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### Progress on Tune-stable Nonscaling FFAGs

C. Johnstone, Fermilab

FFAG08

Sept 1-5, 2008

University of Manchester

Manchester, U.K.

Fermilab

Abstract

- Fueled by recent advances, electron, proton and heavy ion accelerators are playing increasingly important roles in science, technology, and medicine including accelerator-driven subcritical reactors, industrial irradiation, material science, neutrino production, and cancer therapy. The drive for higher beam power, high duty cycle, high reliability and precisely controlled beams at reasonable cost has generated world-wide interest in Fixed-field Alternating Gradient accelerators (FFAGs).
- FFAGs are unique in their high repetition rates, and large acceptances characteristic of cyclotrons, yet they also embody the advantages of the synchrotron: focusing is predominately “strong’, with low injection and extraction losses. By breaking the magnet into sectors to provide edge and strong focusing, and abandoning isochronism in favor of synchrocyclotron-like operation, FFAGs are capable of multi-GeV accelerated energies. Combining, gradient, edge and weak focusing, the FFAG variants represent, in principle, the most general fixed-field accelerator.

- Mike Craddock 2003?

Fermilab

Advances in Medical FFAG accelerators

- Scaling FFAGs – primarily under development in Japan and recently France
- Nonscaling FFAGs
- Linear-field FFAGs
- International effort (EMMA )
- Tune-stablized, linear-field FFAG
- Developed at Fermilab with collaborative design support from TRIUMF and more recently John Adams Institute, Oxford.

Fermilab

Goals of FFAG designs for Medical Accelerators

- Ultimate design consistent with carbon therapy
- Preliminary lattices capable of 400 MeV/nucleon for protons
- 10-20 mm-mr normalized acceptance – not yet optimized
- Small footprint: ~40m normal conducting, 20 m superconducting (protons)
- Synchrotron-like features
- Variable extraction energy
- Resonant or kicker extraction
- Low losses and component activation
- Multiple extraction points – multiple treatment areas
- Cyclotron-like features
- High current output
- Ease of operation – no pulsed components or supplies

Fermilab

Challenge: Adapting the linear-field, nonscaling FFAGs for slow acceleration ; a medical accelerator

- Tune is strongest indicator of stable particle motion – allowing particles in the beam to execute periodic motion and eventually return 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;
- simpler magnets, strong vertical focusing, for example

Fermilab

The concept of a tune-stabilized nonscaling FFAG

- Linear-field gradients
- Magnets are modified to constrain tune only

Control of tune variations in a nonscaling FFAG

Fermilab

Extraction reference orbit

Injection reference orbit

D

F

F

Injection reference orbit

FFAG Variants:Radial Sector “triplet” (Japan) scaling FFAG:

1½ cell of a nonscaling, linear-field FFAG for muon acceleration showing the compression of orbits in particular in the center magnet.

1½ cells of a nonscaling, linear-field FFAG which is tune-stabilized for medical therapy.

Fermilab

Controlling Tune in a linear-field nonscaling FFAG

- Unlike a synchrotron, reference orbits in a fixed-field accelerator always move radially outward with energy.
- Using this property, tune can be controlled in a linear-field FFAG by applying edge shaping to a Combined-Function (CF) magnet.
- Three focusing terms are available for tune manipulation in the horizontal: quadrupole, weak and edge focusing.
- Two of the terms, quadrupole and edge are available for tune control in the vertical

Fermilab

Background

- The relevant strength terms in a CF magnet are most easily understood in the “thin-lens” representation
- In the horizontal, the three terms are
- In the vertical only the quadrupole gradient, kDl, and the edge term are available

Fermilab

Concept

- With a wedge-shaped CF magnet and correct choice of the position of the 0-field point, all three terms increase with radial position and, therefore, energy.
- The new approach here is to make use of a quadrupole gradient and an edge angle on the CF magnet to enhance quadrupole, weak (or centripetal), and edge focusing as a function of radius and therefore momentum.
- The increase in strength tracks the increase in momentum and stabilizes the tune

Fermilab

leF

eF

F

D

leD

B>0, large

B=0

B <0

B >0

injection bend

liF

liD

iD

Injection reference orbit

eF

Contributions from the different terms in a wedge CF magnet – initial design- Contributions from the different strength terms vary with radial position in the two CF magnets:
- The optimal configuration and alignment for a linear edge is shown in the diagram showing half-cell optics and sector bends

Fermilab

Linear edge (wedge CF) Nonscaling FFAG

- With a linear edge, or a wedge-shaped CF (off-center quad) magnet lattice, the tune at two energies can be fixed:
- The nominal choice is of course injection and extraction.
- Constraint equations are set-up and solved
- Matematica is presently used to search the parameter space and find solutions first in the thin and then in the thick lens expansions

