Trapping of Neutral Molecules by the Electromagnetic Beam Field

Neutral uncharged molecules are affected by the electromagnetic field of a charged particle beam if they carry either an electric or a magnetic dipole moment. The residual gas in an accelerator beam pipe consists of such molecules. In this paper we study their dynamics. Under a few approximations, whose validity we explore and justify, we derive the equations of motion of neutral molecules and their invariants, determine the conditions for these neutral molecules to become trapped in the field of the beams as function of beam-pipe temperature, and compute the resulting enhancement of molecule density in the vicinity of the beam. We demonstrate that large agglomerates of molecules, "flakes," are much more likely to be pulled into the beam than single molecules, and suggest that this phenomenon might help explain some beam observations at the Large Hadron Collider.