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12 janvier 2013
NON-EQUILIBRIUM WORLDS
Jean Pierre PETIT – Former research director – CNRS FR.
When the man of the street thinks about equilibrium of a system, he usually sees a ball
standing at bottom of a well, or something like.
The basics of thermodynamic equilibrium theory contain something more subtle: the dynamic
equilibrium. The simplest example is the air we breathe. Its molecules are shaken in every
direction, showing a mean thermal velocity of 400 m/s. At a tremendous rate, these
molecules collide, interact. These shocks change their speed. However, the physicist will
translate this into statistical stationary (the used word is “detailed balancing”). Imagine a
goblin who, at any time and any point of room can measure molecular speed in a certain
direction, modulo a slight angular uncertainty. At every time increment, our goblin counts V
and V + AV, algebraic value. Then he plots these values on a graph, and sees growing a nice
Gaussian curve, with a top mean value near 400 m/s. Then, the faster or slower are the
molecules, the smaller is their population.
He repeats this work, aiming his measuring device towards any space direction, and, surprise,
surprise, gets the same result. Molecules agitation in the room is isotropic. More, nothing can
disturb this dynamic equilibrium, if temperature remains constant, because gas temperature is
exactly the mean kinetic energy coming from this thermal agitation. The physicist will
describe this gas in thermodynamic equilibrium. This state is multifaceted: air molecules
have no spherical symmetry. Di-atomic molecules, oxygen or helium, are peanut shaped.
Those of carbonic gas or water vapor have other shapes. All those objects, when rotating, can
store energy as tiny flywheels. These molecules can also vibrate. Energy even-distribution
concept says energy must be distributed equally into all these various “modes”. During a
collision, some kinetic energy can be converted into vibrational or rotational energy of a
molecule. The reverse is also valid. Then all this is statistics and our goblin can count how
many molecules are in such and such state, have such kinetic energy, are in such vibrating
state. Back to our breathing air, this census leads to the stationary status. This medium is then
said to be in thermodynamic equilibrium, namely relaxed. Imagine a wizard having power to
stop those molecules, stays put their rotation or vibration moves, modifying them at will,
creating a new statistic law, deforming that beautiful Gaussian curve, even creating some
anisotropic event, where for example thermal speed in one direction is increased two fold
relative to transverse directions. After all, he would let the system evolve following further
collisions. How many of these should be necessary for the system to go back towards
thermodynamic equilibrium? Answer: very few. The mean free travel time of a molecule, in
between two collisions, gives an idea of relaxation time in a gas, of its return time towards
thermodynamic equilibrium.
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Does-it exist non-equilibrium media, where molecular statistic speeds go notably out of this
comfortable isotropy and beauty of these nice Gaussian curves?
Oh yes! And it’s even case majority in universe. A galaxy, this “universe-island”, comprised
of many hundreds billions stars, whose mass are more or less some, can be seen as a gaseous
medium, in which molecules should be… stars. In this precise case, one discovers a
disconcerting world where the mean time free travel of a star, before any encounter with
neighbor star, is ten thousand times age of universe. What do we mean by encounter? Should
it be a collision where the two stars heavily smashed? Not even! In the theoretical physics
domain we call kinetic theory of gases, we will consider collision when star trajectory is
noticeably modified while crossing neighbor star.
However, calculation proves these events are extremely rare, and our hundreds billions stars
system can be seen as usually no-colliding.
Since billions years, trajectory of our Sun is regular, quasi circular. If our Sun was self
conscious, providing he did not change pace due to encounters, he would ignore having
neighbors. He only senses the gravitational field as “smooth”. He walks along his pace like in
a basin, while not sensing any bump created by other stars. Immediately the corollary
surfaces: place our goblin, now an astronomer, in the vicinity of Sun in our Galaxy and ask
him to build a speed statistic of neighbor stars in any direction. Obvious fact comes now. The
medium, dynamically speaking, is strongly anisotropic. It does exist a direction where the
stars’ agitation speeds (called residual speed by astronomers, relative to the mean rotation
drive of the galaxy, quite circular and at 230 km/s near Sun) are practically two times more
than in any other transverse direction. In our breathing air, this was called spheroid speed
distribution – Now, this becomes ellipsoid speed distribution. So far, so good? How this does
affect our vision, our understanding of the world? Change everything! Because by far we
cannot deal with theories of so drastically non equilibrium systems.
