Lattice Design for PRISM-FFAG Akira Sato Osaka University 4th Aug. 2004 : NP04 at Tokai
Lattice Design for PRISM-FFAG
Akira SatoOsaka University
4th Aug. 2004 : NP04 at Tokai
contents
• PRISM overview
• PRISM-FFAG dynamics study
• method
• acceptance
• current parameters
• summary
PRISMPhase Rotated Intense Slow Muon source
muon intensity 1011-1012μ/sec
kinetic energy 20MeV
energy spread +-(0.5-1.0)MeV
beam repetition 100-1000Hz
pion contamination < 10^-18
Anticipated PRISM beam design characteristics
high intensity muon beamnarrow energy-spread high purity
dedicated for the stopped muon experiments
LFV : mu-e conversion sensitivity of 10-18
PRISM LayoutPion capture sectionThe highest beam intensity in the world could be achieved by large-solid angle capture of pions at their production. Decay sectionπ − μ decay section consisting of a 10-m long superconducting solenoid magnet.Phase rotatorto make the beam energy spread narrower. To achieve phase rotation, a fixed-field alternating gradient synchrotron (FFAG) is considered to be used.
FFAG advantages:synchrotron oscillation
need to do phase rotationlarge momentum acceptance
necessary to accept large momentum distribution at the beginning to do phase rotation
large transverse acceptance muon beam is broad in space
Construction of the PRISM-FFAG
Among the all PRISM components, the phase rotator section can be constructed from japanese fiscal year (JFY) of 2003 for five years.
FY2003Lattice design, Magnet designRF R&D
FY2004RFx1gap construction & testMagnetx1 construction & field meas.
FY2005RF tuningMagnetx9 constructionFFAG-ring construction
FY2006Commissioning Phase rotation
FY2007Muon acceleration(Ionization cooling)
5m
RF PS
RF AMP RF Cavity
FFAG-Magnet
Kicker Magnet
for Injection
Optics Design for PRISM-FFAG
Large Transverse Acceptance horizontal > 20000 pi mm mrad
vertical > 3000 pi mm mrad
Long Straight section
to install RF cavities
Requirements
magnets : large aperture and small opening angle.non-linear effect and magnetic fringing fields are important to study the beam dynamics of FFAGs.
toward the high intensity and narrow energy spread muon beam
conventional method
Dr. thesis of M.YoshimotoPoP-FFAG(KEK)
TOSCA is the best. but takes much time.
New method to study dynamics
to study :acceptance (H,V)tunetune shiftbeam size etc
parameters :number of cellFD,DFD,FDFk valueF/D ratiogap size
quasi-realistic magnetic field
3D tracking by geant3.21
can model realistic fringing field
How to make quasi-realistic 3D magnetic fieldsstep 1 : calculate magnetic field (Bx(~Bθ),Bz) of each z-θcross sections (r1-r5). x-axis is considered as θ-axis (approximation).
step 2 : convert the field (Bθ,Bz) to (Bz,Bθ,Br) by using Maxwell eq.
€
Bz(zi) = By (zi)Bθ (zi) = Bx (zi)
Br(zi) =dBz
dr
(Z i )
(Zi − Zi−1) + Br(Zi−1)
step 3 : to make a fine mesh field map, apply a 2D spline interpolation to the above field map.
r1
r2
r3
r4
r5
r
x(θ) z
F magnetD magnet D magnetfieldclump
fieldclump
MAGNET CYCLE = 3420
FD D
z
x(θ) r
Comparison (field map)TOSCA quasi-realistic
-2000
0
2000
4000
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Bz(gauss)
-4000
-2000
0
2000
4000
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Bt(gauss)
0
200
400
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Br(gauss)
-2000
0
2000
4000
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Bz(gauss)
-4000
-2000
0
2000
4000
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Bt(gauss)
0
200
400
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Br(gauss)
TOSCA quasi-realistic
TOSCA quasi-realistic
TOSCA quasi-realistic
> 8 hours several min.!
Comparison (tracking results)
N=8k=5
F/D = 7.1r0=5m
TOSCA quasi-realistic
Acceptance StudyDFD, N=10, half gap=17cm, w/o field clamps, r0=6.5m for 68MeV/c
Horizontal phase spaces are plotted in a tune diagram.
