We demonstrate that when magnetic field-aligned currents encounter density cavities, double layers (DLs) spontaneously form. The parallel electric field in the double layer (DL) accelerates electrons and ions to maintain the current continuity. However, such double layers are found to be transitory; their growth is initially accompanied by further deepening of a part of the cavity and the decay with subsequent refilling. The bursty acceleration of electrons and ions by the double layer provides a mechanism for the conversion of the electromagnetic energy associated with the currents into kinetic energy of the plasma. Thus the spontaneous double layer formation in plasma density cavities could be an effective dissipation mechanism for Alfven waves which carry substantial currents when they acquire sufficiently short wavelengths perpendicular to the magnetic field.