Authors:Garraffo et alAbstract:A planet orbiting in the "habitable zone" of our closest neighboring star, Proxima Centauri, has recently been discovered, and the next natural question is whether or not Proxima b is "habitable". Stellar winds are likely a source of atmospheric erosion that could be particularly severe in the case of M dwarf habitable zone planets that reside close to their parent star. Here we study the stellar wind conditions that Proxima b experiences over its orbit. We construct 3-D MHD models of the wind and magnetic field around Proxima Centauri using a surface magnetic field map for a star of the same spectral type and scaled to match the observed ~ 600 G surface magnetic field strength of Proxima. We examine the wind conditions and dynamic pressure over different plausible orbits that sample the constrained parameters of the orbit of Proxima b. For all the parameter space explored, the planet is subject to stellar wind pressures of more than 2000 times those experienced by Earth from the solar wind. During an orbit, Proxima b is also subject to pressure changes of 1 to 3 orders of magnitude on timescales of a day. Its magnetopause standoff distance consequently undergoes sudden and periodic changes by a factor of 2 to 5. Proxima b will traverse the interplanetary current sheet twice each orbit, and likely crosses into regions of subsonic wind quite frequently. These effects should be taken into account in any physically realistic assessment or prediction of its atmospheric reservoir, characteristics and loss.