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Muon acceleration by RLA with the non-scaling FFAG. Dejan Trbojevic. RLA for Muons. Introduction: Present design of the muon RLA’s Problems: Matching of the circular non-scaling FFAG to the straight linac. Time of flight adjustments for each pass. Goals :

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slide1

Muon acceleration by RLA

with the non-scaling FFAG

Dejan Trbojevic

rla for muons
RLA for Muons
  • Introduction:
    • Present design of the muon RLA’s
  • Problems:
    • Matching of the circular non-scaling FFAG to the straight linac.
    • Time of flight adjustments for each pass.
  • Goals:
    • Use the permanent magnets for the arcs – Halbach magnets.
    • Try to make four or five times in muon energy by either a race track or dog-bone acceleration with a single arc (2.5-10 GeV or -60%< δp/p< +60%).
    • Match the betatron and dispersion functions from the arc to the linac.
    • Design a chicane to adjust the time of flight for different energy passes.

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

racetrack vs dogbone rla both m and m species
‘Racetrack’ vs ‘Dogbone’ RLA (both m+ and m- species )

m+

m-

m-

m+

m+

m-

m-

m-

m-

m+

m+

m+

m+

m-

m-

m+

DE/2

From Alex Bogacz presentation at the previous LEMC:

  • better orbit separation at linac’s end ~ energy difference between consecutive passes (2DE)
  • allows both charges to traverse the Linac in the same direction (more uniform focusing profile
  • the droplets can be reduced in size according to the required energy
  • both charge signs can be made to follow a Figure-8 path (suppression of depolarization effects) Chuck Ankenbrandt

DE

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

fodo vs triplet focusing flat focusing linac profile
FODO vs Triplet focusing - ‘flat focusing' linac profile*

Bob Palmer*

From Alex Bogacz presentation at the previous LEMC:

Triplet

1-pass, 3-5 GeV

256.82 meters

phase adv. drops much faster in the horizontal plane

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

the linac betatron function dependence on energy
The linac – Betatron Function dependence on energy

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide6

Multipass Linac - racetrack FFAG

Chicane

20 Cavities

Chicane

Non-scaling FFAG arc

Non-scaling FFAG arc

Chicane

Chicane

20 Cavities

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide7

Muon Collider Review Meeting At BNL 2001

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide8

Design of the arcs with Halbach magnets

FODO cells for the 2.5 -> 10 GeV muons

N=170 cells

L=1.606 m

LBD=0.73 m

LQF=0.52 m

For the:

dp/p=+-60%

BBD=2.5 T

GF=40.0 T/m

GD=-50.0 T/m

r=43.42 m

86.85 m

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

arc cell with halbach magnets
Arc cell with Halbach magnets

0.1675 m

xmax=65.8 mm

xmin= -35.1 mm

0.73/2 m

1.606 m

FODO cell for the dp/p=+-60 % -> 2.5 - 10 GeV

0.1675 m

52 mm

0.73/2 m

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

arc cell with halbach magnets1
Arc cell with Halbach magnets

0.1675 m

xmax=52.9 mm

xmin= -12.8 mm

0.73 m

1.606 m

FODO cell for the dp/p=+-60 % -> 2.5 - 10 GeV

0.1675 m

52/2 mm

0.52/2 m

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

arc cells for two different lattices
Arc cells for two different lattices

FODO cell for the dp/p=+-60 % -> 2.5 - 10 GeV

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide13

A total difference in the path length -

10 GeV and the minimum of the parabola

is Dl=0.2465 m

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

halbach permanent magnet
Halbach permanent magnet
  • But in reality it would be limited by:
  • The realistic size
  • The demagnetization effect
slide15

Permanent Magnet for the BNL additional triplets

(K. Halbach)

Material: NdFeBn5563

Br = 15000 G

Hc = -13000 Oe

(www.mceproducts.com)

Y (cm)

Field Quality @ R=6 cm

b2 = 10248.0 Gauss (17 T/m)

b6 = 44.3 Gauss (4.3E-3)

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

X (cm)

halbach permanent magnets available material
Halbach permanent magnets: available material

No-Fe-B Type Rare Earth Magnets:

halbach permanent magnets pictures from the original publication
Halbach permanent magnets – pictures from the original publication:

Bg= Br ln(OD/ID)

