Ultra-compact CW racetrack FFAGs - PowerPoint Presentation

Slide1

Ultra-compact CW racetrack FFAGs

FFAG1313th International Workshop on FFAGsTRIUMFSept 21 2013Vancouver, Canada

Dr. C.

Johnstone

,

FermilabSlide2

OutlineMotivation and BackgroundNext generation ultra-compact, high-energy fixed field acceleratorsMedical, security, energy applications CW FFAGs ; i.e. strong-focusing cyclotronsRelativistic energies: ~200 MeV – 1 GeV Ultra-compactConstant machine tunes (optimized gradients)High mA currents (low losses)

These machines require high gradient acceleration; and SCRF for high currentsCompactnessLow extraction lossesLarge horizontal aperture of the FFAG, like the cyclotron, is a challenging problem for SCRF design2Slide3

Cyclotrons: general commentsCyclotrons are the highest current, most compact solution, but only up ~200 MeV for protonsAs the energy becomes relativistic, orbit separation becomes smaller and smaller for CW operationHigher energies require separated sectors (like the 590-MeV PSI or 500-MeV TRIUMF machines) – in order to insert strong accelerating (RF) systems.

Stronger acceleration is required to minimize beam losses and radioactivity particularly during beam extraction Fewer acceleration turns and larger between different acceleration orbits facilitate efficient extraction. However, once space is inserted between the magnetic sectors of the cyclotron, the footprint grows rapidly. At relativistic energies, above 200 MeV, cyclotrons do not scale. Field profile must be nonlinear at relativistic energies for CW operationSlide4

Tunes in a relativistic ultracompact cyclotron

One of the most important indicators of stability is called machine tune; the no. of oscillations a particle makes about the energy-specific reference orbit in one translation around the ringDA problems occur when the tune is an integer or fraction of an integer (units of 2 rad) because particles retrace through nonlinearities and imperfectionsThe tune in a cyclotron must vary as it enters relativistic energies. A gradient must be imposed to keep the beam CW

Predicted tune from an

ultracompact

medical cyclotron(left) and ZGOUBI (middle) and COSY (right).. Predicted problems are marked with red arrows

Begin position = end

Begin position



end Slide5

So what is a FFAG?Next generation cyclotronA Fixed Field Alternating Gradient Accelerator is a ~ a cyclotron with strong synchrotron-like focusing

The ns-FFAG combines all forms of transverse beam (envelope) confinement in an arbitrary, optimized magnet field:For the horizontal, the three terms are The power of the FFAG is that the confinement terms can be varied independently to optimize machine parameters such as footprint, aperture, and tune in a FFAG AND DC beam can be supported to very high energies

synchrotron

cyclotronSlide6

Quick Guide to Fixed-Fielding Alternating Gradient FFAGsSimplest Dynamical Definition: FFAG is ~ a cyclotron with a gradient; beam confinement is via:Strong alternating-gradient (AG) focusing, both planes: radial sector FFAG normal/reversed gradients alternate (like a synchrotron)Gradient focusing in horizontal, edge focusing in vertical:

spiral sector FFAG vertical envelope control is through edge focusing (like a cyclotron)the normal gradient increases edge focusing with radius /momentum (unlike a cyclotron) A cyclotron can be considered the lowest-order FFAG Types of FFAGs:Scaling:B field follows a scaling law as a function of radius - rk (k a constant;) present-day scaling FFAGs: Y. Mori, Kyoto University Research Reactor InstituteNonscaling:Linear (quadrupole) gradient; beam parameters generally vary with energy (EMMA FFAG, Daresbury Laboratory, first nonscaling FFAG)Nonlinear-gradient; beam parameters such as machine tune can be fixed (as in a synchrotron)Slide7

FFAGs and their VariationsScaling FFAGs (spiral or radial-sector) are characterized by geometrically similar orbits of increasing radius, imposing a constant tune (field and derivative gradient scale identically with r). Magnetic field follows the law B 

rk, with r as the radius, and k as the constant field index. Field expansion: k determines multipole order;Comments: the lower the k value, the more slowly field increases with r and the larger the horizontal aperture, but the more linear the field composition and dynamics.

