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This paper presents an experimental and numerical study of the dynamics and structure of an atmospheric-pressure helium discharge with nitrogen admixture propagating through a thin dielectric tube surrounded by two ring electrodes. The experimental unfiltered optical emission of the discharge has been compared to the computed emission of the second positive system of nitrogen and shows very good agreement. In all studied cases, the discharge ignition occurs inside the tube at the outer edges of the high-voltage electrode ring, and the discharge propagates outward of both sides of the high-voltage ring with a rather homogeneous discharge front structure. When the discharge approaches the grounded ring, the emission is enhanced and moves from the symmetry axis to the tube surface. In both simulation and experiment, an initial front propagation velocity of about 3 ×106 cm/s is observed as the plasma traverses the first part of the electrode gap. This velocity increases in the later part of the electrode gap as the plasma approaches the grounded ring, and the observed velocity in the experiment is slightly higher than that in the simulation. In experiments, when the admixture is decreased, the discharge constricts close to the tube axis during its propagation between the electrode rings before moving to the tube surface close to the grounded ring. In simulations, as a first step, we have considered that, in reducing the amount of nitrogen admixture, the efficiency of photoionization decreases significantly. This allows the formation of an electron depleted volume close to the grounded electrode ring, which then constrains the discharge to propagate close to the tube axis, in agreement with experiments.