Ultracompact CW racetrack FFAGs Dr C Johnstone Fermilab

Ultra-compact CW racetrack FFAGs Dr. C. Johnstone, Fermilab FFAG 13 13 th International Workshop on FFAGs TRIUMF Sept 21 2013 Vancouver, Canada

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 Me. V – 1 Ge. V �Ultra-compact �Constant machine tunes (optimized gradients) �High m. A 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 Me. V for protons As the energy becomes relativistic, orbit separation becomes smaller and smaller for CW operation Higher energies require separated sectors (like the 590 -Me. V PSI or 500 -Me. V 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 Me. V, 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 Begin position end � 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 Begin position = end � 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

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 synchrotron – cyclotron 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

� 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 � 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 � � normal/reversed gradients alternate (like a synchrotron) Types of FFAGs: Scaling: � B field follows a scaling law as a function of radius - rk (k a constant; ) presentday 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 Variations Scaling 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. Spiral Sector: example: more compact; positive bend field only. Vertical focusing controlled by edge crossing angle. 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. F D D Radial Sector: example: This is a triplet DFD cell; there also FDF, FODO and doublets. In a radial sector the D is the negative of the F field profile, but shorter.

Linear nonscaling FFAGs for rapid acceleration 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 23 range in momentum. EMMA – world’s first nonscaling FFAG, @Daresbury Laboratory, commissioning, late December, ‘ 09 Extraction reference orbit D F F Injection reference orbit Cartoon of orbit compaction: nonsimilar orbits, nonconstant tune, resonance crossing 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 momentum EMMA –like machine Slow acceleration Control of tune variations in a nonscaling FFAG with a constant gradient NEXT STEP IS NONLINEAR FIELD VARIATIONS REQUIRED FOR: MORE CONSTANT TUNE, LESS RF AND ISOCHRONOUS OR CW OPERATION

Understanding a ns-FFAG Ø Ø Apply a “synchrotron” strong-focusing field profile to each “cyclotron” orbit Strong-focusing allows Long injection/extraction or synchrotron-like straights Ø Strong RF acceleration modules Ø Low –loss profile of the synchrotron Ø DC beam to high energies in compact structure Ø Ø 400 Me. V/nucleon: charge to mass of ½ (carbon) Ø 1. 2 Ge. V protons Ø Avoidance of unstable beam regions Ø constant machine tune straight = or normalized path length

Relativistic CW (DC-beam) ns-FFAGs NS FFAG can maintain isochronous orbits at relativistic energies ü ü ü 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 3500 planes relative to the cyclotron FFAG limit 3000 Cyclotron limit ~ 1 Ge. V protons P (Me. V/c) ü <Br> p/β for isochronous orbits ≥ 2 Ge. V protons 2500 2000 1500 1000 500 or normalized path length 0 0 0, 5 1 1, 5

To further summarize beam envelope control (in the thin Lens Limit): 1. Centripetal (Cyclotrons + FFAGs) : bend plane only, horizontally defocusing or focusing � 2. Edge focusing (Cyclotrons + FFAGs) : Horizontally focusing / vertically defocusing, vice versa, or no focusing depending on field at entrance and entrance angle � 3. Strength (bend angle/bend radius of dipole field component on reference orbit) Strength tan , (or ~ for reasonably small edge-crossing angles) Gradient focusing (Synchrotrons + FFAGs) : Body gradient, fields components > dipole: B= a + bx +cx 2 + dx 3 + … B’= b + 2 cx + 3 dx 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 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 Ø Ø Ø 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 Ø Ø Ø 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 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. Arbitrary shapes, field content, contours HARD EDGE � Various methods of describing complex fields and components are now supported including representation in radiusdependent 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

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; 4 x 2 m straights Stable beam area @injection (200 Me. V) Stable beam area @500 Me. V Stable beam area @1000 Me. V Tracked: 24 cm x 240 mr = 57, 600π mm-mr norm = 39, 460π mm-mr Tracked: 36 cm x 225 mr = 81000π mm-mr norm = 94, 132π mm-mr Tracked: 39 cm x 150 mr = 58, 500π mm-mr norm = 105, 824π mm-mr 300 mr 520 mm Stable horizontal Beam size vs. Energy, tracked in 3 cm steps Stable beam area @injection (200 Me. V) Stable beam area @500 Me. V Stable beam area @1000 Me. V Tracked: 30 mm x 8 mr = 240π mm-mr norm =165π mm-mr Tracked: 33 mm x 6 mr = 198π mm-mr norm =229π mm-mr Tracked: 30 mm x 4 mr = 120π mm-mr norm =216π mm-mr 10100 mrmr 40 mm Stable Vertical Beam size vs. Energy: tracking ends at ± 1 cm, vertical magnet gap, tracked in 3 mm steps

FFAG Tracking summary: 1. 2 m ext. radius, racetrack Stable beam area @injection (200 Me. V) Stable beam area @500 Me. V Stable beam area @1000 Me. V Tracked: 8 cm x 293 mr = 23440π mm-mr norm = 16, 059π mm-mr Tracked: 12 cm x 220 mr = 26400π mm-mr norm = 30680π mm-mr Tracked: 13 cm x 165 mr = 21450π mm-mr norm = 38802π mm-mr 330 mr 180 mm Stable horizontal Beam size vs. Energy Stable beam area @injection (200 Me. V) Stable beam area @500 Me. V Stable beam area @1000 Me. V Tracked: 10 mm x 9 mr = 90π mm-mr norm =62π mm-mr Tracked: 11 mm x 7 mr = 77π mm-mr norm =89π mm-mr Tracked: 10 mm x 5 mr = 50π mm-mr norm =90π mm-mr 10100 mrmr 15 mm Stable Vertical Beam size vs. Energy: tracking ends at ± 1 cm, vertical magnet gap

