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Fusion Energy


100 kg D 150 kg T. 1 GWe for 1 year 10 TWy for 1000 y. Fusion Reaction ... Direct radiation (focusable by mirrors) Diffuse radiation (unfocusable) ... – PowerPoint PPT presentation

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Title: Fusion Energy

Fusion Energy
Binding Energy per nucleon
  • 100 kg D 150 kg T
  • 1 GWe for 1 year
  • gt10 TWy for 1000 y

Mass number A
Main problem how to overcome Coulomb repulsion?
Note 1) D obtained from seawater by
electrolysis 2) T has a half-life of
12.4 years, so is not naturally occurring
in practice, it is produced by a
breeding reaction, eg n 6Li _ 4He T
4.8 MeV or n 7Li _ 4He T
n - 2.9 MeV
3) Stars are powered by fusion
reactions, made possible by
their size, ie the gravitational pressure is
sufficient to withstand the
gas pressure 4) Temperature
required for self-sustaining fusion reaction is
much higher than melting point
of all known materials
How can the hot gas be kept away from the walls
of the container?
Note Number densities of electrons and ions are
approximately equal (except near walls and other
boundaries) ne ni n This near-equality
effectively screens the plasma from external
electric fields. However, magnetic fields do
penetrate plasmas and can be used to control them
(No Transcript)
Mirror Machine
Larmor radius r mv?/qB
exhibits diffusion instability
magnetic moment m ½qv?r conserved as Fq
essentially zero
Fz ??(m.B) -m?B/?z
particle reflection near coil
A helical toroidal field and its effect on the
drift of a particles motion
The direction of the drift is shown by the blue
arrows and its effect is to move the path up and
away from the field line when the particle is
above the axis but back toward the field line
when below the axis with the result that the
overall drift is zero.
Both the neutral beam from charge exchange of 80
keV hydrogen ions and rf injection, 20-50 MHz
for ICRH or 70-140 GHz for ECRH, can also be
used to drive a current within the plasma.
Using high speed pellets of frozen D a high
central plasma density can also be obtained.
To make the poloidal field a current is induced
in the plasma and the resultant field is
helical. The current is induced in the plasma by
varying a large magnetic field that passes
through the centre of the torus. The plasma acts
as the secondary circuit in a transformer. If the
flux linkage is F then VdF/dt and IV/R, where
R is the resistance of the plasma.
Tokamak Fusion Reactor
The fast neutrons (14.1 MeV) pass through the
plasma containment wall and are stopped in a
lithium blanket where they produce tritium.
Enriching the percentage of 6Li enhances the
tritium breeding ratio (TBR), which needs to be
greater than 1 for self sufficiency. The 7Li
reaction produces a neutron which can make
another T nucleus
Energy conservation P Lv?(mass
evaporated)/sec Lv rgvgA where P incident
power, A 4pr2, Lv latent heat of
evaporation, rg gas density, vg gas speed
Radial momentum pr imparted to vapour per unit
area per second pr (rgvg) vg (rgvg) 2/rg
(P/LvA)2/rg jump in pressure
across outer surface of pellet
Density increase of 103 achieved for 10
picoseconds Particle beams also being explored,
instead of lasers
Lawson Criterion
Consider D-T reaction 2H1 3H1 4He2 n
Efusion (Efusion 17.6 MeV)
Ea ( Efusion/5) heats plasma
Total plasma kinetic energy per unit volume is E
2n(3kBT/2) 3nkBT Self-sustaining reaction
requires fusion alpha energy generated gt
rate of plasma energy loss n2ltsvgtEa /4 gt
3nkBT/t where t is the time for the plasma energy
to be lost to the walls when the plasma is in
its operating state or nt gt 12kBT/ltsvgtEa f(T)
Optimum value of T for ltvsgt for the D-T
reaction is about 60 KeV At 20 KeV, a more
realistic temperature, ltvsgt 4.5 10-22 m3/s
which gives nt gt 3.1019 s m-3
Between 10 and 20 keV ltvsgt ? T2 so nt gt
12kBT/ltsvgtEa Lawson Criterion equivalent to a
limit on ntT, the fusion triple product on
diagram Q Ea/Eexternal
t is proportional to characteristic
length squared, if diffusive process, ie to
area. Area in TFR 0.13 m2, in JET 8 m2. t in TFR
20 ms predicts for JET 1.2 s, if diffusive, close
to what was achieved.
Z-Pinch Machine
Bennett Pinch (not on syllabus)
Axial current J gives rise to azimuthal B
field Force per unit volume is JB. If plasma
pressure is P then m0?P (?B)B
as ?B m0J m0dP/dr - (B/r)d(rB)/dr
m0?r2(dP/dr)dr -? (rB)d(rB) m0r2P - 2
m0?rPdr -1/2(rB)2
If P(R) 0 at edge of axial plasma current, then
as P (n n-)kT and n n- n, the electron
number density, then 2m0?rPdr 2m0kT?2nrdr
1/2(rB)2rR Number N per unit length N
?2pnrdr So 2m0NkT p/2(rB)2rR
?B m0J so (1/r)d(rB)/dr m0J rBrR
(m0/2p) ?2pJrdr m0I/(2p) So 2NkT m0I2/(8p)
108 oC, n 1020, A 1 m2 so N 1020 requires I
2.5 MA for equilibrium
Photovoltaic Electricity Generation
Incident solar power density 1 kW m-2
(max) Total solar power incident on planet 104
(Global power consumption) Actual utilisation of
solar power 0.01 of global power consumption

