The Exotic Power Sources Today I'll wrap up my discussion of power plants Except for hyper-controversial nuclear, which I'll return to a bit later I'll

The Exotic Power Sources

Today I'll wrap up my discussion of power plants

Except for hyper-controversial nuclear, which I'll return to a bit later

I'll first cover the more "exotic" power generation technologies already in use:

- Tidal Barrage - Tidal Stream

- Wave - Geothermal

Then move to more exotic proposed technologies:

- Wind Generators IN the atmosphere

- Solar Cells ABOVE the atmosphere

- Nuclear Fusion

An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm

Tidal Power

Tidal power is really just a different form of hydro power

And as discussed in the earlier lecture on hydro and wind powers

Hydro is ultimately about gravitational potential energy:

D Egravity = M g Dh

Which for a continuous steady flow F (volume / second) gave us:

Phydro = 9.8 (kW-seconds / m4) x F x Dh (kW = kilowatt)

(Nitpicking: salt water can be a few percent more dense than pure water)

However, big difference: For tides and waves, flows are NOT steady at all!


Alternative forms of tidal power generation

The simplest / oldest might have been some variation of this:

Floating boat / buoy tied via rope and pulleys to onshore counter weight

With movement of onshore weight or pulley used to do some sort of work

But can get a lot more power from a variation of a dam

Ocean: Dammed inlet or manmade basin:

Power generated when tide coming in Power generated when tide going out

Also has potentially big benefits of moving power generation mechanism onshore

Or at least into dam which is connected to shore

And of concentrating / simplifying that mechanism (e.g. into single turbine)

Here recognizing the severe difficulty of keeping mechanisms working in saltwater

(Just ask Stephen Spielberg!)

(a.k.a. "Tidal Barrage")

How much power out?

With density of water ρ, reservoir area A, surface gravity of g:

Say tide raises sea level h, then lowers it h: net change in height = 2h

So full tidal rise => Gravitational energy of M g 2h. With mass of raised water:

M = density of water x its volume = ρ (2 h Area) (2h enters again!)

Putting in values for water density and surface gravity:

Egravitational = ρ g (2 h Area) 2h = (1000 kg/m3)(9.8 m/s2) 4 Area h2

= (9800 kg m2/s2 x 1/m4) 4 Area h2

= 39.2 kiloJoules /m4 x Area h2

Tidal cycle is ~ 12 hours ~ 43,200 seconds, so cycle averaged power is:

Powertides = 0.91 Watts / m4 x (Area h2)An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm

Note: Book gets 2X my number = Power out DURING falling tide (with 0 out during rising tide)

But it's actually 6 hours of rising tide + 6 hours falling:

But can extract power whichever direction tide is pushing water:

Get power when rising tide PUSHES water into reservoir

AND

Get power when falling reservoir PUSHES water back out to sea

So, it turns out that answer above is still about right

But because salt water is a little denser than fresh water, fair to round up to:

Powertides ~ 1 Watt / m4 x (Area h2) where h = half tide

Of which we could recover a fraction: εgenerator (efficiency of our hydro generator)


But there is also the "pumping trick"

As described in "Sustainable Energy without the Hot Air – David J.C. MacKay:"

Make your dam a bit TALLER than the high tide level, and add some pumps

At HIGH tide, pump extra water UP into reservoir (expending energy!)

At LOW tide that SAME water will fall LARGER DISTANCE = More energy back! Tide provided PART of energy to get

extra water up into reservoir

But YOU then get all the energy back


Thereby expending/recovering additional power:

Say at (about) high tide, you pump water UP a further height b:

With pump efficiency = εpump and generator efficiency= εgenerator

That requires you to expend an energy:

Eexpended = (1/εpump) M g height =(1/εpump) (ρ A b) g b = ρ g A b2/εpump

But then, at low tide, that water falls not b but b + 2h:

Erecovered = εgenerator M g height = εgenerator (ρ A b) g (b + 2h)

Giving ratio of added power out to added power invested

Ratio out / in = (εgeneratorεpump) (b + 2h)/b call εgeneratorεpump

= εtotal

If efficiencies were 1, ratio would always be better than 1 => net gain

If efficiencies less than 1, ratio => 1 when b = 2h (εtotal)/(1- εtotal)


