  Electron beam probe (EBP) is a new principle detector, which makes use of a
low-intensity and low-energy electron beam to measure the transverse profile,
bunch shape, beam neutralization and beam wake field of an intense beam with
small dimensions. While can be applied to many aspects, we limit our analysis
to beam distribution reconstruction. This kind of detector is almost
non-interceptive for all of the beam and does not disturb the machine
environment. In this paper, we present the theoretical aspects behind this
technique for beam distribution measurement and some simulation results of the
detector involved. First, a method to obtain parallel electron beam is
introduced and a simulation code is developed. And then, EBP as a profile
monitor for dense beam is simulated using fast scan method under various target
beam profile, such as KV distribution, waterbag distribution, parabolic
distribution, Gaussian distribution and halo distribution. Profile
reconstruction from the deflected electron beam trajectory is implemented and
compared with the actual one, and an expected agreement is achieved.
Furthermore, Instead of fast scan, a slow scan, i.e. step-by-step scan, is
considered, which lows the requirement for hardware, i.e. Radio Frequency
deflector. we calculate the three dimensional electric field of Gaussian
distribution and simulate the electron motion under this field. In addition,
fast scan along the target beam direction and slow scan across the beam is also
presented, and can provide a measurement of longitudinal distribution as well
as transverse profile simultaneously. Final, simulation results for China
Accelerator Driven Sub-critical System (CADS) and High Intensity Heavy Ion
Accelerator Facility (HIAF) are given to investigate the quantitative behavior
of EBP.
