  The extreme nonlinear optical process of high-harmonic generation (HHG) makes
it possible to map the properties of a laser beam onto a radiating electron
wavefunction, and in turn, onto the emitted x-ray light. Bright HHG beams
typically emerge from a longitudinal phased distribution of atomic-scale
quantum antennae. Here, we form a transverse necklace-shaped phased array of
HHG emitters, where orbital angular momentum conservation allows us to tune the
line spacing and divergence properties of extreme-ultraviolet and soft X-ray
high harmonic combs. The on-axis HHG emission has extremely low divergence,
well below that obtained when using Gaussian driving beams, which further
decreases with harmonic order. This work provides a new degree of freedom for
the design of harmonic combs, particularly in the soft X-ray regime, where very
limited options are available. Such harmonic beams can enable more sensitive
probes of the fastest correlated charge and spin dynamics in molecules,
nanoparticles and materials.