Can also pump water OUT near low tide

Putting this ALL together, "Sustainable Energy without the Hot Air" shows:

Net gain for pumping is a "boost factor" of (εtotal)/(1- εtotal)

For εtotal ~ 0.76 (corresponding to pump and generator efficiencies of ~ 87%)

Book generates table (averaged over tidal cycle):

Tidal Half Optimum PowerPower

Amplitude (h) Boost Height (b) with pumping without pumping

1 meter 6.5 meter 3.5 W/m2

0.8 W/m2

2 meter 13 meter 14 W/m2 3.3 W/m2

3 meter 20 meter 31 W/m2 7.4 W/m2

4 meter 26 meter 56 W/m2 13 W/m2

http://en.wikipedia.org/wiki/Rance_Tidal_Power_Station

However (paralleling conventional hydropower):

Above demands BUILDING those coastal reservoirs

By damming up bays or estuaries. Thereby modifying coasts with ecological value

E.G. water purification and animal rearing value of coastal marshes

And/or: visual / leisure time / vacation residence value

And/or: harbor / industrial value "Worlds First" tidal power station (1966) in Rance River estuary,

in Brittany France

62 MW average (240 MW peak)

~ 1/10 average U.S. power plant

Thoughts regarding tidal barrages:

It's worrying to note that while the above Rance tidal barrage claims to be oldest

Its output power level cited by most sources as STILL being the largest

(Also, misleadingly, they mostly cite its peak rather than average power)

Suggesting, over fifty years, that a lot of people decided against this option

As relatively attractive, and relatively high power, as it appears

In addition, regarding the preceding pump enhancement trick:

That calculation assumes ALL the water is pumped up AT high tide

Or out AT low tide (i.e. all the extra water moved in ~ ½ hour)

But optimum "boost heights" were 5-7 times tidal height, making this unlikely

And pumping before or after peak tides => diminished energy gain

Of which a few exist:

Strangford Loch, N. Ireland: 1.2 MW

~ 1/500 average U.S. Power Plant

Or, with some added artwork:http://en.wikipedia.org/wiki/

Strangford_Lough

Leading to alternative of "tidal stream" power generation

http://subseaworldnews.com/2012/01/17/uk-seagen-tidal-turbine-gets-all-clear-from-

environmental-studies/


With a lot more contemplated, or at least imagined:

http://www.darvill.clara.net/altenerg/tidal.htm

http://climatekids.nasa.gov/tidal-energy/

http://www.bbc.co.uk/news/uk-wales-north-west-wales-

11037069

http://www.global-greenhouse-warming.com/tidal.html

http://www.fujitaresearch.com/reports/tidalpower.html

Including some very questionable proposals:

http://www.esru.strath.ac.uk/EandE/Web_sites/10-11/Tidal/

tidal.html

http://www.ecofriend.com/eco-tech-nasa-s-jpl-develops-a-

cost-effective-way-to-harness-ocean-energy.html

A proposal to use water turbines to mechanically pump water into necessarily BIG LONG BIG PIPES to an onshore hydro power station?

But producing electricity AT those turbines, and then just running electrical cable to shore, would seem immensely simpler and more efficient!

This appears to be the simple of a copy of a vertical axis wind turbine whose advantage is using winds from any direction. But tides will flow in one direction (and its opposite), so what is the advantage?

And with 1000X more dense water flow, its structure would have to be MUCH more strongly built than the wind turbine design it copies!

http://www.marineturbines.com/3/news/article/37/anglesey_tidal_energy_plan_moves_forward_

In fact, a particularly good idea might be to "lay low:"

That is, DON'T build a tall structure resembling ANY sort of wind turbine

Instead, just sink to / cling to the bottom

Removing any surface obstruction to navigation (i.e. target for collisions!) AND

Removing the need for VERY hard to construct undersea foundations (=$$$)

I.E. instead of this (foundations added): Something that could just be sunk on site:

http://news.bbc.co.uk/2/shared/spl/hi/pop_ups/07/uk_enl_1193829329/html/1.stm

http://www.pressherald.com/2012/07/21/maine-company-leading-way-as-tidal-energy-comes-of-age_2012-07-22/

Which is being pursued up in Maine:

Intended for Maine's Passamaquoddy and Cobscook bays:

Press Herald headline: "Maine company leading way as tidal energy comes of age:"

HOWEVER: 50 kW prototype ( ~ 1/10,000 average U.S. Power Plant)

"Much of the industry’s near-term expansion is expected to be in Nova Scotia . . .

