Design Considerations for Proposed Fermilab Integrable RCS
DDESIGN CONSIDERATIONS FOR PROPOSED FERMILABINTEGRABLE RCS
J. Eldred and A. Valishev, FNAL, Batavia, IL 60510, USA
Abstract
Integrable optics is an innovation in particle acceleratordesign that provides strong nonlinear focusing while avoid-ing parametric resonances. One promising application ofintegrable optics is to overcome the traditional limits on ac-celerator intensity imposed by betatron tune-spread and col-lective instabilities. The efficacy of high-intensity integrableaccelerators will be undergo comprehensive testing over thenext several years at the Fermilab Integrable Optics Test Ac-celerator (IOTA) and the University of Maryland ElectronRing (UMER). We propose an integrable Rapid-Cycling Syn-chrotron (iRCS) as a replacement for the Fermilab Booster toachieve multi-MW beam power for the Fermilab high-energyneutrino program. We provide a overview of the machineparameters and discuss an approach to lattice optimization.Integrable optics requires arcs with integer-pi phase advancefollowed by drifts with matched beta functions. We providean example integrable lattice with features of a modern RCS- long dispersion-free drifts, low momentum compaction,superperiodicity, chromaticity correction, separate-functionmagnets, and bounded beta functions.
INTRODUCTION
Integrable optics is a development in particle acceleratortechnology that enables strong nonlinear focusing withoutgenerating parametric resonances [1]. A promising appli-cation of integrable optics is in high-intensity rings, whereit is necessary to avoid resonances associated with a largebetatron tune-spread while simultaneously suppressing col-lective instabilities with Landau damping. The efficacy of ac-celerator design incorporating integrable optics will undergocomprehensive experimental tests at the Fermilab IntegrableOptics Test Accelerator (IOTA) [2] and the University ofMaryland Electron Ring (UMER) [3] over the next severalyears. In this paper we discuss a potential Fermilab inte-grable rapid-cycling synchotron (iRCS) as a high-intensityreplacement for the Fermilab Booster.At Fermilab, a core research priority is to improve theproton beam power for the flagship high-energy neutrinoprogram [4]. In the current running configuration, a 700 kW120 Gev proton beam is delivered to a carbon-target for theNuMI beamline that supports the NOvA, MINERvA, andMINOS neutrino experiments. Next, the Proton Improve-ment Plan II (PIP-II) will replace the 400 MeV linac with anew 800 MeV linac that will increase the 120 GeV protonpower of the Fermilab complex to 1.2 MW [5].The next flagship neutrino experiment at Fermilab will bethe LBNF/DUNE [6]. The P5 Report referred to LBNF as“the highest priority project in its lifetime” and set a bench-mark for a 3 σ measurement of the CP-violating phase over 75% the range of its possible values [7]. The P5 benchmarkfor the CP-violating phase corresponds to a 900 kt · MW · yearneutrino exposure requirement [4, 6]. For a 1.2 MW protonpower and a 50 kt LAr detector, 15 years are required tomeet that benchmark. For a 3.6 MW proton power and a 36kt LAr detector, 7 years are required.In order to achieve a 120 GeV proton power significantlybeyond the 1.2 MW delivered by PIP-II, it will be necessaryto replace the Fermilab Booster with a modern RCS [4]. TheFermilab Booster is over 45 years old and faces limitationsfrom its magnets and its RF alike. There is no beampipeinside the dipoles and the magnet laminations generate animpedance instability. The impedance instability provides ∼ RCS DESIGN CONSIDERATIONS
