The amount of carbon dioxide released (Kg CO 2 /kWh) annually in the UK .

The amount of carbon dioxide released (Kg CO2/kWh) annually in the UK.

Do we need Nuclear Reactors?

Patterns of fuel flow around the World

World Situation

B ~1.5 MeV per A

The Energy released in Fission

The Idea of a Chain Reaction

The Four Factor Formula

In a sense a nuclear reactor is simply a controlled chain reaction – a system arranged so that it is stable and produces constant power.

Initially we consider an infinitely large system. - In effect we ignore the loss of neutrons from the surface.

We define a Neutron Reproduction Factor k∞

No.of neutrons in a generation No.of neutrons in preceding generation

k∞ =

In other words it gives the net change in the number of thermal neutrons from one generation to the next. On average each thermal neutron produces k∞ new thermal neutrons

If a chain reaction is to continue we must have k∞ ≥ 1

However although 2.5 neutrons are produced on average in each fission they are fast neutrons.

Fission Cross-sections

Here we see the cross-sections for neutron-induced fission and neutron capture on235U and 238U

In the thermal (low energy) part of the spectrum the cross-section falls with energyas 1/ v.

For 235U the cross-section for fission = 584 b, much larger than for scattering 9 b or for capture 97 b. Overall the cross-section falls by 3 orders-of-magnitude from thermal to fast energies.

For 238U no fission occurs until the neutronreaches an energy of 1 MeV.

Thermal

The Four Factor Formula

Why are fast neutrons ”bad” in this context? The cross-section for fission is ~1000 times for slowed down neutrons compared with the fast neutrons created in fission.

We need to slow down the neutron energy so that the average energy drops from a few MeV to 0.025eV.

BUT….in the moderation process we can lose neutrons either by absorption on e.g., 238U.

Neutron energies are moderated (slowed down) by elastic collisions with nuclei.

The best choice for a moderating material is a light element (e.g., Hydrogen) because then the neutron transfers the largest possible energy in a collision.

The Mass Distribution of Fission frgaments

A typical result of thermal neutron induced fission in 235U leads to the result n + 235U 93Rb + 141Cs + 2n

This is not a unique split and there is a wide distribution of masses for the two resulting fission fragments.

Note that fission into almost equal mass fragments is less probable than the maximum yield by 600.

Aside:- Fission induced by fast particles shows a distribution which centres on equal mass fragments.

The Energy released in Fission

The Idea of a Chain Reaction

If we try to use natural Uranium ( Now 0.7% 235U ) we cannot get k> 1 because the dominant 238U absorbs too many neutrons.

However if we can enrich the sample highly in 235U then we can get k > 1 and the chain reaction can be sustained. This is the basis of the fast reactor, namely a reactor that operates with fission being initiated by neutrons that have not been slowed down much following their production. If the enrichment is high enough it is also the basis of an explosive weapon.

The Four Factor Formula

For 235U f = 584 b and a = 97 b so = 2.08 fast neutrons per thermal neutron

For 238U f = 0 for thermal neutrons and a = 2.75 b

Natural U contains 0.72% 235U

For natural Uranium we have effective cross – sections for fission and capture

f = f (235) + 0.72

100 100

99.28f (238) = 4.20 b

a = 0.72100

a (235) +99.28100

a (238) = 3.43 b

So the effective value of for natural U is 1.33 This number is rather close to 1 so we have to do something to ensure we have a critical system.

One “simple” thing we can do is enrich the U to 3% in 235U This increases to 1.84

A natural Reactor in Oklo, GabonA. The fraction of 235U in natural Uranium is found to be very precisely 0.00720 +/- 0.00001

error reflects the variation found in samples from places where U is mined.

B. This ratio varies on a geological timescale. 235U and 238U have half-lives of 7.0 x 108 years and 4.5 x 109 years respectively.

Note:- 2 x 109 y ago the ratio would have been ~ 3%

C. 1972 – a sample was found in Gabon with a 235U abundance 0.00717.

Other samples from the same place were found with values as low as 0.00440

D. Hypothesis was that 2 x 109 y ago a natural reactor operated in Oklo. Moderation would have been by groundwater.

E. The reactor would have worked intermittently with the heat boiling off the water and it would then start again when enough water accumulated.

The Oklo reactor is interesting in itself but it is also highly relevant to the discussionof dealing with present day waste. Neither the fission fragments nor the Pu migrated from the site in 2 x 109 y.

A more advanced kind of reactor is the breeder reactor, which produces more fissionable fuel than it consumes.

The chain reaction is:

The plutonium is easily separated from uranium by chemical means. Fast breeder reactors have been built that convert 238U to 239Pu. The

reactors are designed to use fast neutrons. Breeder reactors hold the promise of providing an almost unlimited

supply of fissionable material. One of the downsides of such reactors is that plutonium is highly

toxic, and there is concern about its use in unauthorised weapons production.

Breeder Reactors

Normal reaction235U + slow n fission fragments + 2(fast)n

“Parasite” reaction238U + fast n 239U* 239Np (neptunium) 239Pu (fissile)

Pu/U fuel cycleProcess “used” fuel to extract 239Pu to be mixed with U(or to make bomb!)

Other parasite reaction232Th + fast n 233Th* 233Pa (protactinium) 233U (fissile)

Th/U/Pu cycleLace natural Uranium with Thorium to extract 239Pu and 233U to be re-injected into natural Uranium.

The re-cycling of spent fuel