Download Nuclear and Particle Physics SubAtomic Physics

Notes
Nuclear
and Physics
Particle
SubAtomic
Nuclear
Physics
Physics
Lecture 9
3rd Year Junior
Honours
Course
Dr Daniel Watts
Notes
Notes
Fission continued...
Applications of nuclear decay: Radioactive Dating
Uranium occurs in natural minerals e.g. pitchblende UO3UO2PbO
Natural Abundance
238U(99.28%), 235U
(0.71%), and
234U
(0.006%)
n+
Obtain information on age of rock from radioactive series
e.g 238U
τ1/2=4.5109 years
238
234
4
92
Ratio of
238U
U → 90Th + 2 He
235U
→ 236U* → 139Xe + 95Sr + 2n
The probability (cross section) for such induced processes
depends on energy of projectile and the initial nucleus
Rate determining step as
other half lives are smaller
(10-4s to 105 yrs)
to 206Pb gives information on age of sample
Appreciable cross section
for induced fission even
at lower energies – “fissile”
Other “clocks” with geological time scales also used e.g.
87
37
87
Rb→38
Sr + −10e
τ1/2=4.91010 years
Other techniques for archaeological time scales – e.g.14C dating
continuously formed in
earths atmosphere
14
7
N + 01n→146C +11p
Carbon in living organisms exchanged
with atmospheric carbon – ceases when
organism dies
Need ~1 MeV minimum for fission of 238U
Why?? 238U(Z=82) is even-even → Additional binding from pairing
effects is lost when neutron is added (δ term in SEMF)
Oldest rocks measured to date: ~ 4.5 billion years old !
14C
Induced fission – the nucleus is induced to fission by external
interaction e.g. Projectile neutron
cosmic
ray
proton
n
Fissile nuclei are even-odd 235U ,239Pu
Aside: the neutron energies from fission
are on order of ~1 MeV → need to slow
neutrons down (in moderator) to get to
larger fission cross sections
Neutron
energies
Following
fission
of 235U
Notes
Notes
Fission power: Delayed neutrons
Fission reactor budget – thermal reactor
The intrinsic time scales of the nuclear chain reaction are fast.
Probability that neutrons will be thermalised
rather than captured in the moderator
p typically ~ 0.4-0.9. Depends on the type of
moderator and the moderator/fuel ratio
Multiplication
of neutron flux
(>1 to enable
chain reaction)
Kinf = η × p × f × ε
Control is achieved by exploiting beta delayed neutron emission
Before being thermalised
some neutrons may induce
fast fissions – increasing
the number of neutrons
ε typically ~ 1.03
Average number of neutrons
produced by thermal neutron
during fissions of reactor fuel
Probability that once thermalised the
neut. interacts with a U nucleus
η = ν × Pf
f typically ~ 0.9
ν −average No. Neut. fission-1
Pf – probability for fission
Pf = σf/σf+σc where σf, σc are the
cross sections for fission and
capture reactions (averaged
over the isotopes in the fuel)
Natural uranium η=1.33
3% enriched 235U η=1.84
Useful figures at
thermal energies
(20oC)
The above equation is known as the infinite
reactor equation - neglects losses of
neutrons out of the edges of the reactor
Finite size reactors → Kinf reduced by a
factor dependent on the reactor geometry
Nucleus
Density
(gcm-3)
235U
18.7
238U
18.9
natU
18.9
σf
579
4.17
σc
ν
101
2.42
2.72
--------
3.43
--------
The prompt (undelayed) fission neutrons are sub-critical i.e. not of
sufficient number to maintain a chain reaction.
The (typically ~1%) delayed neutrons have second to minute time
scales and can be controlled
Neutron flux removed/controlled in reactor using absorbing control
rods
Notes
Notes
Practical thermal fission reactors
Fast Breeder reactors
With water as a moderator then p is too small to produce
the chain reaction (K>1) for naturally occurring Uranium
Therefore the fissile component of Uranium needs to be
enriched to ~3% to increase η and enable a water moderated
reactor
Thermalising the neutrons is not the only possibility - fast
reactors use higher energy neutrons > ~1 MeV. Therefore do not
need moderator - smaller
Energetic neutrons → exploit to breed fissile fuel
n+
238U
239Np
Light water
reactors
→ 239U → 239Np + β− + ν
→ 239Pu + β− + ν
Enable over 50% of Uranium reserve to yield energy (not just the
0.7% fissile component).
Potential to provide energy needs for ~1000 years.
