  We update our previous search for trapped magnetic monopoles in LHC Run 2
using nearly six times more integrated luminosity and including additional
models for the interpretation of the data. The MoEDAL forward trapping
detector, comprising 222~kg of aluminium samples, was exposed to 2.11~fb$^{-1}$
of 13 TeV proton-proton collisions near the LHCb interaction point and analysed
by searching for induced persistent currents after passage through a
superconducting magnetometer. Magnetic charges equal to the Dirac charge or
above are excluded in all samples. The results are interpreted in Drell-Yan
production models for monopoles with spins 0, 1/2 and 1: in addition to
standard point-like couplings, we also consider couplings with
momentum-dependent form factors. The search provides the best current
laboratory constraints for monopoles with magnetic charges ranging from two to
five times the Dirac charge.
