USPAS 2005 Recirculated and Energy Recovered Linacs 1 &+(66/(33 &+(66/(33 USPAS Course on Recirculated and Energy Recovered Linacs I. V. Bazarov Cornell University G. A. Krafft and L. Merminga Jefferson Lab Emittance and energy spread growth due to synchrotron radiation
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USPAS Course on Recirculated and Energy Recovered Linacs
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USPAS 2005 Recirculated and Energy Recovered Linacs 1&+(66/(33&+(66/(33
USPAS Course on
Recirculated and Energy Recovered Linacs
I. V. Bazarov
Cornell University
G. A. Krafft and L. Merminga
Jefferson Lab
Emittance and energy spread growth due to synchrotron radiation
USPAS 2005 Recirculated and Energy Recovered Linacs 2&+(66/(33&+(66/(33
Contents
• Coherent vs. incoherent emission
• Energy spread
- dipole magnets
- insertion devices
• Emittance growth
- dipole magnets
- H-fuction
- examples of calculation
- insertion devices
USPAS 2005 Recirculated and Energy Recovered Linacs 3&+(66/(33&+(66/(33
Quantum excitation
‘Quantum excitation’ in accelerator physics refers to diffusion of
phase space (momentum) of e– due to recoil from emitted photons.
Because radiated power scales as ∝ γ4 and critical photon energy
(divides synchrotron radiation spectral power into two equal halves)
as ∝ γ3 , the effect becomes important at high energies (typically ≥ 3
GeV).
Here we consider incoherent synchrotron radiation primarily (λ <<
σz, so that the radiation power scales linearly with the number of
electrons). When radiation wavelength becomes comparable with
the bunch length (or density modulation size), radiated power
becomes quadratic with peak current. This coherent synchrotron
radiation (CSR) effects can be important at all energies when bunch
length becomes is sufficiently short.
USPAS 2005 Recirculated and Energy Recovered Linacs 4&+(66/(33&+(66/(33
Circular trajectory in the “rest” frame
Lorentz back-transform 4-vector ),( kc&
ω
USPAS 2005 Recirculated and Energy Recovered Linacs 5&+(66/(33&+(66/(33
Coherent radiation from a bend magnet
∞→
=
Ω−+=
Ω ∫ NdzzSc
zif
dd
IdfNNN
dd
Idfor ,)(exp)( ,)]()1([
2
0
22 ωω
ωω
ω
rms
( )222 /4exp)( λσπω −=f
Form factor
Gaussian Uniform
)/2(sinc)( 2 λπω lf =
half length
USPAS 2005 Recirculated and Energy Recovered Linacs 6&+(66/(33&+(66/(33