The reaction above is a breeder reaction – which breeds fissile
fuel (239Pu) → can be extracted and reused
If deuterium is used as moderator rather than water then the
value of p is increased significantly (neutron capture
probability reduced). Can then use naturally occurring Uranium
as the fuel
For breeding need to design a reactor with η>2.
One neutron to keep the reaction going (produce
more neutrons from the fissile component)
One (at least) to go to the breeder reaction
where the neutron is lost.
Canadian heavy water
Reactors (CANDU)
FBRs built in UK, USA, Russia,
Japan - recent projects in
India and China.
Material
Useful figures at
thermal energies
(20oC)
σs
density
σa
H2O
1.0
49.2
0.66
D2O
1.1
10.6
0.001
Graphite
1.6
4.7
0.005
Need to use coolants which
have high heat capacity Na, NaK, Pb used.
Notes
Notes
Accelerator driven systems
Fusion in the sun
Fusion - combining nuclei to form heavier nucleus with higher B/A
Consists of a nuclear particle accelerator (protons or deuterons)
injected into a sub-critical (K~0.95) fission reactor
B/A larger in the fused nucleus (smaller fraction of nucleons
near the surface)
The energetic particles result in production of large amounts of
neutrons in the reactor
Fusion is the energy source of stars (see next semester course)
Gravitational potential energy converted into kinetic & radiation
energy of gas → Temperature of gas rises & fusion ignites
Nuclear power keeps star interior hot enough to stop the collapse
(at least for a while! e.g ~9 billion years in the case of our Sun)
Some cause further fission, others used to convert waste, breed
new fuel and generate energy
Can be used with conventional thermal reactor or with fast
reactor
Need high beam fluxes for transmutation – technological
challenges
p +11p→12D + ν e + e + + 0.42MeV
D +11p→ 23He + γ + 5.49 MeV
He+ 23He→ 24He+11p +11p + 12.9 MeV
1
1
2
1
3
2
First step is rare
(involves weak
interaction)
Sets long timescales
For stellar life
Get energy release of 26.7MeV per 4He nucleus formed
Notes
Notes
Terrestrial Fusion power
Can fusion be harnessed as a terrestrial energy source?
Fusion power research
Tokamak attempts to magnetically confine and heat the plasma
ITER
Fuel supply practically unlimited – naturally abundant or created in
fusion/fission reactors
p + p → d +e+ ν
d + d → 3He + n
d + d → T +p
d + T → 4He + n
(0.7 MeV)
(3.27 MeV)
(4.04 MeV)
(17.06 MeV)
D-T fusion best – higher energy yield
and lower ignition temperatures
Rate of fusion reactions (W) is given by:
W = (n2 <µσ>)/4
n
µ
σ
<>
Reaction rate <µσ> m3s-1
Coulomb barrier for fusion to occur – but energy releases are large
electron density per unit vol. (D,T density = n/2)
Relative velocity of the two nuclei
The (velocity dependent) fusion cross section
Indicates average over all possible relative
velocities of the fusing nuclei (Maxwell-Bolt distn.)
The fusion energy delivered in a time τ is therefore
E = (n2<µσ>τQ)/4
For a net energy gain this must exceed the total energy you put
in to heat the system (~3nKT)
nτ > 12kT/(<µσ>Q)
This is known as the Lawson criterion
Present designs of fusion reactors give temperatures kT~10keV.
For D-T fusion therefore need nτ > 0.7 x 1015 scm-3
Toroidal field along direction of plasma provided by coil and poloidal
field along the surface of the plasma provided by currents induced in
the plasma.
Additional heating supplied
energetic H-D atoms
by
microwave
sources/injections
of
Inertial confinement fusion –
Pellet containing D-T struck from many
directions by laser pulses. Compresses and
heats the pellet - exceed Lawson criteria
Energy to heat pellet 0.1mm diam. to 10 keV (density
NIF (US)
DT-~1025cm-3)
E = 4/3π x (0.05cm)3 x 1025cm-3 x 10x103 x e ~ 105J
Need to achieve density and temp above Lawson criterion before pellet blows
apart (~10-10s) 1015 W !!
Lasers inefficient 1-10% of power to light - 1017 W more realistic -
Notes
Questions from past exam papers
Write an essay on the topic of the “Strong nuclear force”. In your essay you should
indicate the main properties of the strong nuclear force, comment on their physical
significance and relate them to observational facts such as the stability of the deuteron
and the features of the curve of binding energy per nucleon. Use sketches where
appropriate
[20]
Some other past exam questions were set as tutorial questions