Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010

Bunch Compressors

John Byrd (based on a talk by P. Piot)

Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010

Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010

Magnetic bunch compression

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.

Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010

Linear Effects

Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010

Nonlinear effects

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?

Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010

(Single wiggler period)

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.

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

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 << 1,

In a linear approximation for RF,

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⎟⎟⎠

⎞⎜⎜⎝

⎛≈⎟⎟⎠

⎞⎜⎜⎝

⎛

0

0

66651

1 01δδz

RRz

( )RFRF

EeVR φcos1

066 −=

Longitudinal particle motion in bunch compressor: matrix formalism

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 << R56,

Total transformation

For frf = p/2 (i.e. no acceleration), R66=1, the transformation matrix is sympletic, which means that longitudinal emittance is a conserved quantitiy.

αεδσγε,δσβε,σσσε δδδδ >==<>==<>==<−= zzs zzzz2222222 ,

Longitudinal particle motion in bunch compressor: matrix formalism

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

Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010

s = 2acos(θ)

+ b = 2a cos θο

1+ δ⎛⎝⎜

⎞⎠⎟

⎡⎣⎢

⎤⎦⎥

−1

+ b ≈ 2a + a θο

1+ 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

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 2

οο Raasss

Path length dispersion in Chicane

For large d, d2 and d3 terms may cause non-linear deformations of the phase space during compression.

Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010

Ballistic bunch compression

Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010

SDL Experiment

Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010

UCLA Experiment

Short Bunches in Accelerators– USPAS, Boston, MA 21-25 June 2010

Homework

•  Calculate bunch compression for the Zeuthen Chicane –  Calculate R56 –  Compute