The Physics of Energy sources Nuclear Reactor Practicalities

The Physics of Energy sources Nuclear Reactor Practicalities B. Maffei Bruno.maffei@manchester.ac.uk www.jb.man.ac.uk/~bm Nuclear Reactor 1

Commonalities between reactors All reactors will have the same essential elements! Fuel: fissile material! Moderator to thermalise the neutrons! Excepted for reactors using fast neutrons! A reflector surrounding the core (fuel+moderator)! To reduce neutron leakage! Containment and shielding vessel! To prevent radioactive material escaping! Coolant! Cool and transfer the heat from the core to the turbine! Control system! Material that will allow to keep the reaction under control Nuclear Reactor 2

Various types! Power reactors! Main aim: generating large amount of energy Transformation of the kinetic energy from the fragments into heat and electricity the most efficiently possible. Design considerations: special attention to thermodynamic design Typical output 1-2 GW! Research reactors! Designed for neutron production for research purposes Low power range: 1-10MW Steady and accurate neutron flux for nuclear and solid-state Physics! Converters! Convert non fissile material into fissile elements.! Breeder reactors (see later) Nuclear Reactor 3

Fuel! Most commonly used are 235 U, 233 U, 239 Pu! 235 U can be found: Natural U (0.72% 235 U, the rest is 238 U) Needs to be enriched to sustain chain reaction! 233 U, 239 Pu cannot be found From converters or breeder reactors! Neutron energy! We have seen that it is more efficient to use thermal neutrons for 235 U Due to the fission cross section decrease with increasing neutron energy.! However, that does not stop us to use slow or fast neutrons In this case we need Richer fuel in 235 U Larger amount of fuel to provide the same power (x10-100)! We do not have the same problem with 233 U, 239 Pu! Trade-offs They will work with faster neutrons! The main advantage/disadvantage of using fast neutron reactor are: No use of moderator making the reactor more compact (submarine engines) More expensive: better enrichment Higher power density core at a higher temperature needs a good thermal transfer Nuclear Reactor 4

Enrichment! In order to increase the ratio of 235 U in natural uranium, we need a way to separate the 2 isotopes 235 U and 238 U.! Their chemical properties are the same no differentiation possible! Need to use physical processes: mainly mass difference Their mass difference is small ~ 1% of their total mass! There are several methods. Here are the main two.! Both methods use uranium hexafluoride UF 6 in gas phase (under pressure)! Gas diffusion Use the difference in diffusion rate UF6 gas is forced through a porous material (semi-permeable membrane). The slightly smaller molecules of 235 UF 6 will diffuse faster than the 238 UF 6 ones. The gas has to go through hundreds of membranes before reaching a good enough enrichment. Fairly expensive process but has been the only large scale process until the 70s! Gas centrifuge UF 6 is put into a rotating centrifuge. The heavier 238 UF 6 will tend to move towards the outside of the cylinder while the lighter 235 UF 6 will collect closer to the centre. Nuclear Reactor 5

Moderator! We have seen that a moderator is needed to thermalise the fast neutrons! The ideal moderator:! Cheap and abundant! Have a low atomic mass (see previous calculations)! Be chemically stable! High density (liquid or solid)! Have a minimal neutron capture cross section and a good scattering cross section! Ideal moderators do not exist. The closest are:! Graphite (used by Fermi in 1942 in the first nuclear reactor)! H 2 O! D 2 O Deuterium (Heavy water)! Not possible:! Boron would have been better than C (A=11 instead of 12) but σ a too large! Beryllium (A=9) but too dangerous poison Nuclear Reactor 6

Graphite as moderator! 12 C is reasonably light and cheap From previous lecture, we found out with a simple model taking into account scattering in the opposite direction only: 1 2 m v 2 2 n 1 2 M m n 11 = = = 0.72 if we assume M = 12 1 2 m v mn + M 13 n 2 If we want to thermalise the neutrons from 1MeV to 0.025eV we need many collisions: E E final initial 11 = 13 2N = 0.025 6 10 N being the number of collisions N~50 However this simplified model overestimates the energy loss (180deg only). Averaged over all scattering angles, we need about twice as many collisions and N~100 is more realistic value as we can see from the results of a more complete model. Nuclear Reactor 7

