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EG21001 Nuclear Physics
Fission & Fusion
Allan Gillespie
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Nuclear Fission
Steps in the Discovery of Fission:
We have seen that neutron-capture by a nuclide with atomic number Z, followed by--decay, gives a new nuclide with Z+1. Fermi attempted to produce a transuranicelement, Z = 93, from Uranium (Z=92) by this process. The result was indeed neutron
capture, butproduct nuclide was -unstable with 4 separate half lives.
Experiments of Hahn & Strassmann (1939) in Berlin showed that the products were
isotopes of Ba, La and Ce - i.e. much lighter nuclides.
Meitner and Frisch gave correct interpretation of experiments - uranium nucleus is
unstable after neutron capture, and may divide into two nuclei of roughly equal size.Energy released is very large, corresponding to Q of approx 200 MeV. The term
fission(borrowed from description of cell division in biology) was coined.
Fission results primarily from competition between nuclear and Coulomb forces inheavy nuclei. It can occurspontaneously as a natural decay process (like decay),
or it can be inducedby the absorption of a relatively low-energy particle, such as aneutron or photon. Induced fission much more important than spontaneous fission.
Although any nucleus will fission if we provide enough excitation energy, the
process is only important in practice forheavy nuclei (thorium and beyond).
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Key to obtaining large total energy releases from fission - both in nuclear reactors
and nuclear weapons - is the concept of a chain reaction, where incoming neutronproduces several further neutrons as reaction products, and these in turn induce
newfission events, and so on ...
Fission in isotopes of UraniumBoth common isotope (99.3%) 238U and uncommon (0.7%) isotope 235U (plusseveral other nuclides) can be split by n-bombardment -- 235U by slow neutrons but238U only by neutrons with min energy of ~1 MeV. Fission resulting from neutron
capture is called induced fission, and materials like 235U are called fissile materials.
In general,
cross section
probability of
fission
[unit: barns (b)]
= thermal
neutrons
Ek = 0.025 eV
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Some nuclides can also undergo spontaneous fissionwithout initial n-capture, butthis is quite rare.
When 235U captures a neutron, the resulting nuclide 236U* is formed in a highly
excited state and splits into 2 fission fragmentsalmost instantaneously, releasingan (enormous) kinetic energy of about 200MeV per nucleus, and on average 2.5
neutrons.
Strictly speaking, it is 236U* and not 235U that undergoes fission, but it is usual to
speak ofthe fission of235U.
Fission is a catastrophic reaction for a nucleus, and consequently there is nounique fission reaction. A typicalreaction channel for235U is:
235 1 236 * 140 94 1
92 0 92 54 38 0( ) 2 200+ + + + +U n U Xe Sr n MeV
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Over 100 different nuclides, representing more than 20 different elements, have
been found among fission products (leading to a major problem with nuclear waste
from reactors). Figures show distribution of mass numbers in fission fragments:
Mass distribution of possible fission fragmentsof235U. Splitting into two fragments of unequalmass is more likely than symmetrical fission.
Note logarithmic vertical scales.
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Fission fragments always have too many neutrons to be stable (why?), and
usually respond by undergoing a series of- decays until finally a stable value of
N/Z is reached:
140 140 140 140 14054 55 56 57 58 ( ) ( )Xe Cs Ba La Ce stable four decays
94 94 9438 39 40 ( ) ( )Sr Y Z stable two decays
The neutron excess of fission fragments also explains why 2 or 3 free neutrons
are released during the fission process.
Fission Chain Reaction
Since fission triggered by n-bombardment releases neutrons that can triggerfurther fissions, there exists possibility of a chain reaction. This can be made toproceed slowly and in a controlled manner in a nuclear reactor, or explosively in a
nuclear weapon. Energy release in a nuclear chain reaction is far greater than in
any chemical reaction. e.g. U burned to uranium dioxide in chemical reaction:
U + O2 UO2
Heat of combustion is 4500 J/g. Expressed as energy per atom, this is ~11 eV.
By contrast, fission liberates about 200 MeV per atom/nucleus, nearly 20 milliontimes as much energy.
