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Nuclear physics
Dr. Jay Maron


Nuclei

Proton = 2 up quarks + down quark
Helium atom
Neutron = 1 up quark + 2 down quarks

Particle   Charge    Mass

Proton       +1     1          Composed of 2 up quarks, 1 down quark,  and gluons
Neutron       0     1.0012     Composed of 1 up quark,  2 down quarks, and gluons
Electron     -1      .000544
Up quark    +2/3     .0024
Down quark  -1/3     .0048
Photon        0     0          Carries the electromagnetic force and binds electrons to the nucleus
Gluon         0     0          Carries the strong force and binds quarks, protons, and neutrons
Charge and mass are relative to the proton.

All of these particles are stable except for the neutron, which has a half life of 886 seconds.

Proton charge  =  1.6022 Coulombs
Proton mass    =  1.673⋅10-27 kg
Electron mass  =  9.11⋅10-31 kg
Hydrogen mass  =  Proton mass + Electron mass  =  1.6739⋅10-27 kg

Isotopes

Isotopes of hydrogen

An element has a fixed number of protons and a variable number of neutrons. Each neutron number corresponds to a different isotope. Naturally-occuring elements tend to be a mix of isotopes.

Isotope   Protons   Neutrons   Natural fraction

Hydrogen-1    1        0        .9998
Hydrogen-2    1        1        .0002

Helium-3      2        1        .000002
Helium-4      2        2        .999998

Lithium-6     3        3        .05
Lithium-7     3        4        .95

Beryllium-9   4        5        1

Boron-10      5        5        .20
Boron-11      5        6        .80

Carbon-12     6        6        .989
Carbon-13     6        7        .011
Teaching simulation for isotopes at phet.colorado.edu
Radiation

Beta and gamma rays are harmful and alpha particles are harmless.
Beta decay

Alpha particle  =  Helium nucleus  =  2 Protons and 2 Neutrons
Beta particle   =  Electron
Gamma ray       =  Photon


Alpha decay:   Uranium-235  ->  Thorium-231  +  Alpha
Beta decay:    Neutron      ->  Proton       +  Electron  +  Antineutrino     (From the point of view of nuclei)
Beta decay:    Down quark   ->  Up quark     +  Electron  +  Antineutrino     (From the point of view of quarks)
Beta decay is an example of the "weak force".

Teaching simulation for beta decay

Half life

For a radioactive material,

Time                           =  T
Half life                      =  Th
Original mass                  =  M
Mass remaining after time "T"  =  m  =  M exp(-T/Th)

Suppose an element has a half life of 2 years.

Time    Mass of element remaining (kg)

 0            1
 2           1/2
 4           1/4
 6           1/8
 8           1/16

Weak force (beta decay)

The weak force can convert a neutron into a proton, ejecting a high-energy electron.

From the point of view of nucleons:     Neutron     ->  Proton   + electron + antineutrino

From the point of view of quarks:       Down quark  ->  Up quark + electron + antineutrino
Teaching simulation for beta decay

Stellar fusion

Fusion of hydrogen into helium in the sun

Hydrogen fusion requires a temperature of at least 4 million Kelvin, which requires an object with at least 0.08 solar masses. This is the minimum mass to be a star.

P    + P    →  D    +  Positron + Neutrino +   .42 MeV
P    + D    →  He3  +  Photon              +  5.49 MeV
He3  + He3  →  He4  +  P   +  P            + 12.86 MeV

Helium fusion

As the core of a star star runs out of hydrogen it contracts and heats, and helium fusion begins when the temperature reaches 10 million Kelvin

He4  +  He4  ->  Be8            -   .092 MeV
Be8  +  He4  ->  C12            +  7.367 MeV
C12  +  He4  ->  O16  +  Gamma  +  7.162 MeV

Fusion of carbon into oxygen through the CNO cycle

At temperatures above 17 million Kelvin, carbon-catalyzed fusion happens faster than proton-proton fusion. This occurs in stars more massive than 1.3 solar masses.


