Around the experimental regions of the Large Hadron Collider (LHC) beams
travel in a common vacuum chamber and therefore experience the fields of
the opposing beams, so-called long range interactions. These are
unavoidable and, being nonlinear, limit the LHC's luminosity. Studies of
this effect are essential for designing the ``luminosity upgrade''; a
factor of 10 performance improvement, due to begin operating in 2025.
The usual method of investigating the effect is by multiparticle
simulations, and TRIUMF is part of the international collaboration
charged with these calculations. These are compute-power limited and so
it is highly desirable that an alternative analytic model be
found. Recently, we have discovered such a model[1]. This has the
potential of making beam-beam calculations more tractable.
[1] D. Kaltchev, Fourier Coefficients of Long-Range Beam-Beam
Hamiltonian via Two-Dimensional Bessel functions, Proc. Int. Particle
Accelerator Conf., Vancouver BC, Canada (2018).