Ultra-compact CW racetrack FFAGs

FFAG1313th International Workshop on

FFAGsTRIUMF

Sept 21 2013Vancouver, Canada

Dr. C. Johnstone, Fermilab

Outline Motivation and Background

Next generation ultra-compact, high-energy fixed field accelerators Medical, security, energy applications CW FFAGs ; i.e. strong-focusing cyclotrons

Relativistic energies: ~200 MeV – 1 GeV Ultra-compact Constant machine tunes (optimized gradients) High mA currents (low losses)

These machines require high gradient acceleration; and SCRF for high currents

Compactness Low extraction losses

Large horizontal aperture of the FFAG, like the cyclotron, is a challenging problem for SCRF design

2

Cyclotrons: general comments Cyclotrons are the highest current, most compact solution,

but only up ~200 MeV for protons As the energy becomes relativistic, orbit separation

becomes smaller and smaller for CW operation Higher 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 operation

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 ring

DA problems occur when the tune is an integer or fraction of an integer (units of 2 rad) because particles retrace through nonlinearities and imperfections

The 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

So what is a FFAG?Next generation cyclotron

A 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

field.order arbitrary an for gradient local"" theis andlength magnet -half F theis , length, ed),approximat is tangent so

small assume is angle (edge angle edge the angle, bendsector theis with

/1

F

FFFF

kl

lkf

synchrotron cyclotron

Quick Guide to Fixed-Fielding Alternating Gradient FFAGs

Simplest 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 Institute

Nonscaling: 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)

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.

DF

D

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

DF 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 buckets

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

Linear-fields, constant gradient F and D magnets Magnets are shaped with a linear edge contour with only

tune constrained Dramatic improvement in tune stability – to over a factor of

6 in momentum30-400 MeV Linear-field "Muon" Accelerator

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.2 0.4 0.6 0.8 1

Momentum (GeV/c)

tune

/cel

l

nux/cellnuy/cell

Control of tune variations in a nonscaling FFAG with a constant gradient

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.2 0.4 0.6 0.8 1Momentum (GeV/c)

tune

/cel

l

nux/cell-modelnuy/cell-modelnux/cell-approxnuy/cell-approx

EMMA –like machine Slow acceleration

NEXT STEP IS NONLINEAR FIELD VARIATIONS REQUIRED FOR: MORE CONSTANT TUNE, LESS RF AND ISOCHRONOUS OR CW OPERATION

Understanding a ns-FFAG Apply a “synchrotron” strong-focusing field profile to each

“cyclotron” orbit Strong-focusing allows

Long injection/extraction or synchrotron-like straights Strong RF acceleration modules Low –loss profile of the synchrotron DC beam to high energies in compact structure

400 MeV/nucleon: charge to mass of ½ (carbon) 1.2 GeV protons

Avoidance of unstable beam regions constant machine tune

straight =

or normalized path length

Relativistic CW (DC-beam) ns-FFAGs NS FFAG can maintain isochronous orbits at relativistic energies

Pathlength of isochronous orbits are proportional to velocity Orbits 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 DESIGNS Nonlinear field expansion + edge angle can constrain the tune Nonlinear gradient provides very strong focusing at high energy in both

planes relative to the cyclotron

0 0.2 0.4 0.6 0.8 1 1.20

500

1000

1500

2000

2500

3000

3500

or normalized path length

FFAG limit ≥2 GeV protons

Cyclotron limit ~ 1 GeV protons

P (M

eV/c

)

<Br> p/β for isochronous orbits

To further summarize beam envelope control (in the thin Lens Limit):

1. Centripetal (Cyclotrons + FFAGs) : bend plane only, horizontally defocusing or focusing

Strength (bend angle/bend radius of dipole field component on reference orbit)

2. Edge focusing (Cyclotrons + FFAGs) : Horizontally focusing / vertically defocusing, vice versa, or no focusing

depending on field at entrance and entrance angle Strength tan , (or ~ for reasonably small edge-crossing angles)

3. Gradient focusing (Synchrotrons + FFAGs) : Body gradient, fields components > dipole: B= a + bx +cx2 + dx3 + … B’= b + 2cx + 3dx2 + …

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 FFAGs

Arbitrary 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.