Heavy element fusion

A heavy star continues to fuse elements until it reaches Iron-56. Beyond this, fusion absorbs energy rather than releasing it, triggering a runaway core collapse that fuses elements up to Uranium. If the star explodes as a supernova then these elements are ejected into interstellar space.


Stars

Star type    Mass   Luminosity    Color   Temp   Lifetime   Death      Remnant       Size of      Output
            (solar   (solar             (Kelvin) (billions                           remnant
            masses) luminosities)                 of years)

Brown Dwarf    <.08                       1000  immortal
Red Dwarf       .1        .0001   red     2000   1000      Red giant   White dwarf  Earth
The Sun        1         1        white   5500     10      Red giant   White dwarf  Earth         Light elements
Blue star     10     10000        blue   10000       .01   Supernova   Neutron star Manhattan     Heavy elements
Blue giant    20    100000        blue   20000       .01   Supernova   Black hole   Central Park  Heavy elements
Fate of stars, with mass in solar masses:
       Mass <   9   →  End as red giants and then turn white dwarf.
  9 <  Mass         →  End as supernova
  9 <  Mass <  20   →  Remnant is a neutron star.
 20 <  Mass         →  Remnant is a black hole.
130 <  Mass < 250   →  Pair-instability supernova (if the star has low metallicity)
250 <  Mass         →  Photodisintegration supernova, producing a black hole and relativistic jets.

Nuclear fission

Fission chain reaction

A neutron triggers the fission of Uranium-235 and plutonium-239, releasing energy and more neutrons. The released neutrons trigger further fission.

Chain reaction simulation at phet.colorado.edu

Critical mass

Less than a
critical mass
Critical
mass
More than a
critical mass
Chain reaction in
a supercritical mass
Almost a critical
mass of plutonium

A fission of uranium-235 releases on average 1.86 neutrons, some of which trigger fission in nearby nuclei and some of which escape without triggering fission. If a sphere of uranium-235 is small then most of the neutrons escape before triggering fission and the sphere doesn't blow up. If the sphere is large then most of the neutrons trigger more fission, a chain reaction occurs and the sphere blows up. The threshold for a chain reaction is the "critical mass".

The nuclei that are capable of undergoing a chain reaction are:

           Protons  Neutrons  Critical   Halflife   Neutrons per
                              mass (kg)  (106 yr)     fission

Uranium-233    92     141        16         .160      2.48
Uranium-235    92     143        52      700          1.86
Plutonium-239  94     145        10         .024      2.16

Uranium detonation

Two pieces of uranium-235, each with less than a critical mass, are brought together in a cannon barrel.
If the uranium is brought together too slowly, the bomb fizzles.

If you bring two pieces of uranium-235 together too slowly, a chain reaction begins in the near side of each piece, generates heat, and blows the two pieces apart before they can come completely together. Only a small amount of uranium undergoes fission and this is referred to as a "fizzle". Using gunpowder and a cannon is fast enough to properly detonate uranium and this is technologically easy to do.


Plutonium detonation

Plutonium is more difficult to detonate than uranium. Simply bringing two pieces together, no matter how fast, results in a fizzle. To detonate plutonium you have to shape it as a sphere and implode it, which is technologically difficult.

In World War 2 the U.S. produced enough uranium for 1 bomb and enough plutonium for 2 bombs. One of the plutonium bombs was tested in the "Trinity" test before being used in the war, and the second bomb was dropped on Nagasaki. The uranium bomb was dropped on Hiroshima without previously being tested.

When Hans Bethe, a physicist on the Manhattan project, was asked why they didn't test the uranium bomb he replied "Because we were perfectly sure it would work".