Radial Sector: example: This is a triplet DFD cell; there are also FDF, FODO and doublets. In a radial sector the D is the negative of the F field profile, but shorter.

Spiral Sector: example: more compact; positive bend field only. Vertical focusing controlled by edge crossing angle.

D

F

DSlide8

Linear nonscaling

FFAGs for rapid acceleration

Injection reference orbit

Extraction reference orbit

Linear-field,

nonscaling

FFAGs

. Ultra-compact magnet aperture,

proposed and developed for High Energy Physics (Neutrino Factories and

Muon

Colliders), relaxes optical parameters and aims only for stable acceleration. In general they are not suitable for an accelerator with a modest acceleration system and accelerate only over a factor of 2-3 range in momentum.

Cartoon of orbit compaction: nonsimilar orbits, nonconstant tune, resonance crossing

D

F

F

EMMA – world’s first nonscaling FFAG, @Daresbury Laboratory, commissioning, late December, ‘09

Characteristics– tune sweep/unit cell, parabolic pathlength on momentum (small radial apertures); serpentine (rapid) acceleration – beam “phase-slips”, crossing the peak 3 times, accelerating between rf bucketsSlide9

Tune Stability in a linear-gradient nonscaling FFAG with an edge contour

Linear-fields, constant gradient F and D magnetsMagnets are shaped with a linear edge contour with only tune constrainedDramatic improvement in tune stability – to over a factor of 6 in momentumControl of tune variations in a nonscaling FFAG with a constant gradientEMMA –like machineSlow acceleration NEXT STEP IS NONLINEAR FIELD VARIATIONS REQUIRED FOR:

MORE CONSTANT TUNE, LESS RF AND ISOCHRONOUS OR CW OPERATIONSlide10

Understanding a ns-FFAGApply a “synchrotron” strong-focusing field profile to each “cyclotron” orbit

Strong-focusing allows Long injection/extraction or synchrotron-like straightsStrong RF acceleration modulesLow –loss profile of the synchrotronDC beam to high energies in compact structure400 MeV/nucleon: charge to mass of ½ (carbon)1.2 GeV protonsAvoidance of unstable beam regions constant machine tune

s

traight =

 or normalized path lengthSlide11

Relativistic CW (DC-beam) ns-FFAGsNS FFAG can maintain isochronous orbits at relativistic energiesPathlength of isochronous orbits are proportional to velocityOrbits as a function of momentum follow, therefore the B field must scale with velocity

At relativistic energies, momentum is an increasingly nonlinear function of velocity; therefore B field transitions from a linear slope to nonlinear, non-relativistic to relativistic as an approximate function of radius.THIS HAS BEEN ACHIEVED IN RECENT NONLINEAR NS FFAG DESIGNSNonlinear field expansion + edge angle can constrain the tuneNonlinear gradient provides very strong focusing at high energy in both planes relative to the cyclotron or normalized path lengthFFAG limit ≥2 GeV protons

Cyclotron limit

~ 1

GeV

protons

P (

MeV/c)

<Br>



p/

β

for isochronous orbits Slide12

To further summarize beam envelope control (in the thin Lens Limit):Centripetal (Cyclotrons + FFAGs) :

bend plane only, horizontally defocusing or focusing Strength   (bend angle/bend radius of dipole field component on reference orbit) Edge focusing (Cyclotrons + FFAGs) : Horizontally focusing / vertically defocusing, vice versa, or no focusing depending on field at entrance and entrance angleStrength  tan  , (or ~  for reasonably small edge-crossing angles)Gradient focusing (Synchrotrons + FFAGs) :Body gradient, fields components > dipole: B= a + bx +cx2

+ dx

3

+ …

B’= b + 2cx + 3dx

2

+ …

Linear field expansion, constant gradient

Synchrotrons + linear-field

nonscaling

FFAGs (

muon

accelerators)

Nonlinear field expansion up to order k, magnitude of gradient increases with r or energy:

