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Using interferometry, we investigate the dynamics of interaction of a relativistically intense 4-TW, 400-fs laser pulse with a He gas jet. We observe a stable plasma channel 1 mm long and less than 30 μm in diameter, with a radial gradient of electron density ∼5×1022 cm-4 and with an on-axis electron density approximately ten times less than its maximum value of 8×1019 cm-3. A high radial velocity of the surrounding gas ionization of ∼3.8×108 cm/s has been observed after the channel formation, and it is attributed to the fast ions expelled from the laser channel and propagating radially outward. We developed a kinetic model which describes the plasma channel formation and the subsequent ambient gas excitation and ionization. Comparing the model predictions with the interferometric data, we reconstructed the axial profile of laser channel and on-axis laser intensity. The estimated maximum energy of accelerated ions is about 500 keV, and the total energy of the fast ions is 5% of the laser pulse energy.