A tube rectifier works differently to a solid state rectifier (as pointed out by PRR).
An SS diode rectifier works by only allowing current to pass in one direction, so when the VAC voltage swing goes -ve, the current is blocked through that diode. The diodes on each side of the PT's High Tension (HT) winding allow high voltage +ve current pulses to pass, which correspond to the high voltage AC wave which is in opposite phase to each other end of the HT winding.
For a tube rectifier, the ends of the HT winding are each connected to one of the rectifier's plates.
The tube rectifier's cathode is heated so that it frees electrons into a 'space charge' 'floating' just above the surface of the cathode (like a conventional tube cathode). The tube rectifier's cathode isn't grounded, but is connected to the B+ reservoir cap.
On the +ve 1/2 of each end of the HT winding's VAC cycle, the corresponding tube rectifier's plate that it is connected to, swings positive. This pulls electrons away from the cathode's 'space charge', and this causes the cathode to rise to a high +ve voltage, which in-turn sucks electrons out of the reservoir filter cap's "B+" side, causing the filter cap to become positively charged. The 'internal resistance' resulting from the interaction between between the cathode and the plate (and the space between them, and their relative sizes, and the amount of cathode heater energy, and the amount of VAC swing at the plate, and the amount of reservoir capacitance) is referred to as the plate resistance, and this causes a voltage drop between the maximum +ve voltage swing at the plate and the corresponding maximum cathode voltage. Different tube rectifiers exhibit different amounts of this 'forward' voltage drop.
To return to the current cycle, when the rectifier plate swings to the -ve 1/2 of the cycle, nothing happens at the cathode as a result of that -ve plate voltage swing, BUT at this same time, the other rectifier plate is reaching its +ve 1/2 of the VAC cycle, causing electrons to flow from the cathode to that other plate. So the cathode is experiencing continuous back-to-back +ve pulses of charge, which is sucking electrons out of the reservoir filter cap, encouraging that filter cap to remain at a high +ve voltage (albeit at a voltage that's lower than the peak VAC swing on the plates, due to the forward voltage drop exhibited by the rectifier tube).
The final part of this is that the reservoir filter cap takes longer to 'discharge' (than it takes to 'charge' to a +ve voltage). The current that occurs in the corresponding 'charging' segments of the filter cap's charging cycle are referred to as 'charging' current. This charging current is not constant, but is in little discrete (but more-or-less instantaneous) pulses that correspond to the timing of the rectifier's cathode +ve pulses. Of course, once the filter cap charge equals the cathode's charge, the filter cap's charging current stops, and resumes again when the capacitor's charge falls to a sufficiently lower voltage to encourage another 'burst' of charging current. The bigger the reservoir capacitance of this filter cap, the more stress this charging current places on the rectifier. That is why tube rectifiers are rated for a maximum recommended reservoir capacitance.
The 'discrete' bursts of charging current going into the reservoir cap don't in themselves produce a steady B+ voltage at the reservoir cap, but produce what is known as 'ripple current' at that cap. This requires further filtering (e.g.; with a resistor and another filter cap) to get a smooth B+ voltage.