(for units) that are community-owned"

However, power outputs to date are disappointing:

But they still might be very important for more remote/isolated locales

Isolation IS a typical enabling factor for many/most of these "exotics"

Also, it could be practical in special locales where geography favors installations:

Rance River Barrage: Not much more than short bridge => low dam

Bay of Fundy (Nova Scotia): World's highest tidal range, up to 16 meters

Moreover, if costs and reliability COULD be improved . . .

There IS the fact (from Hydropower / Windpower lecture) that FOR flows:

Energy_Density_Waterkinetic = 0.5 (kg/liter) x v2

Energy_Density_Airkinetic = 0.59 (g/liter) x v2

Implying: Offshore hydro could be 1000X more power dense than offshore wind!

For a larger impact, I'd suggest:

Float-into-place / sink / cling-near-to-the-bottom (foundationless) designs

for "farms" that might then be compatible with ship navigation

in narrow very high tidal flow mouths of large bays

For instance these (where I've experienced the force of tidal flow):

(Just a suggestion . . .)

Google Earth

Name sort of says it all (and we have all experienced it)

Trick is HOW to capture it. Actually built:

Or extrapolated:

http://www.biggreensmile.com/green-glossary/wave-power.aspx

An alternative: Wave power:

http://www.biggreensmile.com/green-glossary/wave-power.aspx

http://www.bluebird-electric.net/wave_power_energy_generation.htm

Common Theme:

Flexing at joints / pivot points => Pumps fluids => Drives generators

In other words, hydropower => hydraulic power => electric power

However, flaws (possibly fatal) that I perceive:

1) Water's power is ONLY collected from immediate vicinity of mechanism

That is why whole fleets of the units are envisaged

Vs. Tidal Barrage where turbine collected power from whole reservoir

2) (Red mechanism): All of mechanism is exposed to highly corrosive seawater

Multiple joints vs. single propeller shaft seal of Tidal Flow turbine

3) (Red mechanism): Floating on surface, it completely obstructs navigation

4) (Yellow mechanism): Massive toilet bowl floats, from shore? (gimme a break!)

What power outputs have actually been achieved?

Wikipedia identified a couple of dozen projects (http://en.wikipedia.org/wiki/Wave_power)

But cited power outputs for only a handful:

2.25 MW of Povao de Varzim, Portugal

3 MW off Scotland (exact location / ID not provided)

20 MW (expandable to 40 MW) off Cornwall UK

19 MW of Portland, Victoria, Australia

1.5 MW off Reedsport Oregon

Meaning LARGEST was ~ 4% the size of single average US Power Plant

(of which we currently require ~ 5800)

1) Orkustofnun – National Nower Authority: www.nea.is/geothermal/2) www.geysers.com/geothermal.aspx

So it's time to move on to: Geothermal Power

Which resurrects last lecture's theme of getting heat (from somewhere)

Using it to boil something

With fluid to vapor expansion then driving turbine generator

Source of heat: Earth's molten core (thought partly heated by radioactive decay)

So it gets hotter with depth = "Geothermal Gradient" ~ 25-30°C / km of depth

However, that's highly averaged number, applicable away from tectonic boundaries

NEAR tectonic boundaries (e.g. in Iceland) gradient can be much higher

Allowing Iceland to generate 25% of its power from geothermal1 OR

California's 15 geothermal plant "Geysers" system2 to reach 725 MW (!)

Source: http://ec.europa.eu/research/energy/eu/index_en.cfm?pg=research-geothermal-background

Geothermal energy is thus all about maps:

From the European commission: Extrapolated temperatures at 5 km depth

Conclusion? Not much - Turkey, a bit of Spain, plus the Balkans . . .

Source: http://www.nrel.gov/gis/images/geothermal_resource2009-final.jpg

Or for the U.S.