Separation of Uranium-235 from Uranium-238

Magnetic separation. Dark blue = uranium-235. Light blue = uranium-238. Yellow = magnetic field.
Magnetic separation machines during the Manhattan Project

Natural Uranium is .72% Uranium-235 and 99.3% Uranium-238. Only Uranium-235 undergoes a chain reaction and so it has to be separated from the Uranium-238. Several methods exist for doing this. In World War 2 the isotopes were separated magnetically with calutrons. Gas diffusion and centrifuges can also be used.


Centrifuge separation of uranium-235

UF6
UF6
Light blue: uranium-235. Dark blue: uranium-238
Centrifuges

Uranium is converted to gas form by forming uranium hexafluoride (HF6). HF6 is a gas above 64 Celsius. In a centrifuge, the lighter uranium-235 concentrates at the center and the heavier uranium-238 concentrates at the edge.


Nuclear isotopes relevant to fission energy

Abundance of elements in the sun, indicated by dot size

Blue elements are unstable with a half life much less than the age of the solar system and don't exist in nature.

The only elements heavier than Bismuth that can be found on the Earth are Thorium and Uranium, and these are the only elements that can be tapped for fission energy.

Natural thorium is 100% Thorium-232

Natural uranium is .7% Uranium-235 and the rest is Uranium-238.

Plutonium has a short half life and doesn't exist in nature. It can be created by subjecting uranium-238 to neutrons in a nuclear reactor. Fissionable uranium-233 can be created from thorium-232.

Uranium-238  +  Neutron  →  Plutonium-239
Thorium-232  +  Neutron  →  Uranium-233

Detail:

Uranium-238 + Neutron  →  Uranium-239
Uranium-239            →  Neptunium-239 + Electron + Antineutrino          Halflife = 23 minutes
Neptunium-239          →  Plutonium-239 + Electron + Antineutrino          Halflife = 2.4 days

Thorium-232 + Neutron  →  Thorium-233
Thorium-233            →  Protactinium-233 + Electron + Antineutrino       Halflife = 22 minutes
Protactinium-233       →  Uranium-233      + Electron + Antineutrino       Halflife = 27.0 days

Fusion bomb

Fusion bombs use the reactions:

Neutron    +  Lithium6  →  Tritium  +  Helium4  +   4.874 MeV
Deuterium  +  Tritium   →  Helium4  +  Neutron  +  17.56  MeV
Leaving out the neutron catalyst, this is
Deuterium  +  Lithium6  →  Helium4  +  Helium4  +  22.43  MeV

Fusion bomb design

Fusion of deuterium and lithium requires high temperature and pressure, which is achieved by compressing the fuel. This is done by detonating a fission bomb and using the generated X-rays to compress the fusion fuel. X-rays strike the outer layer and expel atoms, and the recoil compresses the fuel. This is called "ablation" and the design was developed by Teller and Ulam.

             X-ray     Plasma    Ablation
            pressure  pressure   pressure
              TPa       TPa        TPa

Ivy Mike       7.3       35        530
W-80         140        750       6400
Teller
Ulam
Ulam

Energy

The practical limit for the energy/mass of a fusion bomb = 25 TJoules/kg or .0062 Mtons of TNT per kg.

1 ton of TNT                        =   4⋅109  Joules
1 ton of gasoline                   =   4⋅1010 Joules
Massive Ordnance Air Blast bomb     =   .000011 MTons TNT  (Largest U.S. conventional bomb)
Trinity plutonium-239 test          =   .020 MTons TNT
Hiroshima uranium-235 fission bomb  =   .015 MTons TNT   "Little Boy". 60 kg Uranium-235
Nagasaki plutonium-239 fission bomb =   .021 MTons TNT   "Fat Man".     6 kg Plutonium-239
Ivy King fission bomb               =   .5   MTons TNT   Largest pure fission bomb
B83 fusion bomb                     =  1.2   MTons TNT   Largest bomb in active service
Castle Bravo fusion bomb            = 15     MTons TNT   Largest U.S. test
B41 fusion bomb                     = 25     MTons TNT   Largest U.S. bomb created
Tsar Bomba                          = 50     MTons TNT   Largest USSR test

