Reacceleration of Galactic Cosmic Rays Beyond the Knee at the Termination Shock of a Cosmic-Ray-Driven Galactic Wind

The origin of cosmic rays above the knee in the spectrum is an unsolved problem. We present a wind model in which interstellar gas flows along a non-rotating, expanding flux tube with a changing speed and cross-sectional area. Cosmic rays from Galactic sources, such as supernova remnants, which are coupled to the plasma via Alfv\'{e}n waves, provide the main pressure source for driving this outflow. These cosmic rays are then subject to diffusive shock reacceleration at the Galactic wind termination shock, which is located at a distance $\sim200\,{\rm kpc}$. Some of the highest-energy reaccelerated particles propagate upstream against the wind and can contribute to the PeV-EeV range of the spectrum. We analyze the conditions under which efficient reacceleration can occur and find that rigidities $\sim$ 10-40 PV can be obtained and that the termination shock may account for half of the proton spectrum measured in IceCube/IceTop experiment. The highest-energy particles that escape downstream from our termination shock, and similar shocks surrounding most galaxies, can be further accelerated by intergalactic shock fronts.