U.S. National Renewable Energy Lab (NREL) map:

Conclusion? Build geothermal plants in the West/Northwest


But how MUCH power?

Let's first try to read the fine print:

Black dots – "Identified hydrothermal site"

"Map does not include shallow EGS sourceslocated near hydrothermal sites"

Huh? Aren't those the best locations?

Is intent here to find only NEW power sites?

Of new "deep" class called out in title?

"Includes temperature at depth of 3 to 10 km"

"N/A regions have temperatures less than 150°Cat 10 km depth

Clearly need better understanding to guess at likely power out

Coverage of geothermal in my textbook collection is very thin

But the best of them identifies three classes of geothermal:

Class 1: Shallow plants for sole purpose of heating surface buildings

Which would SAVE power but not produce it => Geothermal Heat Pump

Class 2: Systems using naturally produced steam (e.g. from geysers)

That is, minimal drilling and letting steam come to you

Occurring in very limited locales like Iceland, Geysers CA, Yellowstone

Class 3: Systems reaching depths deep enough / hot enough to boil piped in water

Called "Enhanced Geothermal Systems" or EGS

So we are mostly interested in EGS = What NREL map was also focusing on!

Source: http://en.wikipedia.org/wiki/Geothermal_electricity

Diagram of EGS (enhanced geothermal system):

With detailed components given as:

1) (Surface) Reservoir

2) Pump house

3) Heat exchanger

4) Turbine Hall

5) Production Well

6) Injection Well

7) Hot Water to District Heating

8) Porous Sediments

9) Observation Well

10) Crystalline Bedrock

We've been over this ground enough to figure out the rest:

Pump house (2) => To push supply water down into the

Injection Well (6) to then diffuse through the deep extremely hot

Porous Sediments (8) causing the water to boil, exiting as steam via the

Production Well (5) from where it is then routed to the

Heat exchanger (3) boiling clean mineral-free water with THAT steam going to

Turbine Hall (4) with small diversion to nearby shivering people via

Hot Water to District Heating (7) and rest of steam continuing on to

Surface Reservoir (1) where steam condenses (~ cooling tower/river/lake) with

Crystalline Bedrock (10) to keep most injected water from wandering away and

Observation Well (9) being the only thing still in need of explanation:

Which Wikipedia forgot to explain but I'd guess could monitor how much plant is cooling earth (and thus be used to fine tune plant operation)

But what is Geothermal's potential?

Thermodynamics' Carnot cycle gives maximum "heat engine" efficiency of

Max efficiency (%) = (1 – Tlow / T high) x 100

For geothermal heat engines, Tlow ~ earth surface temperature ~ 300°K

And Thigh might be 200°C higher, e.g. 500°K giving theoretical limit of

Max geothermal efficiency ~ (1- 300 / 500) x 100 ~ 40%

Compared to wind's 40%, IGCC fossil fuel's 50% or hydroelectricity's almost 90%

But heck, with geothermal the "fuel" IS free!

So, 40% of WHAT? Of the thermal power flowing up through the earth's crust:

Wikipedia specs this as 65 mW / m2 on land (vs. 110 ocean bottom)

USGS and book "Hot Air" give about the same at ~ 50 mW / m2


From which:

Carnot limited extraction = (~ 40%) x (50 mW / m2) = 20 mW / m2

Total dry land area of world ~ 150 x 106 km2

Multiplying this land area by the capturable geothermal flow:

Powermax ~ (20 mW / m2) x (150 x 106 km2) ~ 3 x 1012 Watts

Divide this by world population of ~ 7 billion

Max personal geothermal power ~ 428 Watts

Which, while not trivial, is certainly not that impressive, especially when it requires

Geothermal power from TOTAL land area, at max efficiency possible

1) Source: http://www.eia.gov/electricity/monthly/epm_table_grapher.cfm?t=epmt_1_01_a

Reality check?

US Energy Information Agency gives1 2013 geothermal total of 16,517 GW-hr

=> Total US Geo power of 1.88 GW (~ 4 average US power plants)

Out of total US renewable sourcing of 522,464 MW-hr (=> Geo ~ 3.16%)

But, from intro of Hydro / Wind Power lecture, US renewables ~ 9.1% of total

So Geothermal contributed about 0.28% of US power in 2013

What about new deep water injected EGS (Enhanced Geothermal Systems)?

