andutilizing example case of the simulation where, ∆ T tr /T tr = 138 /
488 = 0 .
28, one arrives atthe useful frequency range f cut < f ext < (12 − /T tr ). The amplitude of excitation shouldbe significantly higher than the inherent ripple amplitude such that it forces the particlerelease ahead of inherent ripples. On the other hand, it should be low enough such thatparticles released in the previous cycle are not re-captured (the same argument as for highfrequency modulation) and the total length of spill is not affected due to associated tunemodulation. The optimal value in simulation is a factor of 10 times higher than the inherentripple amplitude which corresponds to 2% of total current change during the slow extractiontune ramp in our experiment. The amplitude and frequency dependence reported in Fig. 5 isrelated with dependence between spiral step and transit time, i.e. for smaller transit times,the spiral step is larger and thus a larger amplitude excitation can be employed withoutrecapturing particles. At much higher frequencies f ext (cid:29) /T tr , most particles would notbe able to follow the introduced oscillations of stable area and no periodic release of parti-cles at the introduced frequency will occur and thus spill quality is not affected by externalmodulation. Further, in a quadrupole driven extraction process, where T tr varies during theextraction, the exciting frequency should follow it during the extraction.Figure 6 shows the spill spectra and duty factors with and without tune modulation fora high energy beam of 1.58 GeV/u Ag corresponding to the highest rigidity at SIS-18 for11 − − − − Frequency (kHz) N o r m a li ze dp o w e r ( a r b . un i t s ) Without external modulationWith external modulation . . . . D u t y f a c t o r Without external modulationWith external modulation .
55 14 .
552 14 .
554 14 .
556 14 .
558 14 . P a r t i c l ec o un t s i n µ s b i n s Without external modulationWith external modulation
FIG. 6: Comparison of beam spill (bottom), its duty factor (middle) and the powerspectra (top) with and without external modulation of tune.the HADES experiment [15]. In this case, the duty factor does not improve from start to endof extraction (unlike shown in Fig 4). The reason for that is the insufficient voltage on theelectrostatic septum at the highest SIS-18 rigidity. Insufficient kick from the septum leadsto loss of particles with smaller spiral step ∆ X (or larger transit time) and thus the effectivetransit time spread distribution ∆ T tr remains roughly the same for the whole extraction.In Fig. 6 (top), the wiggly shape of spectrum in the ”passband” is due to transit timedependent septum losses. This also results in a spill quality of F ≈ . . ≈
10 dB in the power spectrashown in Fig. 6 (top). This led to a factor 2.5 improvement in the duty factor and a muchsmoother spill as shown in Fig. 6 (middle and down respectively). The HADES experimentreported an increase by a factor of 1.5 in cumulative statistics. The corresponding eventrates (courtesy of HADES collaboration) are shown in Fig. 7. The smoother spill structureis further expected to reduce the number of discarded events during post processing andincrease the effective event rate useful for the experiment.FIG. 7: The event rate registered in the HADES detector with tune modulation (from 300to 600 s) and no modulation (0 - 300 s). The x-axis shows elapsed time in seconds withrespect to the last measurement. Each extraction spill lasted for 20 s.(Courtesy: J.Pietraszko and M. Traxler from the HADES collaboration).The transit time dependent tune modulation method for spill smoothing is describedin this report. It is operationally straightforward and immediately renders itself to otherfacilities and experiments facing issues with micro-spill non-uniformity. In summary, thesteps to be followed are; an estimate of the cut-off frequencies at the start and end of spillis made from the spill spectrum. A frequency sweep between the two optimal frequenciessatisfying the criterion f cut < f ext < (3 − · f cut with an amplitude of 1 −
