Fusion

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© 1998-2008 by Glenn Elert -- A Work in Progress
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Discussion

introduction

The sun has been around for some five billion years and is expected to shine for another five billion years to come.

Size is related to energy. Nuclear energy is to chemical energy as atomic dimensions (10−10 m) are to nuclear dimensions (10−15 m). Nuclear reactions have energies on the order of 100,000 times the energy of chemical reactions.

Paraphrase needed …
F. W. Aston discovered in 1920 the key experimental element in the puzzle. He made precise measurements of the masses of many different atoms, among them hydrogen and helium. Aston found that four hydrogen nuclei were heavier than a helium nucleus. This was not the principal goal of the experiments he performed, which were motivated in large part by looking for isotopes of neon. The importance of Aston's measurements was immediately recognized by Sir Arthur Eddington, the brilliant English astrophysicist. Eddington argued in his 1920 presidential address to the British Association for the Advancement of Science that Aston's measurement of the mass difference between hydrogen and helium meant that the sun could shine by converting hydrogen atoms to helium. This burning of hydrogen into helium would (according to Einstein's relation between mass and energy) release about 0.7% of the mass equivalent of the energy. In principle, this could allow the sun to shine for about a 100 billion years. In a frighteningly prescient insight, Eddington went on to remark about the connection between stellar energy generation and the future of humanity:

If, indeed, the subatomic energy in the stars is being freely used to maintain their great furnaces, it seems to bring a little nearer to fulfillment our dream of controlling this latent power for the well-being of the human race -- or for its suicide.

Bethe described the results of his calculations in a paper entitled "Energy Production in Stars".


Light nuclei join to form a heavier nucleus. Energy is released in the process. Fusion powers the stars and "large" thermonuclear weapons. [magnify, animate]

Light nuclei join to form a heavier nucleus. Energy is released in the process. Fusion powers the stars and high yield thermonuclear weapons.

solar fusion

Stars begin as a cloud of mostly hydrogen with about 25% helium and heavier elements in smaller quantities. The sun, 107 K core, hydrogen fuses to form helium through a process known as the proton-proton chain (often shortened to the p-p chain).

Overall


The Proton-Proton Chain [magnify]

More on stellar fusion in the Nucleosynthesis section of this book.

thermonuclear weapons

The first fusion bomb used liquefied deuterium (heavy hydrogen). Current "h-bombs" are dry thermonuclear weapons. The fuel of choice is lithium deuteride (lithium-6 deuteride to be more precise).


Lithium Deuteride in Action [magnify]

More on fusion bombs in the Nuclear Weapons section of this book.

fusion reactors

magnetic confinement
tokamak -- toroidal chamber and magnetic coil

inertial confinement?
laser systems

Approaches to Nuclear Fusion
method density (kg/m3) temperature (K) confinement time
magnetic confinement 0.000001 100 million several seconds
inertial confinement 1,000,000 100 million 10−11 s
solar core 100,000 16 million as old as the sun
hydrogen bomb ? ? ?
Source: Lawrence Livermore National Laboratory

 

Selected Isotopes of the Light Elements
Z element A mass (u) abundance   Z element A mass (u) abundance
–1 [electron] 0 0.000549     5 boron 8 8.024605  
                9 9.013328  
0 [neutron] 1 1.008665         10 10.012937 19.9
                11 11.009305 80.1
+1 [proton] 1 1.007276         12 12.014352  
                13 13.01778  
1 hydrogen 1 1.007825 99.985   6 carbon 10 10.01686  
  [deuterium] 2 2.0140 0.015       11 11.01143  
  [tritium] 3 3.01605         12 12 98.9
                13 13.003355 1.1
2 helium 3 3.01603       14 14.003241  
    4 4.00260 100       15 15.010599  
    5 5.01222     7 nitrogen 12 12.018613  
                13 13.005738  
3 lithium 5 5.01254         14 14.003074 99.63
    6 6.015121 7.5       15 15.000108 0.37
    7 7.016003 92.5       16 16.006099  
    8 8.022485         17 17.008450  
    9 9.026789     8 oxygen 14 14.008595  
                15 15.003065  
4 beryllium 7 7.016928         16 15.994915 99.76
    8 8.005305         17 16.999131 0.04
    9 9.012182 100       18 17.999160 0.20
    10 10.013534         19 19.003577  
    11 11.021658         20 20.004075  

Summary

Problems

practice

  1. Hydrogen fusion in the sun is a multistep reaction, but the net result is that four hydrogen atoms fuse into one helium atom.
     
     
    The mass of the sun is 1.99 × 1030 kg, 91% of which is hydrogen. Its power output is 3.85 × 1026 W. Determine …
    1. the mass of four hydrogen atoms,
    2. the mass defect when four hydrogen atoms fuse into one helium atom (in atomic mass units and megaelectronvolts),
    3. the rate at which the sun's mass is decreasing,
    4. the total mass destroyed if all the sun's hydrogen were converted into helium, and
    5. the expected lifetime of the sun (assuming its power output will remain constant).
    Solutions …
    1. The mass of four hydrogen atoms is …
       
       
    2. The mass difference between four hydrogen atoms and one helium atom is …
       
       
    3. The rate at which mass is destroyed is related to the rate at which energy is produced.
       
       
      About four million tons of the sun vanishes every second.
    4. The fraction of the sun's mass lost if every hydrogen nucleus was used to produce helium is the same as the the ratio of the mass defect to the original mass.
       
