Nuclei

Contents

Binding Energy

		A nucleus is specified by its number of protons Z, number of neutrons N, and the mass number A = Z+N. The nucleons (protons and neutrons) in a nucleus are bound together -- their total energy is less than the total energy of the separated particles. The binding energy is the amount of energy given up when the nucleus is formed. Plotting the binding energy per nucleon versus the mass number A (Figure 14-01) shows that starting from Hydrogen, nuclei become more stable as there are more
Figure 14-01 Nuclear Binding Energy [view large image]	Figure 14-02 Proton/Neutron & Decay [view large image]	protons and neutrons, until Iron. After that, the trend reverses.

The curve of stable nuclei portrays in Figure 14-02 is the result of the balancing act between the various repulsive and attractive effects:


1. Electric force (repulsive) : There is the obvious electric repulsion between the protons each carrying a positive charge.
2. Uncertainty principle (repulsive) : According to this principle at short distance (equivalent to reduced uncertainty in position) the uncertainty in momentum becomes correspondingly large giving rise to higher kinetic energy and a tendency to disperse.
3. Exclusion principle (repulsive) : Since identical particles cannot be in same state, close proximity between similar particles also implies higher kinetic energy and a tendency to disperse.
4. Strong Interaction (attractive) : This is the short range nuclear force that operates on all the protons and neutrons. It is this force that holds the nucleus together.
5. Neutrons (attractive or repulsive) : Adding neutrons to the nucleus tends to minimize the repulsive effects. However, too many of them in there would favor the beta decay reaction, which turns neutron into proton and makes the nucleus unstable. Isotopes are elements with varying number of neutrons but same number of protons in the nucleus. If there are too many protons in the nucleus, there is no way to add neutrons to overcome the electric repulsion. This kind of elements would become unstable via alpha decay or other processes to reduce the number of positive charge.

Origin of Elements

Light elements (mainly hydrogen, helium and trace of deuterium, lithium) were generated in the first few minutes of the Big Bang, which was not able to produce more complex elements as the universe rapidly cooling off. Since then hydrogen and helium contribute by mass of respectively 70 and 28 per cent of all baryonic matter in the universe. Most of the remaining 2% of the elements up to iron and nickel are made in the interior of the stars. The resulting elements are thrust into space by booming stellar winds or when a star explodes as a supernova. Carbon, nitrogen and oxygen are the most abundant heavy elements. Oxygen is created by supernovae, while carbon is created in low-mass stars (red giants, planetary nebulae) and nitrogen is made by both processes mentioned above.

Figure 14-03 Element Abundance [view large image]

The Liquid-Drop and The Shell Models

		The liquid-drop model assumes that the constituents of the nucleus interact only with their nearest neighbors, and the density is constant inside the nucleus, like the molecules in the liquid. Using this analogy, a semiempirical formula has been developed to describe the binding energy as a function of the mass number A (shown by the solid curve in Figure 14-01). The result is not particularly accurate for the lower value of A. The expression is useful in discussing stability, radioactivity, and the fluctuations from the average behavior due to shell effects. The top diagram in Figure 14-04a shows two vibrational energy levels, which split into finer structures due to rotation.
Figure 14-04a Liquid Drop Model [view large image]	Figure 14-04b Fission [view large image]	Figure 14-04b shows the deformation of the liquid drop, which eventually separates into two pieces (caused by the electrostatic repulsion of the protons).

		There is extensive experimental evidence of the contrary hypothesis that the nucleons move in an effective potential well created by all the other nucleons. Since the nucleons are densely packed into a small region, it is expected that the chance of collision is very high. However, the interaction by collision is minimized by the Pauli exclusion principle, which forbids two fermions to occupy the same quantum state. If there are no nearby, unfilled quantum states that can be reached by the available energy for an interaction, then the interaction will not occur.
Figure 14-05a Nuclear Potential [view large image]	Figure 14-05b Nuclear Energy Levels [view large image]

• Enhanced abundance of those elements for which Z or N is a magic number.
• The stable elements at the end of the naturally occurring radioactive series all have a "magic number" of neutrons or protons.
• The neutron absorption cross-sections for isotopes where N = magic number are much lower than surrounding isotopes.
• The binding energy for the last neutron is a maximum for a magic neutron number and drops sharply for the next neutron added.
• Electric quadrupole moments (a measurement for deviation from spherical distribution) are near zero for magic number nuclei.
• The excitation energy from the ground nuclear state to the first excited state is greater for closed shells

		even if it happens to be located right in the middle of the island of stability. Figure 10-05d presents all the trans-uranium elements synthe-sized artificially. It shows the steady decrease in half-life with increasing atomic number (# of protons), then this sudden jump in the disputed claim. The color of the square represents the
Figure 14-05c Nuclear Island [large image]	Figure 14-05d Trans-uranium Elements [view large image]	chemical property of the element as indicated in the traditional periodic table (see also insert in the figure).

A more realistic nuclear (nucleon-nucleon) potential is the empirical curve shown in Figure 14-05e. As originally proposed by H. Yukawa, the longest range part of the strong internucleon force can be attributed to exchange of the mesons (pions). At shorter distances, exchanges of heavier mesons become important. However, the origin of the repulsive hard-core below 1 fermi (10-13cm) remains unclear until recently in 2007, when numerical results convincingly demonstrate that it is a consequence of QCD. The numerical computation is actually rather involved because of the virtual gluons and quark-antiquark pairs surrounding the three quarks (the components of the nucleon). The required computational power is only available now to reproduce the empirical potential from first principles. This potential represents the residual force derived from the more fundamental forces (as prescribed in QCD) between the constituent particles. The form of this potential is remarkably similar to the molecular

Figure 14-05e Nucleon-Nucleon Potential [view large image]

potential curve even though these residual forces originated from different sources - one from quantum chromodynamics, while the other from quantum electrodynamics.

Nuclear Decay

Unstable nuclei, called radioactive isotopes, will undergo nuclear decay to make it more stable. There are only certain types of nuclear decay which means that most isotopes can't jump directly from being unstable to being stable. It often takes several decays to eventually become a stable nucleus. When unstable nuclei decay, the reactions generally involve the emission of a particle and or energy. Half-lives are characteristic properties of the various unstable atomic nuclei and the particular way in which they decay. Alpha and beta decay are generally slower processes than gamma decay. Half-lives for beta decay range upward from 10^-2 sec and, for alpha decay, upward from about 10^-6 sec. Bismuth-209 has the longest half-life of 2x10¹⁹ years. Half-lives for gamma decay may be too short to measure (~ 10^-14 second), though a wide range of half-lives for gamma emission has been reported.

There are five types of nuclear decay:



Alpha Decay - The strong force, despite its strength, has a very short range; it can't even reach from one end of a fair-sized atomic nucleus to the other. If a proton is at the edge of a big nucleus, it can feel the pulling strong force only from the particles in the neighborhood, but there is an electromagnetic force, which tends to push it out, all the way from the other side of the nucleus. There is a sensitive balance between these two competing forces. The nucleus needs not to acquire extra energy to escape; the quantum mechanical effect called tunneling allows a certain probability of escape through a potential wall. Alpha decay, in which just a small chunk breaks off from the main nucleus, is a rather mild case of fission; in more dramatic examples, the nucleus can break more or less in half. The broken-off chunk most often is packed into a helium nucleus (alpha particle) because it is in a more stable form. Figure 14-06 shows the effect of tunneling

Figure 14-06 Alpha Decay [view large image]

through the Coulomb barrier; the nucleus has a small probability of escape to the outside depending on the height and width of the wall.

Beta Decay - The weak interaction is responsible for the instability of "free" neutrons, which decay according to the reaction: n p + e + electron-anti-neutrino with a lifetime about 15 minutes in a process known as beta decay. Neutrons in a nucleus are subject to the protection of the nuclear and the electromagnetic forces from the other nucleons, and they will remain stable provided there are not too many of them. If there are too many, such protection would not be sufficient for all of them to remain stable, and the nucleus would undergo beta decay. Figure 14-07

Figure 14-07 Beta Decay [view large image]

shows that in the beta decay process, the down quark turns into an up quark (thus changes the neutron to proton) by emitting a W- meson, which decays into an electron and an electron-anti-neutrino.

Gamma Decay - In gamma decay, a nucleus changes from a higher energy state to a lower energy state through the emission of electromagnetic radiation. It happens usually after the transmutation of the nucleus; the end product has to re-arrange the occupancy of energy levels in order to arrive at a more stable state. The number of protons (and neutrons) in the nucleus does not change in this process, so the parent and daughter atoms are the same chemical element. In the gamma decay of a nucleus, the emitted photon and recoiling nucleus each have a well-defined energy after the decay. Figure 14-08 shows the adjustment of energy level by emitting gamma ray after Mg has transmuted into Al.