History of nuclear physics

Leo Szilard
Enrico Fermi
Johnny von Neumann, Robert Oppenheimer, and the EDVAC computer
Niels Bohr

1885        Rontgen discovers X-rays
1899        Rutherford discovers alpha and beta rays
1903        Rutherford discovers gamma rays
1905        Einstein discovers that E=mc2. Matter is equivalent to energy
1909        Nucleus discovered by the Rutherford scattering experiment
1932        Neutron discovered
1933        Nuclear fission chain reaction envisioned by Szilard
1934        Fermi bombards uranium with neutrons and creates Plutonium
1938 Dec19  Hahn and Strassmann discover uranium fission
1939 Jan 6  Hahn and Strassmann publish uranium fission
1939 Jan25  Fermi begins conducting nuclear fission experiments at Columbia University
1939 Jan26  Bohr and Fermi report on uranium fission at the Washington Conference
            on theoretical physics
1939 Jul 4  Szilard, Wigner, and Einstein discuss nuclear fission
1939 Aug 2  Szilard, Teller, and Einstein discuss nuclear fission. Szilard drafts
            the the "Einstein letter" that is later delivered to President Roosevelt
1939 Oct11  Alexander Sachs briefs President Roosevelt on Einstein's letter.
1939 Oct12  Alexander Sachs meets again with President Roosevelt and this time
            Roosevelt gives the order to commence the development of a nuclear bomb.
1942 Dec 2  Fermi and Szilard achieve the first self-sustaining nuclear fission
            reactor at the University of Chicago
1942 Aug    Manhattan project commences
1942-1945   German nuclear bomb project goes nowhere
1945 Jul16  Trinity test of a plutonium bomb yields a 20 kTon TNT equivalent explosion
1945 Aug 6  A uranium bomb is deployed at Hiroshima, yielding 15 kTons TNT equivalent
1945 Aug 9  A plutonium bomb is deployed at Nagasaki, yielding 21 kTons TNT equivalent
Hans Bethe, a physicist on the Manhattan Project, was asked why the uranium type bomb was not tested before deployment and he replied "Because we were perfectly sure it would work".
World War 2

Trinity plutonium test
Trinity plutonium test
Little Boy
Little Boy
Hiroshima

The Enola Gay, the bomber that deployed "Little Boy"
Fat Man
Nagasaki


Nuclear fission products
               Parts    Halflife     Decay    Neutron   Result of      Halflife
                per     (thousand    energy   absorb    neutron        (thousand
              thousand  years)       (MeV)    (barns)   absorption     years)

Caesium-135     69      1500          .27       8.3     Barium-136     Stable
Caesium-137     63          .030    1.2          .11    Barium-138     Stable
Technetium-99   61       210         .29       20       Ruthenium-100  Stable
Zirconium-93    55      1500          .091      2.7     Niobium-94     20.3
Strontium-90    45          .029    2.8          .90    Zirconium-91   Stable
Palladium-107   12.5    6500          .033      1.8     Silver-108     .418
Iodine-129       8.4   15700          .194     18       Xenon-130      ?
Samarium-151     5.3        .097     .077   15200       Europium-152   .0135
Krypton-85       2.2        .011     .69        1.7
Tin-126          1.1     230        4.0        < .1
Selenium-79       .447   330         .15       < .1
Europium-155      .80       .0048    .25     3950
Cadmium-113       .008      .014     .32    20600
Tin-121           .0005     .044     .39        ?
"Neutron absorption" is the cross section for a nucleus to capture a thermal neutron.

All of the radioactive fission products decay by beta decay.

If the neutron cross section is 8 barnes or higher then the nucleus can potentially be transmuted into a nonradioactive nucleus.

Strontium-90 is ideal for Radioisotope Thermoelectric Generators (RTGs). www.jaymaron.com/rockets/rockets.html

The most troublesome fission products are the ones that can't be transmuted. Chief among these are Caesium-137, Zirconium-93, Niobium-94, Strontium-90, Zirconium-91, and Palladium-107.


