[Enthalpy]

Finally I checked what other Sapiens do already to transport electricity over continents.

Very long powerful lines exist, they use DC, but with bare conductors at really tall towers. 12GW at ±1100kV over 3000km between Changji and Guquan
  hvdcnewschina.blogspot.com
almost what continental Europe needs to distribute windpower, except the vulnerability and aspect of the aerial line.

Most isolated lines are underwater. 2250MW at ±600kV over 422km between Hunterston and Wirral for 1.2Ggbp (1.46G€)
  assosubsea.com - wikipedia
The UK has links with many neighbours. 1400MW at ±515kV over 720km between Cambois and Kvilldal for 2G€
  wikiwand.com
about the same with Denmark and next with Germany for 1.9G€
  nsenergybusiness.com

Few HV lines are buried in continents. "Corridor A" will transport 2GW at ±525kV in Germany, comprising 300km "Corridor A-Nord" for 1G€ and 340km "Ultranet"
  nsenergybusiness.com

The usual dielectric is XLPE, cross-linked polyethylene. 1GW cables can make coils <3m wide. The central conductor is often multi-strand copper. The return current uses generally a separate cable, not the sheath, and generally at high voltage.

==========

Can buried isolated cables of this technology transport 50GW over 2000km land? Not easy!

According to the appended scaling factors, from 2250MW over 422km to 50GW over 2000km, identical radii need 105× as many cables, 499× as much conductor and insulator volume, and if it were proportional, 1.46G€ would extrapolate to 729G€. Even if the amount reduces the price by 40%, 437G€ are twice the cost of the wind turbines that produce the electricity, excluded. Or else if keeping two cables, with radii and voltage ×3.2 (that's ±1.9MV!), the volumes increase ×49 and a proportional price reaches 71G€, or much less because the production cost doesn't increase like the cross area.

Cooling is a limit to flexible cables with plastic insulation (formula appended). Take a dissipation 30MW/300km = Q/L = 100W/m and R/r=2 in XLPE insulator, the drop is 29K there. In the soil, taking R≈1.5m r=0.1m, the drop is 108K if dry, 18K if wet, so favourable conditions leave little margin. Now if dissipating 1GW over 2000km = 500W/m, the insulator fails. The design can be tweaked, uneasily.

An algebraic solution exists for the wave impedance, hence the lineic capacitance, of a round conductor over a ground plane. Adapting it to heat conduction would give a better formula than "taking R≈1.5m". Detail, I won't do it.

[Enthalpy]

The materials are cheap at a long powerful line. As unoptimized arbitrary example, r=0.14m R=0.30m L=2000+2000km need 670kt aluminium costing 2G€ (plus the sheath) and 810kt processed vegetable oil costing 1.5G€. The amounts are much less than the EU's yearly production. Lukewarn aluminium resists 1.14+1.14Ω. At ±960kV DC, these dimensions transport 50GW with 3.1% losses.

The installation of a line through the Ocean justifies an expensive high-tech cable. I believe a continental line should be low-tech, resembling more a pipeline where the parts cost little more than the materials, and the installation should accept some assembly work. Like: a dumb conductor in a tube, with transportable sections screwed or welded together on site, and oil in between. Tens of G€ saved pay easily for assembly work: that's 30k€ per joint.

==========

Oil cools well the conductors at powers inaccessible to solid dielectrics.

I take again r=0.14m R=0.30m L=2000+2000km and 50GW×3.1% losses, or 390+390W/m. Vegetable oil weighs 920kg/m³ and absorbs 2400J/kg/K, so an axial flow at gentle 2m/s exiting 10K warmer removes 10MW lost in a 25km long section. The coolers can clean and monitor the oil. The soil remains cool for normal uses. Easy, known.

A transverse flow by natural convection can also move heat from the central conductor to the sheath. I find that a 20mPa×s oil climbs in a 2.7mm thin layer around the central conductor, up to 9mm/s with a quadratic profile, and leaves only 11K warmer from 390W/m. I am unreliable here: a design needs an expert and experiments.

But then, the soil can't remove 390W/m from the sheath, and aluminium heat spreaders would add too much metal, so passive cooling needs smaller losses or about 3× as many cables. The spreaders are rather strips to let groundwater through. Or put oil loops in the soil?

Marc Schaefer, aka Enthalpy

[Enthalpy]

[...] Detail, I won't do it.

Finally I did it myself. The algebraic solution for the thermal resistivity between a cylinder and a plane is appended.

The characteristic impedance for a balanced line is from wiki. Versus the symmetry plane it's one half.
  wikipedia

Marc Schaefer, aka Enthalpy

[Enthalpy]

The Russian Rosatom won't build a nuclear power plant Hanhikivi, Finland
  CNN
due to "significant delays and inability to deliver the project".

