Albert's Series: Basic stuff, but serious.
I. Short and simple Math notes:
A few words on Nuclear weapons.Date: 22/06/2017
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1. Quick overview on "generations" of Nuclear weapons.This is a small note on the various architectures, as well as current implementations on various carriers
(like ICBM's, or for example the small B61 tactical weapon etc..), as in use by nuclear capable nations.
Let me immediately make clear that I do not want nuclear weapons at all. They must go away, and all research,
which I personally believe is ongoing and very extensive, should be stopped.
Warning: About that research: not all folks (scientists, politicians, military) might share such a view.
Furthermore, I think we are approaching (or are already in) a rather dangerous time, and even management/control
of those weapons, seem to slip away. You may believe that, or maybe you don't. But you might agree, that the leaders
of the Superpowers (USA, Russia, China) are not exactly Einsteins.
Also, some other countries are almost desperately climbing the nuclear ladder (like, e.g., India).
Some have not even signed any treaty.
1.1 The 1st, the 2nd and 3rd generations.The 1st and 2nd generations.
Although some idea's on nuclear bombs already existed, early in the former century (e.g. H.G Wells, 1914),
it all became much more serious shortly before the start of WWII (around '39 of the former century).
As we all know, the first "pure fission" weapons (A-bomb) were developed in '44/'45, and two of them
were actually really dropped on two Japanese cities. Due to immense respect of the victims, I dare not say anything
about the "socalled" neccessity as to why they were really used, but it resulted in an absolute, complete total horror.
Then, in the early '50's. the first "thermonuclear" devices were tested.
In a way, you might call the thermonuclear device, a multi-stage weapon.
In the thermonuclear class, quite some variants exists, like e.g. the socalled "fusion-boosted fission" weapon,
and other morphologies. In this note, I collect them all together into one class
If we take a look at the "fusion-boosted fission" weapon, it's main principle is actually fission, but
lighter elements (like tritium) are embedded in the architecture, to produce neutrons, and thereby greatly enhancing
the efficiency of fission.
So, some folks would still characterize it as a fission weapon.
Multi-Staged thermonuclear weapons fits the thermonuclear class better, since the fusion role is certainly prominent.
However, today, a true "pure" fusion weapon does not exist yet. There is always (up to now) a first "fission component".
Some people call the devices above, the "first"- and "second" generation.
Today, the "thermonuclear" device (in all sorts and shapes) is the most abundant type of weapon.
They can be used in tactical situations (the accent here is "local regions"), or strategic deployments
(the accent here is on long distance, like in rather large ICBM rockets, or long range bombers).
The thermonuclear class has made "downsizing" possible, that is the physical dimensions, resulting in much
smaller devices, compared to the "pure fission" devices.
The 3rd generation.
In time, knowledge grew on how to utilize neutron absorbers and enhancers inside the device,
and refinenments in stages.
From the early '60's, up to the '70's, '80's, the "ERB" weapons were in development. ERB is short for
"Enhanced Radiation, Reduced Blast". Sometimes they are also called "ERW", or Enhanced Radiation Weapons.
A popular variant is the "neutron bomb", where indeed the primary weapon function is radiation,
accompanied with a lower "blast" (but there will always be a rather significant blast).
Some people call such devices (like the ERW weapons), nuclear weapons of the "third" generation.
In this same generation, other variants were present too, like one focused on Blast, and reduced radiation (RRR).
Also, in this same generation, some really strange (or rather insane) variants were proposed.
For example, the "Cobalt bomb", would use a thermonuclear device as it's core, and a very large quantity
of Cobalt surrounding it, producing (on detonation) a radioactive Cobalt isotope, that potentially
could cover (fall-out) on a whole continent, or even a large part of Earth (depending on the amount of Cobalt).
It's an absurt scenario, ofcourse, but I am sure that some "deep studies" were indeed performed.
1.2 The 4th generation.These are not a reality yet. However, science is rather unstoppable. Also, when sufficient funds are provided,
and/or facilities are provided, then this generation may come into existence.