Leaving aside paradoxical status where stand galaxies due to this damned effect of dark
matter (missing mass), discovered in 1930 by the American, Swiss originated, Fritz Zwicky,
and in any case we could produce any model of self gravitating, punctual mass (orbiting in
their own gravitational field). Our physics stands always near a state of thermodynamic
equilibrium. Obviously, any deviation of this or that represents a deviation against
equilibrium, for example temperature gap between two gaseous areas, which will lead to heat
transfer, a transfer of kinetic energy from thermal agitation. In this case, if we put back to
work our goblin, he would conclude that medium, dynamically speaking, is “almost
isotopic”. This will be case of our atmosphere, even crossed by the utmost windstorms.
Well then, is that impossible to encounter, “to put the fingers on” situations where a gaseous
medium, a fluid, are frankly out of equilibrium? One will found such occurrences when
crossing shock waves. They are limited areas, as precisely the thickness of shock wave has
order of magnitude of small number of mean free path.
When it is crossed by a shock wave, a gas switches between states very abruptly, considering
a state near thermodynamic equilibrium, in the “shocked” gas, is recovered after some mean
free path times.
We reported an observation, forty years ago, in the laboratory where I worked, now
dismantled, the “Institut de Mécanique des Fluides de Marseille”. We had then some sort of
gas guns we called “shock tubes”. Outline is: using an explosive, we ignited a shock wave,
propagating at several thousand meters/sec in a rare gas – Initially this gas was at some
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millimeter mercury pressure. The shock wave move did recompress gas, increasing its
density.
We could follow easily and precisely the increase in density using interferometry. At the
time, we also measured the heat flow at surface of Plexiglas mock-ups. As the experiments
did last only fractions of milliseconds, our measuring devices must have fast response time.
Precisely they where metallic films of some micron thickness, vacuum coated on the wall,
they acted as thermistors. We evaluated heat flow by recording resistance of these wall
sensors while they heated.
One day we placed a sensor straight on the tube wall. Then we observed the heat flow was
reaching the sensor after a certain delay following shock wave passage, materialized by an
abrupt density jump. Yet we made sure the thermal lag of the sensor was small enough for
this delay was not coming from it. In fact we put the finger on a return phenomenon towards
a quasi thermodynamic equilibrium, downstream the shock wave.
We can compare this one to a hammer slam. Not only the density is brutally increased, also
we observed a temperature jump, meaning an increase of thermal speed of molecules. But
behind this wave, isotropy is only seen after several mean free path times. Immediately
before density front, increase of thermal agitation is translated by movements starting
perpendicular to wave direction.
When our sensor collects heat, this results from impact of air molecules on its surface. Yet
immediately before the density front, on some distance, thermal agitation was developing
parallel to the wall. The gas was well “heated” but momentarily unable to transfer this heat to
the wall. Over the collisions the “ellipsoid of speeds” was transforming itself into “spheroid
of speeds”, and the sensor ended in giving return of the heat flow it received. I believe
remembering, with the experimental setup we had, that we recorded this heat flow near one
centimeter before density front.
So the shock waves represent tiny thickness areas, where the gaseous medium is strongly out
of equilibrium.
How do we manage this? To make equal these areas to no thickness surfaces. And this
works since almost one century.
I am old enough to have known almost all of the computer history, since beginning. When I
was a student at “Ecole Nationale Supérieure de l’Aéronautique”, there was no computer in
house. These ones were installed inside sanctuaries called “calculation centers” we could not
access. We were calculating using sliding rules, curiosity objects for today’s generation. In
superior school classes we all had our logarithm book, and every examinations include a
boring numeric calculation test using these items, which are by now exposed in museums.
When I leaved Sup Aero School were just coming mechanical calculators (FACIT), hand
powered. To multiply numbers your turn crank one way, to divide you turn opposite.
The professors, or department managers, had electrical machines, which were breaking the
silent’s office with their cog noise at Institut Mécanique des Fluides, 1964. Computers had
the place of honor, as distant gods only seen through a window, in these calculation centers.
These computers, having the power of a today’s pocket computer, were served by priests in
white cassocks. You could only communicate with them via a thick amount of punched cards
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noisily read by a mechanical “card reader”. We bought “calculation time” by the second, so
costly it was. It is Neolithic vision for young people of today.
Micro Computers invasion has changed all this. More, the increase of computers power being
eruptive, the Net is now full of pictures where you see vast rooms filled with mysterious
black cabinets, managing jaw dropping quantities of data.
Megaflops, gigaflops, petaflops, galore! Back into seventies, you could easily read the
content of an Apple II RAM, which was entirely written as a small booklet.
We are in a promethean world. Can we say these modem tools increase our physics
mastering? An anecdote is coming to my mind. In France, I have been a pioneer for micro
computing, having managing one of the first centers (based on Apple II) dedicated to this
technology. By this time, also sculpture professor to Ecole des Beaux Arts of Aix en
Provence, one day I presented a system, which a flatbed plotter which drew at will master
perspective drawings. An old professor, raising eyebrows, said then “don’t tell me computer
will replace artist?”
Paraphrasing this we could imagine any fellow who, after visiting a mega data center,
claimed: “Don’t tell me computer will replace brain?”
In spite of unstoppable computing power escalation, and massive multi processors, we are far
away from it. However, in certain areas, these systems have sent to scrap our logarithm books
and sliding rules, amongst others. Who is still playing to calculate integrals, pen and paper?
Who is still juggling with differential calculus, apart pure mathematicians?
Nowadays we believe in “computer’s doing everything”. We built algorithms, we supply
data, we run until we receive results. If it is to draw any building or nice engineering work,
this works so well. Theory of fluids is also a success.
We can place a surface element, of any shape, perpendicularly to some gaseous flow, and
compute the whirling flow pattern past it, whatever its aspect. Does it fit the experiment? Not
always. Qualitatively, we master the event, for example we can compute a reliable
aerodynamic drag figure as a result of this gas swirling. Same, we compute the burning
efficiency inside a cylinder, the convection current in an enclosure. Predictive meteorology is
gaining fast, providing a time frame of few days, except “micro events”, very localized,
which are not yet manageable. Is that the case in every domain?
There are bodies who refuse to be kept in leash by this modern times lion tamer so-called
computer. These are “non equilibrium” plasmas, title holder, all categories. They also drift
away from fluid’s theory, in spite of a family semblance with, because they are subject to
distance action, due to electromagnetic field whose action can only be evaluated in taking
account all ionic particles constituting the system.
Don’t matter, said you. It is enough to consider plasma as N-bodies system. Easier to say
than to do! We spoke earlier about galaxies, as examples of collision free worlds. Tokamaks
are another kind (ITER is a giant tokamak). The gas they contain is extremely scarce. Before
starting, filling pressure inside the 840 cubic meter of ITER would be less than fractions of
mercury millimeter pressure. Why so low a pressure? Because we are to heat this gas more
than 100 millions degree. Yet you know the pressure is expressed as: p = nkT - k being
Boltzmann constant, T absolute temperature and n the number of particles per cubic meter.
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Plasma confinement is due only to magnetic pressure, this last increasing as the square of the
magnetic field.
With a field intensity of 5, 2 Tesla, magnetic pressure is 200 atmospheres. In view of
plasma confinement, its pressure must remain far below this value. Due to use of a
superconductor device, the magnetic field cannot be increased indefinitely, then plasma
density inside the reactor chamber stay limited to very low values. From these facts we see a
totally collision-free body, escaping to any reliable macroscopic definition. Can we manage it
like N-bodies problem? Don’t even dream about, present or future – it is not possible to
calculate locally, as we could do it with neutral fluids mechanics. Every area is coupled with
any other via electromagnetic field. Take for example the problem of energy transfer from
plasma core to walls. Besides a mechanism looking like conduction phenomenon, besides
what belongs to turbulence, is coming a third modality, named “abnormal transport”, using…
waves.
In brief as in the only one, a tokamak is an absolute nightmare for a theorist.
Plasma in itself, apart its uncontrollable behavior, is not the only one involved. There is
everything else: amongst them is the unavoidable ablation of particles from the wall. Those
who practice glider know the basic parameter of these machines is the lift- to- drag ratio: it
express the number of meters flown per meter of height lost (the glide ratio). The sailplane
wing, at a given speed, is producing a certain lift force. At same speed we get a drag force,
which is twofold: first is induced drag: a loss of energy due to vortices at wingtips.
You cannot avoid it unless infinite wingspan… It is to decrease it that gliders have so large
wingspan, frequently more than 20 meters, associated with aspect ratio – ratio of half wing
span on mean wing width – larger than 20. Second source of drag is viscous drag. It will be
reduced in seeking the smoothest wing surface. Due to a nice polish we delay starting
turbulence in the immediate vicinity of wing surface. This phenomenon is a basic fluid
instability, the excellence of surface polish can only delay its coming. Inversely, this
turbulence can be started by a perturbation. If we look at a line of smoke in a calm
atmosphere, it is an upstream of hot gas, colored by its particles content. This thread of
smoke, calm at first, will become intensely turbulent after a tenth of centimeters rise,
whatever the quietness of ambient air. By introducing an obstacle, as a needle, in this rising
flow we could trigger an irreversible turbulence. The same is done by a minute harshness on
the polished surface of sailplane wing, which will trigger turbulent phenomena, locally
increasing by an easy hundredth factor air friction, thus total drag. In modern sailplanes, we
succeed in keeping a laminar airflow (non turbulent, parallel layers) over 60% of the chord
line. If by chance a mosquito crashes on leading edge, this minute asperity will start
turbulence in a more or less 30 degrees further zone. For this reason, in contest sailplanes,
whose glide ratio is more than 50, there is a leading edge cleaning device, started
automatically and timely, which can be compared to a linear wind shield, a sort of brush is
traveling along leading edge, back and forth, and comes back to rest in a hidden place.
Considerable works have been spent to increase overall glide ratio of airliners, in order to
reduce their fuel consumption. Back in the sixties the “Caravelle”, which was able to sail
between Orly and Dijon, had a glide factor of 12. Nowadays, even these monstrous Airbus
380 have a glide factor more than 20.
That is, when missing propulsive force, with their four motors idle, starting from 10 thousands
meters height they can glide over 200 kilometers.
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Back to plasmas and tokamaks : in these machines, a micro volume of turbulence can be
triggered by minute particles, torn from walls, and will invade the reaction chamber.
Turbulence speaking, the range is extremely large and spreads from this micro turbulence to
electro-dynamic plasma convulsions involving entire volume.
As a conclusion, engineers are not at all managing the machine unless using approximated
empiric “engineer’s laws”, of weak reliability, about running system. In this domain where
non-equilibrium is the king, where measurements are extremely difficult, computer is of no
help. Experiment is the only leader. Also extrapolation leads to discover new unforeseen
phenomena, as the vertical plasma movement (VDE, Vertical Displacement Event), which
appeared when size jumping from Fontenay aux Roses TFR to Culham JET.
The recent fiasco of the NIF (National Ignition Facility, based at Livermore, Ca) is a good
example of sounding failure in large and costly facilities, with help of the most powerful
computers in the world. It is the conclusion of NIC (National Ignition Campaign) after 2 years
trials, from 2010 to 2012. The system, comprised of 192 lasers, delivers 500 terawatt (more
than thousand times USA electrical grid power) in a hand- full of nanoseconds, on a spherical
target 2 mm diameter, filled up with Deuterium – Tritium mixture, itself inserted at center of a
cylindrical box 2 cm long and 1 cm diameter, called Holraum (oven in German).
The plan is following: half of the lasers’ disc-shaped beams burst into opening one side of
Holraum, the other half barge into hole opposite side. These ultrathin U.V. beams strike the
inner walls of the oven, built from Gold. This one re-emits X radiation. Laser beams, precisely
focused, created 3 rigs of spots on the inner wall. The re-emitted X radiation then hits the
spherical target. We talk now about indirect irradiation. This system has been devised basically
to mimic the fusion stage of a hydrogen bomb, where the X radiation (generated this time by a
fission device) strikes the walls of a shell called ablator, containing the fusion explosive
(Lithium deuterure). In the NIF, this last was replaced with mixture of Deuterium – Tritium in
which fusion starts at a lower temperature, order of 100 million degree. Envelop (the ablator,
thin spherical shell) sublimates and explodes both directions external and internal. We use this
back compression to create a “hot spot” at target center, hoping to start ignition in an inertial
confinement scheme.
All this had been calculated under direction of John Lindl. In 2007, a paper devoted to this
scientist, during Maxwell prize-giving, described finely what would happen. Theorists were so
self-convinced than Lindl did not hesitate to claim ignition would be the starting point of a vast
series of experiments. It is same for the test manager, who even had fixed a dead line for the
operational success, October 2012, which was supposed to crown thirty years of efforts, both
theoretical and technologic.
The result has been an immense fiasco, pinned out by a 19 July 2012 report, emanated from
D.O.E. (US Department Of Energy) and written under supervision of Davis H. Crandall.
What must remain of this observation report, related to this paper very mater, is that in spite of
excellence of this work, both technology and measurement speaking, nothing what emerged
from this experiment was exhibiting any relation with computed data and predictions obtained
with help of the most powerful computers.
Up to the point where some observers were asking if these simulations could represent any
investment for further experiments.
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The NIF crisis is evident – it is impossible to increase the number of lasers (Neodymiumdoped glass) for cost reasons. Impossible again to increase their unity power – in fact, when
they are drenched with energy, above a certain level, they are prone to blow up, whatever the
homogeneity and glass quality are.
To succeed in starting ignition and inertial confinement fusion, implosion speed must be at
least 370 Km/sec.
Not only this speed is not reached, but, serious by far, when the shell constituting ablative
device, is turned to plasma, and pushes its D-T content, “the piston is mixing up with fuel”, due
to a well known instability, the one of Raleigh Taylor. To minimize its effects, we must make
thicker the ablator. But then it would increase its inertia and the speed implosion threshold
would not be reached again.
Simulations done on computer have given false results in all domains. As written in the D.O.E.
report, modeling of interactions between laser and walls (impact of X rays on gold walls) is not
satisfying, in spite of tenths of years studies spent on this subject, and hundredths of thesis and
papers. Same thing for interaction between X rays beams, following a law named “inverse
Raman Scattering”, with the gold plasma, coming from sublimation of parietal gold inside
chamber. Interaction of X radiation with ablator is also not correctly simulated. Last, the
calculation algorithms (LASNEX) totally under–estimated the weight of Raleigh Taylor
instability, the deformation of the contact surface of ablator, Deuterium–Tritium, recalling
intestinal villosities.
These mishaps show confidence limits we can set into superb simulation computerized results,
once these machines try to attack frankly out-of-equilibrium problems, mostly non-linear,
where a bunch of mechanisms, poorly modeled, play a role in the game.
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