This paper presents a combined 2D numerical and experimental study of the influence of N$_2$ admixture on the dynamics of a He–N$_2$ discharge in the 10 cm long dielectric tube of a plasma gun setup. First, the comparison between experiments and simulations is carried out on the ionization front propagation velocity in the tube. The importance of taking into account a detailed kinetic scheme for the He–N$_2$ mixture in the simulations to obtain a good agreement with the experiments is put forward. For the μs driven plasma gun, the two-and three-body Penning reactions occurring in the plasma column behind the ionization front, are shown to play a key role on the discharge dynamics. In the experiments and simulations, the significant influence of the amplitude of the applied voltage on the ionization front propagation velocity is observed. As the amount of N$_2$ varies, simulation results show that the ionization front velocity, depends on a complex coupling between the kinetics of the discharge, the photoionization and the 2D structure of the discharge in the tube. Finally, the time evolution of axial and radial components of the electric field measured by an electro-optic probe set outside the tube are compared with simulation results. A good agreement is obtained on both components of the electric field. In the tube, simulations show that the magnitude of the axial electric field on the discharge axis depends weakly on the amount of N 2 conversely to the magnitude of the off-axis peak electric field. Both, simulations and first measurements in the tube or within the plasma plume show peak electric fields of the order of 45 kV·cm$^{−1}$ .