Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).

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Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). Neutron Life Cycle Why should we worry about these? How? Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). Controlled Fission k = fp(1-lfast)(1-lthermal) Thermal utilization factor f can be changed, as an example, by adding absorber to coolant (PWR) (chemical shim, boric acid), or by inserting movable control rods in & out. • Reactors can also be controlled by altering neutron leakages using movable neutron reflectors. f and p factors change as fuel is burned. • f, p, η change as fertile material is converted to fissile material. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). Controlled Fission Attention should be paid also to the fact that reactor power changes occur due to changes in resonance escape probability p. If Fuel T↑, p↓ due to Doppler broadening of resonance peaks. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). Controlled Fission • Note that  is greater than 2 at thermal energies and almost 3 at high energies. • These “extra” neutrons are Used to convert fertile into fissile fuel. • Efficiency of this process is determined by neutron energy spectrum. Variations in  Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). Controlled Fission Conversion ratio CR is defined as the average rate of fissile atom production to the average rate of fissile atom consumption. For LWR's CR  0.6. CR is called BR for values > 1. Fast breeder reactors have BR > 1. They are called “fast” because primary fissions inducing neutrons are fast not thermal, thus η > 2.5 but σf is only a few barns. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). Controlled Fission Time scale for neutron multiplication Time constant  includes moderation time (~10-6 s) and diffusion time of thermal neutrons (~10-3 s). Time Average number of thermal neutrons t n t +  kn t + 2 k2n For a short time dt Show that Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). Controlled Fission k = 1  n is constant (Desired). k < 1  n decays exponentially. k > 1  n grows exponentially with time constant  / (k-1). k = 1.01 (slightly supercritical)  e(0.01/0.001)t = e10 = 22026 in 1s. Cd is highly absorptive of thermal neutrons. Design the reactor to be slightly subcritical for prompt neutrons. The “few” “delayed” neutrons will be used to achieve criticality, allowing enough time to manipulate the control rods. Dangerous Cd control rods Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). Fission Reactors Essential elements: Fuel (fissile material). Moderator (not in reactors using fast neutrons). Reflector (to reduce leakage and critical size). Containment vessel (to prevent leakage of waste). Shielding (for neutrons and ’s). Coolant. Control system. Emergency systems (to prevent runaway during failure). Core Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). Fission Reactors Types of reactors: Used for what? Power reactors: extract kinetic energy of fragments as heat  boil water  steam drives turbine  electricity. Research reactors: low power (1-10 MW) to generate neutrons (~1013 n.cm-2.s-1 or higher) for research. Converters and breeders: Convert non-thermally-fissionable material (non-fissile) to a thermally-fissionable material (fissile). What are neutron generators? Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

How??? Fission Reactors What neutron energy? Thermal, intermediate (eV – keV), fast reactors. Large, smaller, smaller but more fuel. What fuel? Natural uranium, enriched uranium, 233U, 239Pu. How??? From converter or breeder reactor. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). Fission Reactors What assembly? Heterogeneous: moderator and fuel are lumped. Homogeneous: moderator and fuel are mixed together. In homogeneous systems, it is easier to calculate p and f for example, but a homogeneous natural uranium-graphite mixture can not go critical. What coolant? Coolant prevents meltdown of the core. It transfers heat in power reactors. Why pressurized-water reactors. Why liquid sodium? Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). More on Moderators What moderator? Cheap and abundant. Chemically stable. Low mass (high  logarithmic energy decrement). High density. High s and very low a. Graphite (1,2,4,5) increase amount to compensate 3. Water (1,2,3,4) but n + p  d +   enriched uranium. D2O (heavy water) (1!) but has low capture cross section  natural uranium, but if capture occurs, produces tritium. ….. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Good absorber, bad moderator. More on Moderators For a compound? Moderating power Never consider this only! Moderating ratio  Calculate both moderating power and ratio for water, heavy water, graphite, polyethylene and boron. Tabulate your results and comment. HW 12 10B Good absorber, bad moderator. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). More on Moderators Recall  After n collisions After one collision Total mean free path = n s Is it random walk or there is a preferred direction??? f th Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). More on Moderators HW 13 (or 6\) E Recall (head-on). Then the maximum energy loss is (1-)E, or E  E\  E. For an s-wave collision: show that Obviously Assumptions: Elastic scattering. E Target nucleus at rest. E Spherical symmetry in CM. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). Scattering Kernel?

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). More on Moderators HW 13 (or 6\) continued… (Re)-verify For doing so, you need to verify and use Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). More on Moderators HW 13 (or 6\) continued… Forward scattering is preferred for “practical” moderators (small A). If isotropic neutron scattering (spherically symmetric) in the laboratory frame  average cosine of the scattering angle is zero. Show that Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). More on Moderators HW 13 (or 6\) continued… Spherically symmetric in CM Show that Try to sketch. Neutron scattering is isotropic in the laboratory system?!  valid for neutron scattering with heavy nuclei, which is not true for usual thermal reactor moderators (corrections are applied). Distinguish from Angular neutron distribution. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).