This paper reports high-precision Stokes V spectra of HD 191612 acquired using the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope, in the context of the Magnetism in Massive stars (MiMeS) Project. Using measurements of the equivalent width of the Halpha line and radial velocities of various metallic lines, we have updated both the spectroscopic and orbital ephemerides of this star. We confirm the presence of a strong magnetic field in the photosphere of HD 191612, and detect its variability. We establish that the longitudinal field varies in a manner consistent with the spectroscopic period of 537.6 d, in an approximately sinusoidal fashion. This demonstrates a firm connection between the magnetic field and the processes responsible for the line and continuum variability. Interpreting the variation of the longitudinal magnetic field within the context of the dipole oblique rotator model we obtain a best-fit surface magnetic field model with obliquity beta=67pm 5 deg and polar strength Bd=2450pm 400 G . The inferred magnetic field strength implies an equatorial wind magnetic confinement parameter eta*~50, supporting a picture in which the Halpha emission and photometric variability have their origin in an oblique, rigidly rotating magnetospheric structure resulting from a magnetically channeled wind. This interpretation is supported by our successful Monte Carlo radiative transfer modeling of the photometric variation, which assumes the enhanced plasma densities in the magnetic equatorial plane above the star implied by such a picture. Predictions of the continuum linear polarisation resulting from Thompson scattering from the magnetospheric material indicate that the Stokes Q and U variations are highly sensitive to the magnetospheric geometry, and that expected amplitudes are in the range of current instrumentation. (abridged)
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