Figure 14-08 Gamma Decay [view large image]

• Positron Emission - Positron emission is a type of beta decay, referred to as "beta plus"(ß+ ) or inverse beta decay. In beta plus decay, a proton is converted to a neutron, a positron and a neutrino via the weak interaction. This spontaneous nuclear process releases an amount of energy equal to the energy equivalent of the rest mass that disappears in the process. The positron and neutrino are created in the nucleus at the moment of disintegration. The "endothermic reactions" receives the energy from the nuclear fission. That positron decay is a nuclear process is consistent with the fact that the decay of free protons by positron emission is not observed in nature. On the other hand, the beta decay of free neutrons is a familiar fact. The positron is made of anti-matter and does not last very long in the world of ordinary matter. As soon as the positron meets an ordinary electron the two particles annihilate and

the energy contained in their mass appears as two gamma-rays of 0.5 MeV each, flying off in opposite directions. Positron radioactivity is therefore always accompanied by the emission of gamma rays with an energy of about 0.5 MeV in addition to any other gamma-rays which might be emitted. Example isotopes, which emit positrons are C-11, N-13, O-15 and F-18. These isotopes are used in positron emission tomography (PET). Figure 14-09 shows the transmutation of C-11 into B-11 by positron emission.

Figure 14-09 Positron Emission [view large image]

• Electron Capture - Electron capture is a decay mode for nucleus that will occur when there are too many protons in the nucleus of an atom, and there isn't enough energy to emit a positron. In this case, one of the orbital electrons is captured by a proton in the nucleus, forming a neutron and a neutrino. Since the proton is essentially changed to a neutron, the

	number of neutrons increases by 1, the number of protons decreases by 1, and the atomic mass remains unchanged. By changing the number of protons, electron capture transforms the nucleus into a new element. Electron capture is also called K-capture since the captured electron usually comes from the atom's K-shell. Figure 14-10 shows another way of transmuting C-11 into B-11 by electron capture.
Figure 14-10 Electron Capture [view large image]

Type	Emission	Penetrating Power	Example
Alpha Decay	Helium nuclei	1, stopped by skin, very damaging due to ionization	92U238 90Th234 + 2He4 Applicable to nuclei with Z>83, see Figure 14-02
Beta Decay	Electron, high speed	100, penetrates human tissue to ~ 1 cm	53I131 54Xe131 + -1e0 Applicable to nuclei with high neutron-proton ratio
Gamma Decay	Photons, high energy	10000, highly penetrating but not very ionizing	92U238 90Th234 + 2He4 + 2 photon Energy lost from settling within the nucleus after transmutation
Positron Emission	Positron	100	6C11 5B11 + 1e0 Applicable to nuclei with a low neutron-proton ratio
Electron Capture	Electron, inner shell	~ Infinite for Neutrino	37Rb81 + -1e0 36Kr81 + neutrino Applicable to nuclei with a low neutron-proton ratio

Table 14-01 Types of Nuclear Decay

Nuclear Fission

• Release of the Binding Energy - If a massive nucleus like uranium-235 breaks apart (nuclear fission), then there will be a net yield of energy because the sum of the masses of the fragments will be less than the mass of the uranium nucleus. If the mass of each fragment is equal to or greater than that of iron at the peak of the binding energy curve (see Figure 14-01), then the products of the decay will be bound more tightly than they were in the uranium nucleus, and that decrease in mass comes off in the form of energy according to the Einstein's equation E = mc², where m is the loss of mass in the reaction. For elements lighter than iron it is the process of fusion that releases the binding energy.



• Theory of Fission - A stable nucleus is in a state of minimum energy in a potential well with a barrier further out as shown in Figure 14-11a. Classical theory dictates that the system can break apart only when it is excited with energy beyond the barrier height. In quantum theory there is a certain probability to tunnel out under the barrier as shown in Figure 14-11b. The transmission coefficient T for a one dimensional rectangular barrier is given by the formula:
  T = 16(p₁/p₂)² e^-2p₂a/
  for p₂a/ >> 1, where p₁ = (2mE)^1/2, and p₂ = [2m(V-E)]^1/2.

  		This formula provides a crude approximation in estimating the probability of alpha decay, which depends inversely on the height "V" and width "a" of the barrier. Alpha decay is a process of asymmetric fission because it usually involves a larger nuclear fragment and the much smaller alpha particle.
  Figure 14-11a Nuclear Potential [view large image]	Figure 14-11b Quantum Tunneling [view large image]

• Neutron Induced Fission - When an uranium-235 nucleus captures a neutron, the newly formed isotope uranium-236 turns into an excited state with excitation energy about 6 Mev, which is a bit more than the barrier height and splits into two fragments as shown by the equation below (also see illustration on top of Figure 14-11a, and schematic in Figure 14-11c). Actually, the products in the fission process can be any two in each of the humps shown by Figure 14-11d as long as charge conservation is observed (thus called symmetric fission). There are about 90 different isotopes that can be produced by the fission. The most probable and radioactive product is iodine-131 (half life 8 days), that's why the run on iodine pills and iodized salts during the Fukushima incident. They are supposed to prevent further intake of radioactive iodine by the thyroid. Another dangerous by product is cesium-137, which has a half life of 30 years, but the biological half-life (elimination from the body) is much shorter at about 70 days. Anyway, the following equation is an example of the neutron induced reaction :
  
  ₉₂U²³⁵ + n ₉₂U²³⁶ ₅₆Ba¹⁴⁴ + ₃₆Kr⁸⁹ + 3n + 166 Mev

  		For uranium-238, the excitation energy is about 1 Mev less, so fission is not possible with slow neutrons; it can take place only for neutrons with 1 Mev energy or more. An isotope like uranium-235 that can be split by both slow and fast neutrons, is called "fissile", while uranium-238 which can be split only by fast neutrons, is called "fissionable".
  Figure 14-11c Neutron Induced Fission and Chain reaction [view large image]	Figure 14-11d Symmetric Fission [view large image]

• Cross Section - The neutron released immediately (about 10^-14 sec) in the fission process is called prompt neutron. There are three possibilities for further reaction for such neutron (in descending possibility):

  It bounces off the nucleus by elastic scattering, which occurs 5 times more often than the next process. It induces fission of another nucleus. The least probable is for the neutron to be captured with the emission of radiation or slower neutron (inelastic scattering). Geometrical cross section is defined by the area of the nucleus (~ 3x10-24cm2). The cross section for the various process is the fraction that leads to such process times the geometrical cross section. Figure 14-11e show the fission cross section as a function of neutron energy. The astonish U235

  Figure 14-11e Fission Cross Section [view large image]

  fission cross section of 640x10-24cm2 for slow neutron (at 0.025 ev) is due to quantum effect. While the threshold of 1 Mev for U238 has been explained already above.

  Thus, "hydrogenic materials" are used in nuclear reactor to slow down the neutrons for producing more power. However, slow neutrons are not suitable for nuclear weapons because the explosion is over in microseconds before they have a chance to participate in the fission process.



• Chain Reaction and Critical Mass - According to Figure 14-11c one fission produces 3 neutrons to initiate more fissions. Since not all the neutrons in such reactions are available for fission, let's take 2 neutrons as example (actually a good choice). This means that in the next generation 4 neutrons are produced and in the next, 8, and so on and on - a chain reaction. After 80 generations the number of neutrons has grown to 2⁸⁰ ~ 10²⁴ ~ the number of U²³⁵ nuclei in 1 kg with each fission releasing about 166 Mev energy for a total of 1.66x10²⁶ Mev = 2.65x10¹³ joules, which corresponds to the explosive energy of 10,000 ton of TNT (in comparison, 2.5 tons of high explosives is used to blow up the Murrah Building in Oklahoma City). However, this amount of energy from 1 kg U²³⁵ would not be released because it has a radius of only 2.3 cm (assuming a spherical shape), all the induced neutrons would have escaped the assembly before initiating more fissions. That is because the mean free path of neutron in U²³⁵ is equal to 16.5 cm.

  Therefore, chain reaction can be maintained only when the diameter of the sphere is at least equal to that length. From the known density of 18.9 gm/cm3 for U235, the critical mass is 44 kg. The arithmetic to produce all these numbers is very simple via the formula: M = [(4/3)R3] where is the density, R the radius, and M the mass of the isotope. The time scale can be estimated from: (# of mean-free-path)/(average velocity of fast neutrons ~ 2x109cm/sec). See Figure 14-11f for the neutron spectrum from the fission process. Prompt neutron is the one released together with the fission.

  Figure 14-11f Neutron Spectrum [view large image]

  Table 14-02 displays the critical (bare) mass, half-life, number of neutrons generated in spontaneous fission, and the rate of heat generation by radioactive decay for various fissionable isotopes. They all undergo transmutation via alpha decay. For comparison, the table also includes the two major fertile materials, Thorium-232 and Uranium-238, which in the presence of neutrons can produce the fissionable isotopes Uranium-233 and Plutonium-239, respectively.
  