7.5G€ from Rosatom was much more expensive than renewables. The other suppliers of NPP have stopped their activity or are even more extremely expensive (EDF, 12 to 19G€).

Time to consider the biomass, as proposed here?

[Enthalpy]

Just before the war in ukraine, some politicians promoted nuclear power plants - the same politicians who promoted natural gas as a "transition away from fossil fuels". Few weeks after the combats for the Chernobyl and Zaporizhia nukes, some of these politicians hope citizens have already forgotten and try to insist. Time to say: No, we haven't forgotten Chernobyl, Fukushima, and we know the hideous risks of nuclear power plants in a war.

All power plants are primary targets in a war, remember Yugoslavia and elsewhere. But nuclear ones (NPP) render a huge land area unusable for centuries when they burst, just like in Chernobyl in 1986. The AIEA's report claimed that graphite burned there to spread more radioactive pollution. That's a lie to downplay the risk of water-moderated reactors. Graphite does not burn. Averyone can try with lubricating graphite nanopowder on a candle. That's why graphite makes liners at kilns.

This time at Chernobyl and Zaporizhia, the Russian armed forces tried not to damage the reactors because Belarus and Russia are near. In France they wouldn't hesitate. With 18 plants spread evenly, the country would be uninhabitable. An enemy, not even Russia, even without weapons of mass destruction, can exert the ultimate blackmail on a country equipped with NPP.
  aljazeera

Read how "experts" downplay the risk:
  aljazeera
"sturdy concrete and steel structure"... "can withstand an explosion caused by a shell"
=> Lie. The French NPP have a 20cm steel vessel and a 90cm concrete dome
  fr.wikipedia
90cm concrete resist as little as 20cm steel. Already the stone-old T72 battle tank shoots shaped charges and flechettes that pierce 25-45cm steel
  shaped charge - kinetic energy penetrator - T-72 at Wikipedia

The EPR NPP claims 1.3+1.3m concrete. WWII howitzers pierced 3.5m concrete, known present bunker busters pierce 6m concrete, while hypersonic gliders break bunkers from 3000km distance
  Karl-Gerät - bunker buster - Kh-47M2 Kinzhal at Wikipedia
A ballistic kinetic energy penetrator, present or future, is much worse. Battle tanks throw only 8kg flechettes at 1800m/s, but a penetrator launched by a truck-mounted missile can weigh 3000kg and fall at 5000m/s from 3000km distance.

[Enthalpy]

To cool a buried Hvcd line, heat pipes are better than oil loops and metal heat spreaders in every aspect.

Heat pipes evaporate and condense a fluid in a pipe to transport much heat with very little temperature drop and materials
  wikipedia
Here a small slope can move the liquid, so the tubes are smooth. AA5083 or AA5754 would be cheaper than the usual copper. The ends can be pressed or twisted close, then sealed by TIG, brazing, diffusion welding, or a cap be  welded by friction, etc. Added n-propanol or isopropanol can prevent water freezing.

The lengths of line elements and heatpipes shall ease the offroad transport, I take 6m. The heatpipes are assembled with the sheath on site with no oil leak risks. More contact area transfers less power than at a Cpu maybe an AA5083 part welded on the AA5083 sheath encircles the heat pipe firmly with a screw. The central conductor, the oil and the sheath spread heat lengthwise well, so the line survives broken heat pipes.

Two <10mm 6m heatpipes per metre and per side carry 98W each. Spreading to h=0.25m in 0.4W/m/K soil drops 30K as per previous message. Conduction over 0.75m to the surface drops 61K. Comfortable for oil and aluminium. The soil isn't as bad everywhere, and as a mean, cooler aluminium loses less power.

Optional small metallic heat spreaders on the heatpipes spread heat better and can save heatpipes. No obvious advantage, cost shall decide.

Maybe the trench is 12m wide to lay the heatpipes, or it's narrower with long narrow holes to hoist the heatpipes. The conductor can lay deeper for safety, with only the heatpipes at -1m.

50GW would rather transit over several lines. Below 35GW, +960kV and -960kV can share one trench to save costs and reduce the magnetic field. They can even be twisted. If economical, both conductors can share the oil and the sheath, or 3 or 6 conductors to carry AC.

Design now, try, produce and install?
Marc Schaefer, aka Enthalpy

[Enthalpy]

To monitor a power line, stations along the line can listen to the electric noise created by corona or by arcs. Cross-correlating the signals received by different stations increases the sensitivity and locates the source accurately. I suppose this is long done.

Accepting 100dB losses over 25km distance (to the oil cooling stations if any) lets the line propagate up to 5MHz roughly, but I ignore the dielectric losses. Fine, since discharges create noise from audible up to GHz.