Nuclear fusion

Fusion power

Deuterium + Tritium fusion

The easiest fusion reaction to achieve is

Deuterium  +  Tritium  →  Helium  +  Neutron
The optimal temperature is 500 million Kelvin and other fusion reactions require higher temperatures. This temperature can be achieved either with a tokamak, which confines a hot plasma with magnetic fields, or with "inertial confinement", which heats the material through compression. The fuel density should be as high as possible to produce a satisfactory fusion rate.
Plasma tokamak fusion

Madison Symmetric Torus
ITER participants
Joint European Torus

A tokamak uses magnetic fields to steer hot plasma around a donut-shaped vessel. The International Thermonuclear Experimental Reactor (ITER) in France is scheduled to begin operation in 2018. It will be the first tokamak that produces more fusion power than is required to operate the machine. There are numerous international participants and the experiment is as important for its superconducting magnet technology as it is for fusion. For the ITER reactor,

Fusion power     =  500 MWatt
Input power      =   50 MWatt
Temperature      =  500 MKelvin
Confinement time = 3000 seconds
Plasma current   =   17 MAmps
Magnetic field   =  5.3 Tesla
Inner radius     =  2.0 meter
Outer radius     =  6.0 meter
The "Lithium Tokamak Experiment" at the Princeton Plasma Physics Laboratory uses flowing liquid lithium walls to absorb hydrogen that escapes the plasma. This improves the plasma confinement and is potentially a means for absorbing the heat generated by fusion neutrons.
Inertial confinement fusion

1: Lasers strike target.     2: Outer shell blasted off.     3: Recoil compresses fuel     4: Fusion ignites
Lasers

National Ignition Facility

In inertial confinement fusion, lasers are fired upon a spherical target from all directions, causing the outer layer to explode and deliver a compressive impulse to the fusion fuel inside the target. It is important that the compression be spherically-symmetric to achieve high compression density. For this reason a large number of lasers are used.

After the fuel has been compressed it can be further heated by a second laser pulse, which is the goal of the "HiPer" experiment.

                            Electric   Laser    Fusion   Target
                             energy    energy   energy   density
                               MJ        MJ       MJ      g/cm3

National Ignition Facility    330       1.85      20      1000
HiPer                         422        .27      25       300


Electric energy        Energy supplied to the system
Laser energy           Laser energy delivered to the target
Fusion energy          Energy produced by fusion of the traget
Target density         Density of the target after laser compression

Neutron damage

The fusion of deuterium and tritium produces neutrons with an energy of 14.1 MeV. These neutrons dislodge atoms in materials, weaking the material.

In the following sequence of frames a 30 keV Xenon ion crashes into gold, disrupting the positions of atoms.

Liquid lithium wallls are being considered for stopping the neutrons. Lithium also absorbes hydrogen that escapes the plasma and improves the plasma confinement properties.

Lithium Tokamak Experiment
International Fusion Materials Irradiation Facility


Fusion without neutrons

The fusion reactions that don't produce neutrons are

                                 Energy  Coulomb
                                 yield   energy
                                 (MeV)

P   + P    ->  D   + Positron     .42      1   Slow because it requires the weak force
P   + D    ->  He3 + Photon      5.49      1   Slow because it requires the electromagnetic force
D   + He3  ->  He4 + P          18.353     2   D+D side reactions produce neutrons
P   + Li6  ->  He4 + He3         4.0       3
P   + Li7  ->  He4 + He4        17.2       3
D   + Li6  ->  He4 + He4        22.4       3   D+D side reactions produce neutrons
He3 + He3  ->  He4 + P   + P    12.860     4   He3 is rare
P   + B11  ->  He4 + He4 + He4   8.7       5
He3 + Li6  ->  He4 + He4 + P    16.9       6
P   + N15  ->  C12 + He4         5.0       7
"Coulomb energy" is the product of the charges of the two reactants, in units of proton charge. The lower the energy, the easier it is to fuse the nuclei. This can be seen with the Rutherford scattering simulation.