OD=85 cm

ID =14 cm

ln(OD/ID)=1.8

Bg=2.7 T

Br=1.5 T

QLD = 52 cm

BL = 16.75 cm

QLF = 73 cm

GF = 2.7 T/0.068 m = 40 T/m

GD= -2.7 T/0.054 m=-50 T/m

14 cm

85 cm

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

halbach permanent magnets
Halbach permanent magnets

35 cm

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

matching cell geometrical constraint arc to linac
Matching cell – geometrical constraint - arc to linac

The matching cell length

is: L=3 * 1.605 m = 4.815 m

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

ieee transactions on nuclear science vol ns 30 no 4 august 1983
IEEE Transactions on Nuclear Science, Vol. NS-30, No. 4, August 1983

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide21

Yoshiharu Mori – Fermilab FFAG workshop:

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide22

Yoshiharu Mori – Fermilab FFAG workshop:

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide23

Yoshiharu Mori – Fermilab FFAG workshop:

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide24

Yoshiharu Mori – Fermilab FFAG workshop:

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide25

Shinji Machida – Fermilab FFAG workshop

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

new matching cell
New matching cell

Input parameters are:

xmaxand xminfrom the arc NS-FFAG

pmax, po, and pmin, Dx, bx, by,

Unknowns: BD, BF, Ffo, Fdo , andlo

rfmax

ffo

rfo

amax

fdo

amin

rfmin

lo

ffo

fdo

umax

rdmin

xmax

umin

fdo

rdo

xmin

fdo

rdmax

To be matched to the input

parameters of the linac: bx, by, ax,ay

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

matching cell @ zero dispersion end
Matching Cell - @ zero dispersion end

amax

amin

lo

rdmin

fdmin

umax

rdo

umin

fdo

rdmax

fdmax

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

matching cell @ entrance
Matching Cell @ entrance

w

Ffmax

rfmax

j

rfmax

Ffo

amax

amin

Ffo- Ffmax

rfo

Ffo- Ffmax= Fdo- Fdmax

Ffmin

lo

Ffmin- Ffo

rfmin

Ffmin- Ffo= Fdmin- Fdo

umax

pmin

umin

xmax

umax=amax+lo tan(Ffo-Ffmax)

po

xmin

umin=amin+lo tan(Ffmin-Ffo)

pmax

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

mike craddock s approach
Mike Craddock’s approach:

D/2

rfmax

xd+=0

ffo

rfo

Xd+

xd-=0

fdo

Xd-

rfmin

lo

ffo

fdo

umax

rdmin

xfp+

umin

fdo

high p+

rdo

xfp-

fdo

po

rdmax

F/2

low p-

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

matching to linac zero dispersion for each momentum
Matching to linac -> zero dispersion for each momentum

Orbit offsets

by

bx

Dispersion

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

matching to linac zero dispersion for each momentum1
Matching to linac -> zero dispersion for each momentum

10 GeV

2.5 GeV

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

p p cent orbits matched to linac zero dispersion for each momentum
p>pcent orbits matched to linac -> zero dispersion for each momentum

p=pmax

p=pcent

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

matching cell to the non scaling ffag arcs
Matching cell to the non-scaling FFAG arcs

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

matching cell to the non scaling ffag arcs1
Matching cell to the non-scaling FFAG arcs

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide35

Non scaling FFA arcs with matching cells without linac

Orbits from 2.5 – 10 GeV

through the matching cells and arcs:

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide36

Non scaling FFA arcs with matching cells without linac

Betatron Functions from 2.5 – 10 GeV

through the matching cells and arcs:

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide37

Non scaling FFA arcs with matching cells without linac

Dispersion from 2.5 – 10 GeV

through the matching cells and arcs:

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide38

Matching cell with linac – arc to linac

Orbits magnified 100 times

From 2.5 GeV- 10GeV

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide39

Multipass Linac with combined function triplets

Details of the orbits with

Chicanes:

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide40

-2q

L

q

Lo

Details of the chicane calculations:

Lo /L=cos q

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide41

Details of the Chicane

CAVITY

TRIPLET

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide42

Summary:

  • A combination of the non-scaling FFAG with linac is possible.
  • Time of flight adjustments is necessary –maximum of 0.493 m delay.
  • The simulation of acceleration can be set-up by the PTC (Polymorphic Tracking Code).
  • Thanks to Muon Inc. for the support

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide43

Shinji Machida – Fermilab FFAG workshop

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide44

Shinji Machida – Fermilab FFAG workshop

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide45

Yoshiharu Mori – Fermilab FFAG workshop:

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009

slide47

Yoshiharu Mori – Fermilab FFAG workshop:

Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009