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One of the aims of new circular collider projects is further increase in their luminosity. The high space charge electromagnetic field at the meeting points limits the achievable current densities and consequently the luminosity. Nonlinear focusing compensation in a storage ring done by the opposite-charge beam circulating in another storage ring was proposed and tested many years ago. Ya. S. Derbenev has shown that such a scheme suffers from tune shifts of coherent betatron oscillations, which move betatron frequencies toward the nearest integer or half-integer resonance. In this paper, the collider based on electron energy recovery linac (ERL) and "figure-8" positron storage ring with beams of equal currents is considered. Positrons are circulating in a two-loop storage ring (positron-positron collider), and electronelectron collider uses ERL, as in original Tigner's proposal. Thus, a collision of four bunches and space-charge compensation in a multi-bunch mode can be ensured. The mathematical and numerical analysis of this configuration is presented.

Beam-beam compensation in a collider based on energy recovery LINAC and storage ring