Reducing the Footprint Reverse gradient required for vertical envelope Isochronous or CW (serpentine channel relaxes

tolerances) Stable tune, large energy range The footprint of CW FFAG accelerators is decreasing

rapidly Stable, ~identical tunes are maintained With small straights, extraction and RF modules for high

gradient acceleration are now an issue.Hard edge and full fringe fields

Race-track CW high-energy FFAGs

Incorporate a 1-2 m opposing straight Refit isochronous orbits and recover stable tunes Periodicity of 2 Decreases footprint without compromising

acceleration and stability Most compact design- with SCRF has the dynamics of

a RLA

80 0 100 0 1200 14 00 160 0P , MeV c1.0

1.5

2.0

2.5

3.0v

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

Modeling Cyclotrons in COSY Supplied OPERA field data Two approaches:

A highly accurate tracking through a high-order field map using FACT/COSY Field maps are constructed by expressing the

azimuthal fields in Fourier modes and the radial in Gaussians wavelets for accurate interpolation

Particle 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.

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 FIELDS

Arbitrary shapes, field content, contours

Modeling, Design and Optimizing

Most advanced modeling, design, and optimization of fixed-field accelerators – both FFAGs and cyclotrons - production runs advanced optimization

The 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 computation Performance can be optimized and iterated with magnet

design

FFAG Tracking summary: 3.7 m radius, 4-cell; 4x2m

straights

300 mr 

520 mm 

100 mr 

40 mm 

Stable beam area @injection (200 MeV)

 Tracked: 24 cm x 240 mr

= 57,600π mm-mrnorm = 39,460π mm-mr

 

Stable beam area@500 MeV

 Tracked: 36 cm x 225 mr

= 81000π mm-mrnorm = 94,132π mm-mr

 

Stable beam area@1000 MeV

 Tracked: 39 cm x 150 mr

= 58,500π mm-mrnorm = 105,824π mm-mr

 

Stable horizontal Beam size vs. Energy, tracked in 3cm steps

Stable beam area @injection (200 MeV)

 Tracked: 30 mm x 8 mr

= 240π mm-mrnorm =165π mm-mr

  

Stable beam area @500 MeV

 Tracked: 33 mm x 6 mr

= 198π mm-mrnorm =229π mm-mr

  

Stable beam area@1000 MeV

 Tracked: 30 mm x 4 mr

= 120π mm-mrnorm =216π mm-mr

  

Stable Vertical Beam size vs. Energy: tracking ends at ±1cm, vertical magnet gap, tracked in 3mm steps

10 mr

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-mrnorm = 16,059π mm-mr

 

Stable beam area@500 MeV

 Tracked: 12 cm x 220 mr

= 26400π mm-mrnorm = 30680π mm-mr

 

Stable beam area@1000 MeV

 Tracked: 13 cm x 165 mr

= 21450π mm-mrnorm = 38802π mm-mr

 

Stable horizontal Beam size vs. Energy

Stable beam area @injection (200 MeV)

 Tracked: 10 mm x 9 mr

= 90π mm-mrnorm =62π mm-mr

  

Stable beam area @500 MeV

 Tracked: 11 mm x 7 mr

= 77π mm-mrnorm =89π mm-mr

  

Stable beam area@1000 MeV

 Tracked: 10 mm x 5 mr

= 50π mm-mrnorm =90π mm-mr

  

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

10 mr

Comparing fixed-field Dynamic Apertures

cyclotroncyclotron

FFAG: 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-mrnorm =90π mm-mr

  

FFAG Stable beam area @1000 MeV vs. DA of 800 MeV Daealus cyclotron*: factor of 4 larger for ~ a factor of 4 smaller footprint

 

  80 mm x 293 mrH = 23,440π mm-mr

norm = 16,059π mm-mr 

  10 mm x 9 mr

V = 90π mm-mrnorm =62π 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.

