  For a magnetised plasma in a straight magnetic guide field, we derive a set
of four-dimensional kinetic equations, which can capture electromagnetic
turbulence in the drift kinetic limit. To do so, we start from the gyrokinetic
equations, employ a Laguerre decomposition in the perpendicular velocity
direction, retain only the dominant gyroaverage contributions and only the
first two Laguerre moments that source the electromagnetic fluctuations. The
model conserves free energy, and can describe electromagnetic turbulence for a
plasma at the transition between fluid and gyrokinetic regimes ($k_\perp
\rho_i\approx 1$ range of scales), as dominant finite-Larmor-radius (FLR)
effects are considered. In addition to the three dimensions in positions space,
we retain the parallel velocity dependence, which we describe via a Hermite
representation. Employing this system, but without any other physics based
assumptions for the plasma species that can bias results, will allow us to
investigate how fluid effects transition into the kinetic range, and analyse
the interplay between spatial and velocity space mixing for electromagnetic
plasma turbulence.