  

  Fissionable Isotope	Crtiical Mass (kg)	Half Life (years)	Neutron Generation (# / sec-kg)	Power Generation (Watts / kg)
  Protactinium-231	162	3.28x104	nil	1.3
  Thorium-232	Infinite	1.41x1010	nil	nil
  Uranium-233	16.4	1.59x105	1.23	0.281
  Uranium-235	47.9	7.0x108	0.364	6x10-5
  Uranium-238	Infinite	4.5x109	0.11	8x10-6
  Neptunium-237	59	2.14x106	0.139	0.021
  Plutonium-238	10	88	2.67x106	560
  Plutonium-239	10.2	2.41x104	21.8	2.0
  Plutonium-240	36.8	6.54x103	1.03x106	7.0
  Plutonium-241	12.9	14.7	49.3	6.4
  Plutonium-242	89	3.76x105	1.73x106	0.12
  Americium-241	57	433	1540	115
  Americium-242	9 - 18	-	-	-
  Americium-243	155	7.38x103	900	6.4
  Curium-244	28	18.1	1.1x1010	2.8x103
  Curium-245	13	8.5x103	1.47x105	5.7
  Curium-246	84	4.7x103	9x109	10
  Curium-247	7	1.55x107	-	-
  Berkelium-247	10	1.4x103	nil	36
  Californium-251	9	898	nil	56

  Table 14-02 Critical Mass for Fissionable Isotopes

  A nuclear device with mass close to the critical limit would most probably produce a "fizzle" with the chain reaction terminated prematurely in less than 1 microsecond by an explosion, which is sizable by most standards but not in nuclear scale. A workable nuclear bomb requires special design such as adding more fissile material to make it super-critical, increasing the density (i.e., to decrease the mean free path) through implosion, or using tamper to retard the expansion. These considerations lead to the topic of nuclear bomb construction in the next section.

Applications of Nuclear Fission

• Nuclear Fuel Production - Uranium is as common as tin or zinc on Earth. About 63% of the world's production of

  		uranium comes from Kazakhstan, Canada and Australia (Figure 14-12a). Worldwide production in 2009 amounted to about 50000 tonnes. This is the only nuclear fuel that can be mined naturally. Other nuclear fuels such as plutonium are derived from uranium in breeder reactor. The
  Figure 14-12a Worldwide Uranium Production [view large image]	Figure 14-12b Uranium Processing [view large image]	various production processes are illustrated in Figure 14-12b and explained in more details below:

  
  
  1. Uranium ore - The primary uranium ore is uraninite (UO₂), and pitchblende (UO₃, U₂O₅ - collectively referred to as U₃O₈). A range of other uranium minerals can be found in various deposits. Some of the highest grade uranium ores in the world were found in the Democratic Republic of Congo.
  
  
  
  2. Milling and refining - After mining the ores, they are crushed and then leached with sulfuric acid in the mill. The uranium oxides are separated to yield a substance in dry power form called "yellowcake" (see Figure 14-12c), which is sold on the market as U₃O₈.
  3. Conversion - Natural uranium is 99.274% U²³⁸, with the fissile U²³⁵ only constituting about 0.7205% of its

     weight. The rude material has to go through a process to increase the U235 percentage. But many of the enrichment processes require the substance in gaseous form, which only exists in uranium hexafluoride (UF6). Uranium hexafluoride can be solid, liquid, or gas depending on temperature and pressure. It is a solid or gas depending on whether temperature is below or above 57oC. It is in liquid form at 1.5 atmospheric pressure or higher and temperature greater than 64oC. Thus, the yellowcake has to be converted to uranium hexafluoride by treating it with strong acids and alkalis. Figure 14-12c shows a sample of uranium hexafluoride in crystal form and gas phase in a vial.

     Figure 14-12c U- Compounds

  4. Enrichment - According to cost and efficiency the enrichment methods are referred to by number of generation. The 0th generation is the calutron (California University Cyclotron) used in World War II, the 1st generation

     	employing gaseous diffusion is being phased out presently, the 2nd one is the method of choice currently using the centrifuge techniques. Figure 14-12d shows these three methods schematically. Future generation is still in development using infrared laser to separate the isotopes. Regardless of
     Figure 14-12d Enrichment Methods [view large image]	enrichment methods, uranium fuel has to contain 3 to 4% U235 for nuclear reactors. Bomb grade uranium requires purification of U235 greater than 90%. Following is a brief description for the above-mentioned enrichment methods:

     
     
     • Calutron - It is essentially a mass spectrometer. The device is shown in Diagram a, Figure 14-12d with a magnetic field B pointing toward the page. The method relies on the fact that charged particles with different mass move in different circular paths perpendicular to a magnetic field according to the formula:
       
       R = (v/qB)m
       
       where v is the velocity, q the charge, m the mass of the particle, and R the radius of the circular path. Uranium ions are generated from solid uranium tetrafluoride, UF4, that is heated to produce a vapor and then bombarded with electrons to produce U⁺ ions.
     
     
     
     • Gaseous Diffusion - This method forces the uranium hexafluoride through semi-permeable membrane under pressure gradient as shown in Diagram b, Figure 14-11d. Since the rate of effusion is inversely

       	proportional to the square root of mass, this process allows the smaller constituents with U235 to pass through more to one side of the membrane. Denoting the rate of effusion by R, then R(U235)/R(U238) = (352/349)1/2 = 1.004 which implies 2000 stages to achieve a purity of 99% U235. The
       Figure 14-12e Diffusion Plant at Oak Ridge	huge facility in Oak Ridge, Tennessee was built to enrich uranium through 2 steps of diffusion and 2 steps of Calutron (Figure 14-12e). The plant is to be demolished completely by the end of 2011.

     
     
     • Gas Centrifuge - This process uses rotating cylinder to create a strong centrifugal force F (a fictitious force associated with rotating frame). For angular velocity , distance r from the rotational axis, and m the mass of the object:
       

       F = mr2 so that the heavier UF6 molecules containing U238 move toward the outside and the lighter ones rich in U235 is collected close to the center (Diagram c, Figure 14-11d). This technique produces about 54% of the world's enriched uranium now. All the above methods require cascade of identical stages to successively produce higher concentrations of U235 until it reaches the specification as shown in Figure 14-12f for a gas centrifuge plant.

       Figure 14-12f Cascade of Gas Centrifuges

     • Laser Isotope Separation - The atomic energy levels through (electron)spin-orbit interaction split

       	into fine structures of the order 10-3 ev, which in turn split further into hyperfine structures of the order 10-6 ev by (nuclear)spin-orbit interaction (Diagram a, Figure 14-12g). The amount of hyperfine splitting depends on the mass of the nuclei inversely. By tuning a laser on the hyperfine
       Figure 14-12g Laser Isotope Separation	levels of the U235 atom or its molecular compound, it can be excited or ionized selectively and gathered into collector by appropriate action (direction of the gas flow is perpendicular to the page in Diagram b, Figure 14-12g).

       The Atomic Vapor Laser Isotope Separation (AVLIS) feeds uranium-iron metal alloy into the system. Uranium vapor is produced by heating. It is eventually ionized by the tunable laser and collected into the negatively charged plate.
       In Molecular Laser Isotope Separation (MLIS) the uranium hexafluoride gas is selectively excited for only U²³⁵F₆ molecules. A second laser knocks out a fluorine atom leaving an uranium pentafluoride (U²³⁵F₅) to be precipitates out of the gas.
       No details is available for the technique of "Separation of Isotopes by Laser Excitation" (SILEX) as it is a commercial secret. No laser separation uranium enrichment plants are currently (2011) in operation.
     
     
  5. Fuel Fabrication - The UF₆ gas is chemically treated to form uranium dioxide (UO₂) powder. This

     powder is then processed into ceramic pellets and loaded into metal tubes (fuel rod), which are subsequently bundled into fuel assemblies (Figure 14-12h) for use in nuclear reactor. Weapon grade uranium was enriched to 90% U235 by two steps of gaseous diffusion and two steps of calutron at Oak Ridge in 1945 to produce the bomb dropped on Hiroshima. Since then the majority of fission weapons have used plutonium. Uranium enrichment is currently used to produce fuel (3 to 4% U-235) for civilian nuclear reactors.

     Figure 14-12h Fuel Fabrication

• Nuclear Reactors - For efficient production of energy in nuclear reactors, the neutrons must be slowed down by moderation to increase their capture probability in fission reactors. Specifically, the initial fission of U-235 produces neutrons with mean energy of 2 Mev (see Figure 14-11f). Neutron with this energy has a fission probability about 1000 times less than a neutron with energy of 0.025 ev. So they need to be slowed down, on average, by a factor of 100 million. Some nuclear reactors use heavy water (D₂O) to slow down (moderate) the neutrons, while ordinary water can be used to minimize neutron loss (via the H₂O + 2n D₂O reaction), which is harmful to health. The control rods used to regulate the rate of reaction are mainly composed of stainless steel tubes encapsulating silver-indium-cadmium (neutron) absorber material.
  
