The pressure balance equation for a plasma sheath made up of fictitious fuel ions, electrons and α-particles is solved. The ions are assumed to be electrostatically confined which turns out to imply quasi-neutrality for sufficiently diffuse boundaries. The α-particles are assumed to satisfy the Vlasov equation and to be produced mono-energetically with a spatial source distribution proportional to the square of the fuel ion density. The final steps of the calculation are performed numerically and results for a few sets of parameters are shown. The α-particle pressure is dominant in all regions of space for cases of practical interest.