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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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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.
http://en.wikipedia.org/wiki/Image:Nova_laser_repairs.jpg


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National Ignition Facility, LLNL, CA, USA
http://en.wikipedia.org/wiki/Image:NIF_building_layout.jpg


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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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