  The world's first atomic pile, now called nuclear reactor, was constructed inside a squash court at the university of Chicago. It consisted of 57 layers of pure graphite blocks to slow down the neutrons. Slugs of natural uranium (with only 0.7% of the fissile U-235) are located in between forming a cube-like lattice within the pile. Cadmium rods (the absorbers of neutrons) were used for controlling the reaction rate. The design has a final cadmium rod to drop down automatically into the pile should the neutrons rise above a certain level. If that fails to stop the reaction, another rod could be released from the balcony by cutting a rope. As an extra insurance against an unwanted nuclear explosion, three young physicists stood on an elevator platform above the pile, ready to flood it with a cadmium-salt solution, just in case something went very wrong. These three were known as the "suicide squad". The pile was activated successfully without accident on December 2, 1942 at 2:20 p.m. after a lunch recess. No photographers were present

  		to witness the arrival of nuclear age. Figure 14-12i is the re-creation of the occasion by an artist in 1957. Enrico Fermi (captain of the team of 42 scientists) is the half-bald individual standing next to Walter Zinn who is leaning with his elbow on the rail. A
  Figure 14-12i First Reactor [view large image]	Figure 14-12j Modern Nuclear Reactor [view large image]	schematic diagram of a modern nuclear reactor (type PWR) running on the same principle is shown in Figure 14-12j.

  
  

  While uranium-235 is the naturally occurring fissionable isotope, there are other isotopes which can be induced to fission by neutron bombardment. Plutonium-239 is also fissionable, and both types have been used to make nuclear fission bombs. Plutonium-239 can be produced by breeding from non-fissionable uranium-238 (by absorbing a neutron and then transmuted via the beta decay process). Spent fuel is taken out of the reactor after four years and can be recycled in a reprocessing plant. Some of the nuclear reactors at Hanford, Washington and the Savannah-River Plant, SC are designed for the production of bomb-grade plutonium-239. Figure 14-12k shows the different pathways for the two different types of reactors.

  Figure 14-12k Two Fission Pathways

  In a breeder reactor, the fuel consists of 90% U-238 together with 10% Pu-239. There is no graphite to moderate the reaction by slowing down the neutrons hence it is sometimes referred to as fast breeder - meaning fast neutrons. The fast neutrons are absorbed by U-238, which is then transmuted into fissionable (fissile) plutonium. The great advantage of this type of reactor is that, rather than merely burning uranium to create energy, the naturally abundant U-238 is used in a cyclical process that simultaneously generates both fission energy and more nuclear fuel than there was in the first place. It is called breeder because it breeds fuel. Figure 14-12l shows a breeder reactor. It is rather similar to the conventional nuclear reactor except that there is an U-238 blanket to capture and reflect the

  Figure 14-12l Breeder Reactor [view large image]

  neutrons back to the core, and liquid sodium is used as coolant in extreme temperatures surrounding the reactor.

  Table 14-03 below lists the types of nuclear reactors in commercial operation (in order of decreasing popularity) according to "World Nuclear Association". The classification is mainly by the kind of fuel, heat transportation, and moderating material. There is a total of 435 of these kinds of reactors in the world with 386.4 giga-watts capacity.
  
  

  Reactor Type	Countries	#	Capacity (giga-w)	Fuel	Coolant	Moderator	Comment
  Pressurized Water Reactor (PWR)*	US, France, Japan, Russia, China	265	251.6	Enriched UO2	Water	Water	2 cooling circuits, 1st use in submarine
  Boiling Water Reactor (BWR)	US, Japan, Sweden	94	86.4	Enriched UO2	Water	Water	1 cooling circuit, heat transported by steam
  Pressurized Heavy Water Reactor (PHWR)	Canada (known as CANDU), India	44	24.3	Natural UO2	Heavy Water (D2O)	Heavy Water (D2O)	2 cooling circuits, 0.7% U-235 fuel
  Gas-cooled Reactor (AGR)	UK	18	10.8	Enriched UO2	CO2	Graphite	2 cooling circuits - CO2 and water
  Light Water Graphite-moderated Reactor (RBMK)	Russia	12	12.3	Low-enriched UO2	Water	Graphite	Tendency to overheat as the one in Chernobyl
  Fast Neutron Reactor (FBR)	Japan, Russia	2	1.0	PuO2 and UO2	Liquid Sodium	None	Power from PuO2, plutonium from UO2

  Table 14-03 Types of Nuclear Reactor

  * The Westinghouse AP1000 is the generation III+ pressurized water reactor built on passive safety system, which relies on natural forces to supply cooling water for a few days (in the absence of electricity or human intervention).
  
  The incidents at Three Mile Island in 1979 and at Chernobyl in 1986 had slowed down the building of nuclear reactors. Currently, they generate 17% of the world's electricity. Global warming and rising energy needs has prompted a consortium of ten nations to plan the future reactor (~ 2035). The next generation reactors should be a lot cheaper to run, produce much less radioactive waste at accident-proof facilities, and perhaps eliminate reprocessing waste (into

  plutonium for assembling bombs). Unlike today's water-cooled reactors, which tend to run at about 300 oC, the new design will operate at temperatures from 510 oC to 1000 oC. This allows for more efficient conversion of heat to electricity. But these higher operating temperatures mean that the reactors will need new coolants. One of the most popular concepts is the supercritical-water-cooled reactor, which uses extreme pressures to prevent water from boiling at temperature up to 500 oC. The most advanced concept is helium gas cooling, which can achieve temperature in the range of 700 - 900 oC. Hydrogen can be split from water thermo-chemically at this temperature. The hydrogen gas can be used as fuel to convert into electricity for cars and homes. Operating at high temperatures also rules out conventional fuel systems in the form of metal rods as they melt at fairly low temperatures. Instead, the gas-cooled reactors will hold fuel pellets either in a honeycomb graphite structure, or fused into billiard-ball-sized graphite spheres, known as pebbles (Figure 14-12m).

  Figure 14-12m Next Generation Nuclear Fuel [view large image]

  	A powerful earthquake at 9.0 Richter scale hit Northern Japan (130 km East of Sendai) on March 11, 2011 at 2:46 pm (JST). The quake and subsequent tsunami severed cooling water to 3 of the 6 nuclear reactors (Unit 1, 2, and 3, see Figure 14-12n) in the Fukushima nuclear plant causing explosions that blown off the
  Figure 14-12n Fukushima Incident [view large image]	concrete shielding (in unit 1 and 3). The other 3 units were shutdown before the quake for regular inspection. Following is a summary of the sequence of events leading up to the crisis (as of March 15, 2011):

  1. Immediately after the earth quake, the Fukushima reactors (BWR type) went into an automatic shutdown mode.
  
  
  
  2. Although the neutron induced fission has been stopped by inserting the control rods automatically, elements transmuted into radioactive isotopes in the nuclear fuel continue to generate a great deal of heat by spontaneous decay (about 1.5% of the full production power), and there is no way to turn them off.
  
  
  
  3. The water pumps used to carry the excessive heat away stopped working with the failure of the backup generators as its fuel tanks and power lines were washed away by tsunami. The core began to heat up.
  
  
  
  4. The zirconium alloy holding the fuel pellets is inactive at temperature up to hundreds of degree Celsius. However, when temperature reaches to two thousand degrees, it reacts with the steam and created hydrogen gas according to the formula : Zr + 2H₂O ZrO₂ + 2H₂. The hydrogen molecules combine with oxygen in the air to explode violently - obviously a fault in design that has reportedly been fixed in the latest generation called ESBWR (Economic Simplified Boiling Water Reactor).
  
  
  
  5. This kind of explosion blew the concrete shielding (outer casing) of the reactors apart. Unit 1 went off on March 12, followed by unit 3 on March 14. At 6:14 a.m. on March 15, the pressure-suppression pool beneath the containment vessel (the donut-shaped structure at the bottom of the core used to vent overpressure, see Figure 14-12n) in unit 2 was rocked by a blast. Unlike previous explosions, this one was much closer to the reactor core, releasing more radioactive substances and raising fears of damage to the core and the surrounding containment vessel. At around the same time, unit 4 unexpectedly caught fire when old fuel rods, supposedly stored in deep water pools, became exposed and overheated, releasing explosive hydrogen.
  
  
  
  6. Seawater mixed with boronic acid (boron is excellent neutron absorber to slowdown any possible neutron induced fission) are pumped into the emergency cooling system by fire trucks to prevent a complete meltdown. This action effectively ruins the reactors forever, but prevented a much worse catastrophe.
  
  
  
  7. From the release of hydrogen and the fission products, it is fairly clear that all of these reactors have probably had fuel rods exposed for significant periods of time over a portion of their length and may have suffered partial meltdown. The real danger is the melted fuel to gather at the base of the reactor. It could burn through the concrete containment vessel. In a worse case scenario, the fuel could form a critical mass outside the core and restart the power-generating process, but in a completely uncontrolled way leading to a full-scale nuclear meltdown. However, the danger will subside with each passing day, as radioactive elements in the fuel decay, and cool down gradually.
  
  Every nuclear disaster reveals some loopholes in safeguard. This particular one teaches that the backup facility (like the diesel-electric generator) should be located as far away as possible to prevent damage by the same catastrophic event.
  
  Table 14-04 below is an update for the damaged reactors as of March 25, 2011.
  
