Etude de lìnjection dans lànneau de décroissance dùne usine à

Transcription

Presentation of the realized design for the
injection system
03/01/2005
A. Chancé, J. Payet CEA DAPNIA/SACM
1
Summary
I.
The injection system
II.
Example of an injection system in the arc
III.
Example of an injection system in the straight line
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2
I.
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The injection system
3
β-beam layout
6He2+
18Ne10+
γ
60
100
Half-life
time
(at rest)
0.8s
1.67s
Energy
345GeV
1.7 TeV
Injection
intensity
1013
5.1012
CERN
2.5 km
2GeV Protons
300 m
SPL :
ISOL :
PS :
SPS :
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Super Proton Linac
Isotope Separation On-Line
Proton Synchrotron
Super Proton Synchrotron
Same rigidity for the 2
ions ≈ 600 T.m
4
Principle of the injection system
Optical functions adapted
Chromatic orbit :
H = ∆E/E.Dm = hI+es+hS
injected
beam
hI
deviated beam
SEPTUM
XDOF : gap between the axis of the
deviated and stored beams
hS : gap between the septum and
the stored beam axis
es : septum thickness (≈1.2 cm)
hI : gap between the septum and
the injected beam axis
Dm : dispersion
∆E/E : energy difference
es
hS
kicker
XDOF
Dispersive area
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Mathematical model
The stored ions number after n injections is :
N n +1 = a 2
−
T
γτ
a=
Nn + NI
∫
n mσ
−∞
f σ ( x )dx
fσ corresponds to the
beam distribution
(supposed Gaussian)
a transmission coefficient of the stored beam after the losses on the septum
T repeat rate (8s)
τ half-life time of the ion at rest
NI injected ions number at each injection
The stored ions number tends towards :
NS =
1
1 − a2
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−
T
NI
γτ
6
Limit due to the deposit of ions
Deposed energy by the stored beam on the septum :
1− a
Edéposed =
1 − a2
1000000
−
T
NI 2
−
T
γτ
(γ − 1)E0
γτ
4 standard deviations
seem reasonable :
100J deposit
100000
Edéposée (J)
10000
Hélium
Néo n
1000
100
10
1
0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
5
We will preserve 3
standard deviations
for the injection line
N IHe = 1.1013 ions
N INe = 5.1012 ions
N SHe = 8.1013 ions
N SNe = 15.1012 ions
nb écarts type s ma chine s
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Conclusion
With these injection parameters :
nm = 4 and nj = 3.5 for the Helium and εHerms = 0.38 mm.mrad
⇒ HHe ≈ 3.3 cm for βx = 20 m
nm = 4 and nj = 3 for the Neon and εNerms = 0.47 mm.mrad
⇒ HNe ≈ 3.3 cm for βx = 20 m
The distance between the axis of both beams is the same for the Neon and
Helium.
⇒ H ≈ 3.3 cm
⇒ XDOF ≈ 3.2 cm
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II. Example of an injection system in the
arc
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Line structure
Injection in one of the arcs
Possible structure :

Lattice with some quadripole families in order to maximize the dispersion around
the injection septum
Constraints on the structure :

