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The effects of diode structural parameters, input voltage, and external magnetic field on the space-charge-limiting currents of a magnetically immersed foilless diode are studied by analysis and particle-in-cell (PIC) simulations and are verified with experiments. The effects of longitudinal anode-cathode (A-K) gap and anode-cavity radius on space-charge-limiting current and critical external magnetic field are obtained. A scaling law for diode current is given, which is in good agreement with the PIC simulations and experiments. This is important for the design of this kind of diode because the expected current and impedance of the foilless diode is obtained by changing the longitudinal A-K gap in practice. The I-V relation obtained is applicable in practice and in good accordance with the experiments.