Advanced FFAG and Cyclotron Design and Modeling Software using COSY infinity

1. Advanced FFAG and Cyclotron Design and Modeling Software using COSY infinity Dr. C. Johnstone, Fermilab FFAG13 13th International Workshop on FFAGs TRIUMF Sept 23 2013 Vancouver, Canada

2. Recent Advances in Lattice Design and Optimization • A powerful new methodology has been pioneered for all fixed-field accelerator optics design (FFAGs and cyclotrons) using control theory and optimizers to develop executable design scripts. These procedures allowed global exploration of all important machine parameters in a simplified lattice. • WITH THIS METHODOLOGY, the stable machine tune for FFAGs, for example, was expanded over an acceleration range of 3 up to 6 in momentum with linear fields and up to 44 with nonlinear fields and this included optimization of complex edge contours, footprint, and magnetic components. • Full evaluation of the simple starting lattice, however, required new advanced simulation tools not existing in most accelerator codes. Such tools have been developed by P.A.C. and implemented as an add-on (FACT)to COSY INFINITY. The FACT (FFAG And Cyclotron Tools) fully develop and expand the complex field and edge profiles to accurately predict and optimize machine performance. An accurate 3D field expansion in polar coordinates is one of the output formats which can be used by other codes. • Starting points from the design scripts are directly imported into and modeled in COSY INFINITY using FACT software. • This starting input format is simple and can be used by other design approaches

3. Description of New Tools in COSY INFINITY for Fixed-field Accelerators • Modern extensions of the transfer map-based philosophy as implemented in the arbitrary order code COSY INFINITY remedy the limitations in order and in the accuracy of the dynamics. • However, standard configurations based on pre-selected field elements like combined function magnets with edge angles, are not sufficient to describe in full detail the richness of the nonlinearities that can arise in the fields. • New tools which accurately describe complex fixed fields and edge configurations have been developed and tested in COSY INFINITY • Equally important is the ability to perform extended design optimization, and move away from the current standard of local optimization based on starting conditions that are carefully chosen by educated guesses of the designer, and manually adjusted should the resulting local optimization fail. • Recent significant advances in global optimization as illustrated by the various different directions of cutting edge research including genetic optimization, domain and conquer approaches, and verified methods have led to a state of the art in optimization that need to be tapped into in order to simplify and improve the design and optimization procedures. • This and incorporation of a modern user interface to facilitate use of the code is in progress.

4. 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

5. 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.

6. Example of dynamics studies of fixed-field accelerators using new tools in COSY • Below is a sample FFAG having sixfold symmetry, with focusing stemming from an azimuthal field variation expressed as a single Fourier mode as well as edge focusing. The system is studied to various orders of out-of-plane expansion with the results for orders three and five shown below (typical of a conventional out-of-plane expansion in codes like Cyclops). Tracking in a model non-scaling six-fold symmetric FFAG for horizontal (left pairs) and vertical (right, pairs) with 3rd (top), 5th(middle), and 11th-order (bottom) out of plane expansion, with focusing from an azimuthal field variation expressed as a single Fourier mode as well as edge focusing . With (left) and without (right) Expo symplectification is shown.

7. Step-by-step design of FFAGs and Cyclotrons: more details • For a starting design, equations of motion (without the angle or kinematical term in the Hamiltonian) are solved in terms of variables which describe the fields and physical parameters of the magnetic components; • Physical and technical requirements are automated directly into this initial design search and optimization such as field strength or footprint limits, component lengths, edge contours, and inter-magnet straights. • The output of the design parameter search is imported directly into COSY INFINITY for dynamics, and final optimization about this initial design point • COSY INFINITY also generates a realistic field map (with contours and end fields) in polar coordinates from the initial design specifications which can be imported into field-tracking codes such as CYCLOPS and ZGOUBI

8. Advanced design and simulation of anIsochronous 250-1000 MeVNonscaling FFAG 2m General Parameters of an initial 0. 250 – 1 GeV non-scaling, near-isochronous FFAG lattice design Clockwise: Matematica: Ring tune, deviation from isochronous orbit (%), and radius vs. momentum • Comments and further work • Tracking results indicate ~50-100 mm-mr; relatively insensitive to errors • Low losses

9. Field Map and Tracking: 250-1000 MeV Proton Driver • Immediate large DA aperture: • 0.1-1% error tolerance –typical magnet tolerances • Final isochronous optimization can be performed using advanced optimizers in COSY Dynamic aperture at 250, 585, and1000 MeV – step size is 1.5 cm in the horizontal (left) and 1 mm in the vertical (right).

