Dr. C. Johnstone, Fermilab
FFAG13
13th International Workshop on
FFAGs
TRIUMF
Sept 23 2013
Vancouver, Canada

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


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.

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
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.
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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.
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


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.

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-ofplane 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.

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
Advanced design and simulation of an
Isochronous 250-1000 MeV Nonscaling FFAG
2m
v
DRad
3.0
0.07
2.5
0.06
cA
5.0
4.5
C
4.0
3.5
cD
E
F
3.0
2.5
cC
B
cE
D
G
cF H
cG
cH
0.5 1.0 1.5 2.0 2.5 3.0 3.5
0.05
2.0
cB
A
A 1. ,4.88616
B 2.674 ,4.20703
C 3.03267 ,3.85867
D 3.43662 ,3.43662
E 1. ,3.2672
F 2.00856 ,2.8764
G 2.2306 ,2.67393
H 2.45023 ,2.45023
0.04
1.5
0.03
0.02
1.0
0.01
cA 1. ,5.37477
cB 3.25798 ,5.37477
cC 3.31087 ,4.2696
cD 3.79024 ,3.79024
cE 1. ,2.58876
cF 1.86471 ,2.58876
cG 2.03113 ,2.37929
cH 2.20521 ,2.20521
P, MeV c
800
1000
1200
1400
Cell  x / y (2 rad)
Ring.
Field F/D (T)
Magnet Size F/D Inj
250 MeV
3.419
0.380/0.237
1.520/0.948
1.62/-0.14
1.17/0.38
1000
1200
1400
1600
Ravg
5.0
General Parameters of an initial 0. 250 – 1 GeV non-scaling, nearisochronous FFAG lattice design
Parameter
Avg. Radius (m)
P, MeV c
1600
585 MeV
4.307
1000 MeV
5.030
0.400/0.149
1.600/0.596
0.383/0.242
1.532/0.968
2.06/-0.31
2.35/-0.42
1.59/0.79
1.94/1.14
4.5
4.0
P , MeV c
1000
1200
1400
1600
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
P ar ti cl e A ccel erat or
C or por at ion

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).

B field with Enge function fall
off

tune per cell (radial, horizontal)

tune/cell (z, vertical)

frequency change, isochronous
to +/- 3% using simple hardedge model: progress will
require the advanced codes;
agrees with COSY results
The FACT FFAG GUI program provides a graphical front end to the COSYFACT 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 detailed 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.

“Software as a service” distribution model

Accelerator design management
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Field grid export
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Automated iterative closed orbit fitting for given energy
High order map computation (currently capped at order 15)
Symplectic particle 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

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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
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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
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

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).

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.
Import a previously exported accelerator design or
field map into this system.

Information about the currently selected accelerator
design.
The information dialog is used to view the information
associated with an existing accelerator in the system.

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.

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.

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.


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
•
•
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