- The 2D computational code Z* is used to simulate physical phenomena in a hollow cathode triggered low-pressure capillary discharge at different phases of the process: electron beam generation, formation of a channel by an ionization wave and discharge dynamics together with ionization kinetics and plasma emission, particularly in the EUV band, which is interesting for applications. Runaway electrons in a gas-filled capillary discharge with a hollow cathode play an important role both in ionization wave propagation and in ionization of multicharged ions in a discharge plasma. The electron beam prepares a tight ionized channel. The fast electrons shift the ionization equilibrium in the discharge plasma, increasing the EUV emission from the relatively low-temperature plasma of argon or xenon. At the ionization wave stage, the electron flow is simulated in an electron-hydrodynamic model. At the discharge stage, the plasma is described by the radiative magnetohydrodynamics with ionization kinetics and radiation transfer. The universal method for calculation of cross-sections of electron–ion inelastic impact processes in a plasma of multicharged ions in a wide range of plasma parameters is realized in computational code on the basis of the Hartree–Fock–Slater quantum-statistical model of a self-consistent field for the average atom and the distorted wave approximation.