We report on the performance and planned upgrades to the Fermilab Accumulator Stacktail Stochastic Cooling System. The current system has achieved a maximum flux of 16.5e10/hour, limited by the input flux of antiprotons. The upgrades are designed to handle flux in excess of 40e10/hour

Cullerton, Ed

Derwent, P. F.

McGinnis, David

Pasquinelli, Ralph

Sun, Ding

Tinsley, David

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Performance and Upgrades of the FermilabAccumulator Stacktail Stochastic CoolingP.F. Derwent, Ed Cullerton, David McGinnis, Ralph Pasquinelli, Ding Sun,David TinsleyFermi National Accelerator Laboratory, P. O. Box 500, Batavia IL 60510-0500Abstract. We report on the performance and planned upgrades to the Fermilab Accumulator Stack-tail Stochastic Cooling System. The current system has achieved a maximum flux of 16.5e10/hour,limited by the input flux of antiprotons. The upgrades are designed to handle flux in excess of40e10/hour.Keywords: Stochastic Cooling, Antiproton BeamsPACS: 41.75.LxTHE FERMILAB ACCUMULATORThe Fermilab Accumulator is an 8 GeV ring designed for the colle tion, cooling, andstorage of anitprotons. The Tevatron Collider program requir s 1e13 antiprotons for thestudy of proton-antiproton collisions at√s = 1.96 TeV. Antiprotons are produced byimpinging a 120 GeV proton beam on an nickel alloy target and colle ted through alithium focussing lens and the Fermilab Debuncher ring [1].As the number of antipro-tons collected per pulse (which occur every 2 seconds) is on the order of a few×108, itis necessary to have a storage ring to collect and compress thphase space. For the last20 years of the Tevatron Collider complex, the Fermilab Accumulator has served as thatring. With the advent of electron cooling in the Fermilab Recycler [2], the Accumulatorwill not be the final storage ring but will still play a significant role in the compressionof the antiproton phase space.THEORY OF STOCHASTIC STACKINGStochastic stacking with a constant flux is achieved by designing a system with gain as afunction of energy that falls exponentially, with characteristic energyEd. The resultingdensity distribution then rises exponentially with the same characteristic energy [3]. Theresulting maximum fluxΦ can be expressed as:Φ =W 2|η|Edf0pln(FmaxFmin)(1)whereW is the electronic bandwidth of the system,η is the phase slip factor,f0 isthe beam revolution frequency,p is the beam momentum, andFmax and Fmin are themaximum and minimum frequencies in the system electronic bandwidth. Planar pickupsFERMILAB-CONF-05-457-ADFIGURE 1. Current stacktail profile, which fits to aEd of 10 MeV.have a response that followsexp(−πxd ) wherex is the transverse distance from the centerof the pickup andd is the vertical aperture. If the pickups are located in a region ofhigh momentum dispersion, a system can be designed where thegain response fallsoff exponentially with energy. The region of exponential density increase is called thestacktail and the region where beam accumulates is called the core. As the revolutionfrequency changes with energy so does the flight time betweenpickup and kicker . Thedelay time through the electronics is a constant, hence, it is necessary to use multiplesets of pickups with different gains and delays to build the gain slope across the aperture.Correlator notch filters are used to null the signal at the cor.CURRENT PERFORMANCEThe present Accumulator provides a good example of the basicprin iples. Figure 1shows the antiproton density distribution as a function of the beam revolution frequency,using a longitudinal Schottky pickup. We have 2 sets of pickups, located in a region with10 m of dispersion, separated by 15 mm radially. The pickups and front end amplifiersare cooled by liquid Nitrogen, with an effective noise temperature of 125K. There are256 pickup loops at 15 MeV (with respect to the central energyof the Accumulator)and 48 pickup loops at -8 MeV. There are 128 kicker loops in 8 tanks, with 4 TWTsper tank. There is approximately 150 dB of gain from pickup tokicker. By adjusting therelative gain and phase of the two sets of pickups, we have achi ved an exponential gainslope of 10 MeV. The system bandwidth, accounting for phase vriation as a function offrequency, is measured to be 1.2 GHz. With the machine parameters of the Accumulator,these values support a maximum flux of 29.5e10/hour. Integrain over an hour, our bestperformance has been the accumulation of 16.5e10. The system i still limited by theinput flux.UPGRADE DESIGN APPROACHOf the parameters appearing in Eq. ( 1),Ed , W , and η are the only ones that canreasonably be considered as changeable. The simplest approach to maximize the fluxis to increaseEd . This approach sacrifices the amount of density compaction achievable,since the density grows asexp( EEd ), but has fewer implications for other systems inthe Accumulator. Increasing the bandwidth clearly increases the maximum flux. Bothapproaches will be taken in this upgrade. Changes toη are not being considered at thistime.A two-stage upgrade is planned to handle increased input flux[1]. In the initial stage,the characteristic energyEd is increased from 10 MeV to 18 MeV. This changecan be implemented with a minimal change in hardware throughchanges to pickupposition (moving tanks radially