  The recent detection of a Fast Radio Burst (FRB) from a Galactic magnetar
secured the fact that neutron stars (NSs) with super-strong magnetic fields are
capable of producing these extremely bright coherent radio bursts. One of the
leading mechanisms to explain the origin of such coherent radio emission is the
curvature radiation process within the dipolar magnetic field structure. It
has, however, already been demonstrated that magnetars likely have a more
complex magnetic field topology. Here we critically investigate curvature radio
emission in the presence of inclined dipolar and quadrupolar ("quadrudipolar")
magnetic fields and show that such field structures differ in their angular
characteristics from a purely dipolar case. We analytically show that the shape
of open field lines can be modified significantly depending on both the ratio
of quadrupole to dipole field strength and their inclination angle at the NS
surface. This creates multiple points along each magnetic field line that
coincides with the observer's line of sight and may explain the complex
spectral and temporal structure of the observed FRBs. We also find that in
quadrudipole, the radio beam can take a wider angular range and the beam width
can be wider than in pure dipole. This may explain why the pulse width of the
transient radio pulsation from magnetars is as large as that of ordinary radio
pulsars.