Although a very clear definition of the 4th generation is still missing, it's obvious that it must
be different from all that we have seen above.
The fourth generation is arguably essentially about downsizing. There are multiple roads here.
Increadably, since "pure fusion" is often seen as the coming archetype for 4th generation,
then the true payload then, might be very small, maybe even "pellet" size.
However, the "driver" that makes fusion possible, might still have quite large dimensions.
Ofcourse, the above statement at this point, is still fully hypothetical.
Warning: Again a warning. Many physicists will tell you that "pure fusion" is still a long, long, road to go.
Yes, that might be true. I insert those "warnings" at various places, since I have noticed that my views
might not be in line with the current opinions of many scientists.
However, "pure fusion" is a holy grail. It will have great applications in civil live, but in the military too.
Unless treaties prohibit such thing, which is not the case presently.
You might think of the "Nuclear Non-Proliferation Treaty", but that does not cover a country's own domestic research.
So, what about those treaties then? As I will try to show a little later, current treaties seem to be a bit of
a dissapointment. However, I must say that opinions vary greatly.
Although the principles of "fission" and "fusion" have not been explained yet, usually, for a
"pure" fission device, one need a total amount of fissable material near (or more) the socalled critical mass.
However, many factors determine the needed amount of critical mass to ultimately obtain a chain reaction.
Some factors are tampers, neutron reflectors, or the construction of the bomb to withstand extremely high
pressure/temperature in the pre-phase before explosion, or indeed to use light elements that will produce
a "neutron shower" in order to help the chain reaction.
For "pure" fusion, such a requirement of critical mass is much less stringent.
However, to "start" fusion, an extreme temperature is needed.
One hurdle to solve here, is how to "trigger" the fusion process, without the need for fission.
Even if the appearance of "The 4th generation" is only remotely likely, I would say that the public
on a Global scale, should demand a full and immediate stop on further development of nuclear weapons.
As I see it, current treaties do not cover this at all.
Also, as I see it, the public interest seems to be extremely low (as contrary to the '70's and '80's).
In the next chapter, I like to say something more on the fundamental principles behind fission and fusion,
and architectures. In chapter 3, some real world examples of carriers and devices (per nation) will be shown.
If you like to see more on classifications and types of architectures, here is a nice Cornell (arxiv) article:
Fourth Generation Nuclear Weapons: Military effectiveness and collateral effects (arxiv)
If you like to see some thoughts on using nano-technology in 4th generation nuclear weapons, then you might like:
Nanotechnology and Fourth Generation Nuclear Weapons (cern.ch)
You might find the upper articles a bit coloured, so to speak, but I think they are still good for a reasonable "impression".
The search for fusion (for generating energy) was very hot in the '80's.
Enormous machines were build. Big money and effort was spend. However, the results remained
a bit dissapointing. Fusion worked, but not long enough, and the net gain was ultimately too low.
So, the fusion projects more or less collapsed.
Later, a new kick off was started, as an international project: ITER.
Still later, one article appeared, with some warnings on nuclear proliferation. The overall atmosphere of that article,
somehow fits in my note. You might take a look at that article here.
Again, some criticism is needed here too.
2. The basic principles of fission and fusion.
2.1 Some principles first....
"Chemical energy" versus "Nuclear energy".In just a few words...:
It's certainly not easy to describe chemical energy, or for that matter, describe nuclear energy.
Many factors play a role here.
For example, when studying molecules, one need to take into account many terms like
potential energies, vibrational and rotational energies etc..
However, I can focus on a few important components, thanks to the simple atom model of Rutherford / Bohr.
It can help to see why nuclear processes may yield more energy.
When considering just some "atom" of a certain element, we can describe the energy levels of the electrons,
(in the "outer shells"), and compare it to the binding energies of the protons/neutrons inside the nucleus.
