The Use And History Of The "Shake" Unit

Shake:

An informal unit of time equal to 10^-8 seconds or 10 nanoseconds (ns). This unit originated in nuclear physics. In an atomic explosion, fast-moving neutrons break apart atoms of uranium or plutonium; the fission of these atoms releases additional neutrons which keep the reaction going. The shake is the approximate lifetime of an individual neutron. The word shake and the expression "shake of a lamb's tail" have long been used in English to mean a very brief period of time.

The amount of time taken by each link in the chain reaction is determined by the speed of the neutrons and the distance they travel before being captured. The average distance is called the mean free path. In fissile materials at maximum normal densities the mean free path for fission is roughly 13 cm for 1 MeV neutrons (a typical energy for fission neutrons). These neutrons travel at 1.4x10^9 cm/sec, yielding an average time between fission generations of about 10^-8 sec (10 nanoseconds), a unit of time sometimes called a "shake". The mean free path for scattering is only 2.5 cm, so on average a neutron will be scattered 5 times before causing fission.

10 nanoseconds = one shake, approximate time of one generation of a nuclear chain reaction with fast neutrons

The Use And History Of The "Barn" Unit

From Wikipedia
http://en.wikipedia.org/wiki/Barn_(unit)

Barn (unit)

A barn (symbol b) is a unit of area. While the barn is not an SI unit, it is accepted (although discouraged) for use with the SI. It is used in nuclear physics for expressing the cross sectional area of nuclei and nuclear reactions. A barn is approximately equal to the area of a uranium nucleus.

Definition
1 barn (b) = 10−28 square meters (m²)

Commonly used prefixed versions
The picobarn (pb) = 10−40 m² is frequently used.

Origin
The etymology is clearly whimsical - the unit is said to be "as big as a barn" compared to the typical cross sections for nuclear reactions. It may have been thought as beneficial to use the term to obscure discussions of weapons research during World War 2.

--------------------

The concept of cross section is the crucial key that opens the communication
between the real world of experiment and the abstract, idealized world of
theoretical models. In a high- energy physics experiment, we specify
interactions of elementary particles quantitatively in terms of cross sections.
The cross section is the probability that an interaction will occur between a
projectile particle-say, a proton that has been accelerated in the Tevatron-and
a target particle, which could be an antiproton, or perhaps a proton or neutron
in a piece of metal foil.

We can measure the probability that two
particles will interact in experiments. We can also calculate this quantity in a
model that incorporates our understanding of the forces acting on a subatomic
level. In the famous experiment in which Rutherford studied the scattering of
alpha particles off a foil target, the cross section gives the probability that
the alpha particle is deflected from its path straight through the target. The
cross section for large-angle scattering is the fraction of alpha particles that
bounce back from the target, divided by the density of nuclei in the target and
the target thickness. The comparison of the measured cross section with the
calculated one verified the model of the atom with a minute, massive center,
carrying an electrical charge.

We can picture the cross section as the
effective area that a target presents to the projected particle. If an
interaction is highly probable, it's as if the target particle is large compared
to the whole target area, while if the interaction is very rare, it's as if the
target is small. The cross section for an interaction to occur does not
necessarily depend on the geometric area of a particle. It's possible for two
particles to have the same geometric area (sometimes known as geometric cross
section) and yet have very different interaction cross section or probability
for interacting with a projectile particle.

During wartime research on
the atomic bomb, American physicists who were bouncing neutrons off uranium
nuclei described the uranium nucleus as "big as a barn." Physicists working on
the project adopted the name barn for a unit equal to 10-24 square centimeters,
about the size of a uranium nucleus. Initially they hoped the American slang
name would obscure any reference to the study of nuclear structure; eventually,
the word became a standard unit in particle physics.

Today, although
experimental techniques and theoretical calculations have considerably increased
in complexity compared to the early days of scattering experiments, the concept
which links theory and experiment has not changed. In the Tevatron, for
instance, we measure the probability of producing a pair of top quarks in a
proton-antiproton collision. We measure this production cross section by
counting the number of top quark events observed in the detector and by knowing
the time-integrated luminosity, the product of the number of particles per unit
time in the proton and antiproton beam, per area of the beam. By comparing the
top quark production cross section with predictions, which are based on a model
of elementary particles and their interactions, we probe our understanding of
the strongest known force between elementary particles.

