2. X-Ray SASE FEL
e+e- Linear Colliders

3. Flat Beam Production
In 1998 Y. Derbenev invented a linear optics device for transforming a beam with high ratio of horizontal to vertical emittance (flat beam) to one with a vortex motion (rigid rotor). After injecting such a beam into a matched solenoid this vortex motion can be canceled to create a magnetized beam with equal emittances in the transverse degrees of freedom (round beam) (UM-HE-98-04).
In 1999 R. Brinkmann, K. Flottmann and Y. Derbenev proposed to reverse the process: obtain a flat beam from a round beam produced from a cathode in a magnetic field: A Flat Beam Source for Linear Colliders (TESLA-99-09)
In 2000 H. Edwards and the A0 collaboration have seen the first flat beam from a photo-injector.

4. Vortex Motion

5. This is a flat beam 45o inclined.
Clockwise rotation
Identity matrix in x
90o phase advance in y D1 D2 Q3 Q1 Q2
By choosing b=1/k, particles end up with equal displacement and angles in x and y
This is a flat beam 45o inclined.
D. Edwards

6. Flat Electron Beam Production from A0 Photo-injector
Round beam image on fluorescent screen
Flat beam image on fluorescent screen
Flat beam measurements
Fermilab/NICADD Photoinjector Laboratory (FNPL):
Demonstrated large emittance ratio (50:1)
with small emittance nC
Beam image through slits for emittance measurement