Despite promise, the technology appears to be still in its infancy

With biggest experimental plant (Cooper Basin, Australia)

Only targeting 25 MW output

1) Source: http://volcanoes.usgs.gov/volcanoes/yellowstone/yellowstone_sub_page_53.html2) http://pubs.usgs.gov/gip/dynamic/fire.html

Takeaway message on Geothermal?

Don't try it anywhere, do it where there is a lot more natural heat

USGS1: Yellowstone averaged 50X higher, and peaked 2000X higher

than typical earth surface location

For instance, target "ring of fire" tectonic plate boundary locations2:

But even then:

It's still very hard to estimate cost / potential

Because more site accommodating EGS tech

Has had only small-scale testing

And even less costing out

What about more ambitious and/or futuristic ideas?

To start with, here are two that are variations on existing technologies:

Flying Wind Turbines:

Motivated by earlier discussion of wind speed vs. altitude:

Plus the fact that wind power increases as velocity to the third power!


Early turbines Current turbines: Future Turbines (?):

So to get up into even faster moving winds . . .

Which might actually end up looking more like this:

Being assembled in Massachusetts: The Altaeros Buoyant Air Turbine

- Helium filled cylindrical lifting body

- Altitude to 2000 feet / Winds to 75 MPH

Prototype:

- Fourteen feet long

- Designed for 30 kW power out

- Larger model to produce 200 kW (with megawatt unit envisioned)

Markets?

- Remote sites with weak sunlight (=> grant from Alaska Energy Authority)

- Temporary industrial sites (e.g. construction or well drilling)

- Sites with low ground wind speeds (e.g. India and Brazil)

"The Quest to Harness Wind Energy at 2000 Feet" - Popular Science Magazine – October 2014

Or it might be simpler to just "Go Fly a Kite"

Get rid of balloon (and its expensive lifting helium)

And keep the heavy electrical generator on the ground

Side benefit: Far, far less flying mass to fall on something / someone!

Use the kite's tugs on a rope to power that generator

Prototype kite: Ground generator unit

"Go Fly a Kite" – IEEE Spectrum Magazine, December 2012online at: http://spectrum.ieee.org/energy/renewables/the-benefits-of-airborne-wind-energy

With a lot of such projects going on worldwide:

"Go Fly a Kite" – IEEE Spectrum Magazine, December 2012

Or, going even higher, what about orbiting solar farms?

This one proposed by the Japanese Aerospace Exploration Agency (JAXA)

Said to be possible within twenty five years with 1 GW power output

Beamed down to earth via microwave radio or laser beams

Would weigh more than 10,000 tonnes and be several kilometers across How Japan Plans to Build an Orbital Solar Farm, IEEE Spectrum Magazine, April 2014

online at: http://spectrum.ieee.org/green-tech/solar/how-japan-plans-to-build-an-orbital-solar-farm

Motivation (at least) is crystal clear:

As described in Solar Power lecture:

Atmosphere absorbs ~ 1/4 of sunlight: 1.35 kW / m2 => 1 kW / m2

Remaining is diluted when incident at shallow angles (i.e. not at noon)

And totally blocked by earth itself (for a particular location) half the time

Net result (from U.S. National Renewable Energy Lab calculator website):

But 1 kW-h/m2/day = 41.6 W / m2

So BEST U.S. sites have annual average incident solar power of ~ 200 W / m2 http://rredc.nrel.gov/solar/old_data/nsrdb/1961-1990/redbook/atlas/serve.cgi

Versus orbital solar farm:

Once aimed at the sun, should stay aimed at the sun (ignoring tidal effects)

And, when not blocked by the earth, satellite receives the constant 1350 W / m2

Almost 7X better than our BEST U.S. sites

And ~15X better than our poorer (contiguous 48 state) sites!