Next time, I will get more data on the definition of the "Shake"

Tom Clancy's Three Shakes And Future Topics

Concepts that I am interested in understanding in more detail are that of the unit "barn" and a time quantity known as a shake.

Here is the most incredible chapter in the novel by Tom Clancy called "The Sum of All Fears". The entire chapter details the process that takes place in just 4.4 nanoseconds. Here is the chapter:

THREE SHAKES

The timer just outside the bomb case reached 5:00:00,
and things began to happen.

First, high-voltage capacitors began to
charge, and small pyrotechnics adjacent to the tritium reservoirs at both ends
of the bomb fired. These drove pistons, forcing the tritium down narrow metal
tubes. One tube led into the Primary, the other into the Secondary. There was no
hurry here, and the objective was to mix the various collections of
lithium-deuteride with the fusion-friendly tritium atoms. Elapsed time was ten
seconds.

At 5:00:10, the timer sent out a second
signal.

Time Zero.

The capacitors discharged, sending
an impulse down a wire into a divider network. The length of the first wire was
50 centimeters. This took one and two-thirds nanoseconds. The impulse entered a
dividing network using krytron switches; each of them a small and exceedingly
fast device using selfionized and radioactive krypton gas to time its discharges
with remarkable precision. Using pulse-compression to build their amperage, the
dividing network split the impulse into seventy different wires, each of which
was exactly one meter in length. The relayed impulses required three-tenths of a
shake (three nanoseconds) to transit this distance. The wires all had to be of
the same length, of course, because all of the seventy explosive blocks were
supposed to detonate at the same instant. With the krytrons and the simple
expedient of cutting each wire to the same length, this was easy to
achieve.

The impulses reached the detonators simultaneously. Each
explosive block had three separate detonators, and none of them failed to
function. The detonators were small wire filaments, sufficiently thin that the
arriving current exploded each. The impulse was transferred into the explosive
blocks, and the physical detonation process began 4.4 nanoseconds after the
signal was transmitted by the timer. The result was not an explosion, but an
implosion, since the explosive force was mainly focused inward.

The
high-explosives blocks were actually very sophisticated laminates of two
materials, each laced with dust from light and heavy metals. The outer layer in
each case was a relatively slow explosive with a detonation speed of just over
seven thousand meters per second. The explosive wave in each expanded radially
from the detonator, quickly reaching the edge of the block. Since the blocks
were detonated from the outside-in, the blast front traveled inward through the
blocks. The border between the slow and fast explosives contained bubbles;
called voids; which began to change the shockwave from spherical-shaped to a
planar, or flat wave, which was focused again to match exactly its metallic
target, called "drivers."

The "driver" in each case was a piece of
carefully shaped tungsten-rhenium. These were hit by a force wave traveling at
more than nine thousand eight hundred meters (six miles) per second. Inside the
tungsten-rhenium was a one-centimeter layer of beryllium. Beyond that was a
one-millimeter thickness of uranium 235, which though thin weighed almost as
much as the far thicker beryllium. The entire metallic mass was driving across a
vacuum, and since the explosion was focused on a central point, the actual
closing speed of opposite segments of the bomb was 18,600 meters (or 11.5 miles)
per second.

The central aiming point of the explosives and the
metallic projectiles was a ten-kilogram (22-pounds) mass of radioactive
plutonium 239. It was shaped like a glass tumbler whose top had been bent
outwards and down toward the bottom, creating two parallel walls of metal.
Ordinarily denser than lead, the plutonium was compressed further by the
million-atmospheres pressure of the implosion. This had to be done very quickly.
The plutonium 239 mass also included a small but troublesome quantity of
plutonium 240, which was even less stable and prone to pre-ignition. The outer
and inner surfaces were slammed together and driven in turn toward the geometric
center of the weapon.