21

MAGNETS and modeling Parameter Units ValueNumber of magnets 6Number of SC coils 12Peak magnetic field on coils

T 7

Magnet Beam Pipe gap mm 50Superconductor type NbTiOperating Temperature K 4.0Superconducting cable Rutherfor

dCoil ampere-turns MA 3.0Magnet system height M ~1Total Weight tons ~10One straight section occupied by RF cavities

and injection/extraction in the other

< 3

m

< 5 m

The 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 optimization

Acceleration Gradient required for low-loss extraction

Kinetic 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.

Design specifications Large horizontal beam aperture of 50 cm Cavity 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 MeV Peak magnetic field should be no more

than 160 mT (preferably, 120 mT or less) Peak electric field should be minimized Cavity dimensions should be minimized

FFAG cavity 23September 16, 2013

Cavity options Half-wave resonator H-

Resonators

24

Beamtrajectories

HWR is very dependent on particle velocityCan’t be used efficiently for such a wide range of particle energies

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

Rectangular Cavity Rectangular cavity operating at H101 mode has electric

field concentrated in the center of the wall To concentrate electric field at beam aperture, we

introduced tapers To reduce peak magnetic field the blending was

introduced

FFAG cavity 25

W

L

H

Beamdirection

Gap and Frequency Optimization

The voltage at 160 mT maximum field dependence on gap length was calculated for cavities with different frequencies and lengths

26

150 MHz 1.5 m structure has a potentially higher possible voltage or lower peak magnetic field at 5 MV200 MHz structure is more compact

Beam Energy = 200 MeV

Voltage in the center of the aperture

Peak magnetic field = 160 mT

Cavity shape optimization A taper was introduced to distribute the

magnetic field over a larger volume keeping the electric field concentrated around the beam aperture

Such 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 cm

Final 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

27

RF input coupler design As 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 cavity

28

ANSYS estimations show no significant overheating

80K

4K126K

133K300K

Heat Flows:To 4K = 9.8WTo 60K = 92.0WFrom 300K = 18.8W

Magnetic power coupling and mechanical design

External Q-factor should be ~ 1.9*106

Preliminary results predict ~1.1mm Nb and ~0.6mm SS deformation at magnetic field area

29

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

Dual-stage ion FFAG proton FFAG with pCT

1st stage 18 – ~250-330 MeV H-

Fixed or swept-frequency RF, DC beam Low intensity for pCT Stripping controls extraction energy and intensity in addition to source modulationOR

9-~70-90 MeV charge to mass ratio of ½ Fixed-frequency RF, DC beam for all ions Variable energy extraction Upstream injector for high-energy ring

2nd stage (~4 m x 5-6 m long) 70/90 MeV – 430 MeV/nucleon Variable energy extraction Adjustable, fast orbit bump magnets/extraction

septum in long straight DC extracted beam Variable energy on scale of tens of microseconds Investigating extracted energy range

1st stage: Cyclotron or FFAG

2nd stage: 70/90 – 430 MeV/nucleon ions

Variable energy selection:Injection/extraction straight

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 C6+

Imaging: proton CT (@330 MeV) Radioisotope Production

<30 MeV FFAGs Hospital units (PET) No nuclear waste(Moly99)

Nuclear Waste Transmutation At reactor site Legacy stockpile Accelerator Driven Subcritical Reactor demo

Heidelberg Ion Therapy Synchrotron

Tracking with space charge @300 MeV

0.3 - 1 GeV @10mA stable

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, Belgium

Summary• The nsFFAG has evolved to an isochronous, high

energy, high current application• With constant strong-focusing machine tunes and

optics that are independent of energy• No resonance crossing• The 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 properly• The racetrack is the most compact

• Large aperture high-gradient cavities including SCRF have been designed

• Ironless, self-supported coil SC magnets are also being developed