  Phase 1 of the vacuum ultra-violet (VUV) free-electron laser (FEL) at the
TESLA Test Facility (TTF) recently concluded operation. It successfully
demonstrated the saturation of a SASE FEL in the in the wavelength range of
80-120 nm. We present a posteriori start-to-end numerical simulations of this
FEL. These simulations are based on the programs Astra and elegant for the
generation and transport of the electron distribution. An independent
simulation of the intricate beam dynamics in the magnetic bunch compressor is
performed with the program CSRtrack. The SASE FEL process is simulated with the
code FAST. From our detailed simulations and the resulting phase space
distribution at the undulator entrance, we found that the FEL was driven only
by a small fraction (slice) of the electron bunch. This "lasing slice" is
located in the head of the bunch, and has a peak current of approximately 3 kA.
A strong energy chirp (due to the space charge field after compression) within
this slice had a significant influence on the FEL operation. Our study shows
that the radiation pulse duration is about 40 fs (FWHM) with a corresponding
peak power of 1.5 GW. The simulated FEL properties are compared with various
experimental data and found to be in excellent agreement.