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Schematic of fission process
Model of nuclear fission
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Control of Fission in a Nuclear Reactor
Nuclear reactor = system in which a controlled nuclear chain reaction is used to
liberate energy. In a nuclear power plant, this energy is used to generate steam,which operates a turbine and turns an electrical generator.
For a steady non-explosive reaction, each fission should cause one additional
fission; two will cause an explosion; less than one on average causes reaction to dieout. Since, on average, each 235U fission produces 2.5 neutrons, 40% of the
neutrons are needed to sustain a chain reaction. The size of the fissile material must
be large enough so that not too many neutrons stray through its surface and are lost
to the reaction. There is therefore a critical size to produce a self-sustainingreaction. The critical size forpure 235U is about the size of a grapefruit.
Dependence on neutron kinetic energy
n-induced fission is most effective when neutrons are moving slowly they shouldhave a small kinetic energy of the order of 1/40 eV referred to as thermalised or
thermal (or slow) neutrons, because their k.e. is roughly same as the k.e. of room
temperature air molecules. Slow-moving n has much greater probability of capture
(cross section) because it spends more time near nucleus.
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Slow neutrons -at thermal energies Ek ~ 0.025 eV, v ~ 2000 ms-1
are much more likely to be captured and cause fission in 235U than
Fast neutrons - at Ek ~ 1MeV, v ~ 2 x 107 ms-1
Hence large part of total volume of a (thermal) reactor consists of a moderator(low atomic number material, e.g. carbon or water) which is a non-reactive passive
material that slows down fission neutrons to thermal velocities by collisions with
moderator atoms.
Neutrons are slowed down ballistically by allowing them to collide with other
nuclei and give up some kinetic energy at each (perfectly elastic) collision. Can
easily show that most effective moderation occurs when moderator nuclei have
smallest values of A (i.e. as close to A=1 as possible).
Nucleus common form No. of collisions
to thermaliseHydrogen Normal water 19
Deuterium Heavy water 32
Carbon Graphite 110
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A moderator separate from the fuel is required because fast neutrons from
fissions (energies around 1 MeV) cannotbe slowed down to thermal energies
within the fissile uranium core itself because the majority 238U componentstrongly absorbs neutrons in the 1 130 eV energy range (fig below).
capture of neutrons in 238U(cross section is probability of neutron-capture)
Solution is to allow the fission
neutrons to enter the separate
moderator then re-enter the
fissile core to generate furtherfissions, once slowed down to
thermal velocities (avoiding the
resonances in the cross section).
resonances
En
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First nuclear reactor Enrico Fermi, Chicago, 1942.
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Instrumentation is required to control a reactor. Rate of reaction is controlled byinserting or withdrawing control rods made of elements (such as boron orcadmium) whose nuclei are good neutron absorbers. These rods can be lowered
into the pile to make it sub-critical. Also have shut-down rods to rapidly closedown reactor in an emergency (or a borated liquid system to flood the reactor core).
Not all neutrons are emitted instantaneously. Most are produced without delay
so-called 'prompt neutrons'. Some of fission products are radioactive n-emitters
that produce 'delayed neutrons' (with delays ranging from seconds to minutes).
Removal of control rodsand overheating can be
catastrophic
Chernobyl, Ukraine, 25 April, 1986
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The integrated Caesium
ground-level air
concentration pattern
four days after the
beginning of theChernobyl accident.
(April 1986)
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A typical sequence of processes in fission. A 235U nucleus absorbs aneutron and gives rise to fission; two prompt neutrons and one delayed
neutron are emitted. Following moderation, two neutrons cause new
fissions and the third is captured by 238U resulting finally in 239Pu.
238
U
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A reaction that is sub-critical for prompt neutrons can be critical from prompt-and-delayed neutrons together (sometimes called delayed-critical). Principle is that byputting reactor together with control rods in place, rods can be carefully withdrawn
at frequent intervals during construction. By seeing to it that reactor never goescritical for prompt neutrons (that is, prompt critical) it is assumed that reactor will be
sufficiently sluggish that human responses can prevent reactor running away
destructively. Basic design of a nuclear power plant is shown below.
