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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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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