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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
Bunch Compressors
John Byrd (based on a talk by P. Piot)
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
Magnetic bunch compression
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
To compress a bunch longitudinally, trajectory in dispersive region must be shorter for tail of the bunch than it is for the head.
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
Linear Effects
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
Nonlinear effects
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
How short can the bunch be compressed?
Can low emittance be maintained?
How large are the effects of space charge and coherent synchrotron radiation in bunch compression?
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
(Single wiggler period)
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
Chicane : Simplest type with a 4-bending magnets for bunch compression
Double chicane : R56 is sum of the R56 values for each chicane.
Wiggler type : This type can be used when a large R56 is required, It is also possible to locate quadrupole magnets between dipole magnets where dispersion passes through zero, allowing continuous focusing across these long systems.
Arc type : R56 can be conveniently adjusted by varying betatron phase advance per cell in the bend plane. The systems chromatic aberrations, introduce large beamline geometry excursions and produce many well aligned components.
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
Longitudinal particle motion in bunch compressor: matrix formalism
)cos(
)cos()1()1(
1
11
0
rfrfo
orfrfrfif
oi
eVEEzkeVEEE
EE
ϕ
ϕ
+=
−+=+=+=δδ
⎟⎠⎞⎜
⎝⎛ −+=
=
00
01
01
2cos zk
EeV
zz
RFRF πδδ
krf = 2pfrf/c
When beam passes a bunch through a RF cavity on the zero crossing of the voltage (i.e. without acceleration)
In general, when reference particle crosses at some frf that is not be zero crossing. Then reference energy of the beam is changed from Eo to E1.
Then,
1)cos(
)cos()1(
0
01 −+
−++=
rfrf
orfrfRFo
eVEzkeVE
φφ���δ
δ
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
( ))cos()cos)cos(100
01
01
rforfrfRFrfRF zkEeV
EeV
zz
φφφ
−−+⎟⎟⎠
⎞⎜⎜⎝
⎛−=
=
(δδ
( ) RFRFRF kEeVR φsin
065 =
To first order in eVrf/Eo
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
⎟⎟⎠
⎞⎜⎜⎝
⎛ +=⎟⎟⎠
⎞⎜⎜⎝
⎛⋅≈⎟⎟⎠
⎞⎜⎜⎝
⎛
6665
66565665
0
0
2
2 1RRRRRRzz
MMδδ
In a wiggler (or chicane),
In a linear approximation T566d1 ======
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
• Zeuthen Chicane : a benchmark layout used for CSR calculation comparisons at 2002 ICFA beam dynamics workshop
B3
B2
B4 B1
LB LB DLc DL DL
qo
• Bend magnet length : LB = 0.5m • Drift length B1-B2 and B3-B4(projected) : DL = 5m • Drift length B2-B3 : DLc = 1m • Bend radius : r = 10.3m • Effective total chicane length (LT-DLc) = 12m • Bending angle : qo = 2.77 deg Bunch charge : q = 1nC • Momentum compaction : R56 = -25 mm Electron energy : E = 5 GeV • 2nd order momentum compaction : T566 = 38 mm Initial bunch length : 0.2 mm • Total projected length of chicane : LT = 13 m Final bunch length : 0.02 mm
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
s = 2acos(θ)
+ b = 2a cos θο1+ δ
⎛⎝⎜
⎞⎠⎟
⎡⎣⎢
⎤⎦⎥
−1
+ b ≈ 2a + a θο1+ δ
⎛⎝⎜
⎞⎠⎟+ b
If a particle at reference energy is bent by qo, a particle with relative energy error d is bent by q=qo/(1+d).
Path length from first to final dipoles is
q
2ο
δθ
δa
ddsR 2
056 −==
=
Path length dispersion in Chicane
a a b
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
......223
565656 −+−≈32 δδδΔ RRRs
56566 23 RT −≈ U5666 ≈ 2R56
By performing a Taylor expansion about d=0
Path length in a chicane is
⎟⎟⎠
⎞⎜⎜⎝
⎛+
−=−⎟⎠⎞⎜
⎝⎛
+≈=−= 256
2
)1(11
21
1((
δθ
δθ0)δδ)Δ 2οο Raasss
Path length dispersion in Chicane
For large d, d2 and d3 terms may cause non-linear deformations of the phase space during compression.
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
Ballistic bunch compression
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
SDL Experiment
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
UCLA Experiment
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Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010
Homework
• Calculate bunch compression for the Zeuthen Chicane – Calculate R56 – Compute
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