(2 in
Solar Energy Distribution
  • Radiation reaches Earths surface by
  • Direct radiation (focusable by mirrors)
  • Diffuse radiation (unfocusable)
  • Flux on cloudy day 1/3 of flux on sunny day
  • Note sky would be black (except for
    stars/planets) in the
  • absence of diffuse radiation

Conductors, insulators and semiconductors
p-n junction
An electric field is set up across the junction
and causes a drift of electrons, which balances
the diffusion due the concentration gradient.
Forward current I ISexp(V/VT) - 1 VT
kT/?e? ? 0.026 volts at room temperature IS is
the saturation current
Operation of Solar Cell
Light generates electron-hole pairs. These
diffuse and are separated by electric field
across depletion layer Produces a reverse current
ie a negative current from p to n region and
increased potential of p relative to n
Photocell current IC IL - ISexp(V/VT) -
1 Open-circuit voltage VOC VTln(1 IL/IS) ?
Circuit layout for testing a Solar Cell
P FF?ISCVOC where FF is fill-factor FF
typically 0.75 0.85
Electron-hole created if hn gt Eg eVg Min
wavelength lmin hc/eVg eg Si lmin (6.6
1034)(3 108)/(1.6 10-19)(1.1) 1.1 mm
36 silicon cells series-connected
0.53 m
1.19 m
Limits to Photocell Efficiency
1 Reflection from top surface Can be reduced from
40 to 6 using quarter-wavelength
thick antireflection coating Silicon has a
complex refractive index, as it is partly
conducting, which is frequency dependent and
averages about 3.5 The reflectance r between two
media with refractive indexes n1 and n2 is r
(n1 - n2)2/ (n1 n2)2
2 Photons too low in energy (23) Energy wasted
as heat 3 Photons too energetic (33) Excess
photon energy (hn Eg) lost as heat
4 Voltage Factor (0.5) Voltage factor eVB/Eg
0.6/1.1 5 Small losses from contacts on front
surface very little loss from photons not
absorbed because of optimising thickness plus
reflecting layers on the back of the cell (total
3) 6 Charge collection efficiency(0.7) Some
electron-hole pairs recombine
Overall efficiency (0.96)(0.44)(0.5)(0.7)
15 Typically 10-15 at present for commercially
available devices Note a) Experimental devices
20-25 efficient should be on
market within 10 years, as market forces drive
prices down b) Theoretical limit to
device efficiency imposed by solar spectrum 47
Overall Process for Producing a Monocrystalline
Silicon Solar Cell
  • New forms of Silicon
  • single crystals (most efficient, most expensive)
  • polycrystals (cheaper, less efficient)
  • polycrystalline thin films (uses light trapping
  • amorphous silicon (currently available a-Si
    cells degrade
  • from 10 to 7)
  • silicon ribbon cells (thin ribbon of
    monocrystalline silicon drawn
  • from a silicon melt)

Annual module cost and incremental installed
Learning rate is the percentage reduction in
costs for a doubling in cumulative production-
for PV modules it is 22
CdS/CdTe Solar Cell
CdS (n-type) Eg 2.4 eV CdTe (p-type) Eg 1.5
Dye-sensitized solar cells
Gratzel cell 20 nm TiO particles coated with a
monolayer of dye
Other materials can be used eg GaAs, CdTe All
devices can be made effectively more efficient if
mirrors are used to focus or collect the suns
direct rays
Applications 1 Low power devices Calculators,
watches, radios, etc (ideal) 2 Remote
locations/hot climates Telecommunications,
satellites, lighthouses, TVs, water pumping, air
conditioning refrigeration (food preservation,
medicines) 3 Large scale power
generation Demonstration projects in progress (eg
Pyrenees) but general prospects are not
favourable at present eg 1000 MW station would
require 10 km2 PV array - backup electricity
generation would also be necessary, due to
weather variations
Maintenance minimal-cleaning, minor circuitry
repairs, security Growth currently 900 MWp/yr
globally by 2010 3300 MWp/yr (mainly
developing world/hot countries)
Solar Power Towers
Temperature of the salt can be raised to 500
C (Solar radiation is approximately Black Body
with temperature 6000K) 10 MW solar power tower
at Barstow in California Max efficiency 1-
(300/873) (Carnot Cycle) 65 Alternatively a
Stirling Engine can be placed at the focus of a
parabolic dish concentrator- operating
temperature 1000 C
Stirling Cycle
  • (W2 - W4)/ (Q1 Q2) eC/1 aeC/ln(V2/V1)
  • where eC (Th - Tc)/Th

