In the framework of the LIGHT project a dedicated test stand is under preparation at GSI for the transport and focusing of laser accelerated ion beams. The relevant acceleration mechanism for the parameters achievable at the GSI PHELIX laser is the TNSA (Target Normal Sheath Acceleration). The subsequent evolution of the ion beam can be described rather well by the isothermal plasma expansion model. This model assumes an initial dense plasma layer with a ’hot’ electron component and ’cold’ ions. We will present 1D and 2D simulation results obtained with the VORPAL code on the expansion of the beam and on the cooling down of the neutralizing electrons. The electrons and their temperature can play an important role for the focusing of the beam in a solenoid magnet, as foreseen in the GSI test stand. We will discuss possible controlled de-neutralization schemes using external magnet fields.