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A proposal is presented in this work for a new type of ion source that employs a hyperbolic potential field for the dual purpose of trapping the plasma ions, and permitting the electrons to impact the trapped ions successively, which by turn render the ions highly stripped. The pvwposed souroe consists of an axially symmetric hyperbolic Penning assembly energized with fixed and cosinusoidal voltage and is immersed in a homogeneous axial magnetic field. The anode and both of the two cathodes follow hyperboloid surfaces of one and two sheets respectively. Extraction of the stripped ions can be accomplished either radially or axially through an extracting system, which is optimized to satisfy Pierce conditions of rectilinear flow. Filtering the extracted ions is done by a quadrupole mass analyzer. Under the influence of the imposed hyperbolic potential field, electrons are allowed to ascillate with bound or unbound trajectories depending on the operating conditions. From the solutions of the equations of motion governing such oscillating electrons, it is possible to optimize the overall performance of the proposed ion source.