2% of thequadrupole current change due to tune ramp during extraction is introduced. Since the fulltransit time distribution is not accessible during experiments, some empirical tweaking ofamplitude and frequency should be performed to obtain the optimal smoothing. As a next13tep, waveforms other than a simple sinusoid for the introduced tune modulation will bestudied. On a longer term, particle amplitude dependent external tune modulation usingnon-linear fields could be beneficial.Horst Welker and Andrzej Stafiniak are gratefully acknowledged for their consistent sup-port in introducing the ripples in quadrupoles power supplies. SIS-18 team provided supportin bringing the technique into regular operation on a very short notice. ∗ Corresponding author: [email protected][1] Ugo Amaldi and Gerhard Kraft, Rep. Prog. Phys. 68 1861, 2005.[2] L. Badano, M. Benedikt, P. J. Bryant, M. Crescenti, P. Holy, A. Maier, M. Pullia and S.Rossi, “Proton-ion medical machine study (PIMMS) part I”, CERN/PS/ 99-010 (DI), Geneva(1999).[3] K. Hiramoto and M. Nishi, Resonant beam extraction scheme with constant separatrix, Nucl.Inst. Meth. A322 (1992), 154-160.[4] K Noda et al., “Slow beam extraction by a transverse RF field with AM and FM”, NIM A,Volume 374, Issue 2, 1996.[5] NUSTAR and HADES/CBM physics case and experience, Proceedings of the first slow ex-traction workshop, https://indico.gsi.de/event/4496/page/6, Darmstadt (2016).[6] C. Krantz et al., “Slow extraction techniques at the Marburg Ion-beam therapy centre”, Proc.of IPAC 2018, Vancouver (2018).[7] S. van der Meer “Stochastic extraction, a low-ripple version of resonant extraction”, CERN-PS-AA-78-6, (1978).[8] H. Stockhorst et al., “Beam extraction at the cooler synchrotron COSY, Proc. of EPAC 1996,Barcelona (1996).[9] W. Hardt, “Moulding the noise spectrum for much better ultra slow extraction,CERN/PS/DL/LEAR note 84-2[10] R. Cappi and Ch. Steinbach, “Low frequency duty factor improvement for the CERN PS slowextraction using RF phase displacement techniques”, IEEE Transactions on Nuclear Science,Vol. NS-28, No. 3. (1981).[11] P. Forck et al., “Measurements and Improvements of the time structure of a slowly extracted eam from a synchrotron” Proc. of EPAC 2000, Vienna, (2000).[12] H. Sato et al., “Analysis of the Servo-Spill control for slow beam extraction”, Proc. Of the9th Symp. On Acc. Sci. & Tech, Tsukuba, 25(1993).[13] C. Schoemers et. al., “The intensity feedback system at Heidelberg Ion-Beam Therapy Cen-tre”, NIM-A 795:92-99, September 2015. DOI: 10.1016/j.nima.2015.05.054[14] J. Shi et al., “Feedback of slow extraction in CSRm”, NIM-A, Volume 714, 21 June 2013,Pages 105-109 (2013).[15] G. Agakichiev et al., The high-acceptance dielectron spectrometer HADES, Eur. Phys. J. A(2009) 41: 243-277.[16] Y. Kobayashi and H. Takahashi, “Improvement of the emittance in the resonant beam ejec-tion”, Proc. Vth Int. Conf. on High Energy Acc., p. 347, (1967).[17] S. Sorge et al., “Measurements and Simulations of the Spill Quality of Slowly Extracted Beamsfrom the SIS-18 Synchrotron”, J. Phys.: Conf. Ser. 1067 052003, (2018).[18] R Singh et al., “Slow Extraction Spill Characterization From Micro to Milli-Second Scale”,J. Phys.: Conf. Ser. 1067 072002 (2018).[19] J. P. Prieto et al., “Beam dynamics simulations of the effect of power converter ripple on slowextraction at the CERN SPS” Proc. of IPAC 2018, Vancouver, (2018).[20] K. Mizushima et al., “Making beam spill less sensitive to power supply ripple in reso-nant slow extraction”, NIM-A, Volume 638, Issue 1, 2011, Pages 19-23, ISSN 0168-9002,https://doi.org/10.1016/j.nima.2011.02.056.eam from a synchrotron” Proc. of EPAC 2000, Vienna, (2000).[12] H. Sato et al., “Analysis of the Servo-Spill control for slow beam extraction”, Proc. Of the9th Symp. On Acc. Sci. & Tech, Tsukuba, 25(1993).[13] C. Schoemers et. al., “The intensity feedback system at Heidelberg Ion-Beam Therapy Cen-tre”, NIM-A 795:92-99, September 2015. DOI: 10.1016/j.nima.2015.05.054[14] J. Shi et al., “Feedback of slow extraction in CSRm”, NIM-A, Volume 714, 21 June 2013,Pages 105-109 (2013).[15] G. Agakichiev et al., The high-acceptance dielectron spectrometer HADES, Eur. Phys. J. A(2009) 41: 243-277.[16] Y. Kobayashi and H. Takahashi, “Improvement of the emittance in the resonant beam ejec-tion”, Proc. Vth Int. Conf. on High Energy Acc., p. 347, (1967).[17] S. Sorge et al., “Measurements and Simulations of the Spill Quality of Slowly Extracted Beamsfrom the SIS-18 Synchrotron”, J. Phys.: Conf. Ser. 1067 052003, (2018).[18] R Singh et al., “Slow Extraction Spill Characterization From Micro to Milli-Second Scale”,J. Phys.: Conf. Ser. 1067 072002 (2018).[19] J. P. Prieto et al., “Beam dynamics simulations of the effect of power converter ripple on slowextraction at the CERN SPS” Proc. of IPAC 2018, Vancouver, (2018).[20] K. Mizushima et al., “Making beam spill less sensitive to power supply ripple in reso-nant slow extraction”, NIM-A, Volume 638, Issue 1, 2011, Pages 19-23, ISSN 0168-9002,https://doi.org/10.1016/j.nima.2011.02.056.