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In this paper, we report on the halo formation and emittance growth driven by a parametric resonance during beam-beam collisions with optically mismatched injection. In the regime of the weak-strong beam-beam interaction, if two beams have the same machine tunes, on-axis head-on collisions between a mismatched strong beam and a weak beam will not cause the formation of halo. However, if the two beams collide with an initial offset, the beam-beam force from the mismatched strong beam can cause halo formation and emittance growth in the weak beam. Meanwhile, if two beams have different machine tunes, for opposite charged colliding beams, when the machine tune of the weak beam is smaller than that of the strong beam, there is emittance growth in the weak beam. When the machine tune of the weak beam is larger than that of the strong beam, there is little emittance growth. In the regime of the strong-strong beam-beam interaction, halo is formed in both beams even when the two beams collide head-on on the axis with equal machine tunes. This puts a strong requirement for a good beam match during the injection to colliders in order to avoid emittance growth if there are no other mechanisms after the injection to decohere the mismatched envelope oscillation

Halo formation due to beam-beam interactions of beams optically mismatched at injection