Coherent Synchrotron Radiation in Particle Accelerators

Rui LiJefferson Lab

To address the questions:

• What is coherent synchrotron radiation (CSR)?

• Why is it a concern in particle accelerators?

• How we investigate the problem?

• What is the present status of CSR research?

Outline• Synchrotron Radiation by a Single Electron

• Coherent Synchrotron Radiation (CSR)by an Electron Bunch

• Collective CSR Interaction for High Brightness Beams

• CSR Effect in Particle Accelerators

• Investigation of the CSR Effects

1. Synchrotron Radiation by a Single Electron

Electromagnetic Field of a Moving ChargeCoulomb Field for a Point Charge at Rest

rrqE 3= v=0

Coulomb Field for a Point Charge with Uniform Motion

2/32223 )sin1(1

ψβγ −=

rrqE v=0.8c

Radiation by an Accelerated Point Charge

Black field line connecting Coulomb fields: radiation fields due to acceleration

Synchrotron Radiation•Electromagnetic radiationemitted by charged particlesmoving with centripetalacceleration

• First discovered by GEin 1947 in a type of acceleratorknown as synchrotron,as an unwanted by-productof storage ring accelerator.

Single Particle Lienard-Wiechert Field

X

ct

),( retret tx

Spacetime trajectory of source electron

),( tX

,

, ,

retret

ret

cv

cv

RRnxXR

==

=−=

ββ

||)(:Conditionn Retardatio

retret xXttc −=−light cone

Observation point

⎪⎪⎩

⎪⎪⎨

⎧

×=

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅−×−×

+⎥⎦

⎤⎢⎣

⎡

⋅−−

=

EnB

Rnnn

ce

RnneE

ret

3ret

232 )1()[(

)1( βββ

βγβ

Lienard-WiechertField:

Features of Synchrotron Radiation

•extremely intense

•wide energy specturm

•highly polarized

•emitted in very short pulses (nanosec)

Spectrum of Synchrotron Radiation

ρω c

mcE

c

3

23 ⎟⎠⎞

⎜⎝⎛=Cutoff at critical frequency:

2. Coherent Synchrotron Radiation (CSR)

by an Electron Bunch

Coherence of Radiation by Many Electrons

•Typically in accelerators, 1010 electrons travel in atight bunch at v~c.

200 EP =•The single particle radiation power is

•What is the radiation power spectrum for N electrons?

•For radiation wavelength << bunch length,

)( z02

0

2

1tot σλ <<=≈= ∑

=

PNENEPN

ii,0=jiEE

radiation incoherent :λσ >s

•For radiation wavelength > bunch length,the radiation from single electron adds coherently,

)( z022

0

2

1tot σλ ≈=≈= ∑

=

PNNEEPN

ii

radiationcoherent :λσ ≤s

Radiation Power Spectrum for N electrons

λπω c2

=

)(ωI

zσλ ≥

radiationincoherent )()( 0 ωω NII =

radiationcoherent )()( 0

2 ωω INI =

Recent Observation of CSR

3. Collective CSR Interaction for High Brightness Beams

Where does the extra radiation power come from?Kinetic energy loss of the electrons due to bunch self-interaction on curved orbit

')','()',';,(),(0

rdtrntrtrEtrE ∫=

NevEeP ∝⋅=

Power loss by one electron:

Power loss by the bunch:

22tot ),,(),,()( eNvdrdtvrftvrPtP ∝= ∫

crrtt |'|' −

−=Radiation emitted from a tail particle at retarded time overtakes the bunch to interact with a head particle

CSR Collective Force on the Bunch

Overtaking Length

m34.1 10m, mm, 1example,For

)24( 3/120

===

=

L

L

z

z

ρσ

ρσ

Bunch tail:lose energy

Bunch head:gain energy

Shielding by Vacuum Chamber•Electron beams in accelerators are surrounded by vacuum chamber

•Simple model: parallel plate shielding

Bunch Self-Interaction in Vacuum Chamber

ConductingPlates

ImageCharges

Retarded t’ Present t

+

+

-

-

-

ImageCharges

Transient Interaction at Entrance of a Bend

As the bunch enters into the bend, in addition to the radiation fields,the bunch also sees Coulomb field emitted from the bunch’spseudo-position as if the particles continue to travel with theirVelocity at retarded time.

4. CSR Effect in Particle Accelerators

Accelerator Facilities with High Brightness Electron Beams

A. Light Sources

•Storage Ring Light Souces

•Linac Based Free Electron Laser

B. Colliders

•Storage Ring Colliders•Linear Colliders

Example of Free Electron Laser:Eenergy Recovery Linac based FEL (Jefferson Lab)

135 MeV

Recirculation Arc

Magnetic Bunch Compressor

Example of Linear Collider:The International Linear Collider (ILC)

Magnetic Bunch Compressor:

X-FEL based on last 1-km of existing SLAC linacX-FEL based on last 1-km of existing SLAC linac

LCLS at SLACLCLS at SLAC

LCLSLCLSLCLS

1.5-15 Å1.5-15 Å

2 compressors2 compressors

14.4 GeV

Magnetic Bunch CompressionMagnetic Bunch Compression

σz0σz0

∆Ε/Ε∆Ε/Ε

zzσzσz

under-compressionunder-compression

V = V0sin(ωτ)V = V0sin(ωτ)

