Effects of space charge force on the beam-beam mode coupling instability

Recent <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>e</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>e</a:mi><a:mo>−</a:mo></a:msup></a:math> colliders operate with very low emittance and high current. The space-charge tune shift is not negligible in tau-charm and B factories. The vertical space-charge tune shift is on the order of 0.02–0.1 and is comparable to the synchrotron tune and the beam-beam tune shift. The beam-beam mode coupling instability has been studied with and without vacuum environment impedance. The mode coupling is influenced by the space-charge force, which exhibits similar characteristics to the beam-beam force. The combined effect of beam-beam, space charge, and vacuum environment impedance is discussed within the framework of the mode coupling theory. Strong-strong beam-beam simulation, considering the space-charge force and the impedance, are conducted to validate the theory and to study general cases such as asymmetric colliders. Published by the American Physical Society 2024