US Particle Accelerator School Unit 8 - Lecture 17 Building blocks of storage rings William A. Barletta Director, United States Particle Accelerator School Dept. of Physics, MIT
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US Particle Accelerator School
Unit 8 - Lecture 17
Building blocks of storage rings
William A. Barletta
Director, United States Particle Accelerator School
Dept. of Physics, MIT
US Particle Accelerator School
In practical units
Dipole magnets to bend the beam
Itotal (Amp turns) =1
0.4B (Gauss) G(cm)
1m 1[ ] = 0.2998
Bo T[ ]
relE GeV[ ]
Ldipole= bend
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Quadrupoles to focus the beam
For a Quadrupole with length l & with gradient B'
x Focal point
f
For Z =1 k m 2[ ] = 0.2998 B T /m[ ]
E GeV[ ]k
=q
E B xl
=
R
B T
m
= 2.51
NI [A - turns]
R [mm2]
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BEAM OPTICS screen
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Magnet input screens
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FODO transport channel
For stability sinµ
2=
L
2 f f > L /2
FODO cell
-ff/2 f/2
LL
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FODO transport
The (symmetric) FODO transport matrix is
Where
Let = f / L
MFODO = 1 2
L2
f 2 2L 1+L
f
1f * 1 2
L2
f 2
= cos sin
1cos
1
f * = 2 1 Lf
L
f 2
and = betatron phase advance
cos =1 2L2
f 2 =2 2
2 or sin2
=1
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More generally for a lens of finite length
The solution is that of a simple harmonic oscillator
For K < 0 the solution is
For the thin lens, let l 0 keeping Kl finite and 1/f
x
x
out
= cos
1
Ksin
Ksin cos
x
x
out
where = K l
x
x
out
= cosh
1
K sinh
K sinh cosh
x
x
out
with = K l
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Symmetric FODO cell
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Simple FODO cell
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12-fold symmetric 1 GeV FODO ring
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RF for 1 GeV FODO ring
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Longitudinal phase space
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The bend magnet can be in the drift:1/12th of 10 GeV DESY ring
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DESY ring parameters
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DESY ring RF
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Example of synchrotron complex: ELSA
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ELSA optical functions
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Achromatic Transport Cells
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Why use achromats?
We may want to deliver the beam to a region with no
residual dispersion (energy dependent orbit displacement)
Interaction regions in colliders
Insertion devices in storage rings
For circulating electron beams we may want a very low
emittance
Synchrotron light sources
We would like many long straight sections
Hence the low-emittance Chasman-Green lattice (1975)
Basis is Double Bend Achromat (Panofsky, 1965)
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Storage ring building blocks:Double Bend Achromat
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12 of the cells make a 2 GeV electron ring
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With a tune in a dangerous position
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The longitudinal phase space is
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