  A bright collimated neutron source is an essential tool for global security
missions and fundamental scientific research. In this paper, we study a compact
high-yield and high-angular-flux neutron source utilizing the break-up reaction
of laser-driven deuterons in a $^9\text{Be}$ converter. The neutron generation
scaling from such a reaction is used to guide the choice and optimization of
the acceleration process for the bulk ions in a low density $\text{CD}_2$ foam.
In particular, the collisionless shock acceleration mechanism is exploited with
proper choice in the laser and target parameter space to accelerate these ions
towards energies above the temperature of the distribution. Particle-In-Cell
and Monte Carlo simulations are coupled to investigate this concept and
possible adverse effects, as well as the contribution from the surface ions
accelerated and the optimal converter design. The simulation results indicated
that our design can be a practical approach to increase both the neutron yield
and forward flux of laser-driven neutron sources, reaching peak angular neutron
flux $>10^{11}$ neutron/sr and yield $>10^{11}$ neutron/pulse with present-day
kJ-class high-power lasers. Such developments will advance fundamental neutron
science, high precision radiography and other global security applications with
the laser-driven sources.
