  Structured vortex waves have numerous applications in optics, plasmonics,
radio-wave technologies and acoustics. We present a theoretical study of a
method for generating vortex states based on coherent superposition of waves
from discrete elements of planar phased arrays, given limitations on an element
number. Using Jacobi-Anger expansion, we analyze emerging vortex topologies and
derive a constraint for the least number of elements needed to generate a
vortex with a given leading-order topological charge.