in the Accumulator tunnel)and electronic gain andphase settings. The second stage requires additional pickups, electronics, and kickers;all covering the frequency range 4-6 GHz.DESIGN CONSTRAINTSThere are drawbacks to increasingEd. The Accumulator has a finite momentum aperture.It is therefore necessary to stop the flux at some point and accumulate it in a ‘core’. Thegain function will then deviate from a pure exponential and other considerations cometo the fore. It is necessary to match the stacktail system gain to the core system gain tohave a smooth transition in the gain profile. As the density increases for a given valueof the gain, diffusive beam heating from other particles (through the cooling systems)eventually dominates the cooling term and the system no longer is able to effectivelyincrease the density. It is generally true that as the density of the core increases itbecomes necessary to decrease the system gain to maintain some margin between thecooling and diffusive terms in the Fokker-Planck equation.Another limitation is the assumption of constant input flux.The input flux is a tran-sient, with large pulses coming every 2 seconds. It is necessary for the input pulse tomove completely into the stacktail region before the next pulse arrives or it will bephase displaced by the RF bucket moving the new pulse onto thedeposition orbit. Thefraction of the input pulse that moves across the aperture isa function of the gain of thesystem and the momentum distribution of the input pulse. Thelarger the gain, the moreefficiently the input pulse moves off of the deposition orbit. The large gain necessaryfor effective stacking of the input pulse is also detrimental (for reasons given above) toaccumulating large amounts of beam in the core.DESIGN CALCULATIONSUsing a numerical integration of the Fokker-Planck equation, including models ofpickup and kicker response, amplifier and notch filter performance, and a full implemen-tation of the beam feedback terms [4], both stages of the upgrade have been simulated.The simulation designs for stage 1 (2-4 GHz bandwidth, 18 MeVcharacteristic energy)FIGURE 2. Stage 2 simulation results. The green dots are the accumulation r te per minute, the blueline is the beam current in the Accumulator. The input flux is approximately 80e10/hour, transfers to theRecycler occur every 30 minutes and take 1 minute to complete.and stage 2 (2-6 GHz bandwidth, 10 MeV characteristic energy) are complete. For stage1, the following changes are necessary:• Move 256 pickups 1mm radially outward from current location(a energy changeof 1 MeV)• Move 48 pickups 7 mm radially outward from current location (a energy changeof 8 MeV)• Adjust system gains and phasesWith these changes, the stacktail can sustain a stack rate of>55e10/hour for 30 minutes.For stage 2, because of the increased bandwidth of the system, it is necessary todecrease the total energy change in the system to avoid Schottky band overlap. Hence,the core energy is closer to the stacktail. Half the 2-4 GHz pickups and kickers areremoved and replaced with 4-6 GHz pickups and kickers. With the increased bandwidth,the characteristic energy is lowered to approximately 15 MeV. The resulting system cansustain 80e10/hour for 30 minutes. The accumulation rate and beam current for thissimulation are shown in figure 2.UPGRADE STATUSThe current configuration of the stacktail is able to handle the current maximum inputflux to the Accumulator. With the coming improvements [1], weanticipate that we willmake use of the staged approach. The 4-6 GHz pickups and kickers have been designedand measured with a stretched wire, with the results agreeing well with microwavestructure simulations. We are currently building a prototype tank to house several designiterations of the pickup loops. This tank will be installed in the Fermilab Debuncher thisfall for beam tests. We anticipate assembly of the 4-6 GHz pickup and kicker tanksto take place during the 2006 calendar year, with installation during an appropriateaccelerator shutdown period.CONCLUSIONSThe Fermilab Accumulator stacktail design and performancehas been described. Thecurrent arrangement can support a theoretical maximum flux of 29.5e10/hour, thoughthe maximum value achieved has been limited by the input flux and is 16.5e10 in onehour. A two stage design approach has been presented, to handle increases of the inputflux to 80e10/hour. Beam measurements are planned and we anticip te installation asthe input flux outperforms the stacktail.REFERENCES1. D. McGinnis, "Antiproton production rate increase", these proceedings.2. S. Nagaitsev, "Antiproton cooling in the Fermilab Recycler", these proceedings.3. D. Möhl,et al., "Physics and Technique of Stochastic Cooling",Physics Reports, 58, No. 2 (1980).4. J. Marriner & V. Visnjic, "Fermilab Stochastic Cooling Code User’s Guide", Fermilab PbarNote 498 (unpublished),http://www-bdnew.fnal.gov/pbar/documents/pbarnotes/pdf_files/pb498.pdf. The Fortran code has been rewritten in C++ for these simulations.

Performance and upgrades of the Fermilab Accumulator stacktail stochastic cooling

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Performance and upgrades of the Fermilab Accumulator stacktail stochastic cooling

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