Two numerical codes have been developed to study the existence and evolutio
n of a charge separation at a plasma edge. In the first code, the finite gy
ro-radius guiding center approximation, which also includes the polarisatio
n drift, is used to describe the ions, and a gyro-kinetic equation is used
for the electrons. In the second code, both ions and electrons are treated
with gyro-kinetic equations. The effect of a small dissipation term on the
solution is studied.