Acoustic noise too can detect and locate corona and arcs, as well as leaks, especially by correlation. Already done against leaks at gas pipes.

Optical fibres can measure the temperature and much more, and transmit the data very far. If inside the sheath, they can detect bubbles, measure the oil's optical properties, sense noise locally, measure the current, the electric field, etc. Outside the sheath, the temperature, the magnetic field hence the current, some acoustic noises, maybe leaked oil, and others are still accessible. Fibre sensors exist for long, a pipe is a perfect use for them.

Marc Schaefer, aka Enthalpy

[Enthalpy]

I suggested here on 20 Apr 2022 some seemingly cheap paths to refine natural triglycerides. But synthetic oils may be purer hence last longer. They can be cheaper than I thought.

A refinery shall provide a mix of 1-alkenes. Hydroformylation makes aldehydes. Oxidation gives a mix of fatty acids, reduction a mix of fatty alcohols if needed. Esterification might use fatty alcohols if the esters have good pour and flash points, or glycerol, or the pentaerythritol more common to synthetic transformer oil. Many-hydroxybenzene? Bigger polyols?

Saturated acids needed for durability tend to make solid fats, but here the lengths of the carbon chains can be nicely tuned, and the mix lowers the pour point. Though hard to predict, a more branched ester (pentaerythritol etc) may broaden the liquid range and reduce the viscosity.

[Enthalpy]

Sources claim that aerial lines are too inductive, buried lines too capacitive, justifying DC for long lines. But for really high power, the characteristic impedance of a submerged or buried line can be matched, neither capacitive nor inductive.

Take one 65Ω coaxial per phase. 30GW need 806kV_rms = 1140kV_pk phase to neutral: such voltages are already in use. 3 or 6 conductors in a common sheath would slightly lower the impedance, still comfortable.

If the power varies and the voltage is constant, the line becomes capacitive for lower power. Solutions:

• Lower the voltage too. But the ohmic losses don't drop at partial power. Neither does this fit well a continent-long line with intermediate taps.
• Compensate the reactive power but the usual methods. But a line matched at almost the maximum power needs less compensation at partial power.

Marc Schaefer, aka Enthalpy

[Enthalpy]

How big is the stray induction created by the strong current?

The appended curve gives the horizontal component divided by 40µT to compare with the geomagnetic field, as a function of the height.

• The line won't go unnoticed with the usual constructions. Passive cooling reveals it anyway.
• Bifilar lines would fool walkers, boats, planes and cars at some 100m, ouch. Only 10m if quadrupolar.
• Bifilar lines may disturb some birds and fish at 400m, ouch again, and 20m if quadrupolar. But experience exists for AC overhead lines, which animals seem to distinguish from the geomagnetic field.
• Antisubmarine boats and planes detect such a bifilar line from many km, a perfect quadrupolar one from many hm.

While a quadrupolar line seems desirable, it costs sqrt(2)× as much metal.

Twisting the conductors squeezes the field at distances greater than the helix period. It can be done at complete cables, or at conductor sets within a straight sheath. Curved extrusion exists, a curved 6m section nears the quarter period of a helix. Maybe extrusion achieves helices too? Or deform the parts into helices at the production. Parts 0.3m off-axis are 0.3% longer, hence expensive and lossy, with 4×6m period, or 4.8% longer with 6m period.

Concentric currents squeeze the field, as limited only by geometric accuracy. As the sheath must be sturdy, flowing the return current in the insulated sheath seems logical. But electric alloys are very soft and not so corrosion-safe. Possible improvements:

• Centrifuge casting can include stiffeners of locally bigger diameter, for instance where the sections are assembled.
• Could extrusion achieve tubes of sandwiched AA5083 / pure Al / AA5083? From a sandwiched feed material or from three feeds co-extruded. Nice research topic if still not done.
• Cold-working hardens the tube and keeps the conductivity. Possibly by oval deformation between rolls. If not, azimuthal cold-rolling is already done at Ariane 5's boosters. Or cold-draw the tube. More processes exist for hot Fe, apply them to cold Al.

Marc Schaefer, aka Enthalpy

[Enthalpy]

The European Commission presented on 18 May 2022 its plan REPowerEU
  aljazeera - REPowerEU - InvestmentsHydrogenBiomethane
meant in undiplomatic terms to end the dependency on Russian fossil fuels and tackle the climate crisis.

Among the 210G€ are 29G€ for electricity grids, 86G€ for renewables, including decentralized biomethane, and zero for nukes

[Enthalpy]

[...] hypersonic gliders break bunkers from 3000km distance [...] a penetrator launched by a truck-mounted missile can weigh 3000kg and fall at 5000m/s from 3000km distance.

