unit 8 - lecture 17 building blocks of storage rings...us particle accelerator school unit 8 -...

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


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


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]


BEAM OPTICS screen


Magnet input screens


FODO transport channel

For stability sinµ

2=

L

2 f f > L /2

FODO cell

-ff/2 f/2

LL


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


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


Symmetric FODO cell


Simple FODO cell


12-fold symmetric 1 GeV FODO ring


RF for 1 GeV FODO ring


Longitudinal phase space


The bend magnet can be in the drift:1/12th of 10 GeV DESY ring


DESY ring parameters


DESY ring RF


Example of synchrotron complex: ELSA


ELSA optical functions


Achromatic Transport Cells


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)


Storage ring building blocks:Double Bend Achromat


12 of the cells make a 2 GeV electron ring


With a tune in a dangerous position


The longitudinal phase space is

unit 8 - lecture 17 building blocks of storage rings...us particle accelerator school unit 8 -...

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