Comparing fixed-field Dynamic Apertures FFAG Stable beam area @200 Me. V vs DA of ultracompact 250 Me. V cyclotron 80 mm x 293 mr 10 mm x 9 mr V = 90π mm-mr norm =62π mm-mr H = 23, 440π mm-mr norm = 16, 059π mm-mr FFAG: Horizontal – 1 cm steps FFAG: Vertical – 1 mm steps FFAG Stable beam area @1000 Me. V vs. DA of 800 Me. V Dae alus cyclotron*: factor of 4 larger for ~ a factor of 4 smaller footprint 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 vert. stable area at aperture limits. *F. Meot, et. al. , Proc. IPAC 2012

MAGNETS and modeling Parameter Units Number of magnets 6 Number of SC coils 12 Peak magnetic field on coils T 7 Magnet Beam Pipe gap mm 50 Superconductor type <3 m Operating Temperature Nb. Ti K Superconducting cable <5 m One straight section occupied by RF cavities and injection/extraction in the other Value 4. 0 Rutherford Coil ampere-turns MA 3. 0 Magnet system height M ~1 Total Weight tons ~10 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 21

Acceleration Gradient required for lowloss extraction 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. Kinetic Energy (Me. V) Acc Gradient per turn (MV) 800 r RS Radius @center of straight (m) 1. 1955 (cm) 785 15 1. 1879 0. 76 775 25 1. 1816 1. 39 765 35 1. 1751 2. 04 For 20 MV/turn, and a 2 m 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 Me. V Peak magnetic field should be no more than 160 m. T (preferably, 120 m. T or less) Peak electric field should be minimized Cavity dimensions should be minimized FFAG cavity September 16, 2013 23

Cavity options � Half-wave resonator H-Resonators Beam trajectories 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 edge 24

Rectangular Cavity � � � Rectangular cavity operating at H 101 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 Beam direction W H L FFAG cavity 25

Gap and Frequency Optimization � The voltage at 160 m. T maximum field dependence on gap length was calculated for cavities with different frequencies and lengths Beam Energy = 200 Me. V Voltage in the center of the aperture Peak magnetic field = 160 m. T 150 MHz 1. 5 m structure has a potentially higher possible voltage or lower peak magnetic field at 5 MV 200 MHz structure is more compact 26

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 m. A beam is accelerated by 4 cavities from 200 to 900 Me. V, each cavity requires about 175 k. W of power One of the 80 K options is to attach 2 100 k. W 126 K to the cavity couplers 4 K 133 K 300 K Heat Flows: To 4 K = 9. 8 W To 60 K = 92. 0 W From 300 K = 18. 8 W ANSYS estimations show no significant overheating 28

Magnetic power coupling and mechanical design � � External Q-factor should be ~ 1. 9*106 Preliminary results predict ~1. 1 mm Nb and ~0. 6 mm SS deformation at magnetic field area The complete mechanical design: 1 – niobium shell, 2 – RF ports, 3 - extra ports, 4 – frequency tuning, 5 – steel jacket, 6 – rails 29

Dual-stage ion FFAG proton FFAG with p. CT 1 st stage: Cyclotron or FFAG Ø 1 st stage Ø 18 – ~250 -330 Me. V HØ Fixed or swept-frequency RF, DC beam Ø Low intensity for p. CT Ø Stripping controls extraction energy and intensity in addition to source modulation OR Ø 9 -~70 -90 Me. V charge to mass ratio of ½ Ø Fixed-frequency RF, DC beam for all ions Ø Variable energy extraction 2 nd Ø Upstream injector for high-energy ring Ø 2 nd Ø Ø Ø stage: 70/90 – 430 Me. V/nucleon ions stage (~4 m x 5 -6 m long) 70/90 Me. V – 430 Me. V/nucleon Variable energy extraction Adjustable, fast orbit bump magnets/extraction septum in long straight Ø DC extracted beam Ø Variable energy on scale of tens of microseconds Ø Investigating extracted energy range Variable energy selection: Injection/extraction straight

Other FFAG Applications Heidelberg Ion Therapy Synchrotron Ø principle collaborators (PAC/ANL/BNL/RAL/U of Huddersfield) ü Proton and Ion Therapy ü ü ü A 0. 33 – 1. 2 Ge. V proton RLA = 400 Me. V/nucleon C 6+ Imaging: proton CT (@330 Me. V) Can you find the carbon FFAG? Radioisotope Production ü ü ü <30 Me. V FFAGs Hospital units (PET) No nuclear waste(Moly 99) ü Nuclear Waste Transmutation ü At reactor site ü Legacy stockpile ü Accelerator Driven Subcritical Reactor demo 0. 3 - 1 Ge. V @10 m. A stable Tracking with space charge @300 Me. V

The FFAG accelerator vs. the MYRHHA Linear accelerator for ADSR waste transmutation A linac accelerator for nuclear waste transmutation MYRHHA Mol, Belgium PAC’s FFAG A FFAG 1 Ge. V high power accelerator facility

• • Summary The ns. FFAG 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