Scaling FFAGsArbitrary nonlinear field expansion, magnitude of gradient increases with r or energy:

Nonlinear Non-scaling FFAGs

Edge crossing angles are kept deliberately small in large multi-cell synchrotron rings. This term becomes increasingly important for and causes problems in small synchrotron rings.Slide13

Reducing the FootprintReverse gradient required for vertical envelopeIsochronous or CW (serpentine channel relaxes tolerances)Stable tune, large energy rangeThe footprint of CW FFAG accelerators is decreasing rapidlyStable, ~identical tunes are maintained

With small straights, extraction and RF modules for high gradient acceleration are now an issue.

Hard edge

and full fringe fieldsSlide14

Race-track CW high-energy FFAGsIncorporate a 1-2 m opposing straightRefit isochronous orbits and recover stable tunesPeriodicity of 2Decreases footprint without compromising acceleration and stabilityMost compact design- with SCRF has the dynamics of a RLA

Machine tunes: r ~1.4 z ~0.8 – factor of ~4 > than compact cyclotron

Slide15

Modeling Cyclotrons in COSYSupplied OPERA field data Two approaches:A highly accurate tracking through a high-order field map using FACT/COSYField maps are constructed by expressing the azimuthal fields in Fourier modes and the radial in Gaussians wavelets for accurate interpolationParticle tracking in the code ZGOUBI using the OPERA data directly and linear interpolation

Opera field data plotted in the midplane for one quadrant and showing spiral sectors.Slide16

Advanced Modeling: Simulations in COSY INFINITY Most accelerator codes provide too-little flexibility in field description and are limited to low order in the dynamics, new tools were developed for the study and analysis of FFAG dynamics based on transfer map techniques unique to the code COSY INFINITY.

HARD EDGE Various methods of describing complex fields and components are now supported including representation in radius-dependent Fourier modes, complex magnet edge contours, as well as the capability to interject calculated or measured field data from a magnet design code or actual components. FULL FRINGE FIELDSArbitrary shapes, field content, contoursSlide17

Modeling, Design and Optimizing Most advanced modeling, design, and optimization of fixed-field accelerators – both FFAGs and cyclotrons -production runs advanced optimizationThe lowest order Fourier mode in the cyclotron, for example, can be re-fit to correct dynamics Simple user interface allows switching fixed-field modes and rapid computationPerformance can be optimized and iterated with magnet designSlide18

FFAG Tracking summary:

3.7 m radius, 4-cell; 4x2m straights300 mr 52

0

mm

100 mr

4

0

mm

Stable beam area @injection (200 MeV)

Tracked:

24

cm

x

240

mr



=

57,600

π

mm-mrnorm = 39,460π mm-mr Stable beam area@500 MeV

 Tracked: 36 cm x 225 mr = 81000π mm-mrnorm = 94,132π mm-mr Stable beam area@1000 MeV Tracked: 39 cm

x 150 mr



=

58,500

π

mm-

mr



norm

=

105,824

π

mm-

mr

Stable

horizontal

Beam

size vs.

Energy, tracked in 3cm steps

Stable beam area @injection (200 MeV)

Tracked:

30

mm x

8

mr



=

240

π

mm-

mr



norm

=

165

π

mm-

mr

Stable beam area

@500 MeV

Tracked:

33

mm x

6

mr



=

198

π

mm-

mr



norm

=

229

π

mm-

mr

Stable beam area

@1000 MeV

Tracked:

30

mm x

4

mr



=

120

π

mm-

mr



norm

=

216

π

mm-

mr

Stable Vertical Beam size vs. Energy: tracking ends at ±1cm, vertical magnet

gap, tracked in 3mm steps

10

mrSlide19

FFAG Tracking summary: 1.2 m ext. radius, racetrack

330

mr

180 mm

100 mr

15

mm

Stable beam area @injection (200 MeV)

Tracked:

8

cm

x 293

mr



=

23440π

mm-

mr

norm = 16,059π mm-mr 

Stable beam area@500 MeV Tracked: 12 cm x 220 mr = 26400π mm-mrnorm = 30680π mm-mr Stable beam area@1000 MeV 

Tracked: 13

cm

x 165

mr



=

21450π

mm-

mr



norm

=

38802π

mm-

mr

Stable

horizontal

Beam

size vs.

