  The production of intense neutron beams via thermonuclear reactions in
laser-generated plasmas is investigated theoretically. So far, state-of-the-art
neutron beams are produced via laser-induced particle acceleration leading to
high-energy particle beams that subsequently interact with a secondary target.
Here we show that neutron beams of two orders of magnitude narrower bandwidth
can be obtained from thermonuclear reactions in plasmas generated by
Petawatt-class lasers. The intensity of such neutron beams is about one or two
orders of magnitude lower than the one of the state-of-the-art laser-driven
neutron beams. We study to this end the reaction $^2$H($d$, $n$)$^3$He in
plasmas generated by Petawatt-class lasers interacting with D$_2$ gas jet
targets and CD$_2$ solid-state targets. The results also shows the possibility
of direct measurements of reaction rates at low temperatures of astrophysical
interests. In addition, the use of CD$_2$ solid-state targets can also lead to
great enhancements on the plasma screening compared to the case of D$_2$ gas
jet targets, opening new possibilities to study this so far unsolved issue in
the field of astrophysics.