Moderator comparison We usually define the logarithm energy decrement ξ as the average energy loss after the 1 st collision ln(e 0 /E 1 ). 2 ( A 1) It can be shown that: A 1 Giving a simpler good 2 4 ξ = 1+ ln 2 2A A+ 1 approximate expression ξ = A 3A A: atomic mass number of moderator After N collisions the average energy is: ln( ) ln( E ) Nξ Nuclear Reactor 8 E N = 0 Applied to the previous case E 0 =1MeV and E N =0.025eV we find N~111 This is the energy loss after collisions. We need to take into account the probability for the scattering to happen the scattering cross section. Comparison! From the data, water seems the most appropriate.! But very high capture cross section! Deuterium is next but:! gives radioactive tritium nasty! Fairly expensive to produce! Graphite! Not the best performances but cheap Material σ s (barn) σ a (barn) ξ Ν H 2 O 49.2 0.66 0.920 19 D 2 O 10.6 0.001 0.509 34 Graphite 4.7 0.0045 0.158 111 Even if some reactors are using water or deuterium, for practical reasons, the most common moderator is graphite

Core design! The core is where the reactions will take place and the energy produced. It comprises the fuel and the moderator (if present)! We have seen that the neutron reproduction factor k depends on:! The thermal utilisation factor, f (capture by moderator) It will decrease as a function of the moderator-to-fuel ratio N M /N F! The resonance escape probability, p (capture by 238 U) It will increase as a function of the moderator-to-fuel ratio! For a given enrichment, there is an optimal value of N M /N F to get k maximal! However p varies with N M /N F more quickly than f need to optimise p A way of increasing p is by optimising the design: to clump the fuel in form of rods which are well separated from each other à heterogeneous core - The neutrons produced in one rod will travel to the next rod with moderator only in between p is optimum as the neutrons being thermalised travel mainly in the moderator (short distance inside the rod) thus reducing the resonance absorption due to 238 U. A heterogeneous graphite-natural uranium reactor can be made to be self-sustained Nuclear Reactor 9

n+ 239 239 Breeder reactor! Neutron captured by elements that are not fissile (or poorly) can lead to fissile long lived elements through radioactive decays. 238 2.3d Np Pu U 239 23min U 239 4 ( 2.4 10 yrs) 239 Pu + β + ν Np + β + ν 27d Pa 5 ( 1.6 10 yrs) Nuclear Reactor 10 n+ 233 233 232 U Th 233 22min Th 233 U + β 233 + ν Pa + β + ν 233 U and 239 Pu are fissile. Cannot be found naturally Nucleus With thermal neutrons The idea here is that a breeder reactor could 233 U 2.29 2.4 produce more fissile material than it consumes. 239 Pu 2.16 2.9 If B is the breeding ratio defined as number of fissile atoms formed per atom of existing fuel: η a values for fissile nuclei B=1 fuel is replaced B>1 amount of fuel increases. B<1 amount of fuel decreases. With fast neutrons η a : neutrons produced per neutron absorbed 1 neutron is needed for chain reaction Others are lost through leakage & capture (~0.2) So η a = 1+B+0.2 So if we have a fast neutron reactor with 238 U+ 239 Pu or 232 Th+ 233 U as fuels, we could in principle use fairly abundant fuel ( 238 U) which will be transformed into fissile fuel + energy in the same reactor: this is just a project Does not exist yet

Coolant / Design In order to avoid meltdown of the core, we need to extract the generated heat and transfer it efficiently towards the turbine. The coolant needs to have a large heat capacity It can be gas (air, CO 2 or helium) or liquids Figures from Ref 3 Water cooled! Steam has a low heat capacity. So water has to be kept as a liquid.! Typical core temperature: 300C! The water has to be under pressure (~100atm)! Due to neutron absorption, fuel needs to be enriched! Pure water does not become radioactive, but impurities in it yes. In order to avoid contamination two different water circuits are used Nuclear Reactor 11

Design (2) Canada has a supply of natural uranium and can produce deuterium deuterium-uranium reactor. Deuterium is also used as a coolant CANDU reactor Gas cooled reactor: Helium as a good heat capacity For high power density reactors (high enrichment or breeder reactors) the core temperature is higher. Water is not efficient enough. Use of sodium as coolant: no need for high pressure. But becomes radioactive and is corrosive Nuclear Reactor Figures from Ref 3 12

