Step III - The Radiation Field

In an FEL oscillator the radiation parameter are well defined by the seeding radiation field and the enclosing cavity. Otherwise (FEL amplifier or SASE FEL) they typically need to be optimized. Although SASE simulation significantly reduces the impact of the waist position ZWAIST and the Rayleigh length ZRAYL parameters it is recommended as a pre-optimization step to run steady-state simulation (ITDP = 0). Thus the following is valid for both, FEL amplifier and SASE FEL.

A good estimate of the radiation wavelength is given by the resonant formula

with =XLAMDS, =GAMMA0, _u=XLAMD and a_u =AW0. Anyhow diffraction or emittance effects might slightly change the resonant wavelength. The Raylength length should be chosen so that the initial beam size is similar to the beam size of the gain-guided radiation field in the exponential amplification regime. If the radiation waist is at the undulator entrance (ZWAIST=0) the initial beam size is simply given by with z_r =ZRAYL.

While the input radiation power is a well-defined input parameter for an FEL amplifier its value has to be estimated for steady-state simulation modelling SASE FELs. With the definition of the FEL parameter

an approximation of an equivalent input power (shot noise power) of the SASE FEL is

with f_c =FBESS0 or the value GENESIS 1.3 would calculate in the case that FBESS0 is set to zero in the input deck, _b=(RXBEAM + RYBEAM)/2, I_p = CURPEAK, I_A = 17 kA, P_b =I_pmc ²/e as the electron beam power and N=I_p /ce as the number of electrons per radiation wavelength.

With the parameters for the magnetic field, electron beam and radiation field a run of GENESIS 1.3 should produce some gain. If the results are satisfying the input deck can be used for more advanced simulation (field errors, time-dependent simulation). Otherwise further optimization of the input parameters is needed.

• Setting-up Simulations
• Step I - The Magnetic Lattice
• Step II - The Electron Beam
• Step III - The Radiation Field
• Step IV - Optimization Using the SCAN-Feature
• Step V - Time-dependent Simulation
• Step VI - External Input for the Magnetic Field
• General Tips