  The quality and quantity of 6D stellar position-velocity measurements in the
second Gaia data release (DR2) allows to study small-scale structure in the
orbit distribution of the Galactic disc beyond the immediate Solar
neighborhood. We investigate the distribution of orbital actions
$(J_R,J_\phi=L_z,J_z)$ of $\sim 3.5$ million stars within $1.5~\text{kpc}$ of
the Sun, for which precise actions can be calculated from Gaia DR2 alone. This
distribution $n(J_R,L_z)$ reveals a remarkable amount of sub-structure. The
known moving groups in the $(U,V)$-plane of the Solar neighborhood correspond
to overdensities in $(J_R,L_z)$, as expected. But $n(J_R,L_z)$ also exhibits a
wealth of density clumps and ridges that extend towards higher $J_R$. These
$n(J_R,L_z)$ features are most prominent among orbits that stay close to the
Galactic plane and remain consistently visible out to $\sim1.5~\text{kpc}$, as
opposed to the sub-structure in velocity space. Some of these $n(J_R,L_z)$
ridges resemble features expected from rapid orbit diffusion along particular
($J_R,L_z$)-directions in the presence of various resonances. Several of these
$n(J_R,L_z)$ structures show a dramatic imbalance of stars moving in or out,
suggesting that stars are not phase-mixed along orbits or on resonant orbits.
Orbital action and angle space of stars in Gaia DR2 is therefore highly
structured over kpc-scales, and appears to be very informative for modeling
studies of non-axisymmetric structure and resonances in the Galactic disc.
