Neutron Flux & Reactor Power Lecture Notes PDF

Neutron Flux (continued) Another way to define neutron flux is The total track length traveled by all neutrons in a unit volume per unit time  track length   particles   track length  f   n  v ...

Neutron Flux (continued) Another way to define neutron flux is The total track length traveled by all neutrons in a unit volume per unit time  track length   particles   track length  f   n  v   volume  time   volume   time  In this case the units on Φ would be neutron - cm cm3 - sec We will usually write the units as neutrons/cm2-sec 31  Neutron Flux f  nv Z UO2 H2O R Reactor Core 32  Neutron Flux f  nv Neutrons cm2-sec = Neutron-cm cm3-sec Z φ φ R r 33  Neutron Flux and Reactor Power Example: A research reactor core has a volume of 60 x 103 cm3. Calculate the power of the reactor if the neutron flux is 1.2 x 1013 neutrons/cm2-s and the fission macroscopic cross-section (Σf ) is 0.1 cm-1. Solution: F   ff – Find fission rate in the reactor F = No. of fission interactions per – Energy released per fission = 200 MeV second per cm3 – Power = Energy release per fission x fission rate (Units for power: 1 Watt = 6.242 x 1012 MeV/s) Total Fission Rate  V Σ f f  60 103 (0.1) 1.2 1013  7.2 1016 fission/s 7.2 1016 (200) Power   2.3  10 6 W  2.3 MW 6.242 10 12 34  Neutron Flux (Φ) is very Useful for Calculating Important Reactor Quantities Recall: The macroscopic cross-section depends on -- The target atom density N (a macroscopic quantity) -- Interaction type (i.e., the microscopic cross-section) -- Projectile and target energy Macroscopic total cross section Σt = N t Macroscopic scattering cross section Σs = N s Macroscopic absorption cross section Σa = N a , etc. Therefore: Fission rate = Σf*Φ fissions/cm3-sec Scattering rate = Σs*Φ scattering events/cm3-sec Absorption rate = Σa*Φ absorptions/cm3-sec The rate of “any” interaction = Σany*Φ “any-event”/cm3-sec 35  Neutron Moderation In typical power reactors, neutron-induced fission is more likely when the neutrons have low energy, less than 1 eV (0.025 eV at 20°C, i.e., “thermal neutrons”). Since neutrons from fission events are fast neutrons (born at high energies, up to several MeVs), they must be slowed down to thermal energies (v = 2200 meters/sec) to induce enough fission reactions. The energy of a neutron is reduced (i.e, the its velocity R is “slowed down”) through scattering. This process is known as thermalization or moderation. The material used for the purpose of reducing neutron energies is called a moderator. 36  Why We Need to Moderate the Neutrons 235U Fission and Radiative Capture Cross Sections f : 585 barns U-235 fission f : ~1 barn radiative capture 0.025eV 2.0 MeV From NUEN-611 lecture notes. Author: Unknown. 37  Moderator We want a moderator that will slow the neutrons quickly but not absorb them Thus for an ideal moderator, we want material that has a – Large energy loss per collision Need to slow down neutrons in a small number of collisions – Small absorption cross section So most neutrons are not absorbed by moderator 38  Neutron Moderation (continued) Moderator A Average number of collisions to thermalize H2O 17 19 D 2O 18 35 He 4 42 Be 9 86 C 12 114 39  Fission Chain Reaction Fission reactions not only generate an enormous amount of energy but also emit additional neutrons. Some number of the fast neutrons produced by fission in one generation will undergo moderation and eventually cause fission in the next generation. This leads to the possibility of a self-sustaining neutron- induced fission chain reaction Nuclear power plants operate by precisely controlling the rate at which nuclear reactions occur. 40  Steady-State Reactor Operation For a nuclear chain reaction to continue at steady-state, the neutron production rate must be perfectly balanced with the neutron loss rate Any deviation from this balance will result in – A time-dependence of the neutron population – A time-dependence of the power level of the reactor 41  Neutron Balance Equation To safely and efficiently operate a nuclear reactor, we must be able to predict and control the neutron population and changes to that population over time and space. We will use a balance equation of the form  change rate of   rate of   rate of       neutron population   gain   loss  42  Neutron Production and Loss Rates  change rate of   rate of   rate of       neutron population   gain   loss  The production rate is given by – Production rate due to fixed neutron sources – Production rate due to neutron producing reactions [e.g., fission, (n,2n), etc.] R The loss rate is given by – Loss rate due to absorption reactions – Loss rate due to “leakage” 43  Life Cycle of a Neutron Fast Neutrons PFNL 1-PFNL Don’t Leaks Leak p 1-p Slow to Absorbed Thermal while Fast PTNL 1-PTNL 1-uF uF ntherm nfast Don’t Absorbed in Absorbed in Leaks Leak Other Fuel f 1-f 1-PFAF PFAF Absorbed in Absorbed in Capture Fission Fuel Other PTAF 1-PTAF Fission Capture Source: NUEN 611 notes. Author: Dr. W. Charlton, NUEN, TAMU 44  Criticality The effective neutron multiplication factor (k) defines the criticality condition for the system: # neutrons in given generation k # neutrons in previous generation – Without a source present The value of k immediately tells us what the time evolution of the system will be 45  Criticality (continued) # neutrons in given generation k # neutrons in previous generation With a source of fission neutrons present and without any externally injected neutrons (i.e., fission neutrons only) – k < 1, neutron population will decrease called a subcritical reactor R – k = 1, neutron population will stay constant called a critical reactor – k > 1, neutron population will increase called a supercritical reactor 46  Criticality (continued) We will traditionally use a more convenient definition for criticality – Every neutron in a single generation is lost by some mechanism and – The only neutrons in a given generation (when the external source is not present) are those produced from fission – Thus: rate of neutron production k rate of neutron loss Same ratio # neutrons in given generation k as before # neutrons in previous generation 47  Criticality (continued) For an infinitely large reactor, which has no neutron leakage, this is production rate k  absorption rate R For a more realistic system, this will be production rate k absorption rate  leakage rate Question: Neutron Production Comes from ____?____ and _____?____ 48  Role of Delayed Neutrons From fission, neutrons are emitted and fission products are created – From the decay of these fission products, additional neutrons are generated a relatively long time after the fission event – These neutrons from fission products represent only a small fraction (1 We will change the value of 2.5 k