The term "linearity" is often bandied about without a clear indication of what it is that varies in a linear manner with respect to what. Varying in a "linear manner" meaning that one variable varies in direct proportion to another, so that a graph having one variable as the vertical axis and the other as the horizontal axis would be a straight line.
In this case I would feel certain that the reference to linearity has nothing to do with the waveshape of the AC.
Here is the complete relevant statement from the vhaudio website:
First developed in the 1920's, Thyratron tubes are essentially gas controlled rectifiers. Different from typical vacuum tubes, gas-filled Thyratrons are capable of handling much higher current than their vacuum tube cousins, and this is one of the key attributes to their usage in the Plasmatron. The stunning blue plasma glow is created by ionized, xenon gas.
The Plasmatron provides a more linear voltage output by adding negative resistance to the power line source impedance. But thats EE-speak... What that really means is: the voltage supplied by the Plasmatron wont drop. In fact, it can actually go up, when the load is increased. Need more. Get more.
The Plasmatron is an AC power supply for source components.
Heres what its not:
It is not a power conditioner.
It is not a spike or surge suppressor.
It is not a battery back-up.
It is not a power regenerator.
It is not a filter, in the conventional sense.
I would infer from this that it is a sort of a voltage stabilizer, which prevents the AC voltage from sagging down as load current increases, as would normally happen to some degree. The reference to negative resistance being equivalent to the statement that voltage may actually increase to some degree as current demand increases.
So to the extent that the device minimizes fluctuations in voltage that would normally result from fluctuations in current demand, it would seem that what is being linearized is variation of AC voltage as a function of time.
I have no idea, though, what all this may mean with respect to the likelihood of sonic benefit in most systems. I would note, however, that power amplifiers operating in Class AB or Class D generally have by far the greatest fluctuation in current demand among audio components, while also noting that power amplifiers are omitted from the list of components for which the Plasmatron models are recommended. Due undoubtedly, at least in part, to the somewhat limited load capability of the Plasmatrons.
BTW, in case anyone is interested, here are datasheets for the C3J
Thyratrons. They are "grid controlled rectifiers," meaning that they rectify by switching the tube between conducting and non-conducting states via a control voltage applied to a grid in the tube, rather than by the more usual rectification process of a diode tube or diode semiconductor (which have no grid or other control element, and rectify by virtue of being able to conduct in only one direction).
Although of course rectification implies conversion of AC to DC, and obviously both the input and output of the Plasmatrons are AC. So I don't think it's possible to determine how the Thyratrons are being utilized in the design without further information.