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Serious question: was needing two wires holding us back?
Presumably, if you one use one wire, you will save half your money.
Best case, I'm sure there are economies of scale.
Not only that, but if you have two wires at a high potential difference on poles, you have to be careful to keep them separated, even under adverse conditions e.g. high winds.

Presumably, ensuring adequate clearance between a single wire and the ground is comparatively easier.

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Can someone help me understand the importance of this? Seems big but I just don't have the expertise to estimate the significance.
Explanation using my half forgotten physics course: Apparently they are using the overhead wire as waveguide, with high frequency, using only its capacitance, thus avoiding ohmic losses. There are losses only from dielectric polarization, which they claim to be much less than ohmic loss in standard transmission.
Thanks for spending the time but can you give me the 3rd grade explanation?
Gets energy from the power plant to your light bulb without heating up stuff along the way quite as much.
For some reason I thought they had found a way to do DC current over a single wire. This is a way to get AC transmission using latent capacitance in the line if I'm understanding correctly. Still very interesting, but not what I was expecting.
I thought it was SWER (https://en.wikipedia.org/wiki/Single-wire_earth_return ) but in fact it's something closer to "radio current", as explained in this 20-year-old(!) article:

http://amasci.com/tesla/tmistk.html

The biggest problem I see with this is that it will cause a lot of radio interference --- a long wire with that much power going through it at the frequencies they use will basically act like an antenna.

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put it into a waveguide
Like coaxial cable?
Yes, but then you just replace one type of loss for another, as I just understood.

The currents induced in the waveguide itself will be dissipating the power.

> 20 year old (!)

This paper is close to 20 years old too. The (2018) in the title is wrong.

Quasi-superconducting?
Chinese BYD has been trying for years to make an overhead wires free trolleybuses with this technology.

The main advantage is if you make it to operate high enough frequency, this should theoretically be safe to walk on, or at least safe to drive over.

Given that it will soon be 7th years since they first announced that, and there is nothing they offer on the market, there might have been some showstopper issue with it

Tangential, but the formatting on this is awful. It's like a high school lab report - every equation is a different size and aligned differently.
With such high power, how can you do maintenance work on these systems? With two wire systems, it is at least possible to avoid ground and short circuits.
Excerpt: "It was experimentally proved that SWEPS has quasi-superconductivity property for reactive capacitive current flow along the line even at high operation temperature of the electric conductor."