An Eulerian code that solves the gyrokinetic Vlasov equation in slab g
eometry is presented, It takes into account the EXB and polarization d
rifts in the plane perpendicular to the magnetic field, and kinetic ef
fects in the parallel direction. The finite Larmor radius is modelled
by a convolution operator. The relation is established between this mo
del and others proposed previously, and they are shown to be equivalen
t in the limit of long wavelengths and small Larmor radii. The code is
applied to investigate ion-temperature-gradient modes in the quasi-ne
utral regime, with adiabatic electrons. Numerical results are reported
for a wide range of parameters, including density and temperature pro
files, magnetic field strength, and ion to electron temperature ratio.
Normally the plasma evolves towards long wavelength structures, altho
ugh in some cases (when Landau damping is very weak) more strongly tur
bulent regimes are observed. Test particles are used to compute diffus
ion coefficients both in real space and velocity space. For the most s
trongly turbulent regimes, particle diffusion coefficients are of orde
r 20 m(2) s(-1). The saturation mechanism is also investigated. Many p
revious numerical results obtained with particle codes are confirmed,
but the Vlasov Eulerian technique allows a much finer resolution of st
ructures both in real space and velocity space.