Energy

Stable beam area @injection (200 MeV)

Tracked: 10 mm x 9

mr



=

90π

mm-

mr



norm

=

62

π mm-

mr

Stable beam area

@500 MeV

Tracked: 11 mm x 7 mr



= 77π mm-mr



norm

=

89π mm-mr

Stable beam area

@1000 MeV

Tracked: 10 mm x 5

mr



= 50π mm-

mr



norm

=

90π mm-

mr

Stable Vertical Beam size vs. Energy: tracking ends at ±1cm, vertical magnet gap

10

mrSlide20

Comparing fixed-field Dynamic Apertures

cyclotroncyclotronFFAG: Horizontal – 1 cm steps FFAG: Vertical – 1 mm steps

Tracked:

130

mm x 165

mr



=

21450π

mm-

mr



norm

=

38820π mm-

mr

Tracked: 10 mm x 5

mr



= 50π mm-

mr

norm =90π mm-mr  FFAG Stable beam area @1000 MeV vs. DA of 800 MeV Daealus cyclotron*: factor of 4 larger for ~ a factor of 4 smaller footprint 

  80 mm x 293 mrH = 23,440π mm-mrnorm = 16,059π mm-mr   10 mm x 9 mrV =

90π mm-

mr



norm

=

62

π

mm-

mr

FFAG

Stable

beam

area

@

200 MeV

vs

DA of

ultracompact

250 MeV cyclotron

*F.

Meot

, et. al., Proc. IPAC2012

*FFAG vert

. stable area at aperture limits.Slide21

21

MAGNETS and modelingParameterUnitsValueNumber of magnets6Number of SC

coils

12

Peak magnetic field on coils

T

7

Magnet

Beam Pipe gap

mm

50

Superconductor

type

NbTi

Operating

Temperature

K

4.0Superconducting cable

RutherfordCoil ampere-turnsMA

3.0Magnet system heightM~1

Total Weighttons~10

One straight section occupied by RF cavities and injection/extraction in the other

< 3 m

< 5 mThe magnetic field is relatively flat under the F-pole but the angular field length strongly depends on the radius providing the needed range from injection to extraction. The return flux provides the D or reverse gradient but needs careful optimizationSlide22

Acceleration Gradient required for low-loss extractionKinetic Energy(MeV)

Acc Gradientper turn (MV)RSRadius @center of straight(m)r (cm)800 

1.1955

785

15

1.1879

0.76

775

25

1.1816

1.39

765

35

1.1751

2.04

Reference radius in center of straight for

the

energy

orbits preceding extraction. For an accelerating gradient of ~20 MV/m orbits are sufficiently separated for a “clean” (beam size: 1.14 cm; =10 mm-mr normalized) or low-loss extraction through a septum magnet.For 20 MV/turn, and a 2m straight section, we require 10 MV/m – implies a SCRF cryomodule – in order to achieve extraction with manageable shielding, radiation levels, and activation. This requirement drove the design of the high-energy stage.Slide23

Design specificationsLarge horizontal beam aperture of 50 cmCavity should operate at 150 or 200 MHz (harmonic of the revolution frequency)Should provide at least 5 MV for proton beam with energies 200 – 900 MeVPeak magnetic field should be no more than 160 mT (preferably, 120 mT or less)Peak electric field should be minimizedCavity dimensions should be minimized

FFAG cavity23September 16, 2013Slide24

Cavity optionsHalf-wave resonator H-Resonators24

Beamtrajectories

HWR is very dependent on particle velocity

Can’t be used efficiently for such a wide range

of particle energies

Dimensions are very large as is peak magnetic field on the electrode edgeSlide25

Rectangular CavityRectangular cavity operating at H101 mode has electric field concentrated in the center of the wallTo concentrate electric field at beam aperture, we introduced tapersTo reduce peak magnetic field the blending was introduced FFAG cavity

