The distribution of antenna-driven fields of electromagnetic waves in the local Alfvén resonance (AR) region is studied under resonant conditions, when the axial period of the fundamental harmonics of magnetohydrodynamic oscillations in the axial direction is twice as large as the pitch length, and the poloidal number of the fundamental harmonics is twice as small as the polarity of the helical coils. It is shown that taking into account the helical inhomogeneity of the steady magnetic field can remove infinite discontinuity of the wave fields, which is present in the case of a straight confining magnetic field, rather than electron inertia or finite ion Larmor radius. Radio frequency power absorption within the local AR is compared with the case when AR structure is governed by electron inertia or finite ion Larmor radius. Another approach is proposed to explain the helicity induced gap in the Alfvén continuum.