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

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

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

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

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

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

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

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

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

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

Leading to alternative of "tidal stream" power generation 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 http://subseaworldnews.com/2012/01/17/uk-seagen-tidal-turbine-gets-all-clear-from-environmental-studies/ An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm

With a lot more contemplated, or at least imagined: http://www.bbc.co.uk/news/uk-wales-north-west-wales-11037069 http://www.darvill.clara.net/altenerg/tidal.htm http://www.global-greenhouse-warming.com/tidal.html http://www.fujitaresearch.com/reports/tidalpower.html http://climatekids.nasa.gov/tidal-energy/

Including some very questionable proposals: 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! http://www.ecofriend.com/eco-tech-nasa-s-jpl-develops-a-cost-effective-way-to-harness-ocean-energy.html 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.esru.strath.ac.uk/EandE/Web_sites/10-11/Tidal/tidal.html

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://www.marineturbines.com/3/news/article/37/anglesey_tidal_energy_plan_moves_forward_ http://news.bbc.co.uk/2/shared/spl/hi/pop_ups/07/uk_enl_1193829329/html/1.stm

Which is being pursued up in Maine: Intended for Maine's Passamaquoddy and Cobscook bays: http://www.pressherald.com/2012/07/21/maine-company-leading-way-as-tidal-energy-comes-of-age_2012-07-22/ 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): Google Earth (Just a suggestion . . .)

An alternative: Wave power: 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 http://www.bluebird-electric.net/wave_power_energy_generation.htm http://www.biggreensmile.com/green-glossary/wave-power.aspx

However, flaws (possibly fatal) that I perceive: 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)

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

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

Conclusion? Build geothermal plants in the West/Northwest Or for the U.S. U.S. National Renewable Energy Lab (NREL) map: Conclusion? Build geothermal plants in the West/Northwest Source: http://www.nrel.gov/gis/images/geothermal_resource2009-final.jpg

But how MUCH power? Let's first try to read the fine print: Black dots – "Identified hydrothermal site" "Map does not include shallow EGS sources located 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°C at 10 km depth An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm

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!

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

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

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://www.eia.gov/electricity/monthly/epm_table_grapher.cfm?t=epmt_1_01_a

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 1) Source: http://volcanoes.usgs.gov/volcanoes/yellowstone/yellowstone_sub_page_53.html 2) http://pubs.usgs.gov/gip/dynamic/fire.html

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

So to get up into even faster moving winds . . . Early turbines Current turbines: Future Turbines (?):

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 2012 online 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 / T An 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 An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm

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 array An 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

What about the holy grail of power: Nuclear Fusion 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 An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm

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") energy r An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm

So combined forces would look something like this: 1 fm 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)

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

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

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