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									                                                                  Teacher’s Handout 2.31

             Fusion - Physics of a Fundamental Energy Source1
                             Two Important Fusion Reactions
D + T => He-4 + n
For first generation fusion reactors
The "D-T" reaction has the highest reaction rate at the
plasma temperatures which are currently achievable; it
also has a very high energy release. These properties
make it the easiest reaction to use in a man-made fusion
reactor. As the figure shows, the products of this
reaction include an alpha particle (Helium-4 nucleus)
with 3.5 MeV energy, and a neutron with 14.1 MeV
energy. The neutron escapes from the plasma (it has no
charge and is not confined) and can be trapped in a
surrounding "blanket" structure, where the n + Li-6 =>
He-4 + T reaction can be used to "convert" the neutrons
back into tritium fuel.
1 eV = 1.6022E-19 joules;
Average particle thermal kinetic energy is 1 eV per 11,600 K.

"P-P": Solar Fusion Chain
Known as the proton-proton chain, the reaction
process depicted above is the dominant fusion
mechanism in light stars, including our sun.

(In heavier stars, a more complicated process known
as the carbon cycle predominates.)

In the P-P chain, two pairs of protons fuse, forming
two deuterons. Each deuteron fuses with an additional
proton to form helium-3. The two helium-3 nuclei
which then fuse to create beryllium-6, which is unstable and disintegrates into two protons plus a
helium-4 (alpha particle). In addition, the process releases two neutrinos, two positrons, and
gamma rays. The positrons annihilate quickly with electrons in the plasma, releasing additional
energy in the form of gamma rays. The neutrinos interact so weakly that they fly right out of the
sun immediately.

Fusion of light (low-mass) elements releases
energy, as does fission of heavy (high-mass)
Binding Energy per Nucleon as a Function of Nuclear Mass

The relation E = mc2 states the equivalence of mass and energy. In a fusion reaction, some
reactant mass energy is converted to kinetic energy of the products. Binding energy is the energy
equivalent of the mass difference between a whole nucleus and its individual constituent protons
and neutrons. For energy release in fusion or fission, the products need to have a higher binding
energy per nucleon (proton or neutron) than the reactants. As the graph above shows, fusion only
releases energy for light elements and fission only releases energy for heavy elements.
The actual fusion reaction occurs when two nuclei approach within about 1.0E-15 m, so that the
attraction, via the residual strong interaction between the nuclei, overcomes the electrical
repulsion between the protons. Such close encounters only occur when nuclei collide with
sufficient kinetic energy. Only at high temperatures do enough energetic particles exist for there
to be many fusion reactions.

Binding Energies (Low-Mass Elements Only)

                                     Reaction Energy Ef = k*(mi-mf)*c2

                                     This equation follows from Einstein's E = m*c2. The change
                                     in energy Ef of the system is proportional to the mass
                                     difference (mi-mf) between the reactants and the products. In
                                     the equation above,
                                     Ef = Energy per reaction
                                     mi = total initial (reactant) mass
                                     mf = total final (product) mass
                                     The conversion factor k equals 1 in SI units, or 931.466
                                     MeV/c2 in "natural units" where E is in MeV and m is in
                                     atomic mass units, u.

                                    Useful Nuclear Masses
                              (The electron's mass is 0.000549 u.)

                              Species         Symbols     Mass (u)*

                              n               Neutron     1.008665

                              p (H-1)         Proton      1.007276

                              D (H-2)         Deuteron 2.013553

                              T (H-3)         Triton      3.015500

                              He-3            Helium-3 3.014932
                            He-4 (alpha) Helium-4 4.001506

* Note: 1 u = 1 atomic mass unit = 1.66054 x 10-27 kg = 931.466 MeV/c2
Fusion Rate Coefficients

Plasma Fusion Reaction Rate = R * n1 * n2
n1,n2 = Densities of reacting species
(particles/m3); R = Rate Coefficient (m3/s).
Multiply by Ef to get fusion power density.
To calculate the rate of reactions per unit
volume, multiply the rate coefficient, R, by the
particle densities of the two reacting species
(divide by two if there is only one species, in
order to avoid double-counting the reaction
possibilities). The p + p => D reaction rate
coefficient in the sun is much lower than that
achievable with a deuterium-tritium fuel mix,
because the p + p reaction proceeds by the weak
nuclear interaction. Despite the sun's high
density, the low rate coefficient means a proton in the sun will exist for an average of billions of
years before it fuses. By comparison, a deuteron in a magnetic fusion power plant would only
exist for about 100 seconds, and a deuteron in an imploding, fully-burned inertial confinement
pellet only for 1.0E-9 seconds.
                       Creating the Conditions for Fusion

Fusion requires high temperature plasmas confined long enough to release appreciable fusion
                              Heating Mechanisms                        Sample Image
                                                                      Stars and Galaxies

                       Compression (gravity)
  Gravity              Fusion Reactions (such as the p-p chain)

                                                                   Laser-beam-driven Fusion

                       Compression (implosion driven by laser
                        or ion beams, or by X-rays from laser or
  Inertial              ion beams)
                       Fusion Reactions (primarily D+T)

                                                                     Tokamak Schematic
                       Electromagnetic Waves
                       Ohmic Heating (by electric currents)
                       Neutral Particle Beams (atomic
 Magnetic               hydrogen)
                       Compression (by magnetic fields)
                       Fusion Reactions (primarily D+T)

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