But (first) big caveat is "when not blocked by the earth"

Time for a little orbital mechanics:

Want object to orbit distance r above earth's center

Acceleration of object due to earth's gravity = G M / r2

Inducing a centripetal acceleration on object = v2 / r

Where v = orbital circumference / orbital period = 2 p r / TAn Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm

Substituting and equating:

G M / r2 = (4 p2 r2 / T2) / r which yields (4p2 / GM) r3 = T2

G (universal gravitational constant) = 6.67 x 10-11 m3 / (kg – s2)

Earth parameters: M = 5.97 x 1024 kg Radius = 6371 km

So earth's circumference = 40,029 km

I remember as 24,000 miles => Equator spins at 1000 MPH!

Constant (4p2 / GM) in equation then becomes: 9.913 x 10-14 s2 / m3

Some space agency is going to have to launch pieces of solar farm into orbit

Most launches are into LEO (low earth orbit) 160-2000 km above surface

ISS orbits ~ 400 km above earth => orbital radius of 6800 km, calculating period:

T = √[9.913 x 10-14 s2 / m3 x (6.8 x 106 m)3] = 5,583 sec = 93 minutes


Problems with low earth orbit (LEO):

Earth will block the sun half the time

We just lost half of our potential power enhancement

Satellite won't stay above our location

Assuming world not willing to share cost and benefit of satellite

How do WE (builders / financers of farm) get all of its power?

We'd have to store power until farm's orbit passed overhead ≠ once / orbit

Because earth is rotating under orbit:

So we'd also need HUGE orbiting energy storage capacity (!$#$!@$!!)Figure: http://www.universetoday.com/89063/must-see-video-falling-nasa-uars-satellite-observed-while-still-in-orbit/

So, go to a geosynchronous orbit!

Meaning that we now want an orbital period of one day to match our rotation

Put T = 24 hours = 86,400 seconds into (4p2 / GM) r3 = T2 and solve for r:

r = [(8.64 x 104 s)2 / (9.913 x 10-14 s2 / m3)]1/3 = 42,227 km

Subtracting out earth's radius = 35,856 km above earth surface

How much time will orbiting solar farm then spend in earth's shadow?

Orbital circumference is now 2 p x 42,227 km ~ 265,000 km

Width of earth's shadow ~ earth diameter = 2 x 6371 km = 12,742 km

So fraction of time in shadow ~ 12,742 / 265,000 ~ 4.8%

So we would get almost full 7X–15X enhancement of solar energy to arrayAn Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm

But a couple of problems remain:

Cost of launching pieces to orbit:

NASA figure for cost to launch into (unspecified) orbit is $10,000 / kg1

This, almost certainly, refers to low earth orbit only!

Gravitational potential energy goes as 1/r

r for high geosynchronous orbit is ~ 6X r for low earth orbit

If cost scales as potential energy of orbit, geosynchronous cost => ~ 60 k$ / kg

Japanese JAX station was estimated as 10,000,000 kg => $6 x 1011 to launch

If provided 1 GW (106 kW) power for 20 years (limited by cell lifetimes):

Launch cost (only!) = $6 x1011 / [(20x365x24 hours) x (106 kW)]

= 3.42 $ / kW-hour vs. current power cost of 10-20 cents /kW-h

1) http://www.nasa.gov/centers/marshall/news/background/facts/astp.html_prt.htm

AND you are going to beam down 1 GW of radiation:

Which will be aimed at offshore receivers:

But beams inevitably spread out a bit

(And could be diverted as a weapon!)

Proof of RF radiation harm (~ heat) is very slim

But we do worry about cell phones & AC power lines

For which US / Euro power limits are currently

1.6 / 2 W of RF radiation / kg of tissue1

~ 1 GW / (25 km x 25 km) => I sure wouldn't go near the above power station

How Japan Plans to Build an Orbital Solar Farm, IEEE Spectrum Magazine, April 2014

1) http://en.wikipedia.org/wiki/Mobile_phone_radiation_and_health

Fusion typically refers to energy released when H or He atoms combine:

OR

Problem (according to Newton): Positive protons strongly repel one another

Force (direct from 1st Maxwell Equation / "Gauss's Law") = (1/4πεo) (nq)2/r2

Where q = is magnitude of proton charge = 1.6 x 10-19 Coulombs

εo = permitivity of free space = 8.85 x 10-12 Coulombs/Volt-meter

n = number of protons in each nucleus (one or two)

r = separation of the nuclei

What about the holy grail of power: Nuclear Fusion


Integral of this force = Repulsive potential energy

Which would then be = (1/4πεo) (nq)2/r which would plot something like this:

