Extreme-ultraviolet images of Comet Lovejoy (C/2011 W3) from the Atmospheric Imaging Assembly show striations related to the magnetic field structure in both open and closed magnetic regions. The brightness contrast implies coronal density contrasts of at least a factor of six between neighboring flux tubes over scales of a few thousand kilometers. These density structures imply variations in the Alfvén speed on a similar scale. They will drastically affect the propagation and dissipation of Alfvén waves, and that should be taken into account in models of coronal heating and solar wind acceleration. In each striation, the cometary emission moves along the magnetic field and broadens with time. The speed and the rate of broadening are related to the parallel and perpendicular components of the velocities of the cometary neutrals when they become ionized. We use a magnetohydrodynamic model of the coronal magnetic field and the theory of pickup ions to compare the measurements with theoretical predictions, in particular with the energy lost to Alfvén waves as the cometary ions isotropize.