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Electron current flow drawn off a hollow cylindrical cathode in a pinch‐reflex ion diode is observed to have a filamentary structure. Such filamentation can lead to nonuniform anode turn on and ion emission. Consequently, ion beam brightness is degraded. In this context a purely growing thermal‐resistive instability in the cathode plasma is examined. The instability causes current filamentation and grows on a time scale comparable to the electron–ion energy equilibration time. Electron inelastic collisions have a stabilizing influence on the instability.