Though shear Alfven waves have no reflection points, these waves can be partially reflected from sharp field-aligned variations in Alfven velocity. Such a reflection can lead to the formation of quasi-resonators, such as the ionospheric Alfven resonator, in which wave energy can be accumulated. We show that a similar partial reflection of Alfven waves can occur in regions with steep variations of geomagnetic field line geometry. For that, the propagation of Alfven waves in a plasma immersed in a two-dimensional (2-D) curvilinear magnetic field has been investigated. The Alfven waves comprise two modes with different polarization, toroidal and poloidal, which are described by 1-D equations. These equations formally coincide with the equation for the case of a quasi-uniform straight magnetic field with a modified Alfven velocity that takes into account the field-aligned dependence of the Lam¿ coefficients. The toroidal and poloidal modes depend differently on the magnetic field geometry. The poloidal mode is efficiently reflected from regions where the magnetic field lines sharply converge or diverge, when its wavelength becomes comparable to the typical scale of magnetic field convergence. This effect can result in the formation of Alfven quasi-resonators on open field lines. This mechanism can be used to interpret the occurrence of specific polar cap quasi-periodic Pi3 pulsations with periods ~15--20 min observed by the AGO magnetometer array in Antarctica. Also, such a reflection can limit the influx of Alfvenic wave energy along reconnected field lines from the solar wind into the magnetosphere at certain wavelengths. This effect has been observed as the occurrence of a low-pass cutoff period ~10--15 min in the spectral transfer function between conjugate IMF variations and ground magnetic disturbances.