Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 1 Nuclear Fission 1/ v 235 U thermal cross sections  fission  584 b.  scattering  9 b.  radiative capture  97 b. Fast neutrons should be moderated. Fission Barriers

2 Nuclear Fission Q for 235 U + n  236 U is MeV. Table 13.1 in Krane: Activation energy E A for 236 U  6.2 MeV (Liquid drop + shell)  235 U can be fissioned with zero-energy neutrons. Q for 238 U + n  239 U is 4.??? MeV. E A for 239 U  6.6 MeV  MeV neutrons are needed. Pairing term:  = ??? (Fig in Krane). What about 232 Pa and 231 Pa ? (odd Z). Odd-N nuclei have in general much larger thermal neutron cross sections than even-N nuclei (Table 13.1 in Krane). Nuclear Reactors, BAU, 1 st Semester, (Saed Dababneh).

3 Nuclear Fission  f,Th x b Why not use it?

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 4 Nuclear Fission 235 U + n  93 Rb Cs + 2 n Q = ???? What if other fragments? Different number of neutrons. Take 200 MeV as an average. 66 MeV98 MeV miscalibrated Heavy fragments Light fragments

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 5 Nuclear Fission Mean neutron energy  2 MeV.  2.4 neutrons per fission (average)   5 MeV average kinetic energy carried by prompt neutrons per fission. Show that the average momentum carried by a neutron is only  1.5 % that carried by a fragment. Thus neglecting neutron momenta, show that the ratio between kinetic energies of the two fragments is the inverse of the ratio of their masses. HW 45

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 6 Nuclear Fission Distribution of fission energy Krane sums them up as  decays. Lost … ! Enge

7 Segrè Lost … ! Nuclear Fission How much is recoverable? How much is recoverable? What about capture gammas? (produced by -1 neutrons) What about capture gammas? (produced by -1 neutrons) Why c < (a+b) ? Why c < (a+b) ? Distribution of fission energy abcabc Nuclear Reactors, BAU, 1 st Semester, (Saed Dababneh).

8 Recoverable energy release  200 MeV per 235 U fission. Fission rate = 2.7x10 21 P fissions per day. P in MW. Burnup rate Burnup rate : 1.05 P g/day. P in MW. Capture-to-fission ratio: Consumption rate Consumption rate : 1.05(1+  ) P g/day MW reactor. 3.1x10 19 fissions per second, or gram of 235 U per second. Two neutrinos are expected immediately from the decay of the two fission products, what is the minimum flux of neutrinos expected at 1 km from the reactor. 4.8x10 12 m -2 s -1 Nuclear Fission HW 46

9Nuclear Reactors, BAU, 1 st Semester, (Saed Dababneh). Nuclear Fission 3.1x10 10 fissions per second per W. In thermal reactor, majority of fissions occur in thermal energy region,  and  are maximum. Total fission rate in a thermal reactor of volume V Thermal reactor power (quick calculation)

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 10 Controlled Fission 235 U + n  X + Y + (~ 2.4) n Moderation of second generation neutrons  Chain reaction. Net change in number of neutrons from one generation to the next  k  (neutron reproduction factor). k   1  Chain reaction. Water, D 2 O or graphite moderator. k < 1  subcritical system. k = 1  critical system. k > 1  supercritical system. For steady release of energy (steady- state operation) we need k =1. Fast second generation neutrons Infinite medium (ignoring leakage at the surface). Chain reacting pile

Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh). 11 Probability for a thermal neutron to cause fission on 235 U is Controlled Fission 235 U thermal cross sections  fission  584 b.  scattering  9 b.  radiative capture  97 b. If each fission produces an average of neutrons, then the mean number of fission neutrons produced per thermal neutron =   <

12 Controlled Fission 235 U 238 U Assume natural uranium: % 238 U, % 235 U.  f / N = ( )(0) + (0.0072)(584) = 4.20 b.   / N = ( )(2.75) + (0.0072)(97) = 3.43 b. Thermal  f = 0 b584 b Thermal   = 2.75 b97 b Nuclear Reactors, BAU, 1 st Semester, (Saed Dababneh). Using the experimental elastic scattering data the radius of the nucleus can be estimated. Doppler effect?

Moderation (to compare x-section) 1H1H (n,  ) (n,n) 2H2H Resonances?

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 14 Probability for a thermal neutron to cause fission natural uranium For natural uranium If each fission produces an average of = 2.4 neutrons, then the mean number of fission neutrons produced per thermal neutron =  = 2.4 x 0.55  1.3 This is close to 1. If neutrons are still to be lost, there is a danger of losing criticality. enriched uranium For enriched uranium ( 235 U = 3%)  = ????? (> 1.3). In this case  is further from 1 and allowing for more neutrons to be lost while maintaining criticality. Controlled Fission

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 15 Controlled Fission thermalhave produced so far  N fast neutrons. N thermal neutrons in one generation have produced so far  N fast neutrons. Some of these fast neutrons can cause 238 U fission  more fast neutrons  fast fission factor =  (= 1.03 for natural uranium). Now we have  N fast neutrons. We need to moderate these fast neutrons  use graphite  for 2 MeV neutrons we need ??? collisions. How many for 1 MeV neutrons? The neutron will pass through the eV region during the moderation process. This energy region has many strong 238 U capture resonances (up to 1000 b)  Can not mix uranium and graphite as powders. In graphite, an average distance of 19 cm is needed for thermalization  the resonance escape probability p (  0.9).

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 16 Controlled Fission Now we have p  N thermal neutrons. Graphite must not be too large to capture thermal neutrons; when thermalized, neutrons should have reached the fuel. Graphite thermal cross section = b, but there is a lot of it present. Capture can also occur in the material encapsulating the fuel elements. The thermal utilization factor f (  0.9) gives the fraction of thermal neutrons that are actually available for the fuel. Now we have fp  N thermal neutrons Now we have fp  N thermal neutrons, could be > or < N thus determining the criticality of the reactor. The four-factor formula. k  = fp  The four-factor formula. k = fp  (1- l fast )(1- l thermal ) Fractions lost at surface

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 17 x 1.03 Fast fission factor “  ” x 0.9 Resonance escape probability ”p” x 0.9 Thermal utilization factor “f” x x  What is: Migration length? Critical size? How does the geometry affect the reproduction factor? Neutron reproduction factor k = 1.000

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 18 Controlled Fission Time scale for neutron multiplication Time  includes moderation time (~10 -6 s) and diffusion time of thermal neutrons (~10 -3 s). TimeAverage number of thermal neutrons t N t +  kN t + 2  k 2 N For a short time dt Show that Show that

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 19 k = 1  N is constant (Desired). k < 1  N decays exponentially. k > 1  N grows exponentially with time constant  / ( k -1). in 1s. k = 1.01 ( slightly supercritical )  e (0.01/0.001) t = e 10 = 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. Controlled FissionDangerous Cd control rods

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 20 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 and Radiation Physics, BAU, First Semester, (Saed Dababneh). 21 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 (~10 13 n.cm -2.s -1 or higher) for research. Converters: Convert non-thermally-fissionable material to a thermally-fissionable material. Fertile  f,th = 742 b

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 22 Fission Reactors Fertile If  = 2  Conversion and fission. If  > 2  Breeder reactor. 239 Pu : Thermal neutrons (  = 2.1)  hard for breeding. Fast neutrons (  = 3)  possible breeding  fast breeder reactors.  f,th = 530 b After sufficient time of breeding, fissile material can be easily (chemically) separated from fertile material. Compare to separating 235 U from 238 U.

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 23 Fission Reactors What neutron energy? Thermal, intermediate (eV – keV), fast reactors. Large, smaller, smaller but more fuel. What fuel? Natural uranium, enriched uranium, 233 U, 239 Pu. From converter or breeder reactor. How??? HW 47

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 24 Fission Reactors What moderator? 1. Cheap and abundant. 2. Chemically stable. 3. Very low mass (~1). 4. High density. 5. Minimal neutron capture cross section. Graphite (1,2,4,5) increase amount to compensate 3. Water (1,2,3,4) but n + p  d +   enriched uranium. D 2 O (heavy water) has low capture cross section  natural uranium, but if capture occurs, produces tritium. Be and BeO, but poisonous.

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 25 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 and Radiation Physics, BAU, First Semester, (Saed Dababneh). 26 Boiling water reactor Pressurized water reactor Light water reactors. Light water reactors. Both use “light” water as coolant and as moderator, thus enriched (2-3%) uranium is used. Both use “light” water as coolant and as moderator, thus enriched (2-3%) uranium is used. Common in the US. Common in the US.

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 27 CANDU reactor Gas cooled reactor Canada has D 2 O and natural uranium. Canada has D 2 O and natural uranium. Most power reactors in GB are graphite moderated gas- cooled. Most power reactors in GB are graphite moderated gas- cooled.

Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 28 Breeder reactor Liquid sodium cooled, fast breeder reactor. Liquid sodium cooled, fast breeder reactor. Blanket contains the fertile 238 U. Blanket contains the fertile 238 U. Water should not mix with sodium. Water should not mix with sodium.