  

  Reactor #	Reactor Core	Primary Containment	Building	Spent Fuel Pool	Radiation Level
  One	Meltdown*	Not damaged	Damaged	Need water injection	High
  Two	Meltdown*	Damaged	Slightly damaged	Need water injection	High
  Three	Meltdown*	Not damaged	Severely damaged	Water level low	Very high
  Four	Not damaged	Not damaged	Damaged	Damaged	Normal

  Table 14-04 Update on the Fukushima Reactors

  * Status of the reactors have been revised on June 7 according to a report from Japan's Nuclear Emergency Response Headquarters. While tried to avoid using the term "meltdown", Tokyo Electric admitted in May that No. 1 reactor core melted almost completely in the first 16 hours after the disaster struck. Reactors No.3 and No. 2 suffered the same fate within the first 60 hours and at 101 hours respectively. All the nuclear fuels would be sitting at the bottom of the pressure vessel in each reactor building and are now believed to be leaking.
  
  

  Figure 14-12o1 Fukushima Clean-up [view large image]	Figure 14-12o2 Clean-up Flowchart [view large image]	Figure 14-12o3 Robot at Work [view large image]

  As the immediate threat of further damage has receded in mid April, the Fukushima power plant faces a massive clean-up task that some said will take many decades and even up to a century to complete. Meanwhile in the short term there are four areas that needs to be considered as shown in Figure 14-12o1. A flowchart for the tasks has been published by the Tokyo Electric Power Company (TEPCO) (Figure 14-12o2). Following is a brief description for each of the clean-up task (in work flow sequence) :
  
  
  1. Water - As of April 30, cooling water has to be injected through the Emergency Core Cooling system producing contaminated water in the process. The task is to restore the "heat exchange function" (meaning normal cooling water flow). But in the meantime maintains the flooding up to top of active fuel (to prevent overheat). The contaminated water meanwhile will be de-contaminated by running it through zeolite filter which removes the Cs-137 isotope, and will be stored in tanks or barges.
  
  
  
  2. Reactors - While continues to cool the active fuel, robots are sent into the containment area to examine the radioactive level etc. for drawing up an action plan (see Figure 14-12o3, it is not clear why the reflection of 1 or 2 workers are shown in the photo as well). Eventually, new buildings are required to anchor new cranes for the final removal of damaged fuel rods, and to cover up the damaged structures.
  
  
  
  3. Spent fuel - The goal is to stabilize the cooling and then have them removed from the site.
  
  
  
  4. Debris - Remote-controlled excavators and transporters are being used to clear debris around the site, but some people will most likely be needed to work inside the reactor buildings. New cover-up buildings will help to prevent further release of radioactive materials to the environment. There is also plan to solidify the contaminated soil.
  
  There is no mention of a long term plan on decommissioning the damaged reactors.
  
  
• Nuclear Bombs - There are three steps to achieve a nuclear explosion, namely:
  1. Keeping the fissile material in sub-critical state before detonation.
  2. Bring together the sub-critical pieces into a super-critical state before starting the chain reaction.
  3. Initiating the chain reaction with a neutron source when the configuration is at maximum super-criticality.
  
  

  	In order to increase efficiency, a tamper is usually wrapped around the nuclear explosive to retard the expansion and to augment the number of neutrons by reflection. There are two main types of nuclear bombs depending on the fissile material (Figure 14-12p). The two crude drawings in the image come from the "Los Alamos Primer" - The first lectures on "How to Build an Atomic Bomb".
  Figure 14-12p Two Types of Nuclear Bomb	The formula below is very important in the design of the bombs: Mc = (4/3)(m/A)3/2 where Mc is the critical mass, m the mass of uranium nucleus, "A" the fission cross section, and the density of the fissile material.

  
  
  • Gun-type Nuclear Bomb - An ingenious method is to produce a sub-critical state from an U²³⁵ sphere with 3 critical mass M_c1, i.e., M = 3M_c1, by taking away a piece of one critical mass. The withdrawal leaves an empty spot (see drawing in Diagram a, Figure 14-12p), which reduces the average density to 2/3 of the original. Since the critical mass M_c varies as ^-2, the critical mass M_c2 for the hollow sphere of U²³⁵ is equal to 2.25M_c1, which is greater than the total mass of 2M_c1in the hollow sphere - and it is thus in a sub-critical state.
    
    Detonation is initiated by firing the detached piece to the core of the hollow sphere. This process must occur in a time interval much less than the initiation of chain reaction by neutrons from spontaneous decay in the sub-critical mass. Otherwise the bomb will end up as fizzle.
    
    A neutron would be released easily when beryllium-9 is struck by an alpha particle as shown below:
    Be⁹ + He⁴ Be⁸ + n + He⁴
    Thus, to create a neutron source on demand, a strong alpha emitter such as polonium-210 is placed at one end of the hollow sphere while the beryllium is attached to the other end of the "bullet" so that neutrons are only produced when the pieces are close to the optimum position.
    
    The yield of a nuclear bomb y can be computed by the following formula:
    
    y = (# of mole) x (# of nucleus / mole) x (energy released / nucleus) x (efficiency) x (ev to Joules conversion)
    
    where (# of nucleus / mole) = 6.023 x 10²³ is just the Avogadro number, and 1 ev = 1.602 x 10^-19 Joules. The atomic bomb dropped on Hiroshima contains 63.5 kg of U-235 giving (# of mole) = 63500/235, each U-235 nucleus releases 166 Mev, and the efficiency is only 1.38% - meaning only 1.38 out of 100 U-235 nuclei actually underwent fission (the rest of the fissile material so painstakingly prepared is blown off into the thin air). Thus the yield computed by the formula for this particular case is 60 TJ. The actual yield is 63 TJ (1 TJ = 10¹² Joules, 1 ton of TNT = 4.184x10⁹ J).
  
  
  
  • Implosion-type Nuclear Bomb - Plutonium (Figure 14-12q) is the key fissile material for modern nuclear bomb. It has some peculiar properties that required special handling. This element has at least 7 allotropic phases

    (different forms), every one of which has its own density and other physical properties including critical mass. The alpha phase occurs at room temperature, it has a density of 19.86 gm/cm3, a critical mass of about 10 kg., and very brittle - not suitable to shape by machine. The bomb makers now use 0.8% gallium alloy to stabilize the malleable delta phase at higher temperature. Despite of such shortcoming it has become the fissile material of choice, since its enrichment is susceptible of chemical treatment, the cost of manufacturing is greatly reduced. The silvery button in Figure 14-12q was used in the core of

    Figure 14-12q Plutonium [view large image]

    the bomb dropped on Nagasaki (a.k.a. Fat Man). The plutonium (in the same image) in the form of a ring is important for criticality safety. There is enough material in there to make a modern strategic nuclear bomb.

    
    Another problem with Pu-239 is the isotope Pu-240. About 1 in 3 of the irradiating neutrons (as depicted in Figure 14-12k) are absorbed to become Pu-240. The trouble with Pu-240 is the tremendous amount of spontaneous neutrons re-emitted at the rate of 1 million per sec per kg (as shown by Table 14-02). In the gun-type bomb, the assembly into critical mass takes about 10^-3 sec, which is too long. The bomb has not passed into super-criticality sufficiently before it blows itself apart resulting in a predetonation - a frizzle. Bomb-grade plutonium contains fewer than 7% Pu-240, while those used in reactor can have 20% or more Pu-240. In spite of minimizing Pu-240 contamination, Nuclear bomb using plutonium has to be re-designed.
    
    The sketch in Diagram b, Figure 14-12p is one of the many possibilities considered for arranging the plutonium in the method of implosion, which requires precise firing of explosive surrounding the outer surface of the sphere. In the final design, shock wave from simultaneous detonations compresses a solid plutonium sphere from sub-critical to super-critical. The critical mass for delta phase plutonium is 16 kg. The "Fat Man" carried only a 6.2 kg plutonium pit (core). Evidently the combined effects of increasing density and tamper modified the critical mass to less than 1/4 of its value at normal pressure. The initiator contains beryllium and polonium separated by a barrier and placed at the center of the bomb. The barrier in the container is ruptured by the shock wave of the explosive to make it into a neutron source. The fission process proceeds quickly in 10^-6 sec, so that the problem with frizzle is avoided. Diagram b, Figure 14-12p shows the structure of implosion-type nuclear bomb.
    
    The world's first nuclear explosion occurred on July 16, 1945 at 5:30 a.m. at the Trinity test site in New Mexico. It is the cumulative efforts of up to 130000 people over 27 months in the Manhattan Project headed by J. R. Oppenheimer at Los Alamos, where the bombs were designed and made. Many thousands more were involved indirectly, working for big corporations such Union Carbide and Du Pont. Other sites include the Met Lab at Chicago; there was Oak Ridge, where U-235 was separated from U-238; and Hanford, the site of the reactors that created plutonium, and the facilities to separate this from the uranium fuel. The device consisted of a five-foot sphere containing shaped charges of high explosives around a core of plutonium no bigger than a tennis ball. The pieces of plutonium will be imploded to reach critical volume by the conventional explosion. The bomb was winched up a hundred-foot wooden tower at Ground Zero. In Figure 14-12r, a physicist in charge of assembling the high-explosive charges sits next to the bomb. Another image in the same figure shows the display of

    spectacular fire ball and mushroom cloud seconds after the detonation. Unknown to the scientists on the project, the real purpose of the bomb was to target Japan and to intimidate the Soviets according to General Groves, the equivalent of political commissar in the project. Some team members consider such intent to be the betrayal of the original aim of using it on Nazi Germany, which was believed to be on the

    Figure 14-12r First Nuclear Explosion [view large image]

    verge of making similar weapon. Anyway, the development came too late as Germany has already capitulated on May 8, 1945 before the Trinity test.

