  The non-thermal particle spectra responsible for the emission from many
astrophysical systems are thought to originate from shocks via a first order
Fermi process otherwise known as diffusive shock acceleration. The same
mechanism is also widely believed to be responsible for the production of high
energy cosmic rays. With the growing interest in collisionless shock physics in
laser produced plasmas, the possibility of reproducing and detecting shock
acceleration in controlled laboratory experiments should be considered. The
various experimental constraints that must be satisfied are reviewed. It is
demonstrated that several currently operating laser facilities may fulfil the
necessary criteria to confirm the occurrence of diffusive shock acceleration of
electrons at laser produced shocks. Successful reproduction of Fermi
acceleration in the laboratory could open a range of possibilities, providing
insight into the complex plasma processes that occur near astrophysical sources
of cosmic rays.
