Dejan Trbojevic Dejan Trbojevic An Update on the FFAG Minimum Emittance Lattice with Distributed RF D. Trbojevic, J. S. Berg, M. Blaskiewicz, E. D. Courant, A. A. Garren, R. Palmer, and E. Keil The FFAG2003 at KEK 7 – 11 July 2003 CONTENT:   Few remarks on the non-scaling minimum emittance FFAG history.   Checking the tools: SYNCH, COSY, MAD8, TEAPOT.   Scaling or non scaling, FODO or minimum emittance FFAG?   Latest developments:   Basic lattice parameters.   Closed orbit offsets.   Tracking results   Magnet design.   Longitudinal simulation of the acceleration.   Work to be done. 1

When did we start? 2 FFAG Lattice Without Opposite Bends  The first publication was from the Montauk workshop on September 30, 1999: Trbojevic, D., Courant, E. D., and Garren, A., FFAG Lattice Without Opposite Bends, Colliders and Collider Physics at the highest Energies, AIP CONFERENCE PROCEEDINGS, Volume 530, Montauk, New York 1999, pp , American Institute of Physics, Melville, New York, 2000, Editor B.J. King. “FFAG lattice without opposite bends”,  Trbojevic, D., “FFAG lattice without opposite bends”, KEK Workshop on FFAG Synchrotrons, October 11,  Accelerator physics seminar talk at Brookhaven National Laboratory: Dejan Trbojevic, : ”Fixed Field Alternating Gradient Lattice (FFAG) without Opposite Bends”.  Accelerator physics seminar talk at Brookhaven National Laboratory: Dejan Trbojevic, December 14, 2000: ”Fixed Field Alternating Gradient Lattice (FFAG) without Opposite Bends”.  Muon Collaboration Meeting at Berkeley,. Dejan Trbojevic: “Some taught about recirculator”.  Muon Collaboration Meeting at Berkeley, February 2, Dejan Trbojevic: “Some taught about recirculator”.  Collaboration Meeting Neutrino Factory at Brookhaven National Laboratory.  Trbojevic, D., Courant, E., Garren, A. “Fixed field alternating gradient lattice design without opposite bends”. Eighth European Particle Accelerator Conf. (EPAC’02), Paris, France, June 3-7, 2002, pgs (2002) BNL “FFAG LATTICE FOR MUON ACCELERATION WITH DISTRIBUTED RF”,  PAC2003, Portland, Oregon, May 16, 2003, “FFAG LATTICE FOR MUON ACCELERATION WITH DISTRIBUTED RF”, D. Trbojevic, J.S. Berg, M.Blaskiewicz, E.D. Courant, R. Palmer, BNL, Upton, New York, A.A. Garren, LBL, Berkeley, California, USA.  FFAG update at the KEK workshop July 8, 2003.

Required Range of Energies (or dp/p)Required Range of Energies (or dp/p) –the “central” energy or momentum p o is in two examples presented later set to 15 GEV. The muon acceleration would be possible from 10 GeV up to 20 GeV. –Aperture limitation is defined by the maximum value of the DISPERSION function: o  x < +/- 30 mm o if the 0.5 < E/Eo < 1.5 then dp/p < % o o D x < 90 mm Why is the minimum emittance lattice for the electronic storage rings relevant? –The normalized dispersion amplitude corresponds to the 1/2 !!! 3 The basic idea has remained the same:  x = D x  p/p < 30 mm

The minimum emittance lattice: The minimum emittance lattice requires reduction of the function H:The minimum emittance lattice requires reduction of the function H: –The normalized dispersion amplitude corresponds to the 1/2 –Conditions are for the minimum of the betatron function  x and dispersion function D x to have small values at the middle of the dipole (combined function dipole makes it even smaller). 4  min  Ld  15 D xmin =  Ld/24 

5 NSLS reduction of the emittance: 10 times

Normalized Dispersion Plot of the First Montauk 99 Design 6

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TEST data by different tools: Cyclotron made of five combined function dipoles 10  o =C o /2  B  = 50 Tm n= 0.5 C o = 100 meters u = x/  o

TEST data for different tools: Cyclotron 11

TEST data for different tools: a simple cyclotron 12

TEST data for different tools: a simple cyclotron 13

TEST data for different tools: a simple cyclotron 14

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16 Scaling or non- scaling FFAG, Minimum emittance lattice or FODO? Scaling FFAG properties:  Zero chromaticity.  Orbits parallel for different energies.  Large momentum acceptance.  Relatively large circumference.  Relatively large physical aperture.  RF:large aperture-follows the energy.  Tunes are fixed for all energies.  Negative momentum compaction.  Orbits of the high energy particles are at high field, low energy particles at low field. Minimum emittance FFAG properties:  Chromaticity is changing.  Orbits not parallel.  Large momentum acceptance.  Relatively small circumference.  Relatively small physical aperture.  RF:small aperture-at the crest.  Tunes move 0.4->0.1 in basic cell.  Momentum compaction changes.  Orbits of the high energy particles are at high field, low energy particles at low field. FODO or minimum emittance lattice?  For the same magnet properties larger circumference and larger X co.  For the same dispersion [  x=D x  dp/p ] and the same magnet smaller field and larger circumference.  The FODO has larger available free space.

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Maximum of Dispersion function in the FODO cell: D max = [ L  ( sin(  /2) ) ]/sin 2 (  /2) …(1) 0.06 m = (L d m)  … (2) [ L = L d + L1,  = 2  / N d ] 19 L BF BD 0.06 m D max = 0.06 m = ( L d m) (B y L d / BRHO) Ld(m)B y (T)  B y L d /BRHON d =2  /  C =L N d (m) ~ ~ Ld = [ SQRT( *0.158)]/2.0 if B y =7 T L1=0.4 m LdLd BRHO= Tm ( E  15 GeV) FIX the D x

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Two CELLS: 26

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Maximae of the betatron functions during acceleration 28

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Progress in the Minimum Emittance FFAG lattice design: 31  Dynamical aperture was reduced due to sextupoles.  October 2002: the small opposite bend was introduced:  This change allowed removal of the sextupoles.  Very large dynamical aperture.  The tunes are changing but between in the basic cell.  January 2003: Additional defocusing quadrupoles are removed and a larger area for the cavity placement was provided.  The lattice became extremely simple and easy to analyze.  The analytical solutions showed problems with the available codes.  May 2003: Both magnets are complete combined function magnets.  The acceleration requires either additional harmonic or reduction of the path length difference.  The magnets required for this latest design are being investigated by the magnet division at Brookhaven Natioanl Laboratory. It looks like there are simple solutions.

32  QD  min  QF  max

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43 Tracking results with COSY at the central momentum 3 cm 5 cm

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51 ~2.5 ns 200 MHz RF  cm = ns 10 cm = ns 15 cm = ns 20 cm = ns 30 cm = 1.00 ns

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57  Finalize the TOOLS vs. analytical prediction agreement.  Few new tools are to be tested in details: Etienne Forest, Scott Berg, PARMELA, ECOOL.  Tracking with the real magnetic fields in the combined function magnets.  Six dimensional tracking with the RF.  Reduce the path length difference:  Applying partial sextupole strength.  Reducing the closed orbit offsets.  Prepare, analyze and build the first non-scaling FFAG PPO:  Check if the eRHIC electron acceleration makes sense?  Check if the linac-to-AGS FFAG make sense?  Check if there is a possibility of cooling the muons?  Check if there is any connection in reduction of the orbit offsets within the scaling FFAG by following the same minimum emittance lattice principle? What we need to do next: