  By the application of $\phi$-mapping topological theory, the properties of
vortices in quantum R\"ontgen effect is thoroughly studied. The explicit
expression of the vorticity is obtained, wherein which the $\delta$ function
indicates that the vortices can only stem from the zero points of $\phi$ and
the magnetic flux of the consequent monopoles is quantized in terms of the Hopf
indices and Brouwer degrees. The evolution of vortex lines is discussed. The
reduced dynamic equation and a conserved dynamic quantity on stable vortex
lines are obtained.
