Author: Lindberg, R.R.
Paper Title Page
MOPSO49 Numerical Accuracy When Solving the FEL Equations 82
 
  • R.R. Lindberg
    ANL, Argonne, USA
 
  Funding: U.S. Dept. of Energy Office of Sciences under Contract No. DE-AC02-06CH11357
The usual method of numerically solving the FEL equations involves dividing both the e-beam and radiation field into "slices" that are loaded one at a time into memory. This scheme is only first order accurate in the discretization of the ponderomotive phase because having only one slice in memory effectively results in a first order interpolation of the field-particle coupling. While experience has shown that FEL simulations work quite well, the first order accuracy opens the door to two possible ways of speeding up simulation time. First, one can consider higher order algorithms; unfortunately, these methods appear to require all the particle and field data in memory at the same time, and therefore will typically only be important for either small (probably 1D) problems or for parallel simulations run on many processors. Second, one may consistently solving the equations to some low order using faster, simpler algorithms (replacing, for example, the usual RK4). The latter is particularly attractive, although in practice it may be desirable to retain higher order methods when integrating along z. We investigate some of the possibilities.
 
 
THOBNO02 Transverse Gradient Undulators for a Storage Ring X-ray FEL Oscillator 740
 
  • R.R. Lindberg, K.-J. Kim
    ANL, Argonne, USA
  • Y. Cai, Y. Ding, Z. Huang
    SLAC, Menlo Park, California, USA
 
  Funding: Work supported by U.S. Dept.~of Energy, Office of Basic Energy Sciences, Contract No.~DE-AC02-06CH11357.
An x-ray FEL oscillator (XFELO) is a fully coherent 4th generation source with complementary scientific applications to those based on self-amplified spontaneous emission*. While the naturally high repetition rate, intrinsic stability, and very small emittance produced by an ultimate storage ring (USR) makes it a potential candidate to drive an XFELO, the energy spread is typically an order of magnitude too large for sufficient gain. On the other hand, Smith and coworkers** showed how the energy spread requirement can be effectively mitigated with a transverse gradient undulator (TGU): since the TGU has a field strength that varies with transverse position, by properly correlating the electron energy with transverse position one can approximately satisfy the FEL resonance condition for all electrons. Motivated by recent work in the high-gain regime***, we investigate the utility of a TGU for low gain FELs at x-ray wavelengths. We find that a TGU may make an XFELO realizable in the largest ultimate storage rings now under consideration (e.g., in either the old Tevatron or PEP-II tunnel).
* K.-J. Kim, Y. Shvyd'ko and S. Reiche, PRL 100 244802 (2008).
** T. Smith, et al., J. Appl. Phys. 50, 4580 (1979).
*** Z. Huang, Y. Ding, and C.B. Schroeder, PRL 109, 204801 (2012).
 
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