Dejan Trbojevic Dejan Trbojevic

Non-Scaling Fixed Gradient FFAG OptimizationNon-Scaling Fixed Gradient FFAG Optimizationand Proton Therapy Accelerator from 25 – 250 MeVand Proton Therapy Accelerator from 25 – 250 MeV

FFAG04@KEK 12 – 16, October 2004FFAG04@KEK 12 – 16, October 2004

CONTENT:CONTENT:

Again: Why is the Dispersion Action H important?

Optimization: For the Muon Acceleration the priority is the path length. Would not be bad also to get small orbit offsets? We have to be in the “STABLE” region for tunes in the whole

acceleration region for dp/p. Well let’s get the shortest circumference if possible? The vertical tune should be at the end of acceleration larger than 0.1.

Proton Therapy Accelerator – how to get it right?

When did we start?

The first publication was from the Montauk workshop on September 30, 1999: Trbojevic, D., Courant, E. D., and Garren, A., FFAG Lattice Without Opposite BendsFFAG Lattice Without Opposite Bends, Colliders and Collider Physics at the highest Energies, AIP CONFERENCE PROCEEDINGS, Volume 530, Montauk, New York 1999, pp. 333-338, American Institute of Physics, Melville, New York, 2000, Editor B.J. King.

Trbojevic, D., ““FFAG lattice without opposite bends”,FFAG lattice without opposite bends”, KEK Workshop on FFAG Synchrotrons, October 11, 2000.

Accelerator physics seminar talk at Brookhaven National Laboratory: Dejan Trbojevic, Accelerator physics seminar talk at Brookhaven National Laboratory: Dejan Trbojevic, December 14, 2000: : ”Fixed Field Alternating Gradient Lattice (FFAG) without Opposite ”Fixed Field Alternating Gradient Lattice (FFAG) without Opposite Bends”.Bends”.

Muon Collaboration Meeting at Berkeley, Muon Collaboration Meeting at Berkeley, February 2, 2001. Dejan Trbojevic: “Some taught . Dejan Trbojevic: “Some taught about recirculator” .about recirculator” .

Collaboration Meeting Neutrino Factory at Brookhaven National LaboratoryCollaboration 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. 1199-1202 (2002) BNL-69007.

PAC2003, Portland, Oregon, May 16, 2003, “FFAG LATTICE FOR MUON “FFAG LATTICE FOR MUON ACCELERATION WITH DISTRIBUTED RF”,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 p/p)• Aperture limitation is defined by the maximum value of

the DISPERSION function:

• x < +/- 30 mm• if the 0.5 < p/p < 1.5 then:

• Dx < 60 mm

• Why is the Dispersion Action H Relevant?• The normalized dispersion amplitude Corresponds to the

<H>1/2 !!!

The basic idea has remained the same:x = Dx p/p < 30 mm

Basic Dispersion function definitions:Basic Dispersion function definitions:The “dispersion action” H function:

1

KDD

Combined function magnet: dispersion and “twiss” functions

How to obtain the minimum of <H>:

Conditions for the minimum of the <H> functionfor the combined function magnet:

The major conclusions from previously compiled analytical formulas for different lattices like FODO, doublet, triplet, double bend achromat, triple bend achromat etc. comparisons are listed bellow:The FODO cell H function and conditions for the minimum of the average value < H > through the cell are:The dispersion function in the FODO cell:

,2

sin2

,2

sin211

2sin1

2sin

2cos 2

3

2

f

LwhereLH FODO

2cos

2sin

2sin

431

3

2

FODOF a minimum at ~140o

The minimum emittance The minimum emittance lattice:lattice:• The minimum emittance lattice requires reduction of the The minimum emittance lattice requires reduction of the

function H:function H:– The normalized dispersion amplitude corresponds to the The normalized dispersion amplitude corresponds to the

<H><H>1/2 1/2

– Conditions are for the minimum of the betatron function Conditions are for the minimum of the betatron function xx and dispersion function D and dispersion function Dxx to have small values at the to have small values at the middle of the dipole (combined function dipole makes it middle of the dipole (combined function dipole makes it even smaller).even smaller). minLd15

Dxmin=Ld/24

5NSLS reduction of the emittance: 10 timesNSLS reduction of the emittance: 10 times

Comparison between fodo, doublet, and triplet lattices:

Lattice parameter dependence on the H function:

Maximum orbit offsets and path length arround thering dependence on the H function:

Maximum closed orbit offsets for a seriesof muon acceleration lattices made fromconditions for the minimum of <H>

Stability range of betatron tunes for Muon accelerationlattices developed by the <H> minimum condition:

Proton Therapy non-scaling Fixed Gradient25 MeV – 250 MeV accelerator

Required Parameters

Magnet properties

Lattice parameters at reference momentum po

Optimization of the lattice: tunes and orbit offsets

Lattice properties during acceleration

Proton Therapy non-scaling Fixed Gradient25 MeV – 250 MeV accelerator

B 0.7272814 2.4321837

Proton Therapy non-scaling Fixed Gradient25 MeV – 250 MeV accelerator