I've been studying this topic in more detail over the past week. I now see that ringing could occur
whenever you have an LC circuit. In the diagram below of a typical power supply used for a tube amp, I believe there are two opportunities for ringing, labeled 1 and 2.
Considering case (2) first: stepping the current load of I1 in PSUD, or just watching the initial rise of the voltage on C2, I was able to see the ring in simulation caused by this CLC circuit. I realized however, that I might be missing a resonant circuit at (1). This resonance is created by the leakage inductance between primary and secondary windings of the power transformer, along with the winding capacitance (thus another LC circuit, although not obvious at first glance). When current abruptly stops flowing due to the diodes switching off (as part of the rectification process), the circuit rings. It is my belief that these two sources of ringing are audible, at least to some extent.
The apparent typical solution to damp both sources of ringing is to fit in "snubber" circuits. In case (1), the snubber consists of a cap in series with a resistor hung directly across the secondary winding (usually about 0.1 uF + 50 ohms or so, but depends on the transformer). Like so:
Some solutions fit in a second "snubber" capacitor in parallel to the added C+R shown above to swamp out the internal winding capacitance. In any case, the purpose of the snubber is to absorb and release energy in semi-opposite phase to damp the ring.
In case (2), the snubber consists of two back-to-back capacitors (typically .1 uF or so) hung one on each side of the choke and connected together on the other ends, and those two ends are connected to ground at the center tap, and where the snubbing resistance is the internal DC resistance of the choke itself.
In the first diagram above, the capacitors are not .1 uF--they are much larger at 47 uF and 200 uF, but in conjunction with the series resistance of the choke, and the value of R1 (4.7 ohms), as well as the series resistance of the secondary winding, I believe you can find values of R1, C1, and C2 that meet both the criteria for snubbing the ring, as well as offer sufficient capacitive loading for proper ripple rejection and current demand for the output stage of a power amp. (that's my supposition anyway).
So it is my belief that correctly addressing both sources of ringing should make a very clean power supply that responds well to both HF and LF transients, giving a very "clean" sounding power supply for tube audio circuits.
At this point, all of this is just theorizing on my part. Am I on the right track with this thinking? Set me straight if I've wandered off somewhere.