Please realize that the simple atom model of Rutherford/Bohr is not fully consistent with Quantum Mechanics (QM),
or not even with classical theories. For example, "well-defined" positions of electrons are not consistent with QM.
However, the "shells" correspond nicely with an abstract representation of the discrete "energy levels",
which makes the model indeed rather usable.
Captured in "energy levels", some typical energies for an electron to change shells, or to get free, sits in the
order of tens of eV, or hundreds of eV, or thousends of eV etc...
This is an important component of "capturing" chemical energy.
Typical binding energies of protons/neutrons in the nucleus, sits in the ranges of many MeV (mega eV).
This is an important component of "capturing" nuclear energy.
This maybe a nice pointer that typical nuclear processes (per Atom), are much more "energetic" than
What we have seen above, is certainly not good enough. But for my purpose, it is sufficient.
The Atom number.The number of protons in the nucleus of an atom, is called the "atomic number". However, apart from Hydrogen (H), there
will always be a certain number of (neutral) neutrons as well. Since protons are charged positively, you might say that the
classical Electromagnetic force will immediately drive them apart. However, at short distances,
the strong nuclear force "rules".
Ofcourse, today physicists know of a deeper structure (quarks, gluons), but that does not play a role in this simple note.
So, a nucleus of a certain atom (or certain "element"), contains protons and neutrons. The number of neutrons may vary slightly,
resulting in socalled isotopes of that element.
For example, the element Cobald is often written as: 2759Co, meaning that the atom number is "27"
(which is the number of protons), while the total of protons and neutrons is "59" (the mass number).
So, in the upper example, the number of protons is 27, and the number of neutrons is (59-27).
As another example, one isotope of Uranium might we written as 92238U.
The "type" of atom (like Cobalt), is determined by the number of protons. Or stated in an equivalent way:
The atom number (number of protons) defines the sort of "element", like Hydrogen (H), Helium (He), Carbon (C), Iron (Fe) etc...
The total mass of the atom, is determined almost fully by the nucleus (protons+neutrons).
Radioactive decay (natural radioactivity).This subsection is not really neccessary (as I realize myself now), but I leave it anyway.
The advantage is that we get a quick intro in some nuclear "equations".
The "notations" used is in typical "Albert style", so, it really could be better and neater...
If you are new to this all, you better "google" on nuclear equations, and see how it is properly done.
There are several types of "spontaneous" radioactive processes, or you may also say "natural radioactivity".
(Not all are listed here (!))
Example: β decay.
It's possible that in a nucleus, a neutron "flips" into a proton, and thereby emitting a fast electron (e-),
and a "anti-neutrino" (-υ) as well.
It can actually happen with a "free" neutron too.
Ofcourse, "flips" is not an explanation. Particle physicists have a theory that fundamentally describes that process.
In this note, we do not have to go into depth, because it requires a discussion of the "weak" force, the W bosons, and quark types.
A reasonable explanation is this:
The strong force between nucleons (protons/neutrons) acts mostly and attrctively, between nearest neighbours.
At the same time the ElectroMagnetic coulomb repulsion, acts between all protons. So, that's a tendency
to drive them apart.
In such a sense, the presence of neutrons then acts as the glue which hold the particles in the nucleus together.
However, there is a limit to such usefullness of the number of neutrons.
Or in other words (semi-classical): The neutrons acts to screen the protons from each other, making the nucleus stable.
You might say that for effective screening there needs to be a little more neutrons than protons.
As said above, the socalled weak force is responsible for β decay.
However, the resulting proton (from the neutron) must be able to find a free quantum state (Pauli exclusion principle).
The higher the neutron/proton ratio, the more "chance", of having a free state for the "resulting" proton,
and the more chance on β decay.
In β decay, we have:
n -> p + e- + -υ
where "n" is the neutron, "p" is the proton, e- is the electron, and -υ- denotes the anti-neutrino.
If it happens in the nucleus of atom X (or atom of element X), we would have:
ZA X -> (Z+1)A Y + e- + -υ
Since a neutron was "changed" into a proton, we thus have an atom of element "Y".
