Experiments were performed using the Omega EP laser, which provided pulses containing 1kJ of energy in 9ps and was used to investigate high-power, relativistic intensity laser interactions with near-critical density plasmas, created from foam targets with densities of 3-100 mg/cm(3). The effect of changing the plasma density on both the laser light transmitted through the targets and the proton beam accelerated from the interaction was investigated. Two-dimensional particle-in-cell simulations enabled the interaction dynamics and laser propagation to be studied in detail. The effect of the laser polarization and intensity in the two-dimensional simulations on the channel formation and electron heating are discussed. In this regime, where the plasma density is above the critical density, but below the relativistic critical density, the channel formation speed and therefore length are inversely proportional to the plasma density, which is faster than the hole boring model prediction. A general model is developed to describe the channel length in this regime. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3563438]