A Space-charge Compatible "Tomography" of Beam Phase-space Distributions

The well-known 3-gradient method allows accessing to a beam RMS emittance and Twiss parameters at a position A by measuring its rms size at a downstream position B with at least 3 different transport conditions from A to B. We suggest extending this method to access to a beam phase-space distribution model at A from beam profiles measured at B. We propose to use an iterative method which consists in: - defining a parametric model describing the beam distribution in 4D transverse phase-space at a position A, - adjusting iteratively the model parameters by minimizing the difference between beam profiles measured at B and these obtained by transporting the beam generated according to the model with TraceWIN code from A to B. This method allows taking into account space-charge and other transport non-linearities.