While servicing a malfunctioning x-ray machine, the engineer observes that electrical flow within the x-ray tube is alternating back and forth between cathode and anode. What device's failure is likely responsible for this issue?

The observation of electrical flow alternating back and forth between the cathode and anode in an x-ray tube indicates a failure in the rectifier. The rectifier is a crucial component that converts alternating current (AC) from the power supply into direct current (DC) required by the x-ray tube for optimal operation. If the rectifier is not functioning properly, it cannot prevent the reverse flow of current, leading to the situation where the current oscillates between the cathode and anode. This can result in inadequate x-ray production and potentially damage the tube.

In contrast, components like the step-up transformer and autotransformer play significant roles in adjusting voltage levels but are not responsible for the directionality of current flow. The step-up transformer increases the voltage to the levels required for x-ray production, while the autotransformer adjusts the incoming voltage to the required level for the transformer’s operation but doesn't rectify the current flow. The cathode filament, responsible for electron production, would not cause a reversal of current flow in the x-ray tube itself but rather influence the tube's operation based on the current provided to it. Therefore, the failure that causes the described problem lies within the rectifier.