Pressurised-water
reactor (PWR, USA)
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Typical fissionpower reactors
Torness, Scotland
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inside a nuclear power reactor
Sizewell A and B
power stations
Dungeness B
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20Indian Point nuclear plant, New York.
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21Hartlepool, UK
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Enrichment
Depending on the moderator material chosen, it may be necessary to enrich the235U component in the nuclear fuel above its natural value of 0.7%, typically to 3%or so, by isotope-separation processing. Since enrichment is an essential
component of nuclear weapons construction, this can lead to a coupling of nuclear
power programmes and WMDs.
Nuclear Weapons
In (very simplified) essence, a nuclear fission weapon like the Hiroshimaatomic bomb brings together several sub-critical masses of highly enriched
uranium to make a super-critical mass. This requires exotic chemical implosion
technology to overcome the natural forces of thermal expansion. Such
considerations at least ensure that a nuclear reactor cannot produce the densityeffects required to initiate a nuclear weapon.
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Fast Reactors
No cooling down of neutrons: no moderator
Fissile reactor core can therefore be smaller
Core surrounded by 238U (or depleted U)
Coolant often liquid sodium
239Pu + 235U
(fissile)
238U(fertile)
238U + 1n 239Np 239Pu
- : 23 min - : 2.3 days
239Pu in presence of fast neutrons
produces 2.9 neutrons breeder reactor
Easy to separate fissile material created (different Z)
Dounreay nuclearplant
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erenkov
radiation (blue)
from -emission
in Harwellnuclear reactor
N l W
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Small-scale nuclearweapons testing
atomic cannon test, 1953
Trinity tests, 1945
Nuclear Weapons
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N l F i
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Nuclear Fusion
In a nuclearfusion reaction, two or more small light nuclei come together, orfuse, to
form a larger nucleus. Fusion reactions release energy for the same reasons (ofbinding energy) as fission reactions, but the BE/nucleon curve shows that there is
potential foreven greater energy releasein fusion, because of the slope of the curveat small A.
Fusion Reactions in the Sun
(i) Proton Cycle:Fusion of four H nuclei into a He nucleus is
believed to be primary energy source in our Sun.
This reaction is called the proton cycle:
p + p d + e+ + e where p =11H and d =
21H
p + d 32He +
32He +
32He
42He + p + p , ( called helium burning )
Sequence results in a total mass-energy conversion of26.7 MeV. This fusion is
"contained" on the Sun by the enormous gravitational field, and a continuous
reaction takes place.
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fission
fusion
energy
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Fig 1. Temp of Sun is ~ 107 K
(ii) CNO cycle:Another possible cycle (proposed by Bethe) to convert hydrogen into helium in
the Sun involving carbon, nitrogen, oxygen and helium. The net effect is:
4p 42He + 2e+ + 24.7MeV
Fig. 2: Sequence of events in the carbon cycle
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A man-made fusion reaction on Earth might utilise one of the reactions below:
Reaction Energy Released
(MeV)
D(d,p)T 4.02
T(p,)4He 19.6
T(d,n)4He 17.6
6Li(n,)T 4.96
6Li(d,)
4He 22.4
7Li(p,)
4He 17.3
7Li(d,n)
8Be 14.9
Fusion in Sun and stars is contained by tremendous gravitational field of Sun,and a continuous reaction takes place. By contrast, fusion reaction which takes
place in an H-bomb is a destructive explosion, since it is not contained.
At first glance it appears that fusion on Earth is hopeless, not only because we
must achieve enormous temperatures necessary, but at same time we need tocontain reaction at a temperature many orders of magnitude above that at which
earth materials vaporise. In fact, to obtain fusion we do not need high
temperatures as such - what we need are high velocity particles. e.g. any particle
with k.e. = 0.025 eV has a kinetic temperature of 293K , whereas a particle havingk.e. = 1 keV has a kinetic temperature equivalent of 11.6 million K.
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Basic physical and technical problems of fusion power lie in developing systemscapable of producing the heat necessary to create a hydrogen plasma (>100 millionK) under controlled conditions, and maintaining that temperature for a period of up
to several seconds. At these temperatures the fusion reactions are calledthermonuclear reactions.
Critical quantity in a fusion reactor is productof plasma temperature and number
density of particles. Nuclei of heavy hydrogen isotopes - deuterium and tritium - areeasiest nuclei to fuse. Resulting products of fusion are helium gas and neutron
radiation. This process is seen as the most promising, and therefore the
development ofD/T fusion reactors has become focal point of international efforts.
Fusion Power
A. The Tokamak - Magnetic Confinement Fusion
Most promising route towards a nuclear fusion reactor makes use of a powerfulmagnetic field to confine a hydrogen plasma.
At the extreme temperatures involved, the D-T gas becomes completely ionised,
with all the atomic electrons stripped off their atoms, and the resulting plasmaacts like two independent fluids of positive and negative particles.
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Fusion plasma located within toroidal high-vacuum chamber, and magnetic
fields of suitable geometry act through chamber wall to confine plasma and
maintain it in equilibrium. Since there exists no material for the fusion chamber
which would be able to withstand a plasma temperature of 100 million K withoutevaporating, magnetic fields have to be sufficiently powerful and complex to
prevent the hot gas from coming into contact with the chamber wall.
Of various possible magnetic confinement systems, the tokamak (Russian fortorus, or doughnut-shape) represents most promising design. Plasma
conditions which closely resemble those required for fusion reactors are
achieved in largest Tokamak machines. Tokamak has become something of a
standard machine, and a plant such as this can be found in every large plasma
physics research centre.
Essentially, Tokamak is a transformerin which the "secondary winding" is made
up of the annular plasma in which the secondary current flows. Power-carrying
coils around torus produce a toroidal magnetic field to confine the plasma.Plasma temperatures required for fusion process can only be attained if small
quantities of hydrogen locked in the fusion chamber are extremely pure. Any
contamination of the plasma increases the radiation emitted by the plasma
considerably, resulting in cooling. Vacuum vessel ensures vacuum of approximately 10-9 mbar.
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There is a lot of confusion about whether a fusion reactor produces vast amounts
ofnuclear waste, like a conventional fission reactor. The fusion reaction does notproduce waste products as such (like long-lived radioactive waste), but the
enormous neutron and gamma fluxes present activate all of the fusion reactormaterials, rendering structure extremely difficult to maintain or dispose of after use.
B. Inertial Confinement Fusion
Inertial confinement takes the opposite approach by compressing pellets of fuel to
high densities for very short confinement times. In one method, a small pellet of
fuel (0.1 - 1mm in dia) containing deuterium and tritium is struck simultaneously
from many directions by intense laser beams that first vaporise the pellet, convert it
to a plasma, and then heat and compress it to the point at which fusion can occur.
A typical laser pulse might deliver105 J in 10-9 s, for an instantaneous power of
1014 W (which exceeds the instantaneous generating power of the USA by two
orders of magnitude!).
In D-T fusion reaction shown, most of energy is carried by the neutrons (in a
fission reaction only a small fraction of the energy goes to the neutrons). This
presents some difficult problems for the recovery of energy and its conversion into
electrical power. One possibility for a fusion reactor design is shown in Fig.3.Reaction area surrounded by lithium, which captures neutrons by the reaction:
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6 1 4 3
3 3 0 2 2 1 2Li n He H+ +
KE of reaction products is rapidly dissipated as heat, and thermal energy of liquid
lithium can be used to convert water to steam to generate electricity. Reaction hasadded advantage of producing tritium (3H), which is needed as fuel for fusion reactor.
Fig 3: Proposed design for a fusion reactor:
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Fig. 4: Inertial confinement fusioninitiated by a laser
e.g. NOVA laser, Lawrence Livermore
Laboratory, CA, USA.
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National Ignition Facility, LLNL, CA, USA
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European High Power LaserEnergy Research Facility
(HiPER)
Uses intense laser pulses to fuse
small capsules of deuterium-
tritium fuel.
Hold fuel capsules at extremelyhigh pressures for a few
picoseconds using lasers.
Another laser heats dense core
to about 108 K, forcing nuclei to
fuse.
Process known as fast ignition second laser
must heat fuel within 10-11 s of implosion.
2 GW typical for
large power station
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END
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Total neutron cross sectionsversus neutron energy
Note resonances in Cd
and (especially) In.
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