Above is an example of β- decay (there also exists the β+ decay).
Thus in real example, we may have:
53131 I -> 54131 Xe + e- + -υ
Example: Alpha decay.
A relatively "unstable" nucleus, may even emit an α particle, which is essentially a He (Helium) nucleus (24He).
Or stated in other words: α particle decay is the phenomenon whereby an unstable nuclei goes into a stable state,
by emitting an α particle.
92238U -> 90234Th + 24He
Here, an Uranium isotope decays into Thorium, and an α particle is emitted.
Interestingly, a classical potential barrier would not allow that. However, Quantum Mechanical "tunneling"
through barriers, is possible. So, there exists a "means" to go from unstable to stable.
Alpha decay, is often followed by the emission of a high-energy γ photon, since the result nucleus, is often
still in an exited state.
2.2 A short description of Fission.Quite some isotopes of elements, are "unstable". Sometimes, an nucleus can "break up" into two (sometimes 3, 4)
roughly "equally heavy" elements, while also producing radiation, and/or particles of some kind, and energy.
This is often called "fission".
It is generally more often observed with isotopes with higher masses (the "A" number of ZA X).
Since those two parts are more stable than the original, it seems rather logical that energy gets released.
But there must be more than that.
In fact, a full (complete) explanation is not deviced yet, but very good "pointers" go around.
It's even not very obvious to cleary define "stable" and "unstable" elements.
For example, if about half of a certain amount of an isotope of an element, decays in 107 years,
then it is not so very stable, but also not so increadably unstable as well.
But for another isotope, it might be something like 5 years, then we may say that's quite unstable.
A detailed examination of decay requires isobaric spin, other quantum numbers, possibly shell theories, flavours etc..
That's not neccessary for us to do so.
Increadably, for my purpose, we can come away with a few pointers, and one is just the binding energy.
Binding Energy:In semi-classical language:
The mass of a nucleus is always less, than the sum of all of the individual masses of the protons and neutrons.
The mass difference corresponds to an energy E = Δmc2, which is ofcourse one of Einstein's
famous relations. This mass difference is also often called the mass defect.
When protons and neutrons comes close, and react together in making bonds, to form a nucleus, in that process energy is released,
which then (sort of) will "sit" in the "binding energy".
One can talk of the binding energy of an individual particle (proton/neutron), or consider the total binding energy.
As an example of such individual value, you might think of a number like 8 MeV.
In some articles, "binding energy" is characterize as negative energy, which *might* be a bit of an unfortunate term.
It's probably better to say, that if the "binding energy" increases, the particles are "deeper in the well",
thereby making their bonds stronger.
So, if an nucleus has a high binding energy, in general, it's more stable.
In the latter part of first halve of the former century (say 1935), nuclear physicist already did enormously much
experimental work, and many hypothesis were proposed. Gradually, great theories were deviced.
It's pretty useless to give here a fairly accurate equation of calculating the Binding Energy.
However, I think it's a great illustration. It's a formula from around that time (Weizsacker's formula).
It's from around 1935:
EB = av A - as A2/3 - ac Z2 / A1/3 - aA (A-Z)2/ A + δ(A,Z)
There are several terms, like an Area component, a Coulomb component etc..
The formula is partly theoretical (thus created by theory) and empirical (values from measurements).
Except for the very light elements, it works.
The figure below, shows the binding energy (per nucleon, that is, proton or neutron) along all elements.
Note that the figure rises very sharply, then has a maximum for in the "neighboorhoud" of Iron (Fe), and when
the massnumber increases, the slope is pointed downwards.
Ofcourse, pure Hydrogen (11H), only has one proton, so, the binding energy does not really apply here.
Then, for the next light elements, the slope is very steep.
Fig. 1: Average binding energy per nucleon, against the mass number (the elements)
Source: Wikimedia commons (free).
Fission of some specific heavy isotopes: