coherent synchrotron radiation in particle...
TRANSCRIPT
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
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)
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 =
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.
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
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
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 ∆+
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
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.