Helium-3 is rare on the Earth and abundant on the moon.


Astrophysical plasmas
n       =  Electron density
M       =  Electron mass
V       =  Electron thermal velocity
Q       =  Proton charge
k       =  Boltzmann constant
Τ       =  Temperature
T       =  Confinement time
I       =  Plasma current
B       =  Magnetic field in Teslas
Xdebye  =  Debye length                   (k Τ/n/Q2/(4 π Ke))½
Xgyro   =  Electron gyro radius           M V / Q B
Fgyro   =  Electron gyrofrequency


              Electron  Temp  Debye  Magnetic
              density   (K)    (m)   field (T)
               (m-3)
Solar core       e32     e7    e-11   -
ITER          1.0e20     e8    e-4    5.3
Laser fusion  6.0e32     e8           -   National Ignition Facility. Density=1000 g/cm3
Gas discharge    e16     e4    e-4    -
Ionosphere       e12     e3    e-3   e-5
Magnetosphere    e7      e7    e2    e-8
Solar wind       e6      e5    e1    e-9
Interstellar     e5      e4    e1    e-10
Intergalactic    e0      e6    e5     -

Rocket fusion

A rocket ideally produces as much energy per mass as possible, which is reflected in the fusion "energy per nucleon". The reactions that have the best energy per nucleon are

                               Energy   Energy per
                               yield    nucleon
                               (MeV)    (MeV)

D   + He3  ->  He4 + P         18.353    3.67
D   + T    ->  He4 + N         17.590    3.52
D   + Li6  ->  He4 + He4       22.4      2.80
T   + He3  ->  He4 + D         14.320    2.39   41%
P   + Li7  ->  He4 + He4       17.2      2.15
He3 + He3  ->  He4 + P   + P   12.860    2.14
T   + He3  ->  He4 + P   + N   12.096    2.02   59%
The best choice is D + He3 and the next best choice is D + T.
Index of fusion reactions
                                     Energy   Energy per
                                     yield    nucleon
                                     (MeV)    (MeV)
P    + P    ->  D    +  Positron     .42      .21
P    + D    ->  He3  +  Photon      5.49     1.83
P    + T    ->  He3  +  N           -.764
P    + Li6  ->  He4  +  He3         4.0       .57
P    + Li7  ->  He4  +  He4        17.2      2.15
P    + B11  ->  He4  +  He4  + He4  8.7       .72


D    + D    ->  T    +  P           4.033    1.01   50%
            ->  He3  +  N           3.269     .81   50%
D    + T    ->  He4  +  N          17.590    3.52
D    + He3  ->  He4  +  P          18.353    3.67
D    + Li6  ->  He4  +  He4        22.4      2.80
T    + T    ->  He4  +  N   +  N   11.332    1.89
T    + He3  ->  He4  +  P   +  N   12.096    2.02   59%
            ->  He4  +  D          14.320    2.39   41%
He3  + He3  ->  He4  +  P   +  P   12.860    2.14
He3  + Li6  ->  He4  +  He4 +  P   16.9      1.88
N    + Li6  ->  T    +  He4         4.784     .68
N    + Li7  ->  T    +  He4 +  N   -2.467


           Mass of nucleus  Mass of atom   Half life     Binding energy
                (AMU)         (AMU)                      per nucleon (MeV)
Electron      .00054858
Neutron      1.00866492                    886 seconds     0
Proton       1.00727647                                    0
Hydrogen     1.00727647     1.00782504                     0
Deuterium    2.01355321     2.01410178                     1.11226
Tritium      3.01550071     3.01604928     12.3 years      2.82727
Helium-3     3.01493173     3.0160293                      2.57269
Helium-4     4.00150485     4.002602                       7.07392
Lithium-6    6.01347537     6.01512280                     5.33257
Lithium-7    7.01435712     7.01600455                     5.60637
Beryllium-8                                7*10^17 s       7.06244
Beryllium-9                                                6.46278
Boron-10                                                   6.47508
Boron-11                                                   6.92771
Carbon-12                                                  7.68015
Carbon-13                                                  7.46986
Carbon-14                                  5730 years      7.52033
Oxygen-16                                                  7.97622
Oxygen-17                                                  7.75075
Oxygen-18                                                  7.76707
Iron-56                                                    8.79
Uranium-235                                                7.59
Uranium-238                                                7.57