    
    
    The North Korean nuclear test in 2006 seemed to fizzle out with very low yield. Probable causes of the misfiring:
    • Non-symmetrical implosion - The implosion must be extremely symmetrical to be fully successful. Typically a combination of fast and slow conventional explosives surrounds a sphere of plutonium (the "core" or "pit"). Engineers must carefully machine all the pieces that make up this explosive shell into shapes that, when detonated simultaneously, produce a precisely spherical shock wave that compresses the plutonium to two to five times its normal density (the more compression, the greater the explosive yield). At the higher density, what was a subcritical mass of plutonium becomes supercritical, i.e., one in which a sustained chain reaction takes place, producing the blast.
    • Wrong timing of the initiator - The initiator is a small device at the center of the core that emits a burst of neutrons to start the chain reaction reliably at a precise stage of the implosion. An initiator going off early or late or not at all would reduce the yield.
    • Impurity - The fuel rods of nuclear reactors produce the desired isotope, plutonium 239, but the longer it

      remains in the reactor, the more of it becomes plutonium 240. Plutonium 240 constantly emits tens of thousands of times more neutrons per second than plutonium 239. Although neutrons are the key particles in producing a nuclear chain reaction, an excess of them early in the implosion is a recipe for predetonation. Figure 14-12s shows the fuel rods from the Yongbyon nuclear reactor. They probably provided the plutonium 239 needed for the test. North Korea has conducted an underground nuclear test successfully on May 25, 2009.

      Figure 14-12s NK Fuel Rods

Thermo-nuclear Fusion

charged particles have acquired enough energy to overcome the Coulomb repulsion. The stellar interior is the only place where fusion occurs naturally via the proton-proton reaction and the carbon cycle (Figure 14-13a). The amount of energy released is about an order of magnitude lower than fission and many of the reactions takes a long time to occur. Nevertheless, since there are so many charged particles inside the stars, they keep on generating energy for a long time especially

Figure 14-13a Stellar Fusion [view large image]

when the key (initial) step of proton-proton reaction takes an average of 14 billion years to occur (this is lucky for the evolution of life, otherwise the Sun may cease to shine long time ago).

Figure 14-13b shows the dependence of temperature for the p-p reaction and carbon cycle (CNO). The p-p reaction is the dominant process in lower temperature (in million degree K) for most of the main sequence stars. Whereas at higher temperature, the CNO process is important for massive stars with mass greater than 1.5 Msun and in the later stage of all stars. Careful examination of Figure 14-13a reveals that two protons in the p-p chain and one carbon in the CNO cycle act like a catalyze to produce a nucleus of He-4. The time scale in Figure 14-13a is the "mean reaction time per particle", which is proportional to T2/3/ (and other constants) where T is the temperature and is the density of the proton (and He-3 in one of the steps). The entities with no label in the diagrams of Figure 14-13a are the compound nuclei, which exist for a very short time of about 10-16 sec.

Figure 14-13b Temp. & Reaction Rate

Applications of Thermo-nuclear Fusion

The slow reaction rate in the p-p chain and CNO cycle makes them in-practical for any application on Earth. The fusion reactions that seem most promising as terrestrial energy sources are listed in Figure 14-14a. These reactions occur at temperature about 100 times higher than that in the Sun's core. Reactions 5 and 6 are not thermo-nuclear reactions. They are used to produce the triton in reaction 1.

Figure 14-14a Thermonuclear Reactions [view large image]

• Nucleosynthesis - In the Big Bang theory of modern cosmology, there was a period in early universe that was favorable for the aforementioned thermonuclear reactions. Light elements up to beryllium were generated about 3 minutes after

  the Big Bang. The process lasted for about 15 minutes starting at temperature of 1010K (at the high end of the thermonuclear reactions in Figure 14-14a). Figure 14-14b lists the reactions in nucleosynthesis, many of them are identical to those in Figure 14-14a. Initiation of the process depended on the baryon to photon ratio, too many photons would drive the   p + n D + reaction backward leaving no deuteron to proceed. Nucleosynthesis ended when temperature fell off with the cosmic expansion preventing elements heavier than beryllium to form. The calculation of mass abundances follows simple thermodynamic

  Figure 14-14b Big Bang Nucleosynthesis

  arguments and is insensitive to what happened before the process. Its agreement with observation presents a fairly reliable verification for the theory of Big Bang.

• Thermo-nuclear Reactor - In order to release energy at a level of practical use for production of electricity, the gaseous deuterium-tritium fuel must be heated to about 100 million degrees Celsius. This temperature is more than six times hotter than the interior of the sun, which is estimated to be 15 million degrees Celsius. Scientists have already passed the task of achieving the necessary temperatures. In some cases, they have attained temperatures as high as 510 million degrees, more than 20 times the temperature at the center of the sun.
  
  The problem is how to confine the deuterium and tritium under such extreme conditions. A part of the solution to this problem lies in the fact that, at the high temperatures required, all the electrons of light atoms become separated from the nuclei. The fuel is in the plasma state. Because of the electric charges carried by electrons and ions, a plasma can, in principle be confined by a magnetic field. In the absence of a magnetic field, the charged particles in a plasma move in straight lines and random directions. Since nothing restricts their motion the charged particles can strike the walls of a containing vessel, thereby cooling the plasma and inhibiting fusion reactions (but would not damage the wall because of very low number density). In a tokamak, the high-temperature plasma are confined by the magnetic field around the doughnut-shaped nuclear reactor. As shown by Figure 14-14c, the magnetic fields that confine the plasma are provided primarily by cylindrical magnetic field (toroidal magnetic field) and an internal plasma current (poloidal magnetic field). Combining the toroidal and poloidal magnetic fields creates a helical field that contains the plasma.
  
  

  However, long-lived pinched plasmas are extremely difficult to maintain. The plasma column is observed to break up rapidly. The reason for the disintegration of the column is the growth of instabilities. The column is unstable against various departures from cylindrical geometry. Small distortions are amplified rapidly and destroy the column in a very short time. The mechanisms of instability in plasma physics are nearly unlimited. Some instabilities are comparable to examples borrowed from fluid mechanics, as the Rayleigh Taylor’s instability, which consists of superposing two fluids with the heaviest on top. Imagine for example a vessel in which you pour water and then carefully add oil over the top. The system is then in a state of meta-stable equilibrium. The slightest nudge will provoke a change with the heavier fluid dropping to the bottom, which corresponds to a stable equilibrium. Another type of instability are kink instabilities, which occur when a current parallel to the magnetic field cause twisting of the field lines, recalling the effect obtained if we twist a rope too much: the rope twists out and

  Figure 14-14c Plasma Confinement

  kinks. The sausage or neck instability causes a greater inwards pressure at the neck of a constriction. This serves to enhance the existing distortion.

  The Tokamak Fusion Test Reactor has produced significant quantities of fusion power (up to 10 Million Watts) from the fusion of DT (Deuterium and Tritium). However, this has not yet reached the breakeven point when output power equals to the input.
  

  In September 2006, Chinese researchers had, for the first time, managed to inject a plasma of ionized hydrogen into the Experimental Advanced Superconducting Tokamak (EAST, Figure 14-14d), and the plasma sustained currents of 250,000 amps for up to 3 seconds. But no attempt was made to introduce deuterium or tritium into the plasma, so no fusion has taken place. Eventually, the EAST team aims to hold the plasma for study for as long as 1000 seconds. Conventional experimental fusion machines use copper coils, or a combination of copper and superconducting coils, to trap the hot plasma. But copper coils heat up and need to be cooled down regularly, thus limiting operating time. EAST has only superconducting coils so it can be operated

  Figure 14-14d EAST [view large image]

  continuously. This US$25-million machine sets the stage for the multibillion-dollar ITER fusion experiment that is to be built in France, and starts operation in 2016.

  
  
  ITER (Figure 14-14e) is an international project involving The People's Republic of China, the European Union and Switzerland (represented by Euratom), Japan, the Republic of Korea, the Russian Federation, and the United States of America. It is the experimental step between today’s studies of plasma physics and tomorrow's electricity-producing fusion power plants. The location of the reactor has been selected in Cadarache, southern France. The US$5.5 billion

  funding from ITER's six international partners could be in place by the winter of 2005, allowing construction to begin in 2006, and operation in 2016. ITER is designed to heat hydrogen to hundreds of millions of degrees centigrade, and then squeeze energy from the resulting plasma, while holding it stable for minutes at a time. It is based on the tokamak model, which up until today has only one machine that has begun to approach the "break-even point". It is believed that by building a tokamak with bigger size, it will allow the high-temperature high-pressure plasma to remain stable longer (~ 7-10 minutes) producing 500 megawatts of energy within the interval.

  Figure 14-14e ITER [view large image]

  By 2009 the ITER project faced with ballooning costs and growing delays, its seven partners are likely to build only a skeletal version of the device at first. This mini-ITER should be able to run in 2018. The full-scale version would not come alive until the end of 2025.