10. 1-GeV Proton Driver Modeled in CYCLOPS: fine mesh and fringe fields (Yi-N. Raoand M. Craddock, TRIUMF) • B field with Enge function fall off • tune per cell (radial, horizontal) • tune/cell (z, vertical) • frequency change, isochronous to +/- 3% using simple hard-edge model: progress will require the advanced codes; agrees with COSY results

11. FACT Overview • The FACT FFAG GUI program provides a graphical front end to the COSY- FACT tool developed by Particle Accelerator Corporation (PAC) and COSY INFINITY developed by the Beam Theory and Dynamical Systems Group at Michigan State University (MSU). Specically, it currently allows the analysis of two types of accelerator specications, Fourier Gauss and Enge Edge, via de- tailed high-order particle tracking as well as eld data export and visualization. • Any computations, along with all relevant source code and accelerator design specications, are performed on a remote server provided and maintained by PAC. The FACT FFAG GUI uses Oracle JavaWebStart technology to download and run the COSY JavaGUI program that is capable of displaying the GUI to the user and communicating her response to the server using industry standard encrypted SSH channels. • The FACT FFAG GUI is powered by the COSYFACT tool box developed by PAC for the simulation of a variety of FFAG type accelerators. COSYFACT and the FACT FFAG GUI are built on top of the well known COSY INFINITY scientic computation environment, consisting of COSY INFINITY, the COSY INFINITY beam physics package, and the COSY JavaGUI, all developed and licensed by MSU.

12. FACT Implementation “Software as a service” distribution model

13. FACT CAPABILITIES • Accelerator design management • Unlimited number of accelerator designs • Fourier Gauss (FG) and Enge Edge (EE) type accelerator descriptions • Graphical magnet layout representation (EE) • Fringe field (EE) and field smoothing (FG) user settings • Field grid export • Flexible le format specification for easy field export into other tools • Automatic field plotting for quick quality assurance • Powerful particle tracking at a single energy level • Automated iterative closed orbit fitting for given energy • High order map computation (currently capped at order 15) • Symplecticparticle tracking • Customizable tracking pictures generated for x-a and y-b motion • Optional normalized emittance scaling • Batch particle tracking at up to 50 energies in one run • Sequential symplectic particle tracking at various energies • Orbit overview of all tracked orbits • Center tune over energy plot • PDF output of results, ready to be included in reports or papers • Built in locking mechanism to prevent accidental concurrent use by several remote users

14. The Main Interface • After successful login, the main interface of the FACT FFAG GUI comes up: Figure 6: FACT FFAG GUI main window. • The top half of the FACT FFAG GUI main window shows a list of all currently available accelerators in the system. Each accelerator is listed with its name, type (FG or EE) and the accelerated particle (p, e, or H).

15. Accelerator Design Management Add a new accelerator design into the system. • The add new accelerator design dialog is used to upload a new accelerator design into the system.

16. Import Accelerator Design Import a previously exported accelerator design or field map into this system.

17. Accelerator Information Information about the currently selected accelerator design. • The information dialog is used to view the information associated with an existing accelerator in the system.

18. Field Export Field export dialog. • The field export dialog is used to export mid-plane field grid data and to visualize the resulting field profile. The field data is exported as concentric circles at different, equally spaced radii, each with a fixed number of azimuthal data points.

19. Single Energy Tracking Single energy tracking main dialog. • The single energy tracking dialog is used to track particles at a single specified energy through an accelerator system. It is most suitable for quick interactive exploration of the stability properties of a new accelerator system.

20. Batch Tracking Batch tracking dialog with orbits for various energies. • The batch tracking dialog is used to track particles at a various user specified energies through an accelerator system. It is most suitable for a detailed analysis of the stability properties of an accelerator.

21. Tunes in a relativistic ultracompact cyclotron • Below are three tunes predicted for an ultracompact relativistic 250 MeV cyclotron. • Note that the analytical formula and COSY and ZGOUBI agree for horizontal but not at high energy/high spiral angles in the vertical which goes unstable in the more accurate model Predicted tune from an ultracompact medical cyclotron(left) and ZGOUBI (middle) and COSY (right). Predicted problems are marked with red arrows

22. Summary • New tools have been developed for complex FFAG fields and edge contours • High order maps are generated from: • Complex field and edge contours using the Enge function for sector FFAGs • Field maps for spiral sector, AVF cyclotrons and FFAGs which are first expressed in Fourier Gauss expansions • Closed orbits, tracking and optics are generated to arbitrary order in the dynamics • These tools can also be used to modify/optimize the optics, lattice and generate field maps for iterative magnet design • Powerful GUI interfaces have been implemented such that only the simple interface is downloaded to user computers • Software maintenance and code support and updates then are automatic and not the responsibility of the users