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Self-sustained high-pressure pulsed glow discharge is applied to excitation discharge on transversely excited atmospheric (TEA) gas lasers. Influence of shockwaves with Mach number MS of 1.1 and 1.35 on the discharge has been investigated. The normal Shockwave, which is normal to gas flow direction in TEA gas lasers, is produced by a shock tube with gas mixture of helium and argon to simulate reflected shockwave in discharge cavity. Discharge instability depends on both the shock Mach number and the position of shockwave in the cavity. The discharge does not collapse by gas density disturbance caused by the shockwave with MS = 1.1, where the gas densities in front of and behind the shockwave are rho1 = 0.52 kg/m3 and rho2 = 0.60 kg/m3, respectively. In the two shockwaves with identical MS = 1.35 having rho2/rho1 = 0.83/0.55 or 0.67 kg/m3/0.45 kg/m3, the recovery of discharge depends on rho2, and the gas density disturbance caused by oblique shockwave destroys the discharge even if the cavity is occupied by the gas having suitable density in still gas. The discharge may not be disturbed with spatial distribution of preionization electron density due to the shockwave.