ECE 662

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ECE 662

• Free-Electron Lasers
• April 28, 2005

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Applications of High-Power Microwaves,
Gaponov- Grekhov Granatstein, eds.
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Important Features of FEL Sources
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FEL Features
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FEL Features
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FEL Features
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Peak-Power Output of FELs and Other
Representative Sources (Ref Granatstein et.al)
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FEL Brief History
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FEL
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FEL Concepts
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FEL Concepts
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FEL Concepts
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FEL Operation Summary
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FEL Operation Summary
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FEL Operation Summary
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FEL Operation Ref. Benford and Swegle

• Electron beam velocity vz v0
• Wiggler magnetic field period, ?W
• Oscillation motion of electrons, wavenumber, kW
  2?/ ?W , and frequency ?W kW vz
• Note transverse acceleration of the moving
  charges results in forward-directed radiation.
• Beating of radiation with wavenumber kz and
  frequency ? with the pump field of the wiggler
  creates a ponderomotive potential well moving at
  a velocity of ? / (kz kW)
• Assume that the space charge is low and use a
  wiggler-shifted beam line to be ? (kz kW) vz

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FEL Operation Ref. Benford and Swegle

• For the electromagnetic wave, we approximate its
  dispersion curve by using the free-space
  dispersion relation for a wave traveling along
  the z axis ? kz c
• At resonance, ? ?res (kz c) res (kz kW)
  vz
• Or kz c kz ?W or ?W kz (c kz) c kz (1
  ?z) where ?z vz / c, or c kz ?W / (1 ?z)
• ? ?res (kz c) res (1 ?z) ?W / (1 ?z2)
• Use ?2 1 / 1 (v/c)2 1 / (1 ?2) or
• ?2 - ?2 ?2 1 or ?2 1 ?2 (?x2 ?z2 ), or
• 1 ?z2 (1 / ?2 )(1 ?2 ?x2 ), where ?x vx /
  c is the transverse wiggle velocity

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FEL Operation Ref. Benford and Swegle

• From c kz ?W / (1 ?z) (1 ?z) kWvz / (1
  ?z2)
• and 1 ?z2 (1/?2) (1 ?2 ?x2 ), find
• 2?c/? (1 ?z) (2?/ ?W)vz/(1/?2) (1 ?2 ?x2
  )
• Cross-multiply to find
• ?W(c/?2) (1 ?2 ?x2 ) ? (1 ?z) vz, or
• ? (?W) (1 ?2 ?x2 ) / ?z(1 ?z) ?2 ,
• From the force equation in the x direction (vz
  ?By)
• find, ?2 ?x2 ½ aW2 ½ (e BW)/(m c kW) 2 lt
  1,
• If ?z?1, then ? (?W) / 2?2 (1 ½ aW2), or
• ? ? (?W) / 2?2

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FEL Efficiency
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FEL Classes
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Possible Applications of FELs
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Possible Applications of FELs
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FEL Critical Components
The most important and often most difficult task
in any FEL is the generation and transport of
a high-quality electron beam. Beam quality must
be carefully considered when choosing and/or
designing each of the four major components.
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Factors Affecting Beam Quality

• .Cathode effects
• - Emission uniformity
• - Surface roughness
• Cathode temperature
• Electron gun
• - Nonlinear applied electric field
• - Magnetic field aberrations, misalignment, etc.
• Nonlinear space-charge forces
• Beam transport and acceleration
• - Nonlinearities in focusing fields
• - Instabilities
• - Mismatches from gun to focusing channel or
  between
• focusing elements.

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Bifilar Wiggler
- Provides radial focusing for beam - Compatible
with axial magnetic field - Tapering for
efficiency enhancement is difficult - Produces
circularly polarized radiation
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Linear or Planar Wiggler
- Can be electromagnet or permanent magnet -
Tapering is straightforward - Provides focusing
in only one plane - Not compatible with axial
magnetic field - Produces linearly polarized
radiation
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FEL Summary
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FEL Experimental Activity

• At least 25 FEL experiments have been operated
  around the world
• The peak electron beam current in these devices
  varies from 0.1 to 30,000 A and the beam energy
  from 0.25 to 500 MeV
• The output wavelength ranges from 0.1 to 10,000
  microns.
• In the millimeter regime, output power in excess
  of 1 GW has been generated with an interaction
  efficiency of 40

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