Coherent deflection of Gaussian bunches colliding at crossing angle

The coherent deflection of a charged-particles bunch in the field of a counter-propagating bunch is analyzed starting from first principles. The general solution to the equations of motion for Gaussian bunches is obtained. General formulas for the momentum kick and deflection angle are derived. The work extends the conventional Bassetti–Erskine formalism to the domain of arbitrary energies and non-zero crossing angles. Applications in collider physics for beam orbit distortion caused by the beam-beam interaction are discussed, specifically for van der Meer scans.