Dejan Trbojevic
description
Transcript of Dejan Trbojevic
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Dejan Trbojevic
Muon acceleration by RLA with the non-scaling FFAG
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RLA for MuonsIntroduction:
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
3Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
‘Racetrack’ vs ‘Dogbone’ RLA (both m+ and m- species )
m+
DE/2
m+m-
m-
m-
m+
m-
m+
m-
m+
m+ m-m+ m-
m+ m-
DE
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 profilethe droplets can be reduced in size according to the required energyboth charge signs can be made to follow a Figure-8 path (suppression of depolarization effects) Chuck Ankenbrandt
From Alex Bogacz presentation at the previous LEMC:
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1-pass, 3-5 GeV phase adv. drops much faster in the horizontal plane
256.820
Mon Aug 28 23:36:36 2006 OptiM - MAIN: - D:\RLA explore\Dogbone_Triplet\flat\Linac1.opt
0.5
0P
HA
SE
_X&
Y
Q_X Q_Y
256.820
Mon Aug 28 23:35:11 2006 OptiM - MAIN: - D:\RLA explore\Dogbone_Triplet\flat\Linac1.opt
600
50
BE
TA_X
&Y
[m]
DIS
P_X
&Y
[m]
BETA_X BETA_Y DISP_X DISP_Y
Triplet
FODO vs Triplet focusing - ‘flat focusing' linac profile*Bob Palmer*
From Alex Bogacz presentation at the previous LEMC:
256.82 meters
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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The linac – Betatron Function dependence on energy
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Multipass Linac - racetrack FFAG
Chicane
Chicane
Chicane Chicane
Non-scaling FFAG arc
20 Cavities
20 Cavities
Non-scaling FFAG arc
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Muon Collider Review Meeting At BNL 2001
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Design of the arcs with Halbach magnetsFODO cells for the 2.5 -> 10 GeV muons
N=170 cellsL=1.606 mLBD=0.73 mLQF=0.52 m
For the: dp/p=+-60%BBD=2.5 TGF=40.0 T/mGD=-50.0 T/m
r=43.42 m
86.8
5 m
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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x max=65.8 mm
x min= -35.1 mm
1.606 m
0.73/2 m
0.1675 m
FODO cell for the dp/p=+-60 % -> 2.5 - 10 GeV
Arc cell with Halbach magnets
52 mm
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
0.73/2 m
0.1675 m
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x max=52.9 mm
x min= -12.8 mm
1.606 m
0.73 m
0.1675 m
FODO cell for the dp/p=+-60 % -> 2.5 - 10 GeV
Arc cell with Halbach magnets
52/2 mm
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
0.52/2 m
0.1675 m
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FODO cell for the dp/p=+-60 % -> 2.5 - 10 GeV
Arc cells for two different lattices
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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13Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
A total difference in the path length - 10 GeV and the minimum of the parabolais Dl=0.2465 m
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Halbach permanent magnet
But in reality it would be limited by: (1)The realistic size (2)The demagnetization effect
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Material: NdFeB n5563
Br = 15000 GHc = -13000 Oe
(www.mceproducts.com)
Permanent Magnet for the BNL additional triplets
(K. Halbach)Y (cm)
X (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
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Halbach permanent magnets: available material
No-Fe-B Type Rare Earth Magnets:
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Halbach permanent magnets – pictures from the original publication:
QLD = 52 cmBL = 16.75 cmQLF = 73 cmGF = 2.7 T/0.068 m = 40 T/mGD= -2.7 T/0.054 m=-50 T/m
14 cm
85 cm
Bg= Br ln(OD/ID)
Br=1.5 T OD=85 cmID =14 cmln(OD/ID)=1.8
Bg=2.7 T
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Halbach permanent magnets35
cm
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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The matching cell lengthis: L=3 * 1.605 m = 4.815 m
Matching cell – geometrical constraint - arc to linac
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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IEEE Transactions on Nuclear Science, Vol. NS-30, No. 4, August 1983
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
21Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
Yoshiharu Mori – Fermilab FFAG workshop:
22Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
Yoshiharu Mori – Fermilab FFAG workshop:
23Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
Yoshiharu Mori – Fermilab FFAG workshop:
24Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
Yoshiharu Mori – Fermilab FFAG workshop:
25Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
Shinji Machida – Fermilab FFAG workshop
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New matching cell
f fo
f fo
fdol o
xmax
xmin
amax
uminumax
rdo
rdmin
rdmax
rfmin
rfmax
rfo
fdo
fdo
fdo
amin
Df
Ff
F
cfo
Dd
Dd
D
cdo
eBpeBp
eBpeBpeBp
eBp
minmin
maxmax
minmin
maxmax
r
r
r
r
r
r
Input parameters are:xmax and xmin from the arc NS-FFAGpmax, po, and pmin, Dx, bx, by,
Unknowns: BD , BF , Ffo , Fdo , and lo
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
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Matching Cell - @ zero dispersion end
fdo
fdmax
fdmin
amax a
minrdmin
rdmax
rdo
min
minmin
sinsin d
do
do
d af
rf
r -
max
maxmax
sinsin d
do
do
d af
rf
r +
dodo
do
dddo
au
a
ffffrr
-+
-
minminmin
minminmin
tansinsin
maxmaxmax
maxmaxmax
tansinsin
ddoo
dodo
dd
au
a
ff
rffr
-+
-
umax
umin
l o
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Matching Cell @ entrance
pmin
pmax
po
xm
axx
min
a max
a min
rfmax
rfo
rfmin
Ffmax
F fmin
Ffo
fo
f
f
fo uf
rf
rsinsin
max
max
max -
fo
f
f
fo uf
rf
rsinsin
min
min
min +
fo
fffou
ff
rrsinsin max
maxmax -
fofo
ffu r
ff
r -sinsin min
minmin
umax u
min
F fmin- F fo
F fo- F fmax
w
j
fo
f
ffo
wf
rff sinsin
max
max
-
fo
f
fof
jf
rff sinsin
min
min
-
l o
umax=amax+lo tan(Ffo-Ffmax)
umin=amin+lo tan(Ffmin-Ffo)
r fmax
max
maxmaxmax
max
sinsin
ffo
ffoffo
ffo
x
wx
rfff
rr
rr
--
+
-+
fo
fo
foff
fof
x
jx
rf
ffr
rr
-
-+
-+
sinsin
1 minminmin
minmin
Ffo- Ffmax= Fdo- Fdmax
Ffmin- Ffo= Fdmin- Fdo
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Mike Craddock’s approach:
f fo
f fo
fdol o
xfp
+xfp-
Xd+
uminumax
rdo
rdmin
rdmax
rfmin
rfmax
rfo
fdo
fdo
fdo
Xd-
low p-
high p+
poF/2
D/2
oppff
fff G
Bx
n
+-r
D--+- oddd
d
odp ppnnn
nX /411
22r
D--+- offf
f
ofp ppnnn
nX /411
22r
oppdd
dpdod G
BX
n
+-r
dddo
dd
dddpd
nA
AXx
ar
a
sinh1tan
cosh
-
-
fffo
ff
fffpf
nA
AXx
ar
a
sin1tan
cos
-
-
xd+=0
xd-=0
0
tan1sinh
1cosh
cosh
cosh
--
-+
-+
+
+
+
ff
food
do
dd
ddpfpdpd
dddpd
nl
n
XXXx
AXx
ar
ar
a
a
a
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Matching to linac -> zero dispersion for each momentum
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
Orbit offsets
Dispersion
bybx
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Matching to linac -> zero dispersion for each momentum
10 GeV
2.5 GeV
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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p>pcent orbits matched to linac -> zero dispersion for each momentum
p=pcent
p=pmax
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Matching cell to the non-scaling FFAG arcs
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Matching cell to the non-scaling FFAG arcs
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Non scaling FFA arcs with matching cells without linac
Orbits from 2.5 – 10 GeVthrough the matching cells and arcs:
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Non scaling FFA arcs with matching cells without linac
Betatron Functions from 2.5 – 10 GeVthrough the matching cells and arcs:
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Non scaling FFA arcs with matching cells without linac
Dispersion from 2.5 – 10 GeVthrough the matching cells and arcs:
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Matching cell with linac – arc to linac
Orbits magnified 100 timesFrom 2.5 GeV- 10GeV
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Multipass Linac with combined function triplets
Details of the orbits withChicanes:
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Details of the chicane calculations:
...!42
1~cos~,cos
1,1cos122
422 -+-D
--D
r
pklLL
pc
BBlLLLl
o
oo
Lo
-2
L
Lo /L=cos
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Details of the Chicane
CAVITY TRIPLET
Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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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
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Shinji Machida – Fermilab FFAG workshop
44Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
Shinji Machida – Fermilab FFAG workshop
45Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
Yoshiharu Mori – Fermilab FFAG workshop:
46Dejan Trbojevic BNL - Muon Collider Design Workshop Dec 1-3, 2009
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Yoshiharu Mori – Fermilab FFAG workshop: