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• #### Proton transport and auroral optical emissions

The hydrogen lines are the characteristic emissions of proton aurora and have been used to study the impact of protons upon the atmosphere. Observations of hydrogen emission on the long wavelength side of the unshifted lines were not explained by previous theories. To explain the observed optical emissions, a numerical code is developed to solve the one dimensional, steady state, linearly coupled transport equations of H$\sp+$/H in a dipole magnetic field. For the first time, the mirror force is included in the transport equations to produce backscattered particles which are responsible for emission at wavelengths longward of the unshifted lines. Both downward and upward particle intensities of H$\sp+$/H are calculated. The mirror reflectivities of energy and particles are defined, and their dependences on proton input spectra and pitch angle distributions are studied. The results show that the mirror reflectivity increases both with characteristic energy and with pitch angle of the input proton flux, but is more sensitive to angular distributions than to energy spectra. Energy deposition rate, ionization rate, H$\sb\alpha$, H$\sb\beta$ and Nitrogen First Negative bands emission rates and profiles are calculated. Calculated fluxes of H$\sp+$/H and emission properties of Hydrogen Balmer lines are compared with a rocket measurement. The efficiency for production of the Balmer lines and the Nitrogen First Negative bands is obtained in terms of the energy input rate and the H$\sp+$ particle flux. A Doppler shift of about 3.0 A toward the blue for magnetic-zenith profiles of H$\sb\alpha$ is obtained, compared with observational results of $6.0 \pm 2.0$ A. The calculated emissions on the red side of the unshifted hydrogen atomic emission lines when convolved with the instrumental function accounts for the observed emissions on the long wavelength side of the unshifted hydrogen Balmer lines.