Vertical phase spaces are plotted in a tune diagram.
Acceptance dependence on gap size of magnets
DFD, N=10, w/o field clamps, r0=6.5m for 68MeV/c
5cm 10cm 15cm 20cm
Tracking resultsDFD, N=10, F/D=6, k=4.6,
half gap=17cm, r0=6.5m
horizontal vertical
35000πmm mrad
An effective horizontal acceptance is 35000 pi mm mrad in consideration of correlation between horizontal and vertical acceptance
150000πmm mrad 4000πmm mrad
Parameters of PRISM-FFAG
5mRF PS
RF AMP
RF Cavity
FFAG-Magnet
Kicker Magnet for Extraction
Kicker Magnet for Injection
Figure 4: Beam trajectories in horizontal (left) and vertical (right) phase space are plotted on tune diagrams. The area
of each plot indicates the acceptance. In this study the other emittance was set to zero. Therefore correlation between
horizontal and vertical dynamic cannot be seen. Figures beside each plots means F/D ratio in current setting (in BL
integration).
-2000
0
2000
4000
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Bz(gauss)
-4000
-2000
0
2000
4000
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Bt(gauss)
0
200
400
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Br(gauss)
-2000
0
2000
4000
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Bz(gauss)
-4000
-2000
0
2000
4000
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Bt(gauss)
0
200
400
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35
z=0(cm)
z=3(cm)
z=6(cm)
z=9(cm)
z=12(cm)
theta(deg)
Br(gauss)
TOSCA quasi-realistic
TOSCA quasi-realistic
TOSCA quasi-realistic
Figure 3: Comparison between a TOSCA field and a quasi-
realistic field. Bz , Bθ and Br are plotted as a function of
θ.
BEAM DYNAMICS STUDY
In order to search the best optics parameter set for
PRISM-FFAG, the beam dynamics was studied by per-
forming beam tracking using the quasi-realistic field maps.
A tracking program based on GEANT3.21 [5] was used for
particle tracking. Parameters to be studied are:
• Number of sectors,• Combination of magnets: DFD, FDF, FD• Field index (k value)• Ratio of the magnitude of focusing field to that of de-focusing field: (F/D ratio)
Table 1: Present parameters of PRISM-FFAG
Number of sectors 10
Magnet type Radial sector
DFD triplet
Field index (k-value) 4.6
F/D ratio 6.2
Opening angle of magnets F/2 : 2.2deg.
D : 2.2deg.
Half gap of magnets 17cm
Maximum field Focus. : 0.4 Tesla
Defocus. : 0.065 Tesla
Average radius 6.5m for 68MeV/cTune horizontal : 2.73
vertical : 1.58
• Gap size of magnets
Figure 4-(left) and 4-(right) show an example of the
acceptance study of horizontal and vertical respectively.
Beam trajectories in a phase space are plotted on tune dia-
grams. The area of each plot indicates the acceptance.
Taking resonance lines and the transition energy into ac-
count, parameters were selected to be the beam acceptance
as large as possible. Present parameters of PRISM-FFAG
are shown in Table 1.
Figure 5 shows the phase space and the dependence
of tune on the amplitude for horizontal (left) and vertical
(right) respectively using the parameters shown in Table 1.
The initial emittance in the other plane is set to zero. It
is found that the PRISM-FFAG of the present design has a
dynamic aperture of more than about 140,000 πmm·mradin the horizontal plane and about 3,000 πmm·mrad in thevertical in 5 turns. The correlation between horizontal and
Summary
• Beam dynamics were studied and optics design were performed for PRISM-FFAG by new method using quasi-realistic fields.
• This method enables quick iterations in search of the optics parameters such as tune compared with that of using TOSCA fields. That can be used widely to study and design FFAGs with a complex magnetic field. PRISM-II, NuFact-FFAG ...
• The current design has a very large acceptance of 35000 pi mm mrad in horizontal plane. But we still have some items to be studied to finalize the design.
Study items• 6D acceptance with phase rotation.
• zero chromaticity
• gap size optimization
• injection & extraction
• ...