  We do a detailed study on vortex formation in a magnetized plasma within the
spacetime of a moving cosmic string using analytical and numerical methods. The
conical spacetime around the cosmic string causes the frozen-in magnetic field
to deform due to the fluid flow. We find that the overdensity in the wake
region amplifies the magnetic field. This amplification depends on the
direction and the lengthscale of the magnetic perturbations. Alfvens theorem of
flux conservation explains this result. However, our study also shows that the
magnetic field can decay depending on the perturbation lengthscale, due to the
breakdown of Alfvens theorem at a certain lengthscale. This lengthscale is the
gyroradius of the charged particles in the plasma. Our findings are significant
for understanding magnetic reconnection in cosmic string wakes.