Fermilab

Implementation of a linear edge in a nonscaling FFAG

- A linear edge has been successfully implemented in a larger-radius, high-energy ring, <200 MeV/c – >1 Gev/c.
- Magnetic fields were modeled in both the cyclotron code, CYCLOPS, and in the general high-order field code, ZGOUBI
- Tracking has been performed on this machine in ZGOUBI and at individual energies in MAD
- Predicted tunes and performance were reasonably described by the thin and thick lens approaches

Fermilab

Initial tune calculations (Cyclops) and phase space tracking, @injection

Horizontal and Vertical Tune for 14 cells as a function of kinetic energy. ( Edge effects need to be reduced in vertical to increase stable momentum range.)

Horizontal

Vertical

Fermilab

*original author: R. Baartman

Recent modeling and design efforts with Zgoubi*

Design tune of tune-stabilized lattice using analytical approximation (approx) and MAD model (right) vs. lattice implementation in ZGOUBI (left, see references at end of talk)

*T. Yokoi, John Adams Institure, Oxford and British Accelerator Scicence and Radiation Oncology Consortium (BASROC)

Fermilab

Tracking Results with Zgoubi*

For horizontal motion, no significant beam blow up was observed for all sets of accelerating speed and positioning errors. However, for vertical motion, beam blow up was clearly observed at the point which corresponds to an integer resonance in the vertical ring tune.

*T. Yokoi, John Adams Institure, Oxford

Fermilab

Evidence for half-integer resonance extraction

The first integer resonance crossing blows up the beam, then is followed by a region which crosses the half integer resonance more slowly and the beam is slowly lost.

*T. Yokoi, John Adams Institure, Oxford

Fermilab

Results for More Compact Accelerator

- For a larger momentum range (>10) and a more compact aperture, the tune variations become more and more unstable near injection

Region of unstable tune centered @0.5 (over a 0.2 – 9 range in P). This “dip” remains where the field “flips” in the “D” CF magnet and was noted in the vertical tune of the larger-radius, high energy machine.

Fermilab

Simulation Results in TOSCA and COSY

- The region of unstable tune was verified in both the matematica model and the TOSCA field calculations
- Also noted were strong fringe-field effects in the vertical in the D CF magnet @injection using COSY. Both planes stable @extraction

Fermilab

“Variational” Method

- The next approach was to adjust the edge contour of the wedge magnets using a “variational approach” and adjust the edge angle to give a constant tune at each energy- bootstrapping from the previous energy
- For this study injection in the horizontally-defocusing CF was set to 0 field to avoid the field-flip tune issues and the fringe-field tune effects.
- Initial studies set parallel faces at injection.

Fermilab

Variational or bootstrap edge

Flat tune/half cell in both planes

Edge contour

Half length of magnets

Fermilab

Further work

- Variational approach successful, but magnet lengths reached too small a value at certain momenta values
- Next approach was a 2-ring which successfully constrained tunes in two momentum bands with a discrete gradient change between the two rings and a linear edge in both. The gradient change clearly avoided the unstable tune region.

Fermilab

Current Solution

- This two ring approach led to implementing both a gradient change and a varying edge contour combined to control the tune and the edge in a smooth way.
- Edge alignment was “revisited” and changed.
- Tunes are flat at the points

Fermilab

Conclusions

- Approximately an order of magnitude acceleration with stable tune can be achieved with a linear gradient and an edge contour.
- A stable tune has been achieved for more than an order of magnitude with both an edge contour and a gradient change
- Application to a 250 MeV proton therapy machine will be presented in the next talk

Fermilab

Summary of Nonscaling FFAG status and progress

- Simultaneous multiple sources and injection port
- Multiple extraction ports
- Slow or fast resonance or kicker based extraction
- resonance extraction has been demonstrated in simulations
- Variable energy to ~50% of extraction energy – no use of degraders
- Preliminary magnet designs
- CRADA established with Fermilab

Fermilab

FFAGs – General

- Over 30 scaling and nonscaling FFAGs are under design or construction. Applications include
- Accelerator Driven Subcritical Reactor
- Boron Neutron Capture Therapy
- Accelerator-based Neutron Source
- Emittance/Energy Recovery with Internal Target (ERIT)
- The first nonscaling FFAG prototype for rapid acceleration (EMMA) is being built at Daresbury Laboratory, U.K.
- A medical nonscaling FFAG accelerator (PAMELA) is under study in the U.K.

Fermilab

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