       
    5. Setting up another proportion finishes the problem.
       
       
      This is a not a very good estimate, however. Although extremely hot in human terms, most of the sun is just too cool for hydrogen to fuse into helium. Only the central core is hot enough and dense enough. Thus, it is estimated that not more than ten percent of the sun's total hydrogen will ever be available for thermonuclear fusion. Ten percent of 95 billion years 9.5 billion years, which is still a good long time. The earth is some 4.5 billion years old already, placing us somewhere in the middle of the sun's life. The sun is a middle-aged star.
  2. The fuel used in most high-yield thermonuclear weapons is solid lithium 6 deuteride (ρ = 820 kg/m3). These weapons, commonly known as "hydrogen bombs" or "H-bombs", use the energy released when a nuclueus of light lithium and heavy hydrogen fuse to form two nuclei of ordinary helium (a two part process).
     
     
    A typical thermonuclear weapon has a yield on the order of several million tons of TNT or about as destructive one truck bomb for every person in Brooklyn. (One ton of TNT is equal to 4.184 GJ by definition.)
    1. Given the reaction described above, determine …
      1. the mass of one molecule of lithium 6 deuteride, and
      2. the mass defect when one molecule of lithium 6 deuteride is transformed into two atoms of helium (in atomic mass units and megaelectronvolts).
    2. Given a "small" hydrogen bomb with an explosive yield of one megaton, determine …
      1. the mass destroyed in its detonation,
      2. the mass of the fuel required, and
      3. the volume of the fuel required.
    Solutions …
    1. The mass of one lithium 6 deuteride molecule is simple enough to determine.
       
       
    2. The mass difference between the reactants and products of this reaction is also easy to determine.
       
       
    3. Using the mass-energy equivalence gives us the mass destroyed when one of these weapons is detonated. (Recall that the prefix mega means 106.)
       
       
      This may not seem like much mass, but it's an enormous amount of energy.
    4. The ratio of the mass of fuel required to the mass destroyed in a one megaton blast is the same as the ratio of the mass of one lithium 6 deuteride molecule to the mass destroyed in a single reaction.
       
       
      This is about half as heavy as a typical dog.
    5. The volume of fuel required can be determined from its mass and density.
       
       
      This is a bit more than a standard bucket. A bucket of lithium 6 deuteride is sufficient to level all but the largest cities.
  3. The text below describes some of the nuclear reactions that occurred during the detonation of the first hydrogen bomb code named "Mike" at Eniwetok Atoll in 1952. Identify the fusion reactions described in these two paragraphs and rewrite them in symbolic form; that is, as reaction equations.
     
    All these processes, proceeding through microseconds, prepared Mike for thermonuclear burning. Now the escaping X-radiation of the fissioning sparkplug heated the compressed deuterium at its boundaries; the increasing thermal motion of the deuterium nuclei pushed them together until they passed the barrier of electrostatic repulsion between them and came within range of the nuclear strong force, at which point they began to fuse. Some fused to form a helium nucleus — an alpha particle — with the release of a neutron, the alpha and the neutron sharing an energy of 3.27 MeV(1). The neutron passed through the electrified mass of fusing deuterons and escaped, but the positively charged alpha dumped its energy into the heating deuterium mass and helped heat it further.
     
    Other deuterium nuclei fused to form a tritium nucleus with the release of a proton, the triton and the proton sharing 4.03 MeV(2). The positively charged proton dumped more energy into the deuterium mass. The tritium nucleus fused in turn with another deuterium nucleus to form an alpha particle and a high-energy neutron that shared 17.59 MeV(3). The 14 MeV neutrons from this reaction began to escape the hot, compressed deuterium plasma and encountered the U238 nuclei of the vaporized uranium pusher. U238 fissions when it captures neutrons with energies above 1 MeV; so the U238 of the uranium pusher began to fission then under the intense neutron bombardment, flooding more X rays back into the deuterium mass from the outside just as the sparkplug fission reaction was radiating them from the inside, trapping the deuterium between two violent walls of heat and pressure. Deuterium-bred tritium fused with tritium as well, producing a helium nucleus and two neutrons that shared 11.27 MeV of energy(4). At lower orders of probability, deuterium captured a neutron and bred tritium(5); deuterium-bred helium fused with deuterium and made heavy [ordinary] helium plus a highly energetic proton(6), or captured a neutron and bred tritium plus a proton(7). All these reactions contributed to the force of the Mike explosion.
     
    Source: Rhodes, Richard. Dark Sun: The Making of the Hydrogen Bomb. New York: Simon & Schuster, 1995: 507.
     
    Solutions …
    • Seven fusion reactions are described in this passage.
       
       
  4. Write something.
    • Answer it.

numerical

  1. This question is composed of three related parts.
    1. What percentage of the original mass is converted to energy when two heavy hydrogen atoms fuse to form one helium atom?
    2. Calculate the mass destroyed in the detonation of a typical hydrogen bomb if its explosive potential is equivalent to one million tons of TNT. (One ton of TNT possesses 4.184 GJ of chemical energy.)
    3. Using your results from the previous two questions, determine the mass of nuclear fuel needed to make an "H-bomb" capable of leveling hundreds of square kilometers.
  2. For nuclear weapons the yield to weight ratio is the amount of explosive energy released compared to the mass of the nuclear material. Verify the claims of Wikipedia that "the theoretical maximum yield-to-weight ratio for fusion weapons is 6 megatons per metric ton (6 Mt/t)."

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