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Aims. Hydrogen Lyman continuum emission is greatly enhanced in the impulsive kernels of solar flares, with observations of Lyman lines showing impulsive brightening and both red and blue wing asymmetries, based on the images with low spatial resolution. A spate of proposed instruments will study Lyman emission in more detail from bright, impulsive flare kernels. In support of new instrumentation we aim to apply an improved interpretation of Lyman emission with the hydrodynamic radiative code, HYDRO2GEN, which has already successfully explained Hαemission with large red-shifts and sources of white light emission in solar flares. The simulations can interpret the existing observations and propose observations in the forthcoming missions.  Methods. A flaring atmosphere is considered to be produced by a 1D hydrodynamic response to injection of an electron beam, defining depth variations of electron and ion kinetic temperatures, densities and macro-velocities. Radiative responses in this flaring atmosphere affected by the beams with different parameters are simulated using a fully non-local thermodynamic equilibrium (NLTE) approach for a hydrogen 5 levels plus continuum model atom with excitation and ionisation by spontaneous, external and internal diffusive radiation, and by inelastic collisions with thermal and beam electrons. Integral radiative transfer equations for all optically thick transitions are solved using the L2 approximation simultaneously with steady state equations.  Results. During a beam injection in the impulsive phase there is a large increase of collisional ionisation and excitation by non-thermal electrons that strongly (by orders of magnitude) increases excitation and the ionisation degree of hydrogen atoms from all atomic levels. These non-thermal collisions combined with plasma heating caused by beam electrons, lead to an increase in Lyman line and continuum radiation, which is highly optically thick. During a beam injection phase the Lyman continuum emission is greatly enhanced in a large range of wavelengths resulting in a flattened distribution of Lyman continuum over wavelengths. After the beam is switched off Lyman continuum emission, because of its large opacity, sustains, for a very long time, the high ionisation degree of the flaring plasma gained during the beam injection. This leads to a long enhancement of hydrogen ionisation, occurrence of white light flares and increase of Lyman line emission in cores and wings, whose shapes are moved closer to ones from complete redistribution (CRD) in frequencies, and away from the partial ones (PRD) derived in the non-flaring atmospheres. In addition, Lyman line profiles can reflect macro-motions of a flaring atmosphere caused by downward hydrodynamic shocks produced in response to the beam injection reflected in the enhancements of Ly-line red wing emission. These red-shifted Ly-line profiles are often followed by the enhancement of Ly-line blue wing emission caused by the chromospheric evaporation. The ratio of the integrated intensities in the Lyα and Lyβ lines is lower for more powerful flares and agrees with reported values from observations, except in the impulsive phase in flaring kernels which were not resolved in previous observations, in which the ratio is even lower. These results can help observers to design the future observations in Lyman lines and continuum emission in flaring atmospheres.

Non-thermal hydrogen Lyman line and continuum emission in solar flares generated by electron beams