Zolkin, T. Burov, A.V. JACoW Geneva, Switzerland 978-3-95450-180-9 10.18429/JACoW-NAPAC2016-THPOA30 English 1164-1166 THPOA30 ion space-charge impedance dipole feedback Contribution to a conference proceedings 2017 2017-01 http://dx.doi.org/10.18429/JACoW-NAPAC2016-THPOA30 https://jacow.org/napac2016/papers/thpoa30.pdf The space charge (SC) is known to be one of the major limitations for the collective transverse beam stability. When space charge is strong, i.e. SC tune shift much greater than synchrotron tune, the problem allows an exact analytical solution. For that practically important case we present a fast and effective Vlasov solver SCHARGEV (Space CHARGE Vlasov) which calculates a complete eigensystem (spatial shapes of modes and frequency spectra) and therefore provides the growth rates and the thresholds of instabilities. SCHARGEV 1.0 includes driving and detuning wake forces, and, any feedback system (damper). In the next version we will include coupled bunch interaction and Landau damping. Numerical examples for FermiLab Recycler and CERN SPS are presented.