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The velocity-current relation of positive leader discharges is of great importance in the research of lightning physics. However, the measured data in a wide range of current up to several hundred amperes are not available so far. To fill the gap, experiments on positive leader discharges in long air gaps under lightning impulses were carried out on the test site at an altitude of 2.1km. The velocity and current of positive leaders were measured with the synchronized discharge current and high-speed video frames. An empirical formula for the velocity-current relation of positive leaders is given with the leader current up to 500A. The measurements are also compared with the numerical simulations, and it is suggested that the initial tip radius of a propagating leader grows as the leader current increases.

Plain Language Summary Lightning propagates in air in the form of electrical discharges we named as leaders. The leader advances itself by ionizing and heating the air in front of it. It is found that the leader velocity is almost only dependent on the electric current flowing through it. A lot of experiments have been done to obtain the leader velocity-current relation. However, it is doubtful if the extrapolation of the curve is valid since there is a big difference between the current amplitude of laboratory leaders (a few amperes) and that of lightning leaders (up to a few hundreds of amperes). One way to achieve large leader current in the laboratory is to do the experiments under low air pressure. This idea motivated us to perform a series of experiments at an altitude of 2.1km. The maximum leader current we could generate and measure is up to 500A. Based on the data, we propose an empirical formula of the velocity-current relation that can be used to predict the lightning velocity through numerical simulations. The comparison with the published measurements shows that our formula could provide quite accurate estimations, while the previous extrapolation approach fails.