North Korea, not exactly a high-tech country, tested missiles today
  CNN
described by some people as InterContinental Ballistic Missiles, and the newspapers repeated that, optionally with comments by third parties.

The third missile flew 760km at 60km altitude. This isn't a short-range "ballistic" missile with "erratic" trajectory. It's a manoeuvring hypersonic glider, like the Russian Kinzhal that blew a bunker in Ukraine. Using public figures for hypersonic L/D, I estimate a penetrator can retain roughly 1700m/s after steering deeply down from its horizontal trajectory, and still weigh 0.2t depending on the start mass. Big ouch!

The first missile is not a "presumed ICBM". 360km range and 540km apogee don't suffice. It's a short-range missile. A decent ICBM candidate flew in late March: 6000km apogee and 1080km range. The desire not to overfly Japan can explain both abnormally high paths. But there is an other explanation: these ballistic missiles are tested to fall at steep angle on the target, which can be a bunker, or for instance an aircraft carrier, as I keep repeating for years. While one ballistic missile is easily detected, a penetrator is very difficult to destroy or even deflect for being dense, sturdy and possibly passive. Worse: such missiles can be launched in dozens and carry many penetrators each, needing no steering and being then impossible to stop nor avoid. That's why I keep repeating "big surface ships are only targets, not weapons, don't build any more".

What if a hypersonic glider or a big fast ballistic penetrator hit a nuclear power plant? You guessed. 1.3m+1.3m concrete won't stop anything. 540km apogee leave 3.2km/s to a 0.5t to 4t penetrator, 6000km leave 10km/s to maybe 100kg, while an 8kg battletank penetrator hits with 1.8km/s.

[Enthalpy]

[...] 6000km leave 10km/s to maybe 100kg, while an 8kg battletank penetrator hits with 1.8km/s.

6000km leave rather a bit under 8km/s.

[Enthalpy]

More thoughts about tubes of 5xxx/1yyy/5xxx alloys sandwich for a power line's conducting sheath, because conductivity demands "pure" aluminium while strength and corrosion resistance suggest some 5% Mg at the surfaces.

I proposed co-extrusion of the three layers. Maybe continuous casting achieves the same.

Or dip the cold tube of 1yyy alloy in molten 5xxx to deposit layers on it? It depends on how the oxide layer behaves.

• If it separates from the immersed tube, perfect.
• Break it with an arc in argon atmosphere just before dipping?
• Remove it mechanically in the bath?
• Mg can potentially reduce Al₂O₃. The bath could be Mg instead, or rather near the eutectic Al₃Mg₂ (450°C vs Al 660°C and Mg 650°C).

Deposited eutectic layers could diffuse under heat until the surfaces contain some 5% Mg. Or they could serve to solder tubes of 5xxx, 1yyy and 5xxx in an other.

In all cases, lukewarm or cold extrusion of tubes can usefully harden the 5xxx faces.

Marc Schaefer, aka Enthalpy

[Enthalpy]

A nuclear reactor in operation is just critical: it produces as many neutrons as are used or lost. So could a weapon hit a reactor to induce a strong power excursion (= a nuclear explosion), potentially worse than the release of the accumulated radioactivity?

Reactors have passive stability. For instance water expands at heat or boils, less water leaves more energetic neutrons which trigger fewer uranium fissions in usual reactors. Some such feedback loops are fast (hotter uranium absorbs fewer epithermal neutrons), others react in the second time range (water expansion) and can weigh in because a few % of the neutrons are emitted after a delay in the second range. But if the reactivity increases enough to sustain the reaction without the delayed neutrons, the "prompt criticital" reaction can diverge in the nanosecond time scale.

Fast neutrons reactors (=breeders) are worse.

• The loss of their coolant (often sodium) increases the reactivity, like 5%.
• Their plutonium produces fewer delayed neutrons: 0.6%.
• They lose many neutrons exiting the core, like 20%.

A missile launched from a truck can send a 3t kinetic impactor hit the core at 5km/s with an angle depending on the distance. A nuclear enemy wouldn't need to target a reactor, so imagine the impactor is of unreactive material, not plutonium. It passes the concrete dome and steel vessel unhindered, can hit the core eccentered, and creates a shock wave that compresses sodium by 30% or more.

• The compressed part of the core lets fewer neutrons exit.
• Sodium is pushed away faster than plutonium.
• The impactor can bring deuterium and lithium.
• The Superphénix breeder contained 5.7t fissile material, more than the Mk41 bomb did for 25Mt.

I can't go farther with hand estimates. After I mentioned this risk on the Internet, Angela Merkel (PhD for nuclear physics) closed all breeders in Germany. Maybe some computer simulations are still available at the government.

I've read about breeder projects in the USA, China, India.