  We propose a spectral Particle-In-Cell (PIC) algorithm that is based on the
combination of a Hankel transform and a Fourier transform. For physical
problems that have close-to-cylindrical symmetry, this algorithm can be much
faster than full 3D PIC algorithms. In addition, unlike standard
finite-difference PIC codes, the proposed algorithm is free of numerical
dispersion. This algorithm is benchmarked in several situations that are of
interest for laser-plasma interactions. These benchmarks show that it avoids a
number of numerical artifacts, that would otherwise affect the physics in a
standard PIC algorithm - including the zero-order numerical Cherenkov effect.