For high e monotonic gas and large (V2/V1) Sealed
gas engine, external heat supply ? low
pollution, slow response and quiet
Concentrator Systems
A parabolic mirror needs to track the sun A
Winston mirror (cone) accepts light over a range
of angles q Using a trough concentrator
the increase in the light collected within this
range q is D/d (Liouvilles Theorem)
Luz solar collector field Southern California 80
MW output - just competitive
Energy Storage
A variety of solutions to the problem Flywheels C
ompressed air storage Energy stored in phase
changes eg wax in wall cavities Batteries Fuel
cells Pumped storage of water
Flywheels Flywheel on a car to provide kinetic
energy to keep the engine turning between piston
strokes Modern materials - plastics, epoxies and
carbon fibres - light and very strong The kinetic
energy/unit mass for a uniform disc of radius a,
mass m and density r is (1/2)Iw2/m, where I is
the moment of inertia (1/2)ma2, so T/m
(1/4) a2w2 wmax is determined by the maximum
tensile stress of the material smax
The maximum tensile stress in the uniform disc is
ra2wmax2, so Tmax/m (1/4)smax/r Comparing two
flywheels of the same mass, one made of high
tensile steel and the other of a new epoxy or
plastic material, then the latter has an energy
storage about a factor of 10 greater with an
energy density of about 0.5 MJ/kg For a 100 tonne
flywheel, the storage capacity would be 15 MWh
Compressed Air Storage Consider n moles of air
and assume pV nRT If the air is compressed
from V1 to V2 , then the work, W, done is dW -
p dV - (nRT/V) dV so W p1V1 ln(V1/V2)
Typical energy densities are of order 1 MJ/m3 ,
so large underground caverns provide huge energy
storage capabilities There are though significant
heat losses (50) and there can be leaks Salt
caverns naturally seal under pressure, but
concerns over accidental releases of compressed
  • Batteries
  • Lead acid Pb HSO4- _ PbSO4 H 2e-
  • PbO2 HSO4- 3H 2e- _ PbSO4 2H2O
  • Supplying electricity the lead sulphate is
    deposited on the electrodes
  • Charging the lead sulphate changes to lead and
    lead oxide


Lead-acid car batteries can be cycled 300 times
The driving range of a vehicle is roughly
proportional to its specific energy, whereas the
speed capability is nearly proportional to
its specific power
Vanadium Redox Flow Battery
Energy stored in electrolyte which is separate
from electrodes Voltage determined by number of
cells Can smooth out variations in supply from
wind or solar generators eg a 12 MWh battery at
Sorne wind farm in Ireland
Fuel Cell
Vmax 237?103/(2?9.65?104) 1.23 volts
Available energy 237 kJ/mole
PEM fuel cell (schematic)
Fuel cells can be used both to generate
electricity and to store energy in the form of
hydrogen ie run the cell to decompose water into
hydrogen and oxygen Catalysts or elevated
temperatures are required to enhance
the electrode reactions
Fuel Cell
Hydrogen production H2O ? H2 ½ O2 using
electrolysis, light, heat, catalysts or from
hydrocarbons e.g. CH3OH H2O ? CO2 3H2
with CO2 captured
Electrical Energy Stores
Fuel Cell Vehicles
NaBH4 2H2O ?NaBO2 4H2
  • Economic carbon-free production of hydrogen
  • Storage of hydrogen with good energy density

Plug-in Hybrid Electric Vehicles (PHEV)
  • Hybrid
  • Internal Combustion engine
  • can operate more efficiently
  • Power boost from electric
  • motor
  • Regenerative braking
  • Storage batteries
  • supercapacitors
  • ? 50 reduction in CO2
  • Plug-in Hybrid
  • twice fuel economy of
  • hybrid
  • even better using biofuels
  • and green electricity

Fuel cell Battery electric Vehicle Comparison
  • Battery electric car needs established grid and
    fast rechargeable high
  • energy density batteries PHEV an interim low
    CO2 emissions solution
  • Fuel cell car needs good hydrogen production,
    distribution and storage

The Present -Newsweek April 2002
The Future -Newsweek April 2002
Hydrogen Economy, in which hydrogen
is manufactured on a vast scale for a variety of
uses. Production could be by solar, wind
or hydro 2H2 O2 _ 2H2O No Greenhouse
gases just water! No pollution
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