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In a pinched-beam ion diode, an intense electron beam focuses on-axis at the center of the anode and passes through the thin anode foil into a beam dump region behind the anode foil. The beam dump usually consists of an evacuated cylindrical anode-can. Because of energy deposition from the intense electron beam, the interior surfaces of the anode-can are expected to be space-charge-limited emitters. Therefore, the electron space charge from the beam in the anode-can will draw ions off these surfaces. There is evidence from nuclear activation which suggests that ions exist in the anode-can with energies that significantly exceed those associated with the diode voltage. Analysis and particle-in-cell simulations show that a virtual cathode can form in the anode-can that accelerates ions up to the energy associated with the diode voltage. Additionally, a subset of these ions can form current bursts that are driven to the outer wall of the anode-can with ion energies as high as a few times the energy associated with the diode voltage.