Paper 
Title 
Page 
TUP026 
Transverse Coherence Properties of a TGUbased FEL 
429 

 P. Baxevanis, Z. Huang, R.D. Ruth
SLAC, Menlo Park, California, USA
 C.B. Schroeder
LBNL, Berkeley, California, USA



The use of a transverse gradient undulator (TGU) is considered an attractive option for FELs driven by electron beams with a relatively large energy spread. In this scheme, a dispersion is introduced in the beam while the undulator poles are inclined so that the undulator field acquires a linear dependence upon the transverse position in the direction of dispersion. By suitably selecting the dispersion and the field gradient, the energy spread effect can be significantly mitigated, thus avoiding a drastic reduction in the FEL gain. However, adding the dispersion typically leads to electron beams with large aspect ratios. As a result, the presence of higherorder modes in the output FEL radiation can become significant. To investigate this effect, we study the properties of the higherorder eigenmodes of a TGUbased, highgain FEL, using both a simplified, analyticallysolvable model and a variational technique. This formalism is then used to provide an estimate of the degree of transverse coherence for a representative soft Xray, TGU FEL example.



TUP027 
Initial Value Problem for an FEL Driven by an Asymmetric Electron Beam 
433 

 P. Baxevanis, R.D. Ruth
SLAC, Menlo Park, California, USA



FEL configurations in which the driving electron beam is not axially symmetric (round) are important in the study of novel concepts (such as TGUbased FELs) but also become relevant when one wishes to explore the degree to which the deviation from symmetryinevitable in practical casesaffects the performance of more conventional FEL schemes. In this paper, we present a technique for solving the initial value problem of such an asymmetric FEL. Extending an earlier treatment of ours, we start from a selfconsistent, fully 3D, evolution equation for the complex amplitude of the electric field of the FEL radiation, which is then solved by expanding the radiation amplitude in terms of a set of orthogonal transverse modes. The numerical results from such an analysis are in good agreement with simulation and provide a full description of the radiation in the linear regime. Moreover, when the electron beam sizes are constant, this approach can be used to verify the predictions of the standard eigenmode formalism.