If the PIP-II era Booster were to fill the Main Injectorwithout slip-stacking, there would be 0.5 MW available at120 GeV. Table 1 shows how different parameters of a re-placement RCS could modify that beam power. The boldedparameters correspond to the particular scenario that re-lies on integrable optics and a small increase in aperture toachieve 3.6 MW of beam power. a r X i v : . [ phy s i c s . acc - ph ] M a r able 1: Multipliers on beam power relative to PIP-II Boosterwith boxcar stacking in the Main Injector. Bolded valuesshows an integrable RCS scenario that provides 3.6 MW ofbeam power.Booster-MI Beam Power 0.5 MWLaslett Tune-spread ∆ ν / ∆ ν ( ) -0.11 × × × × × βγ /( β γ ) × × × × × (cid:15) N / (cid:15) ( ) N π -mm-mrad × π -mm-mrad25 π -mm-mrad25 π -mm-mrad × × × π -mm-mrad × T ( ) MI / T MI
12 Hz12 Hz12 Hz × × × × × ∆ ν ( z ) ≈ Nr π(cid:15) N βγ (cid:18) λ ( z )(cid:104) λ (cid:105) z (cid:19) F (1)where N is the number of particles, r is the classical ra-dius, (cid:15) N is the normalized transverse emittance, λ ( z ) is thelocal charge density at position z , and F is a transverseform factor [4]. Phase-space painting from PIP-II Linacwill substantially improve the transverse and longitudinalbeam uniformity. Eq. 1 can be rewritten to express the beamintensity as a function of the other three parameters: N ∼ ∆ ν max × (cid:15) N × βγ (2)where ν max is the maximum Laslett tune-spread that can besustained with minimal losses.If integrable optics enable a significantly higher maxi-mum Laslett tune-spread, this would be a very cost-effectiveway to improve RCS performance. The subsequent sectiondiscusses how integrability impacts the RCS lattice opti-mization. Detailed simulations of space-charged dominatedbeams in integrable lattices is an ongoing work [2, 12] andthe ultimate limitation on Laslett tune-spread is not fullydetermined.For a fixed Laslett tune-spread, the intensity of an RCScan be improved by increasing the injection energy. Ta-ble 1 shows how the βγ parameter in Eq. 2 changes withan energy upgrade of the PIP-II Linac. Increasing the injec-tion energy also reduces the transverse emittance relativeto the normalized admittance, through adiabatic damping (cid:15) = (cid:15) N /( βγ ) . The Fermilab Booster has a 95% transverse admittanceof 15 π -mm-mrad, but the 95% admittance of the 5.7cmdiameter beampipe is 20 π -mm-mrad without the restrictionfrom the dipole magnets [4, 13]. On the other hand, the95% transverse admittance of the Main Injector is 40 π -mm-mrad [14].For a fixed lattice design, the transverse admittance in-creases quadratically with increase aperture. Either the mag-net current or the accelerator circumference can be increasedto compensate for the change in the magnet aperture. Table 2shows the transverse emittance as a function of injection en-ergy and aperture. Fermilab has designed RF cavities for anRCS with apertures up to 8.255cm [13].Table 2: 95% Transverse admittance (in π -mm-mrad) ofRCS as a function of aperture and injection energy. Asterisksindicates cases which exceed the Main Injector admittanceof 40 π -mm-mrad.95% Transverse Admittance ( π -mm-mrad)Injection RCS ApertureEnergy 5cm 5.7cm 6.35cm 8.1cm0.8 GeV 15 20 252525 401.2 GeV 20 26 33 53*2.0 GeV 28 38 48* 76*Assuming conventional boxcar stacking, the impact of theRCS ramp rate on the MI beam power can be calculated by: P MI = Nn b E MI / T MI (3) T MI = T Ramp + ( n b − ) T RCS (4)where n b is the number of batches. As long as the MainInjector ramp remains long compared to the Main Injectorfill time, the RCS ramp rate has only a modest effect on theMain Injector beam power. However, the RCS ramp ratewill be an important parameter for any experiments whichreceive the RCS beam while the Main Injector is ramping.An alternate RCS design with an extraction energy of21 GeV should also be considered. Keeping the apertureand acceleration rate constant, the extraction energy of anaccelerator design can be scaled by increasing the integrateddipole length, circumference, and number of RF cavitiesproportionately.For boxcar stacking, increasing the extraction energy hasonly a marginal effect on Main Injector beam intensity. How-ever it should be carefully considered if a higher extractionenergy would enable the RCS beam to be stacked to a greaterMain Injector intensity. For example, slip-stacking is anaccumulation technique currently used to double the inten-sity of the Main Injector, but the feasibility of slip-stackingbeyond the PIP-II era is still under investigation [14, 15].An RCS with an extraction energy of 21 GeV would avoidtransition crossing in the Main Injector and that would ad-dress one of several challenges associated with high-intensityslip-stacking. An alternate accumulation approach could betransverse stacking via nonlinear-resonant injection [16]. RCS EXAMPLE LATTICE