With this repulsion, nuclei would never fuse if not for another force:

Mysterious "strong nuclear force" which binds protons & neutrons

"Mysterious" because is only strong at separations < 1 femtometer (10-15)

At 1 femtometer and below, nuclear force overpowers charge repulsion force

Drawing nuclei together and, in the process,

releasing vast amounts of ("fusion") energyAn Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm

r

So combined forces would look something like this:

To get over that barrier, nuclei must get an incredible running start

= Huge kinetic energy => potential energy while climbing barrier

Temperature must supply that kinetic energy – But how high a temperature?

Kinetic energy of particle (at temperature T is) ~ k T

k = Boltzmann's constant = 1.38 x 10-23 kg-m2/s2 °K

Barrier height ~ (1/4πεo) (nq)2/(1 fm)

r1 fm1 fm

Equating and solving for required fusion temperature:

T = (1/4πεok) (nq)2/(1 fm) Putting in numbers for hydrogen nuclei (n=1):

= (1.6x10-19 C)2/(4π)(8.85 x 10-12 C/V-m)(1.38 x 10-23 kg-m2/s2 °K)(10-15

m)

= 17 billion °K (C-V / kg-(m/s)2) things in parenthesis = Joule/Joule => 1

Temperature to initiate hydrogen fusion ~ 17 billion degrees (K) (!!!)

THIS is what makes fusion so difficult:

1) Must give nuclei HUGE starting kinetic (heat) energy

2) Nuclei must retain that huge energy long enough to collide

Step 1 can be accomplished by using electromagnetic fields to push protons

Step 2 can be the harder part


Keeping nuclei hot long enough for them to collide:

First, must get rid of much cooler ambient gases => ultrahigh vacuum

To which nuclei would otherwise prematurely share their heat

Second, must keep nuclei from colliding with walls of vacuum chamber

Now generally done via a "magnetic bottle"

Which comes right out of our "first right hand rule:"

Magnetic field always pushes protons sideways

With result that they spiral down magnetic field lines:http://www.swapyournotes.com/articledetail/articledetail.html/632/

http://astarmathsandphysics.com/a-level-physics-notes/electricity/a-level-physics-notes-the-magnetic-bottle.html

Magnetic bottle completed by squeezing field together at both ends:

Done well enough, protons should just spiral back and forth

Until they collide and, given enough energy/temperature, fuse

Individual protons have been doing this – for over fifty years

Problem is getting ENOUGH to do this that get more energy out then put in

Promised "within the next decade" since I was in high school

Seems as elusive as ever suggesting (to me) not need for "better engineering"

but a radically different approach and/or fundamental scientific breakthrough

http://astarmathsandphysics.com/a-level-physics-notes/electricity/a-level-physics-notes-the-magnetic-

bottle.html

Conclusions on the "exotic" energy production alternatives?

Many clearly have roles to play (and some are already playing that role)

But, despite decade(s) of development, their contribution is generally very limited

Often to remote locations difficult to otherwise supply with energy

Others (e.g. satellite solar farms) COULD generate huge amounts of energy

But look to be at least an order of magnitude more expensive

Nuclear fusion promises an energy Holy Grail

But, unfortunately, it seems to be as elusive as the original Holy Grail

Which, at least for now, seems to leave us into a bit of a corner

Prompting my upcoming discussion of nuclear fissionAn Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm

Credits / Acknowledgements

Some materials used in this class were developed under a National Science Foundation "Research Initiation Grant in Engineering Education" (RIGEE).

Other materials, including the "UVA Virtual Lab" science education website, were developed under even earlier NSF "Course, Curriculum and Laboratory Improvement" (CCLI) and "Nanoscience Undergraduate Education" (NUE) awards.

This set of notes was authored by John C. Bean who also created all figures not explicitly credited above.

Copyright John C. Bean (2014)

(However, permission is granted for use by individual instructors in non-profit academic institutions)


Documents

The Exotic Power Sources Today I'll wrap up my discussion of power plants Except for hyper-controversial nuclear, which I'll return to a bit later I'll