Reactor poisoning! There is a range of fission fragments that are produced, some of which have a high neutron-capture cross-section! Notably xenon and samarium! 135 Xe as one of the largest neutron capture cross section=2.75x10 6 b! The building up of these fragments will impact the neutron production! However through decay the proportion of 135 Xe will reach a stable level! This fact has to be taken into account in the reaction rate control Fission fraction γ=0.061 135 I 5 1 λ= 2.93 10 s 135 Fission fraction γ=0.003 Xe 5 λ= 2.11 10 s 135 + n 136 Xe! 135 Xe is produced directly by fission and by decay of 135 I! 135 Xe will be lost though decay and neutron capture! At the beginning 135 Xe will build up rapidly then will level off when equilibrium is reached 1 Cs Nuclear Reactor 13

Fission reaction control! In order to regulate the produced energy, we need to control the reaction rate.! Several factors are affecting the energy production! The control is only performed through the variation of k k: change in nb. of neutrons from one generation to next. We want k = 1.0 to have a steady power output! We also need to take into account the fact that over time the number of fissile atoms will decreased (if not re-fuelled).! We also need to take into account the production of reactor poisons.! This control is performed by inserting rods in the core! These rods are made of material that are good neutron absorbers! At the beginning, when the fuel is rich in fissile material the rods are inserted in the core. When the amount of fissile material is decreasing, the rods are slowly removed to keep the power level stable.! They are also used to stop the chain reaction if necessary.! These rods are usually made of boron carbide (σ a =760b) or Cd (σ a =2450b) Nuclear Reactor 14

The role of delayed neutrons! We have seen that to maintain the reaction k=1! If k<1 the reaction is not sustained (sub-critical)! If k>1 super-critical we need to run fast! The calculation of k is only involving the prompt neutrons! Delayed neutrons allow to run a reactor sub-critically! By controlling the reaction with k just below 1 (for safety reasons) the delayed neutrons will help to sustain the reaction! Moreover, the movement of the rods to control the reaction is not immediate the delayed neutrons also help to take into account this time constant. Nuclear Reactor 15

Efficiency The task is to extract heat Q from the core, turn it into useful work W and dump the excess heat energy outside (condenser) heat engine (ref to Carnot cycle) Laws of thermodynamics For an ideal heat engine, the efficiency is given by: W Q = T core T T core condenser The condenser temperature is given by the ambient temperature. We then need a high core temperature to increase efficiency: high energy density reactors T core ~ 600K T condenser ~ 300K W 600 300 Max efficiency(ideal) = = = Q 600 50% In practice, a real reactor will have an efficiency of ~ 30% Nuclear Reactor 16

Pros and Cons! Advantages! Very low level of greenhouse gas release Even taking into account mining of uranium and all other associated activities, nuclear energy produces ~ 1/100 th of coal or oil energy greenhouse gases.! Even if difficult to account for, less casualties than classic energy production! Production of energy in itself is relatively cheap! Disadvantages! Radiations Average radiation released outside by power plant is below natural radiation level However radioactive waste is a big problem Some might be recycled (research, medecine ) Majority will have to be dealt with for thousands of years with all associated issues! Risks Even if there has been only 3 major incidents (UK 1957, USA 1979, Ukraine 1986) so fairly low risk, when an accident happens (Chernobyl) the potential number of casualties is very high (and unknown) as well as impact on ecosystem.! Costs Construction, safety and decommissioning is very costly! It is not a renewable source of energy It is difficult to estimate the fissile fuel resources in the world but some studies are showing that if nuclear energy was to provide 50% or our energy needs, resources would only last for ~50 years. Anyway, at the most will last for 100-200 years at most Nuclear Reactor 17

Summary! General points about fission reactors! Do you know the various types of reactor and their typical power output?! What are the various parts of the reactor?! Would you be able to describe the role of the moderator?! What are the important characteristics of a good moderator and why?! How to optimise a reactor! Enrichment! Right coolant, right moderator, how to control the reaction! Fuel clumping! What is reactor poisoning?! Advantages and disadvantages of nuclear fission Nuclear Reactor 18

References Ref 3: Kenneth S. Krane, Introductory Nuclear Physics (Wiley 1988) Nuclear Reactor 19