About the KEK-FFAG Workshop
11 - 13 October, 2000

Bruno Autin, CERN

Organizers

S. Machida, Y. Mori and T. Yokoi, KEK

Participants

M. Aiba, B. Autin, W. Chou, E. Forest, Fukumoto, A. Garren, J.Goto, Y. Iwashita, C. Johnstone, S.Kamada, K. Koba, M. Kumada, Y. Kuno, S. Machida, Ph. Meads, F. Mills, Y. Mori, M. Muto, K. Nakayama, D. Neuffer, K.Y. Ng, C. Ohmori, Y. Oku, A. Riche, Y. Sato, A. Schnase, H. Schonauer, Y. Shirakabe, M. Sugaya, N. Tagaki, D. Trbojevic, T. Uesegi, Y. Yamazaki, T. Yokoi, M. Yoshii, M. Yoshimoto, M. Yuasa

Perspectives

MURA studies (F. Mills).
FFAG developments (Ph Meads).
Neutrino Factory at Fermilab (D. Neuffer).
Neutrino Factory at CERN (A. Riche).

Scaling FFAG's

Optics design (S. Machida, E. Forest)

Similarity

Same deflection at all momenta.

Proportional magnet radius and beam radius.

Same betatron tunes at all momenta ⟹ Constant integrated focusing strength K l.

Definition of focusing:                            K l = l =

Basic relation between field, momentum and curvature radius:        p = e B ρ

Substitution ⟹ differential equation for field law:            =

Field law:                                B = with k =

Focusing strength at r = :                         K = =

Choice of k based on aperture criterion

Circumference ratio:                             =         
                                    
                                     = - 1

Methods

1. Approximate calculations around the average radius (SAD).
2. Closed orbits determined by numerical intgration in the field map provided by TOSCA.
3. Detailed particle tracking.

Limitations in the choice of k: pole saturation? non-linear dynamics?

KEK Proof Of Principle FFAG machine (Y. Sato, M. Yoshimoto, K. Koba)

Design parameters

Cell                                    Radial sector triplet
Superperiods                                8
k                                    2.5
Energy range                                50  -> 500 keV
Field in F-magnet                            0.14  -> 0.32 T
Field in D-magnet                            0.04  -> 0.13 T
Radius of closed orbits                            0.81  -> 1.14 m
                                    2.17  -> 2.22
                                    1.24  -> 1.26

Operation parameters

Energy range                    50  -> 500 keV                100  -> 1000 keV    

                         F        D            F              D

Field [T]                    0.14 -> 0.35     0.07 -> 0.14         0.2 -> 0.5     0.1 -> 0.2
Maximum Ampere-turns             4260        1900            6020        2690
Maximum current per coil [A]            243        190            344        269
Power per coil [W]                640        240            1280        470
Total power [kW]                10.2        7.6            20.5        15.0
Septum DC voltage [kV]                20                    40
Bumper voltage [kV]                    10                    20
RF frequency [MHz]                    0.61  -> 1.251                1.1  -> 1.97
Synchrotron frequency [kHz]                24.06  -> 16.78            
RF voltage [kV]                    1.3  -> 3                2  -> 6
Peak RF power [kW]                    27                    110
Beam life-time at 0.5 Torr [μs]            85
(limited by charge transfer process)

Experimental aspects

Tune measurements on injection orbit: good agreement with calculations in the horizontal plane for F/D ratios in the (3.4, 4.2) range. In the vertical plane the measured tune is systematically higher by ~ 0.05.

Simultaneous acceleration of two bunches:
RF voltage [V]                800
RF frequencies [kHz]            984, 1068
Synchronous phase []        20

150 MeV proton accelerator

Interest in medical applications (M. Kumada)

Field calculations (M. Aiba)

Main coil around F pole.
Trim coil around D pole.
Magnetic shunts at end faces.
TOSCA.

Field measurements (M. Sugaya)

Pion production, injection and extraction (T. Yokoi)

Pion production

Tungsten target. Proton energy: 50 GeV. Momentum range: 250 - 750 MeV/c. Transverse acceptance: 0.01m. Collection efficiency: 0.5 muon per pion.

Injection and extraction

Yoke free magnet: space for injection and ejection.
injection. Full aperture MA kicker: 500 Gauss. Septum: 1000 Gauss.
Variants: 2 kickers + 1 septum; 1 kicker + 2 septa.
Problem: edge focusing at exit from magnet.

RAL μ Bunch Rotation Ring (G. Rees)

Weak focusing combined function magnets (k < 1)
Proton energy (GeV)    15        μ kinetic energy (MeV)        200
μ bunch spacing (ns)    350                             1.1
Revolution time (ns)    350/9        h                    2
Number of turns    5         (MHz)                51.43
            1.36         (MV)                3
            1.1        Kicker rise or fall time (ns)        20
            0.05        Kicker pulses per cycle (1 + )    7

20 GeV Neutrino Factory based on FFAG rings (Y. Mori)

No phase rotation: immediate acceleration of muons. No cooling (for the time being).