1 MeV = 106 eV  = 1.602*10-13 Joules
If no half-life is given, the nucleus is stable
1 atomic mass unit (AMU)  =  1.660538921*10-27 kg  =  931.494061 MeV

Tokamaks
       Fusion  Input  Temp  Confine  Current  Magnetic  Inner  Outer  Year
       power   power         time              field    radius radius
       MWatt   MWatt   MK     s       MAmp     Tesla      m      m

ITER    500     50           3000    17        5.3*   2.0     6.2   2018  France
JET      16.1   38                    6        4       .96    2.96  1992  UK
JT-60                         100     5.5      2.7*   1.02    3.16  2019  Japan
TFTR     10.7         510             3        6       .8     2.4   1982  Princeton
D III-D                               3        2.2     .67    1.66  1986  San Diego
KSTAR                         300     2        3.5*    .5     1.8   2008  Korea
HL-2M                                 2.5      2.2     .65    1.78     ?  China
Alcator                               2        8       .22     .67  1993  MIT
Tore Supra                    390     2        4.5*    .7     2.25  1988  France
FTU                             1.5   1.6      8       .3      .93  1990  Italy
ASDEX                          10     1.4      3.9     .8     1.65  1991  Germany
TCV                                   1.2      1.4     .7      .88  1992  Switz.

A "*" denotes superconducting magnets.

Neutron-resistant materials
            Cross section (barns)

Magnesium     .059
Lead          .17
Zirconium     .18
Aluminum      .23
Iron         2.56
Stainless    3.1
Nickel       4.5
Titanium     6.1
Cadmium   2520

Critical mass

A fission chain reaction requires that the material produces on average more than one neutron upon fission. The materials that qualify are:

       Nucleons  Critical  Critical  Fission  Neutrons   Decay    Fission   Fission
                   mass    diameter   area    /fission  halflife  halflife   rate
                    kg        cm      barns              Myear     Tyear    F/s/kg

Californium  252     2.73     6.9     2.32     3.73     .0000026
Californium  251     5        8.5     2.43              .000290                     -
Californium  249     6        9       1.74              .000351
Neptunium    236     6.79     8.7                       .154         Inf           0
Curium       247     7.0      9.9                     15.6
Curium       243     8       10.5                       .000029
Plutonium    238     9.5      9.7     1.99              .000088              1204000
Plutonium    239    10        9.9     1.80     2.16     .024        5500          10.1
Curium       245    10       11.5                       .0085
Americium    242    11       12                         .000141
Plutonium    241    12       10.5     1.65              .000014                    <.8
Uranium      233    15       11       1.95     2.48     .159                        -
Plutonium    240    40       15       1.36     2.21     .0066           .116  478000
Uranium      235    52       17       1.24     1.86  704          350000            .0056
Neptunium    237    60       18       1.34             2.14                        <.05
Americium    241    83.5              1.38              .00043                   500
Plutonium    242    95                1.13                                    805000
Protactinium 231  >188                 .83                                        <5
Uranium      238   Inf      Inf        .31     2.07 4470            8400           5.51
Curium       250   Inf      Inf                3.31     .0069
Thorium      232   Inf                 .08                                        <.00005
Uranium      232    >5                2.01                                          .002
Uranium      234   >41                1.22                                         3.9
Uranium      236  >167                 .59                                         2.30
Protactinium 233                       .46
Americium    243                      1.10

