Fermilab CW Isochronous FFAGs Dr Carol Johnstone FFAG
Fermilab CW (Isochronous) FFAGs Dr. Carol Johnstone FFAG 09 Sept 21, 2009 Fermilab 10/21/2009 Dr. Carol Johnstone 1
Understanding FFAGs and their Variations Scaling FFAGs (spiral or radialsector) are characterized by geometrically similar orbits of increasing radius, imposing a constant tune. 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 Comments: ; the lower the k value, 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 (muons) 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-stable nonscaling FFAGs for slow acceleration Tune-stable, nonscaling FFAGs • Tune is strongest indicator of stable particle motion – allowing particles execute periodic motion eventually returning to the same transverse position relative to a reference orbit. Constraining the tune can be sufficient to design a stable machine. • Release of other linear optical parameter allows flexibility and optimization both in cost and complexity of the accelerator design; i. e. simpler magnets, strong vertical focusing, for example • Tune Stable Nonscaling FFAGs have either linear or nonlinear field profiles and/or edge contours Two lattice approaches 1) Machida version - which uses a scaling law truncated at decapole, rectangular magnets , (not discussed here, see PAMELA project) and 2) 2) Johnstone version – The most general form of a radial sector : allowing independent, unconstrained field and edge profiles between two combined-function magnets. 1 40 c m ~17 cm Extraction orbit reference 2 Injection orbit reference
Simulation Challenges New accelerator prototypes are often simulated with conventional tracking codes, – these codes do not provide much flexibility in the field description and are limited to low order in the dynamics. – This limitation is inadequate to demonstrate performance in the presence of strong nonlinearities due to edge fields and other high-order effects appear. – This is particularly true for the FFAGs where edge crossing and strong bends, or “smallring” effects can dominate the optics. In the muon FFAGs, the large beam emittances preclude the use of codes which do not include kinematical (or angle) effects in the Hamiltonian. which implies that codes which fully describe the kinematics are necessary. The current number of supported design and optimization codes that can adequately describe the complex field and magnet contours for both the scaling and nonscaling FFAG variants is limited to the cyclotron code CYCLOPS [1], and the field-map code ZGOUBI [2], and recently COSY INFINITY[3] 1. 2. 3. R Baartman et al. CYCLOPS. Technical report. F. Meot. The ray-tracing code ZGOUBI. Nuclear Instruments and Methods A, 427: 353– 356, 1999 and F. Lemuet and F. Meot. Developments in the ray-tracing code ZGOUBI for 6 -d mul-titurn tracking in FFAG rings, 2005. M. Berz and K. Makino. COSY INFINITY Version 9. 0 beam physics manual. Technical Report MSUHEP-060804, Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, 2006. See also http: //cosyinfinity. org.
Recent Lattice Design and Optimization: Nonscaling FFAGs with stable tune – isochronous lattices – A powerful new methodology was pioneered for FFAG optics design using control theory and native optimizers in Mathematica® to develop executable design scripts usin simple, hard edge linear matrices. These procedures allowed global exploration of all important machine parameters. Starting designs are directly imported into COSY INFINITY – WITH THIS METHODOLOGY, the stable machine tune was expanded over an acceleration range of 3 up to 6 in momentum with linear fields and up to 44 with nonlinear fields. – Full evaluation required new advanced simulation tools not existing in current accelerator codes. New tools have been developed and implemented in COSY INFINITY to describe the exact complex field and edge profiles to optimize and accurately predict machine performance. Other successful public codes for FFAG lattice design include ZGOUBI and a recent upgrade to CYCLOPS – talks on these codes are scheduled for Tuesday.
The Nonlinear Nonscaling Simulation in COSY INFINITY • As conventional 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 •
A 30 -250 Me. V Proton FFAG for Hadron Therapy Mathematica® initial parameters compared with COSY INFINITY and full field description Again strong tune splitting horz/vert, but radial dependence is well reproduced
COSY INFINITY results and DA General Parameters of the triplet 30 -250 Me. V nonscaling FFAG design. Parameter Energy Range Tune/cell ( x / y) Ring tune ( x / y) Average Radius Unit Me. V 2 -rad m Injection 30 Extracti on 250 Energy Range 0. 31 / 0. 16 2. 51/1. 28 0. 31 / 0. 21 2. 51/1. 66 Tune/cell ( x / y) Ring tune ( x / y) 2. 75 3. 39 No. cells Long Straight Peak Field F D Magnet Lengths F D m Apertures F D m 1. 17 0. 646 0. 129 0. 63 0. 55 Average Radius Unit Injection Extractio n Me. V 30 250 2 -rad 0. 31 / 0. 22 2. 48/1. 75 0. 31 / 0. 19 2. 48/1. 55 m 2. 75 3. 39 8 Long Straight m T 3. 13 -3. 41 Peak Field F D m 0. 803 0. 176 Magnet Lengths F D Apertures F D m 1. 17 1. 21 -1. 37 Parameter No. cells 8 m T General Parameters of the triplet 30 -250 Me. V nonscaling FFAG design after tune optimization in COSY – only tune variations are affected. 1. 17 1. 21 -1. 37 3. 13 -3. 41 0. 646 0. 129 0. 803 0. 176 0. 63 0. 55 Dynamic aperture a midpoint, 112 Me. V. , horizontal (left), vertical (right) DA at all energies for both planes is extremely large.
Additional constraint: Isochronous Condition • In addition to stable tune, the condition of “isochronism” was imposed on the orbits: • This equation is useful in determining initial “feasible” apertures and field strengths
Isochronous Lattices: nonscaling nonlinear FFAGs • First 18 Me. V – 150 Me. V isochronous proton FFAG 3 m outer machine radius, 1 m straights, 1. 07 -1. 87 m injection to extraction orbits Physical layout of 18 -150 Me. V 4 sector isochronous NC ring Tune per cell with just quad + sext field profile (top) and then adding octupole (middle) and ring tune (bottom)
Machine Parameters for a 18 -150 Me. V Hisochronous FFAG: Normal conducting 3 2. 8 2. 6 2. 4 2. 2 2 1. 8 1. 6 1. 4 1. 2 1 General Parameters of the triplet 18 -150 Me. V isochronous nonscaling FFAG Energy Range Tune/cell ( x / y) Ring tune ( x / y) Average Radius Unit Me. V 2 -rad m Injection 18 Extracti on 150 0. 30 / 0. 31 2. 51/1. 28 0. 29 / 0. 31 2. 51/1. 66 1. 07 2. 88 No. cells Long Straight Peak Field F D 4 m T Magnet Lengths F D m Apertures F D m 1. 0 1. 21 0 1. 09 -0. 24 1. 068 0. 108 1. 892 1. 120 155 355 455 555 Deviation from isochronicity 0. 03 2. 00 1. 25 255 0. 035 0. 025 Riso-Ravg Parameter Ravg (blue) and Risochronous (red) 0. 02 0. 015 0. 01 0. 005 0 160 260 360 Momentum Me. V/c 460 Isochronous vs. calculated orbits 560 . . .
150 -250 Me. V Superconducting Isochronous Proton FFAG 1. 75 m outer machine radius, 2 m straights, 1. 24 -1. 52 m injection to extraction orbits (0. 28 m orbit separation) Tune per cell with up to duo-decapole (top) and ring tune (bottom)
Machine Parameters for a 150 -250 Me. V isochronous proton FFAG: Superconducting 1. 6 Ravg (blue) and 1. 55 General Parameters of the triplet 150 -250 Me. V isochronous 1. 5 nonscaling FFAG 1. 45 Energy Range Tune/cell ( x / y) Ring tune ( x / y) Average Radius Unit Injection Me. V 2 -rad 150 Extracti on 250 0. 29/ 0. 29 1. 46/1. 45 0. 29 / 0. 29 1. 46/1. 47 1. 24 1. 52 m No. cells Long Straight Peak Field F D Magnet Lengths F D m Apertures F D m 1. 35 1. 3 1. 25 1. 2 550 5 m T 1. 4 2. 0 3. 21 0 3. 52 -1. 81 0. 722 0. 108 0. 892 0. 344 0. 294 0. 218 600 650 700 750 0. 016 0. 014 0. 012 Riso-Ravg (m) Parameter Deviation from isochronicity 0. 01 0. 008 0. 006 0. 004 . . . 0. 002 Higher orders reduced deviation from isochronicity by a factor of 2 0 550 600 650 700 Momentum Me. V/c 750 Isochronous vs. calculated orbits
Hardware Concepts for a Nonlinear Nonscaling FFAG • An innovative new approach to a combined-function 4 T magnet is under design based conventional Nb. Ti superconducting magnet technologyand construction techniques. • For normal conducting/permanent magnets, inset trim coils are being designed for radial field adjustment and fringe field control –very important for vertical tune. You can essentially “buck” fringe field effects.
Conclusions for rf design • For non-isochronous FFAG, s a normal conducting rf system is the only option. The properties of available microwave ferrites for cavity tuning imply a rf frequency below 50 MHz for frequency sweeping. For large-aperture nonisochronous or isochronous FFAGs, and small vertical aperture, the RF leakage from the large horizontal aperture is acceptably small if the device operates below 500 MHz. The large magnet apertures therefore do not present a serious technical issue in terms of an rf structure. • For high-energy –multi. Ge. Visochronous FFAGs (close simplying small apertures), with long straights, superconducting rf is a possibility.
Summary of Work on. S New FFAGs 3. 5 m 5. 5 – 6. 9 p m • FFAG designs are advancing rapidly internationally, particularly for medical and HEP applications • Embedded rings for multi-ion cancer therapy are an exciting compact accelerator chain competitive with cyclotrons. • A CW (isochronous) nonscaling FFAG has been developed -very important for accurate dose delivery, lower intensity beams, reduced shielding • The CW option also has important consequences for the role of FFAGs in high intensity applications. With their high phase advance FFAGs may be able to sustain 10 -20 ma of current limited instead by beam loading in rf cavities rather than space charge. 12 C 6+
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