Transverse%20to%20Longitudinal%20Emittance%20Exchange

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Transverse to Longitudinal Emittance Exchange
Max Cornacchia, Paul Emma Stanford Linear
Accelerator Center

• Proposed by M. Cornacchia (Nov. 2001)

• Analysis taken from similar x-y coupling work by
  W. Spence and P. Emma

• Motivation to reduce transverse and increase
  longitudinal emittance ? faster SASE lasing and
  less CSR micro-bunching in compressors

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SASE FEL needs very bright electron beam
eN lt 1 mm at 1 Å, 15 GeV
sd lt 0.05 at Ipk 4 kA, K ? 4, lu ? 3 cm,
We need ??x lt 1 ?m , but ??z?? ? ??z
lt 300 ?m
RF gun produces ??x ??z few mm
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Emittance Exchange Concept
Electric and magnetic fields
?

• Particle at position x in cavity gets
  acceleration DE/E ? d ? kx

• This energy deviation d in chicane causes
  position change Dx -hd

Must include magnetic field and calculate
emittance in both planes
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Characterize Initial Beam
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Propagate Beam
R 1
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Rewrite emittances
some details
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Introduce Symplectic Condition
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Final Emittance Relations
equal emittances remain equal (i.e., if ex0 ez0
then ex ez)
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Introduce Transverse RF
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Effects of Transverse RF
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Chicane with RF
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Full System Transport Matrix
A 0 ? hk 1
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Final Emittance Relations
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Numerical Example
get nearly complete emittance exchange
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Phase Space Before and After Exchanger
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Normalized Phase Space
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Final Bunch Length and Energy Spread
hk 1, ax az 0
2nd-order ex growth approximated by 2nd-order
dispersion
use small bx and large h
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Bunch Compression
200 mm ? 20 mm
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RF Deflector (cylindrical)
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Cavity Thick-Lens Effect
By Dt
add chirp to compensate thick-lens
initial chirp
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Tracking with Thick-Lens and Chirp
same as thin-lens cavity
l 0.4 m
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Unusual System Characteristics
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Summary

• System potentially reduces transverse emittance

• Also increases longitudinal emittance, possibly
  damping the CSR instability

• Bunch length is compressed (all in last bend)

• Moves injector challenge to longitudinal emittance

• Must avoid CSR energy spread increase in 1st bends

• Scheme may have other uses not yet considered