Fission area  =  Fission cross section in barns (10-28 meters2)
Californium-252    Californium-249    Data    Data
History of nuclear devices
           Fission Fusion

U.S.A.       1945  1954
Germany                  Attempted fission in 1944 & failed
Russia       1949  1953
Britain      1952  1957
France       1960  1968
China        1964  1967
India        1974        Uranium
Israel       1979     ?  Undeclared. Has both fission and fusion weapons
South Africa 1980        Dismantled in 1991
Iran         1981        Osirak reactor to create Plutonium. Reactor destroyed by Israel
Pakistan     1990        Centrifuge enrichment of Uranium. Tested in 1998
                         Built centrifuges from stolen designs
Iraq         1993        Magnetic enrichment of Uranium. Dismantled after Gulf War 1
Iraq         2003        Alleged by the United States. Proved to be untrue.
North Korea  2006        Created plutonium in a nuclear reactor. Detonation test fizzled
                         Also acquired centrifuges from Pakistan
                         Also attempting to purify Uranium with centrifuges
Syria        2007        Nuclear reactor destroyed by Israel
Iran         2009        Attempting centrifuge enrichment of Uranium.
Libya         --         Attempted centrifuge enrichment of Uranium. Dismantled before
                         completion. Cooperated in the investigation that identified
                         Pakistan as the proliferator of Centrifuge designs.
North Korea  2009        Plutonium fission
Libya        2010        Squabbling over nuclear material
Libya        2011        Civil war

Nuclear tests

Redwing Mohawk
Castle Romeo
Operation Upshot Knothole

Crossroads Baker
Crossroads Baker

2400 ton TNT conventional explosive test


Nuclear devices

W87
W83
B41

B61

          Yield   Mass  Mton/  Fission    #   Start  End     Platform
          Mton     kg    kg    primary  built

B41         25     4850  5.15           500   1961   1976    B-52, B-47  Succeeded by the B53
B53          8.9   4010  2.22           340   1962   1997    Titan II    Bunker buster
W56          1.2    272  4.96          1963   1993           Minuteman
B83          1.2   1100  1.09           650   1983  Current  Bomber
W88           .48  <360  1.33  Komodo               Current  Trident
W87           .48  ~235  2.04                 1986  Current  Minuteman
W78           .35  ~340  1.03                 1979  Current  Minuteman
B61           .34   320  1.06    B61   3155   1968  Current  Bomber      Bunker buster. Tunable to .3 kilotons
W80           .15   130  1.15    B61   2117   1984  Current  Tomahawk    Tunable to 5 kiloton
W84           .15   176   .85    B61    530   1983  Current  Tomahawk    Tunable to .2 kilotons
W76           .10   164   .61         >2000   1978  Current  Trident
Tzar Bomba  50    27000  1.85             1   1961  1961
The B41 and Tzar Bomba are three-stage devices (fission-fusion-fusion).
Data
Nuclear fission primaries

W-88
W-87

Fission     Fusion
primary     secondaries

RACER IV    Mark 14, Mark 16, Mark 17
Python      B28, W28, W40, W49
Boa         W30, W52
Robin       W38, W45, W47
Tsetse      W43, W44, W50, B57, W59
Kinglet     W55, W58
B61         B61, W69, W73, W80, W81, W84, W85, W86

Stockpiles
           #

USA      7260    Fusion
Russia   7500    Fusion
France    300    Fusion
China     260    Fusion
UK        215    Fusion
Pakistan  120    Uranium fission.  >1500 kg of uranium-235, 20 kg uranium per bomb
India     110    Plutonium fission
Israel     80    Fusion
N. Korea   20    Plutonium fission

North Korea

North Korea has enough plutonium for an estimated 20 fission bombs.

2006 plutonium test       =  .001 Mtons
2009 plutonium test       =  .005 Mtons
2013 plutonium test       =  .010 Mtons
2016 plutonium test Jan 6 =  .010 Mtons
2016 plutonium test Sep 6 =  .010 Mtons

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