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No dispersion in the straight lines
Reasonable elements in the arc
Problem of the kickers rise time
Arc length as short as possible
10
Optical functions
100
90
fonctions optiques (m)
80
70
60
beta x
beta z
structure arc
Dispersion horizontale
50
40
Injection
30
6 lattices
20
Larc ≈ 880 m
10
Bdipôle ≈ 4 T
0
0
20
40
Dm = 7.6 m for H = 3.4 cm
60
80
100
120
140
abscisse curviligne (m)
⇒∆E/E = 0.5%
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Beam envelopes in the hypothesis of an
injection in the arc
Injected beam
0,08
0,08
0,06
0,06
0,04
0,04
enveloppe (m)
enveloppe (m)
Stored beam
0,02
0,02
0
0
-0,02
-0,02
-0,04
-0,04
0
20
40
60
80
100
120
140
0
20
40
60
80
100
Horizontal envelope with the kickers on
γNe = 100
Horizontal envelope with the kickers off
εNe = 0.47 mm.mrad
Vertical envelope
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120
140
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Quadripole fields for an injection in the arc
γ = 100
LQP = 2 m
QP1
QP2
QP3
QP4
QP5
Pole radius
(cm)
2
2
4
5.5
8
Gradient
(T/m)
10
11
15
20
17
Pole field (T)
0.2
0.23
0.6
1.1
1.4
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III. Example of an injection system in a
straight line
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Optical functions
Structure synoptic
120
1
100
0
fonctions optiques (m)
-1
y (m)
-2
-3
-4
80
betax
betaz
dispersion horizontale
structure ligne
60
40
Bdipole = 3T
20
0
-5
-6
-20
0
50
100
150
x (m)
200
250
0
50
100
150
200
250
For the moment, one of the both straight lines points at no detector.
Possible insertion without braking the received flux by the detector.
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Beam envelopes in the hypothesis of an
injection in a straight line
Injected beam
0,08
0,08
0,06
0,06
0,04
0,04
enveloppe (m)
enveloppe (m)
Stored beam
0,02
0,02
0
0
-0,02
-0,02
-0,04
-0,04
0
50
100
150
200
250
0
50
100
150
200
Horizontal envelope with the kickers on
γNe = 250
Horizontal envelope with the kickers off
εNe = 0.186 mm.mrad
Vertical envelope
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250
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Quadripole fields for an injection in the straight
line
γ = 250
LQP = 2 m
QP1
QP2
QP3
QP4
QP5
QP6
QP7
QP8
Radius
(cm)
2
2
2
3.5
2
2
3
6
Gradient
(T/m)
23
24
30
52
39
62
50
34
Pole field
(T)
0.45
0.45
0.6
1.8
0.8
1.25
1.5
2.1
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Optical functions in the arcs.
5
140
4
QPF
QPD
Dipole
Radius
(cm)
2.5
1.5
2.5
Length
(m)
2
2
12
Pole
field (T)
1.8
0.8
8
Number
25
25
50
3
2
100
1
80
0
60
-1
-2
40
Dispersion (m)
optical functions (m)
120
γ = 250
-3
20
-4
0
-5
0
100
200
300
400
500
600
700
800
900
path length (m)
Dispersion as low as possible.
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Conclusion
Possible injection in the arc for low gammas.
If gamma increases, the quadripole and dipole fields are too high.
⇒It is necessary to inject in one of the straight lines.
For 1 km arcs and γ = 250, we need 8 T dipoles.
If we work with gamma > 250, the magnetic fields become stronger.
We need work on the straight lines and the arcs. The matching sections between
the arc and the straight line introduce chromaticity and we have to find a
compromise between the number of straight line quadripoles and the reached
chromaticity.
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IV. Effect of the desadaptation of the
injected beam
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Effect of the desadaptation of the injected
beam
x’
x’
injected beam ellipse at the
energy ΔE + δ.E
injected beam ellipse at the
energy ΔE
δD
ε (δ ) =
eS
x
g
g
XDOF
XDOF
(
injected beam ellipse at
the energy ΔE
x
g
ΔE/E.D
deviated beam ellipse at the
reference energy
ε i + γ m δ .D
eS
g
Δ.D
)
2
⎧⎪ X DOF = δ i .D + ni β mε (δ i ) + g + eS + g + ni β iε i
⎨
2
⎪⎩∆.D = nm β mε m + (δ m .D ) + g + eS + g + ni β iε i
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Simulation of the beam desadaptation
0,001
0,0008
∆E – δ.E
∆E
∆E + δ.E
0,0006
0,0004
x' (rad)
0,0002
0
-0,0002
-0,0004
-0,0006
-0,0008
-0,001
0,02
0,03
0,04
0,05
0,06
0,07
0,08
0,09
0,1
x (m)
Effectively observed beam swelling
Analytical calculus confirmed by the numerical calculus
Necessity of a guard : The beam is always a little disadapted. Moreover,
swelling due to the errors in the magnetic elements.
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Stored ions number in the dacay ring
1,2
Limit for the stored ions number :
1
Nperm/NS
0,8
Hélium
Néon
0,6
N perm =
NS =
0,4
1
1 − a2
1
1− 2
−
−
T
N inj
τ
T
N inj
τ
0,2
0
0
1
2
3
4
5
nb écarts types préservés
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Filling dynamics
Intensité stockée sur celle nominale en fonction du nombre
d'injections
Cas de l'hélium
Intensité stockée sur celle nominale en fonction du nombre d'injections
Cas du Néon
18-19 min
2,5
1,4
1,2
5-6 min
2
1
N/Ns
N/Ns
1,5
1
pas remplissage 2,5sigma
0,8
0,6
pas de remplissage 3.5sigma
Rempli 20 injections 3.5sigma
0,4
Rempli 5 injections 2,5sigma
0,5
0,2
0
0
0
20
40
nb injections
NInjHe = 1.1013
NSHe = 8.1013
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60
80
0
25
50
75
100
125
150
nb injections
NInjNe = 5.1011
NSNe = 15.1012
It is not necessary to fill faster
24
Limitation due to the deposit of ions by
the injection line
Deposed energy by the injected beam on the septum :
E déposée = (1 − a )N I (γ − 1)E 0
1000000
100000
10000
Edéposée (J)
1000
Hélium
Néon
100
10
1
0,1
We will take 3
standard deviations
for the injection line
N IHe = 1.1013 ions
N INe = 5.1012 ions
N SHe = 8.1013 ions
N SNe = 15.1012 ions
0,01
0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
5
nb écarts types machine
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Problématique de l’injection
⇒
Injection autour d’une déformation de l’orbite fermée (DOF)
Conservation de l’élongation initiale
Déviateurs allumés
Faisceau injecté
Faisceau circulant
SEPTUM
Déviateur rapide
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⇒
Déviateurs éteints
Faisceau injecté
Faisceau circulant
SEPTUM
Déviateur rapide
⇒
Injection « off momentum » dans une région dispersive avec une DOF
Aux tours suivants, le faisceau injecté ne rencontre pas le septum
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⇒
Déviateurs allumés
Faisceau injecté
Faisceau circulant
SEPTUM
Déviateur rapide
⇒
Injection « off momentum » dans une région dispersive avec une DOF
Aux tours suivants, le faisceau injecté ne rencontre pas le septum
⇒ Système RF pour fusionner les faisceaux
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Fusion des 2 faisceaux
3 grandes étapes :
_ injection d’un faisceau à une énergie différente
_ rotation dans l’espace des phases longitudinal
_ gymnastique de phase quand le faisceau injecté est à l’énergie
nominale à l’aide de deux cavités RF dont l’une est à l’harmonique
double :
E
E
φ
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E
φ
φ
29
Injection d’un bucket vide
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Conclusions on the injection in the arc
Advantages of an injection in the arc : strong dispersion area, no insertion in
the straight lines.
But if the ions reference energy increases (for example γNe = 250) , it is not
possible anymore to inject in the arc. In this case, it will be necessary to inject in
one of the straight lines.
We must realize also the design of the straight lines with the matching sections.
But, big neutrinos emission angle (≈1/γ)
⇒few constraints.
We have made some structures but we cannot choose between the different
solutions.
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