• Thermo-nuclear Bombs - Thermonuclear, or hydrogen bombs explode with enormous power via uncontrolled

  		self-sustaining chain fusion reactions (Figure 14-14f). Deuterium and tritium form helium under extremely high temperature, providing the energy: D + T He + n + 17.6 Mev (See Figure 14-14g). In principle, a mixture of D and T heated to very high temperature and in high density will start a chain fusion reaction, liberating an enormous amount of energy. But tritium is an unstable
  Figure 14-14f Thermo-nuclear Explosion [view large image]	Figure 14-14g Fusion [view large image]	element; an ingenious method is to have it produced from lithium deuterate (Li6H2) in the fission phase

  of the explosion -- thus one compound is used for both types of fuels ( D and T). In a thermonuclear bomb, the explosive process begins with the detonation of what is called the primary stage. This consists of a relatively small quantity of conventional explosives, its detonation brings together enough fissionable uranium or plutonium to create a fission chain reaction (sometimes magnified with a smaller fusion reaction), which in turn produces another fission explosion inside the temper in the secondary device and raises the temperature to several million degrees. When the temperature of the mixture reaches 10,000,000 oK, fusion reactions take place. The neutrons from the fusion reactions induced fission in the uranium-238 pieces (highly enriched with U-235) from the tamper and shield, which produced even more radiation and heat and the bomb exploded (See Figure 14-14h). Specialized type of small fusion bombs designed to release neutrons rather than causing further fission reactions are called neutron bombs. This is accomplished by removing the U-238 tamper. Neutrons kill people, leaving the hardware and buildings intact. It is a "clean" bomb. The theorized cobalt bomb is, on the contrary, a radioactively "dirty" bomb having a cobalt tamper. This tamper is made of cobalt-59, which is transmuted into cobalt-60 by neutrons released from the fusion reactions. Cobalt-60 has a half-life of 5.26 years and produces energetic (and thus penetrating) gamma rays. The half-life of Cobalt-60 is just long enough so that airborne particles will settle and coat the earth's surface before significant decay has occurred, thus making it impractical to hide in shelters. This is the "doomsday machine" since it is

  Figure 14-14h Nuclear Detonation

  capable of wiping out life on earth. The whole point about an automated doomsday response to nuclear attack is to let all the world know about its existence, and to demonstrate the viability of the process perhaps in a small scale testing (to show that it's not a bluff). This is the ultimate meaning of deterrence.

  Table 14-05 below lists the various components of the Teller-Ulam H Bomb (see schematic diagram in Figure 14-14i) in sequence of the explosive events.
  
  

  Component	Material	Function
  External Casing	Steel, aluminum, etc.	Outer layer of the bomb
  Primary Device	See Implosion type nuclear bomb	Initial step of the thermo-nuclear explosion
  Radiation Channel	Plastic foam	Confining X-rays for radiation implosion
  Radiation Case	U, W, or Pb (not shown in diagram)	Cavity in the casing for establishing the radiation implosion
  Radiation Shield	Uranium or tungsten	To prevent premature heating
  Tamper	Uranium, tungsten, lead, etc.	Triggering the spark plug by implosion
  Spark plug	Plutonium	Another fission device to ignite the fusion fuel
  Fusion fuel	Lithium-6 deuteride	Fusion lasting for 10-9 sec to release a yield of ~ 50 MT

  Table 14-05 Teller-Ulam H Bomb

  Table 14-06 lists the yield of various types of bomb/device in TJ. (1 TJ = 10¹² Joules, 1 ton of TNT = 4.184x10⁹ J)
  
  

  Type	Yield (TJ)
  First Fission	80
  Hiroshima Fission	63
  Nagasaki Fission	84
  Typical Fission	4000
  Large Fission	84000
  Tactical Fission	~ 60
  Maximum Fusion	210000
  Neutron Fusion	0.4 - 400

  Yields of Nuclear Bomb/Device

  Nuclear warheads don't last forever. The shelf life is about 50 years. In additional to rusting, the plutonium in the primary (the trigger or pit) emits a small but steady stream of radiation, which changes the properties of the plutonium alloy by altering its crystalline structure, ultimately causing the weapon to fail. Over the past 14 years, researchers have studied the warheads with computer simulations and experiments. They are discovering things and seeing things that

  are not expected. The details are of course entirely classified. Because of the nuclear testing moratorium, researchers are trying to design new weapons without a test. It is known as RRW (Reliable Replacement Warhead). New design includes improving the plutonium pit, replacing the toxic materials with other heavier material (for the tamper to amplify the initial explosion), and substituting the volatile explosives (on the outer shell) with an insensitive type (Figures 14-14g). Such ideas have to pass the review of the generals, who have to change the software and hardware systems for delivering the bomb. RRW designers try to reassure the critics that the new warheads will be compatible with existing systems. Figure 14-14i shows the differences in the design of the old and new types.

  Figure 14-14i H Bomb, Old and New [view large image]

  A 2007 study shows that existing warheads will last for at least another 50 years making the new bomb seemingly less necessary. The US House of Representatives will vote on a bill that would eliminate funding for the RRW from the 2008 budget. But the RRW is not done yet. Other plans are working its way through Congress and the Senate.

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  Effects of Nuclear Explosions

  Nuclear weapons are similar to those of more conventional types in so far as their destructive action is due mainly to blast or shock. On the other hand, there are several basic differences between nuclear and high-explosive weapons. In the first place, nuclear explosions can be many thousands (or millions) of times more powerful than the largest conventional detonations. Second, a fairly large proportion of the energy in a nuclear explosion is emitted in the form of light and heat, generally referred to as "thermal radiation". It is capable of causing skin burns and of starting fires at considerable distances. Third, the nuclear explosion is accompanied by highly penetrating and harmful invisible rays, called the "initial nuclear radiation". Finally, the substances remaining after a nuclear explosion are radioactive, emitting similar radiations over an extended period of time. This is know as the "residual nuclear radiation" or "residual radioactivity". Figure 14-15a shows the distribution of energy in a typical nuclear explosion. The detonation of nuclear weapon leads to the liberation

  Figure 14-15a Distribution of Energy [view large image]

  of a large amount of energy in a very small period of time within the casing. Tre-mendous pressures (over million times the ambient pressure) is produced in the form of shock wave. Damage is done at the shock front by the huge difference in air pressure as well as by the drag force (strong winds) trailing behind. The radiation energy are absorbed within a few feet

  in the surrounding to form a hot and highly luminous, spherical mass called fireball. The growth of the fireball becomes the mushroom cloud as shown in Figure 14-15b. It rises to 7200 feet in 10 sec, and eventually attains a height of about

  		4.5 miles. As the shock wave travels in the air away from its source, the overpressure at the front steadily decreases, and the pressure behind the front falls off until it develops a "negative pressure", in which a partial vacuum is produced and the air is sucked in reversing the wind direction. Figure 14-15c illustrates the variation of overpressure with distance at successive times. Its effects on a light structure, a tree, and a small animal are indicated with a series of pictures corresponding to the various
  Figure 14-15b Mushroom Cloud [view large image]	Figure 14-15c Shock Wave [view large image]	times. Speed of the shock front varies from about 1600 ft/sec initially to 1150 ft/sce (slightly faster than the sound speed of 1115 ft/sec) at later time.

  On the microscopic level, the action of radiation is to generate unstable molecular species, or excited molecules by interaction with water or other substances. They are very reactive chemically and soon undergo a number of secondary processes with various molecules present in the living cell. As a result, essential enzyme reactions may be inhibited and

  the behavior of DNA and RNA is modified. There are consequently changes in the cells which may have significant detectable effects on the body as a whole. All radiations apparently induce the same general biological consequences, but neutrons are unusual in the respect that they can convert a N-14 atom in an amino acid into one of C-14. Such a change might inactivate an enzyme or affect a nucleic acid. Certain macroscopic phenomena are soon apparent in the living cell. Among these are breaking of the chromosomes. Figure 14-15d shows the normal plant cell,

  Figure 14-15d Biological Effects [view large image]

  with two groups of chromosomes (left), and changes (right) produced by X-rays. Frequently, the cells are unable to undergo mitosis, so that normal replacement occurring in the living organism is inhibited.

  
  The detonation of a nuclear bomb over a city can cause immense damage. The degree of damage depends upon the distance from the center of the bomb blast, its altitude, and the explosive energy (see Figure 14-15efor the effects on Hiroshima). At the hypocenter (ground zero), everything is immediately vaporized by the high temperature (up to 300 million ^oC). Outward from the hypocenter, most casualties are caused by burns from the heat, injuries from the flying

  		debris of buildings collapsed by the shock wave, and acute exposure to the high radiation. Beyond the immediate blast area, casualties are caused from the heat, radiation, and fires spawned from the heat wave. Figure 14-15f presents two views of Hiroshima before and after an atomic-bomb attack. It occurred in the morning (8:16 a.m.) of August 6, 1945. The bomb detonated at an altitude of 580 meters killing or wounding about half of its 350,000 inhabitants with long-term effects on
  Figure 14-15e Effects of A-Bomb [view large image]	Figure 14-15f Hiroshima	incalculable numbers among the survivors.