The final external act came from a device
called a "zipper." Operating off the third signal from the still-intact
electronic timer, the zipper was a miniature particle accelerator, a very
compact minicyclotron that looked remarkably like a handheld hair-dryer. This
fired deuterium atoms at a beryllium target. Neutrons traveling ten percent of
the speed of light were generated in vast numbers and traveled down a metal tube
into the center of the Primary, called the Pit. The neutrons were timed to
arrive just as the plutonium reached half of its peak density. Ordinarily a
material weighing roughly twice an equivalent mass of lead, the plutonium was
already ten times denser than that and still accelerating inward. The
bombardment of neutrons entered a mass of still-compressing
plutonium.

Fission.

The plutonium atom has an atomic
weight of 239, that being the combined number of neutrons and protons in the
atomic nucleus. What began happened at literally millions of places at once, but
each event was precisely the same. An invading "slow" neutron passed close
enough to a plutonium nucleus to fall under the Strong Nuclear Force that holds
atomic nuclei together. The neutron was pulled into the atom's center, changing
the energy state of the host nucleus and kicking it into an unstable state. The
once symmetrical atomic nucleus began gyrating wildly and was torn apart by
force fluctuations. In most cases a neutron or proton disappeared entirely,
converted to energy in homage to Einstein's law E = MC2. The energy that
resulted from the disappearance of the particles was released in the form of
gamma- and X-radiation, or any of thirty or so other but less important routes.
Finally, the atomic nucleus released two or three additional neutrons. This was
the important part. The process that had required only one neutron to start
released two or three more, each traveling at over ten percent of the speed of
light; 20,000 miles per second; through space occupied by a plutonium mass two
hundred times the density of water. The majority of the newly liberated atomic
particles found targets to hit.

A chain reaction merely means that
the process builds on itself, that the energy released is sufficient to continue
the process without outside assistance. The fission of the plutonium proceeded
in steps called "doublings." The energy liberated by each step was double that
of the preceding one, and that of each subsequent step was doubled again. What
began as a trivial amount of energy and just a handful of freed particles
doubled and redoubled, and the interval between steps was measured in fractions
of nanoseconds. The rate of increase; that is, the acceleration of the chain
reaction; is called the "Alpha," and is the most important variable in the
fission process. An Alpha of 1,000 means that the number of doublings per
microsecond is a vast number, 2'°°°; the number 2 multiplied by itself one
thousand times. At peak fission; between 250 and 253; the bomb would be
generating 10 billion billion watts of power, one hundred thousand times the
electrical-generating capacity of the entire world. Fromm had designed the bomb
to do just that; and that was only ten percent of the weapon's total designed
output. The Secondary had yet to be affected. No part of it had yet been touched
by the forces only a few inches away.

But the fission process had
scarcely begun.

Some of the gamma rays, traveling at the speed of
light, were outside the bombcase while the plutonium was still being compressed
by the explosives. Even nuclear reactions take time. Other gamma rays started to
impact on the Secondary. The majority of the gammas streaked through a gas cloud
that only a few microseconds earlier had been the chemical explosive blocks,
heating it far beyond the temperatures chemicals alone could achieve. Made up of
very light atoms like carbon and oxygen, this cloud emitted a vast quantity of
low-frequency "soft" X-rays. To this point, the device was functioning exactly
as Fromm and Ghosn had planned.

The fission process was seven
nanoseconds 0.7 shakes; old when something went wrong.

Radiation
from the fissioning plutonium blazed in on the tritium-impregnated
lithium-deuteride that occupied the geometric center of the Pit. The reason
Manfred Fromm had left the tritium extraction to last lay in his basic
engineer's conservatism. Tritium is an unstable gas, with a half-life of 12.3
years, meaning that a quantity of pure tritium will, after that time, be
composed half of tritium and half of 3He. Called "heliumthree," 3He is a form of
that second-lightest of elements whose nucleus lacks an extra neutron, and
craves another. By filtering the gas through a thin block of palladium, the 3He
would have been easily separated out, but Ghosn hadn't known about that. As a
result, more than a fifth of the tritium was the wrong material. It could hardly
have been a worse material.

The intense bombardment from the
adjacent fission reaction seared the lithium compound. Normally a material half
the density of salt, it was compressed to a metallic state that exceeded the
density of earth's core. What began was actually a fusion reaction, though a
small one, releasing huge quantities of new neutrons, and also changing many of
the lithium atoms into more tritium, which broke down; "fused"; under the
intense pressure to release yet more neutrons. The additional neutrons generated
were supposed to invade the plutonium mass, boosting the alpha and causing at
least a doubling of the weapon's unboosted fission yield. This had been the
first method of increasing the power of the second-generation nuclear weapons.
But the presence of 3He poisoned the reaction trapping nearly a quarter of the
high-energy neutrons in uselessly stable helium atoms.

For several
more nanoseconds, this did not matter. The plutonium was still increasing its
reaction rate, still doubling, still increasing its Alpha at a rate only
expressable numerically.

Energy was now flooding into the
Secondary. The metallically coated straws flashed to plasma, pressing inward on
the Secondary. Radiant energy in quantities not found on the surface of the sun
vaporized but also reflected off elliptical surfaces, delivering yet more energy
to the Secondary assembly, called the Holraum. The plasma from the immolated
straws pounded inward toward the second reservoir of lithium compounds. The
dense uranium 238 fins just outside the Secondary pit also flashed to dense
plasma, driving inward through the vacuum, then striking and compressing the
tubular containment of more 238U around the central container which held the
largest quantity of lithium-deuteride/tritium. The forces were immense, and the
structure was pounded with a degree of pressure greater than that of a healthy
stellar core.

But not enough.

The Primary's reaction
had already slackened. Starved of neutrons by the presence of the 3He poison,
the bomb's explosive force began to blow apart the reaction mass as soon as the
physical forces reached their balance. The chain reaction reached a moment of
stability, at last unable to sustain its geometric rate of growth; the last two
chain-reaction doublings were lost entirely, and what should have been a total
Primary yield of seventy thousand tons of TNT was halved, halved again, and in
fact ended with a total yield of eleven thousand two hundred tons of high
explosive.

Fromm's design had been as perfect as the circumstances
and materials allowed. An equivalent weapon less than a quarter the size was
possible, but his specifications were more than adequate. A massive safety
factor in the energy budget had been planned for. Even a thirty-kiloton yield
would have been enough to ignite the "spark plug" in the Secondary to start a
massive fusion "burn," but thirty-KT was not reached. The bomb was technically
called a "fizzle."

But it was a fizzle equivalent to eleven
thousand two hundred tons of TN1. That could be represented by a cube of high
explosives seventy-five feet high, seventy-five feet long, and seventy-five feet
thick, as much as could be carried by nearly four hundred trucks, or one
medium-sized ship; but conventional explosives could never have detonated with
anything approaching this deadly efficiency; in fact, a conventional explosion
of this magnitude is a practical impossibility. For all that, it was still a
fizzle.

As yet no perceptible physical effects had even left the
bombcase, much less the truck. The steel case remained largely intact, though
that would rapidly change. Gamma radiation had already escaped, along with
X-rays, but these were invisible. Visible light had not yet emerged from the
plasma cloud that had only three "shakes" before been over a thousand pounds of
exquisitely designed hardware . . . and yet, everything that was to happen had
already taken place. All that remained now was the distribution of the energy
already released by natural laws which neither knew nor cared about the purposes
of their manipulators.

I will post more on my two topics I spoke of at the begining. If anyone has any insight or info please post some comments.

Why This Blog

I have always had some fascination in how atomic weapons worked. I have a degree in physics and found that the actual application of nuclear understanding very exciting, almost as a confirmation of the accuracy of our understanding of the universe. I have a very basic knowledge of the concepts involved with nuclear weapons, and wanted a place to note the basics and grow my understanding.

Since the material I am posting is from publicly available books and websites, this should not pose any type of risk of disclosing any dangerous information. Again, I only enjoy the discussion of the concepts and ideas, of how these devices work.