RF AcceleratingVoltage

RF AcceleratingRF AcceleratingVoltageVoltage

∆z = R56∆Ε/Ε∆z = R56∆Ε/Ε

Path Length-EnergyDependent BeamlinePath LengthPath Length--EnergyEnergyDependent BeamlineDependent Beamline

…or over-compression

…or over-compression

∆Ε/Ε∆Ε/Ε

zz

σE/EσE/E

∆Ε/Ε∆Ε/Ε

zz‘chirp’‘chirp’

Requirement of Accelerator Design

• Colliders: event rate luminosity∝High luminosity Large particle number in

small beam phase space area

or, high brightness electron beam

• Light Sources: high brilliance of photon flux

high brightness electron beam

Pros and Cons of the CSR Effect• Pros (for storage ring light source)

Can enhance radiation power by a factor of Nfor radiation wavelength ~ bunch length

• Cons (for FEL, circular and linear colliders) Collective CSR Interaction on Curved Orbit

Energy Spread of Particles in the Bunch

Particle with different energy being bent differently by

the same external magnetic field

Degradation of Electron Beam Brightness

5. Investigation of the CSR Effect

• Theory

• Numerical Simulation

• Experiment

Theoretical Approach• A bunch of electrons

guided by an external EM field to follow the design orbit

• Due to external and collective interaction, the phase space point (x,x’) of a particle varies along the design orbit

s: pathlength along the orbit

⎪⎪⎩

⎪⎪⎨

⎧

=

=

)](['

'

retcol sfFdsdx

xdsdx

);('),( :y trajectorspace Phase sxsx

Theoretical Approach (con’d)• Phase space distribution at s: x’

x

),',( sxxf

• # of particles within infinitesimal phase space volume:

'),',( dxdxsxxfdN =

•Flow of infinitesimal phase space volume along the design orbit

dx'dx

1dx

1'dx

s ss ∆+

Theoretical Approach (con’d)

• Conservation of Particle Number

'),'('),',( 111,1 dxdxssxxfdxdxsxxfdN ∆+==

Vlasov Equation

0]['

' col =∂∂

+∂∂

+∂∂ fF

xfx

xf

sf

Collective CSR Force

Hamiltonian system: '' 11dxdxdxdx =

• Perturbation )( 0110 fffff <<+=

ion.approximat veperturbati usingEq. Vlasov thefrom solved is ),',( ],[Given col sxxffF

Numerical Simulation

Should be

• Faithful representation of phase space distribution, including fine details

• Accurate calculation of collective forces,including retardation

• Self-consistent• Not slow

A. Macroparticle Model

•Transverse and Longitudinal bunch dynamics

t0

t1

x

y

•Bunch is simulated by a set of macroparticles

Macros: 2D round Gaussian disc

Single macro density distribution:

⎥⎦

⎤⎢⎣

⎡ −+=− 2

20

20

20 2))(())((-Exp

21))((

mmm

tyytx-xtrrnσπσ

Macro sizeMacro centroid vector

))((),( )(0 trrnqtr j

mm∑ −=ρBunch charge distribution:

)( BvEeF ×+=• CSR Force Computation

crrtt

tvtrrFrrrdqtrEtrEtrE jj

mj

j

j

/|'|' timeretardedfor

)]'(),'('[|'|

'),( ),,(),( )(0

)(0

2)()(

−−=

−−

== ∫∑

• Interpretation(r,t)

test particle

jth macro

If we devide jth macro into grid, each grid emits photon(which reaches r at t) at different r’,t’.

Pros and Cons of Macroparticle Model:

• straight-forward calculation of CSR force including retardation• self-consistent

but • slow • noisy

B. Semi-Lagrangian Simulation (low noise, can reveal fine details of phase space)

);,,(

);,,(

Equation Dynamical

⎪⎪⎩

⎪⎪⎨

⎧

=

=

ftqpGdtdp

ftqpFdtdq

mesh on the ),,( Knowing nji tqpf mesh on the ),,( Find ttqpf nji ∆+

q q

p p

);,,()()( );,,()()(

EquationDifference

1

1

⎩⎨⎧

∆−=∆−=

−

−

tftqpGtptptftqpFtqtq

nnn

nnn

nt ttn ∆+

Experimental Observation

Microbunching Instability

Small Initial energy perturbationbend geometry

density modulation

CSR in bend

Stronger energy modulation

bend geometry

Stronger density modulation

Remark: intrinsic energy spread provide natural stabalizing mechanismThreshold of instability

Experimental Observation (con’d)10.5mA

28.8mA

100ms806040200

Time (msec)

40.0mA

10 mA

29 mA

40 mA

Time (msec)

Bolo

met

er s

igna

l (V)

Bursts of far-IR CSR observed on a bolometer. Threshold depends on beam energy, bunch length, energy spread, and wavelength.

CSR can drive a microbunching instability in the electron bunch, resulting in a periodic bursts of terahertz synchrotron radiation, resulting in a noisy source.

Simulated instability showing bunch shape

Simulated ResultsSmall perturbations to the bunch density can be amplified by theinteraction with the radiation. Instability occurs if growth rate is faster than decoherence from bunch energy spread.

z/σz

δ/σδ

Experiment Compared with Theory

Conclusion• Coherent synchrotron radiation is recognized as an important

factor to impact beam dynamics for high brightness beamstransporting in magnetic bends.

• The retardation and sensitivity of this effect pose serious challenge to theory, simulation and experiments.

• Big progress has been made on each aspects. However,more detailed and precise understanding and simulationof CSR are needed in order to have predictive power for machine design.