25

W

L

H

Beam

directionSlide26

Gap and Frequency OptimizationThe voltage at 160 mT maximum field dependence on gap length was calculated for cavities with different frequencies and lengths26

150 MHz 1.5 m structure has a potentially higher possible voltage or lower peak magnetic field at 5 MV200 MHz structure is more compactBeam Energy = 200 MeVVoltage in the center of the aperturePeak magnetic field = 160 mTSlide27

Cavity shape optimizationA taper was introduced to distribute the magnetic field over a larger volume keeping the electric field concentrated around the beam apertureSuch a cavity design has smaller dimensions for the same volume All edges were rounded and improved reentrant nose shape reduced the peak magnetic field by more than 15% and the transverse dimensions by more than 10 cmFinal study was an elliptical cell shape where the magnetic field varies along the cavity wall such that there are no stable electron trajectories and multipacting is inhibited

27Slide28

RF input coupler designAs 1 mA beam is accelerated by 4 cavities from 200 to 900 MeV, each cavity requires about 175 kW of power One of the options is to attach 2 100kW couplers to the cavity28

ANSYS estimations show no significant overheating80K4K126K133K300K

Heat Flows:

To 4K =

9.8W

To 60K =

92.0W

From 300K =

18.8WSlide29

Magnetic power coupling and mechanical designExternal Q-factor should be ~ 1.9*106Preliminary results predict ~1.1mm Nb and ~0.6mm SS deformation at magnetic field area29

The complete mechanical design: 1 – niobium shell, 2 – RF ports, 3- extra ports, 4 – frequency tuning, 5 – steel jacket, 6 – rails Slide30

Dual-stage ion FFAG proton FFAG with pCT1st

stage18 – ~250-330 MeV H- Fixed or swept-frequency RF, DC beamLow intensity for pCTStripping controls extraction energy and intensity in addition to source modulationOR9-~70-90 MeV charge to mass ratio of ½Fixed-frequency RF, DC beam for all ionsVariable energy extractionUpstream injector for high-energy ring2nd stage (~4 m x 5-6 m long)70/90 MeV – 430 MeV/nucleonVariable energy extractionAdjustable, fast orbit bump magnets/extraction septum in long straightDC extracted beamVariable energy on scale of tens of microsecondsInvestigating extracted energy range

1

st

stage: Cyclotron or FFAG

2

nd

stage: 70/90 – 430 MeV/nucleon ions

Variable energy selection:

Injection/extraction straightSlide31

Other FFAG Applications

Can you find the carbon FFAG?

principle collaborators

(PAC/ANL/BNL/RAL/U of

Huddersfield

)

Proton and Ion Therapy

A 0.33 – 1.2

GeV

proton RLA

= 400 MeV/

nucleon

C

6+

Imaging: proton CT (@330 MeV)

Radioisotope Production

<30 MeV FFAGs

Hospital units (PET)

No

nuclear waste(Moly99) Nuclear Waste Transmutation

At reactor siteLegacy stockpile

Accelerator Driven Subcritical Reactor demo

Heidelberg Ion Therapy Synchrotron Tracking with space charge @300 MeV

0.3 - 1 GeV @10mA stable Slide32

The FFAG accelerator vs. the MYRHHA Linear accelerator for ADSR waste transmutation

A FFAG 1

GeV

high power accelerator facility

PAC’s FFAG

A

linac

accelerator for nuclear waste transmutation

MYRHHA

Mol

, BelgiumSlide33

SummaryThe nsFFAG has evolved to an isochronous, high energy, high current applicationWith constant strong-focusing machine tunes and optics that are independent of energyNo resonance crossingThe DA aperture is 10,000 – 100,000

 mm-mr depending on size and tunes In the relativistic regime, the FFAG becomes more compact than the separated sector cyclotron and more stable if designed properlyThe racetrack is the most compactLarge aperture high-gradient cavities including SCRF have been designedIronless, self-supported coil SC magnets are also being developed