  In the long-term, radioactive fallout occurs over a wider area because of prevailing winds. The radioactive fallout particles enter the water supply and are inhaled and ingested by people at a distance from the blast. Radiation and radioactive fallout affect those cells in the body that actively divide (hair, intestine, bone marrow, reproductive organs). Radiation induced DNA damage would increase the risk of leukemia and cancer.
  
  Some of the resulting health conditions include:
  

  		Nausea, vomiting and diarrhea. Cataracts. Hair loss. Loss of blood cells. Infertility. Birth defects. Leukemia. Cancer. Figure 14-16a shows the symptoms of radiation sickness according to the dose received. The radiation unit in Roentgen was originally defined in 1928. It is the energy to produce 2.1 x 109 ion pairs in a volume of 1 cubic centimetre of air, which is equivalent to about 100 ergs per gram
  Figure 14-16a Radiation Sickness [view large image]	Figure 14-16b Sick Survivor [view large image]	of water or tissue irradiated. Although it seems to be a minute amount of energy when one considers that 42 million ergs

  are required to raise the temperature of 1 gram of water by 1^oC. The remarkable property of ionizing radiation is that the small amount of energy represented by a few hundred rontgens can kill a person. For low level irradiation, the effect is similar to premature aging depending on doses and duration of exposure. Figure 14-16b

  shows the consequences from radiation exposure at the median level of 500 rad and the lower level of 100 rad, which is variably expressed as rem or r and is equal to 0.0838 Roentgen. In the U.S., the National Institute of Standard and Technology (NIST) strongly discourages the use of Roentgen as it is not really a SI unit. Another SI unit called Sievert (Sv = 1 J/kg) is also widely used in medical circle to measure the biological effects (1 rad = 0.01 Sv = 10 mSv). Figure 14-16c lists the adverse symptoms related to the levels of radiation (in mSv). Table 14-07 is a short list of the radioactive isotopes and uptakes by various organs. The gamma rays emitters can be expelled out of the body and is super-scripted by the symbol "*". For example, Cs-137 has a half life of 30 years, but half of the substance would be removed from the body in 70 days.

  Figure 14-16c Effects of Radiation [view large image]

  
  
  

  Radioactive Isotope	Half Life	Targeted Organ
  I-131 (Iodine)*	8.3 days	Thyroid
  Rn-222 (Radon) Pu-239 (Plutonium) Kr-85 (Krypton)*	3.8 days 24,000 years 10 years	Lung, (Rn-222 tends to spread over the whole body)
  Co-60 (Cobalt) Pu-239 (Plutonium)	5.3 years 24,000 years	Liver
  U-235 (Uranium) U-238 (Uranium) Pb-210 (Lead) Ru-106 (Ruthenium)*	700,000,000 years 4,500,000,000 years 22.3 years 1 year	Kidney
  Cs-137 (Cesium)* K-42 (Potassium)* C-14 (carbon) T-3 (Tritium) S-35 (Sulfur)	30 years 12 hours 5730 years 12.2 years 87 days	Skin, muscle
  Pu-239 (Plutonium) Sr-90 (Strontium) Ra-226 (Radium)	24,000 years 28.8 years 1620 years	Bone
  Po-210	138 days	Spleen (high toxicity)
  Pu-239 (Plutonium)	24,000 years	Gonads
  K-42*, Co-60*, Kr-85*, I-131*, Cs-137*, Pu-239	12 hours - 24,000 years	Ovaries

  Radioactive Isotopes and Targeted Organs

  
  A global nuclear warfare (many nuclear bombs exploding in different parts of the world) could produce a nuclear winter. In such scenario, the explosion of many bombs would raise great clouds of dust and radioactive material that would travel high into Earth's atmosphere. These clouds would block out sunlight. The reduced level of sunlight would lower the surface temperature of the planet and reduce photosynthesis by plants and bacteria. The reduction in photosynthesis would disrupt the food chain, causing mass extinction of life (including humans). This scenario is similar to the asteroid hypothesis that has been proposed to explain the extinction of the dinosaurs.
  
  
  Protection against nuclear attack:

  Preplanned protection - A massive, reinforced, fireproof shelter structure is required at close distances to protect individuals against the severe immediate effects (blast, thermal, and initial nuclear radiation) of a nuclear explosion. Conventional buildings may also be designed to be blast and fire resistant. Thermal and fire hazard can be minimized by reduction of potential ignition points and by provision for isolation or rapid extinction of ignitions to prevent development of large fires. In those areas where early fallout is expected to be a hazard, shelters may be constructed and provision made for occupying them for considerable lengths of time. Knowledge of warning systems and evacuation procedures will also minimize confusion. Unprepared attack - In the event that shelters are not available, certain evasive actions may prove helpful at distances where the immediate effects are least severe. By instantly falling prone and covering exposed portions of the body or getting behind opaque objects, much of the thermal radiation may be avoided, especially in the case of large-yield weapons. Under no circumstances should an individual look in the direction of the fireball. Staying behind thick walls or lying in a deep ditch may help to avoid initial nuclear radiation. Moreover, persons should avoid areas which have frangible materials, such as window glass, plaster, etc., which may become

  Figure 14-16d Nuclear Protection [view large image]

  flying debris by the action of the blast.

• Aftermath - After the immediate effects of the nuclear explosion are over, certain acts are required to minimize the hazards of the early fallout and from the fires which may result from thermal radiation and secondary blast effects. First, if small fires can be quickly extinguished, extensive conflagrations may be prevented. This must be accomplished before the arrival of the fallout or in areas of low radioactivity levels. Some protection from the fallout may be secured in the basements of buildings or in a quickly constructed shelter, such as placing a sturdy table in a corner adjacent to an unexposed outer wall and covered with 10 to 12 inches of soil, sandbags, solid concrete block, etc., according to what is available. It is important to keep from coming into physical contact with the fallout particles, and to prevent contamination of food and water sources. Monitoring equipment should be used to determine areas which have safe radiation levels and decontamination efforts can proceed to recover necessary equipment, buildings, and areas. Figure 14-16d shows a reinforced precast concrete house before and after a nuclear explosion (under overpressure of 5 psi or wind speed of about 160 mi/hr) at the Nevada Test Site. Note the gas tank, sheltered by the house, is essentially undamaged.

Helium-3

	There are three main energy producing processes in the interior of the Sun. One of them is the proton-proton reaction as shown below:
Figure 14-17 He3-He3 Reaction [view large image]	The He3-He3 reaction (Figure 14-17) in the third step is by far the most frequent of the various alternatives under a central temperature of about 15x106 K.

Another possibility for He3 fusion is via the reaction with D2 (Figure 14-18): He3 + D2 H1 + He4 + 18.4 Mev The fusion reaction rate becomes significant at a temperature of about 10x106 K, and peak about 200x106 K. Researchers see He3 as the perfect fuel source: extremely potent, nonpolluting, with virtually no radioactive by-product. The trouble is, hardly any of it is found on Earth. But there is plenty of it on the Moon.

Figure 14-18 He3-D Reaction [view large image]

Recent reports indicate progress toward making helium-3 fusion. Inside a lab chamber, researchers have produced protons from a steady-state deuterium-helium3 plasma at a rate of 2.6 million reactions per second. That's fast enough to generate fusion power but not churn out electricity. The chamber, which is roughly the size of a basketball, relies on the electrostatic focusing of ions into a dense core by using a spherical grid called Inertial Electrostatic Confinement

Figure 14-19 IEC [view large image]

(IEC) fusion system. Figure 14-19 shows a schematic diagram and the actual construction of an IEC. This one is used for neutron generation.

Meanwhile, news in November 2005 reports that China will make a manned moon landing around 2017. The project includes setting up a moon-based astronomical telescope, measuring the thickness of the moon's soil and the amount of helium-3 on the moon. According to the Chinese announcement: "It will provide the most reliable report on helium-3 to mankind". The United States has unveiled a $104 billion plan in September, 2005 to return Americans to the moon by 2018. Figure 14-20 shows the renderings of a Moon Base by NASA-commissioned artists.

Figure 14-20 Moon Base [view large image]

References:

• Binding Energy -- http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html
• Nuclear Models -- http://csep1.phy.ornl.gov/guidry/Math-9-94html/models.html
• Nuclear Decay, Fission, Fusion -- http://www.lbl.gov/abc/Basic.html
• Nuclear Energy -- http://zebu.uoregon.edu/1999/ph161/l18.html
• Nuclear Reactor -- http://www.npp.hu/mukodes/lancreakcio-e.htm
• Hiroshima, Effect of A-Bomb -- http://www.pref.hiroshima.jp/hiroshima/bunka/htmleng/elegacy3.htm

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Index

Alpha decay Beta decay Binding energy Cobalt bomb Critical mass Doomsday machine Electron capture Fission Fusion Gamma decay Liquid drop model

Magic number Mass number Multiplicity Neutron bomb Nuclear decay Plutonium 239 Positron emission Radioactive series Shell model Uranium 235

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