The iRCS should incorporate the innovations in RCSdesign that have been developed after the FermilabBooster [17]. Periodicity and bounded beta functions in-crease the dynamic aperture. Transition crossing can beavoided by designing the lattice with a low momentumcompaction factor. Modern RCS design also uses separate-function dipole magnets and long dispersion-free drifts. Inthis section we show an example integrable lattice with thesefeatures.An accelerator can achieve integrable optics with alter-nating sections of T-inserts and nonlinear magnets [1]. TheT-inserts are arc sections with π -integer betatron phase-advance in the horizontal and vertical plane. The latticeshould be dispersion-free in the nonlinear section and thehorizontal and vertical beta functions should be matched. Aspecial nonlinear elliptical magnet is matched to the betafunctions to provide the nonlinear focusing.Figure 2 shows an example iRCS lattice and Table 3 showsthe key parameters of this lattice. The lattice is composedof 12 identical achromatic arcs and dispersion-free drifts.Every other drift hosts a nonlinear insert, so the lattice forms6 periodic cells with a T-insert section and a nonlinear insertsection. The drifts in the center of each T-insert arc are usedfor injection, extraction, and RF acceleration.Figure 2: TWISS parameters for one of the six periodiccells. (top) Horizontal and vertical beta functions shown inblack and red respectively. (middle) Location and length ofmagnetic lattice elements where dipoles are shown as shortblue rectangles, quadrupoles shown as tall orange rectangles,and sextupoles shown as green rectangles. (bottom) Lineardispersion function.This example lattice is compatible with the 8-GeV lat-tice described in the previous section. By increasing thecircumference and number of cells, the 8-GeV lattice caneasily be scaled up to 21-GeV lattice with a lower momentumcompaction factor.The effect of linear chromaticity on integrable motion wasexamined in [18] and the effect of nonlinear chromaticity Table 3: Parameters of iRCS LatticeParameter ValueCircumference 486 mPeriodicity 6 (12)Vertical Aperture 5 cmMaximum Energy 8 GeVBend Radius 15.6 mPeak Dipole Field 1.25 TPeak Quadrupole Field 25 T/mPeak Sextupole Field 180 T/m Max Beta Function 35 mMax Dispersion 0.8 mInsertion Length / Cell 8.1 mTotal Insertion Length 97 mSingle Dipole Length 2.8 mNumber of Dipoles 48Number of Quadrupoles 156Number of Sextupoles 48Momentum Compaction 2 × − Extraction Phase-Slip Factor -6 × − Betatron Tunes 19.7Linear Chromaticities -10Second-order Chromaticities 50was examined in [19]. Chromaticity is compatible withintegrability if the horizontal and vertical chromaticities arematched. In the example iRCS lattice the chromaticitieswere matched and reduced in both the first and second order.The chromaticity values shown in Fig. 3 are the result ofcorrection by the sextupole magnets (green in Fig. 2).To preserve integrability, sextupole magnets should alsobe located so that their effect cancels harmonically (separatedby a π -odd phase-advance) [18]. To maintain the flexibilityof the early design, this constraint was not imposed on theexample lattice shown here. This constraint can be met byrequiring a π -odd phase-advance for the 12 linear-periodiccells or by combining into 6 complex linear-periodic cells. SUMMARY & FUTURE WORK
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