Proton energy [GeV]                        50
Proton beam power [MW]                    1 -> 4
Longitudinal acceptance at capture [eV.s]            4.7
Transverse acceptance at capture [m]                
Muons per proton                        0.5
Stored muons per year                        3 -> 1.2
Momentum                    0.5 -> 1    1 -> 3        3 -> 10        10 -> 20
Superperiods                    16        32        32        128
k                        15        63        63        200
Average radius [m]                10        30        90        200
Number of turns                16        21        22        11
Field [T]                    2.8        3.6        4.2        6.3
Tune    h                    5.83        13.7        13.3        18.4
    v                    4.6        4.05        4.24        5.3
Drift length [m]                2.12        3.3        10.05        6.7
Orbit excursion [m]                0.71        0.52        1.55        0.69
                        4        8        8        14

Non scaling FFAG's

Common trend: reduce orbit excursions to less than 10 cm for energy multiplication of the order of 4.
Eliminate the constraint of constant focusing on all orbits.

Combined function sector magnet (A. Garren)

Scaling laws

Same deflection on any orbit.
B = (1 - r).
= -

Machine under study

Energy range [GeV]                16 -> 64
-n                        707
Circumference [m]                1356
Number of turns                30
Superperiods                    4
Number of cells per superperiod        16
Number of insertions per superperiod        4
Insertion length [m]                29.3
Tunes    h                    112.81
    v                    25.9
Orbit excursion     [cm]                (-3.6, 1.8)
RF field [MV/m]                15

Synchronizing bunches with RF using wigglers

Dispersion suppressors

Matching to a "zero" (r < 1 cm) dispersion region with combined function triplets and a pair of bending magnets.

Comparison of RLA's and FFAG's (C. Johnstone)

3-11 GeV RLA

Shape                        Race-track
Linac length [m]                2*200
Path length in RLA [km]            4
Acceleration per turn [GeV]            2
dE/ds [MeV/m]                2
Number of arcs all in the horizontal plane    2*4
Transverse acceptance    [m]            1.1
Central momentum [GeV/c]            4        6        8        10
Momentum spread [%] at 3 σ            ±5.1        ±4.2        ±3.8        ±3.5
Beam size [cm] at 3 σ                ±5.5        ±4.8        ±4.4        ±4.1
Transmission                    0.952        

3-11 GeV FFAG

The idea is to remove the transverse acceptance bottleneck that occurs in the RLA.

Cell                        F, ss, B+D, ss
Magnet design                    H-type with Nb-Ti S.C. coils
-------------------------------------------------------------------------------------------
Magnet type                    F        D
Horizontal aperture [cm]            ±15        ±10
Vertical aperture [cm]                ±4.5        ±6
Pole tip field [T]                4        3.91
-------------------------------------------------------------------------------------------
Central momentum [GeV/c]            9
RF field [MV/m]                1
Acceleration per cell [MeV]            2        3
Cell length [m]                    4.44        5.31
Number of cells                175        209
Number of turns                22.9        12.8
Path length [km]                17.8        14.1
dE/ds [MeV/m]                0.45        0.561
Transmission                    0.837        0.862

What does the entire scheme become if the RLA is replaced by the FFAG?

Green-Chasman lattice (D. Trbojevic)

Ultimate reduction in orbit excursion: 5 cm.

Developments

RF control for MA cavities (A. Schnase)

Integrated SC RF cavity and magnet (Y. Iwashita)

1 kHz kickers (Shirakabe)

Thyratrons replaced by arrays of Insulated Gate Bipolar Transistors (IGBT).
Field [T]            0.1
Rise time (ns)            250
Flat top duration [ns]        200
Field flatness [%]        2.5
Voltage [kV]            35
Intensity [A]            750 -> 1000
Impedance [Ω]            25

KEK - Fermilab development of high field low frequency cavities (W. Chou)

1. 30 kV/m, 7.5 MHz, 50 % duty cycle wide band proton acceleration.
2. 1 MV/m, 7.5 MHz, burst mode operation.

Space charge effects on bunch rotation (K. Y. Ng)

Bow-tie ring (A. Garren)

Lattice. Bypass for a third target. Comparison with triangle.

Distributed cooling (H. Schonauer)

The cooling material can be distributed over a long distance if the β value can be maintained below 2 m. The windows could be suppressed and helium under 1 or 2 bar pressure be used. The idea could be applied to the first FFAG.

1 GeV Synchrotron light sources (Y. Yuasa)

Final remarks

ALL MUON ACCELERATORS ARE FFAG'S !!!

About Linacs and Recirculating Linear Accelerators

Linacs

Fastest acceleration.
Useless at high energy.
Aperture limitations.
Very costly.
Application at low energy.

RLA's

Fast acceleration and good transmission.
Aperture limitations.
Small longitudinal acceptance.
Still too costly.
Comparison with circular machines is open.

About Circular Machines

How to reduce the cost of muon accelerators?

For a given energy gain:
    Increase the number of turns,
    Reduce the RF investment in proportion,
    Accept a tolerable transmission loss.

Can circular machines meet the challenge?

Advantages

Large 6D acceptance: ~ 1 cm in both transverse planes, several eV.s in longitudinal plane.

Broad approach to lattice design:
    Weak focusing (G. Rees, RAL),
    Scaling FFAG's (Y. Mori et al. in Japan),
    Alternating combined function sector magnets (A. Garren, UCLA),
    Low dispersion FODO cells (C. Johnstone and D. Neuffer, FNAL),
    Very strong focusing (D. Trbojevic, BNL).
    CERN will contribute.
    
Ongoing developments:
    Test machine: POP,
    150 MeV scaling FFAG (medical application and, later on, PRISM),
    Low frequency and high field RF cavities,
    High repetition rate kickers.
    
Possible compatibility with machines of the proton driver.

Criteria to be satisfied

Full longitudinal and transverse tracking.

Sufficient transmission.

Magnet and RF cavity design.

Injection and extraction.
    
Competitive cost.