  A numerically efficient framework that takes into account the effect of the
Coulomb collision operator at arbitrary collisionalities is introduced. Such
model is based on the expansion of the distribution function on a
Hermite-Laguerre polynomial basis, to study the effects of collisions on
magnetized plasma instabilities at arbitrary mean-free path. Focusing on the
drift-wave instability, we show that our framework allows retrieving
established collisional and collisionless limits. At the intermediate
collisionalities relevant for present and future magnetic nuclear fusion
devices, deviations with respect to collision operators used in
state-of-the-art turbulence simulation codes show the need for retaining the
full Coulomb operator in order to obtain both the correct instability growth
rate and eigenmode spectrum, which, for example, may significantly impact
quantitative predictions of transport. The exponential convergence of the
spectral representation that we propose makes the representation of the
velocity space dependence, including the full collision operator, more
efficient than standard finite difference methods.
