ULTRA CAVITATION

Newsgroups: sci.physics.fusion
From: terry@asl.dl.nec.com
Subject: Ultra Cavitation
Message-ID: <1993Jan3.043411.2231@asl.dl.nec.com>
Organization: (Speaking only for myself)
Date: Sun, 3 Jan 1993 04:34:11 GMT

--------- Copyrighted document begins with (and includes) this line ----------


                               ULTRA CAVITATION

            -- An Outline of Theoretical and Experimental Issues --

                              December 31, 1992
                                 Version 1.0

                              Terry B. Bollinger
                             2416 Branch Oaks Lane
                           Flower Mound, Texas 75028


                    Copyright 1993 by  Terry B. Bollinger.
                    Unlimited rights  to  duplicate in any
                    form, provided only that the  document
                    and its  copyright  notice  are copied
                    in their entirety. Properly attributed
                    short quotes are also fine.


                        -- DOCUMENT UPDATE HISTORY --

            AUTHOR             DATE                  ACTION
    ----------------------  ----------  ----------------------------------
    Terry B. Bollinger      1992-12-20  Initial outline completed
    Terry B. Bollinger      1993-01-02  Version 1.0 completed and released


1.  INTRODUCTION 

The purpose of this document is to further explore a number of issues related
to how cavitation in a fluid may be capable of generating extraordinarily
high pressures and temperatures that are well beyond the range normally
assumed possible with cavitation.  I refer to this idea of an extended range
of cavitation phenomena as "ultra cavitation."  Ultra cavitation is proposed
to be quantitatively different from ordinary cavitation through its use of a
"wedge-out" mechanism to accelerate a fraction of the imploding molecules to
much higher velocities that are possible in ordinary cavitation.  For this
acceleration effect to apply, the interior of the ultra cavitation void must
contain an extremely hard vacuum, and the surface of the void must maintain a
very high degree of spherical symmetry throughout the collapse process.

This exploration is an extension of the ideas the author first proposed in
Network references [1] and [2].  The issue of cavitation and whether or not
it could induce exceptionally energetic events was first brought to my
attention by Cameron Randale Bass (crb7q@kelvin.seas.Virginia.EDU) in a
private email, and my interest was further increased by some intriguing
recent data on cavitation results that were provided by Steven E. Jones in
Network references [3] and [4]

The style of this document is to provide a broad framework and exploration of
theoretical and experimental issues, rather than a rigorous mathematical
analysis of the relative importance of many of the effects described.  The
style of exploration is perhaps more characteristic more of computer science
than physics, since it emphasizes identification of key abstractions ("what
really makes cavitation work?") followed by exploration of a broad range of
potential theoretical and experimental "free parameters."  The next step is
"implementation," or expansion of the concepts and relationships described
here into specific mathematical formula and numerical analysis methods.

It is my hope that by publishing the outline as quickly as possible, others
on the Net will be able to contribute to directly to the quantification of
the framework I am proposing below.  Also, I think it would be worth looking
at the possibility of synthesizing contributions into a multi-author paper
for submission to a conventional physics journal, so that slow-mail readers
will have easier access to such Network results.

My overall conclusion is that cavitation is an extraordinarily complex and
rich phenomenon.  Based on early reports of cavitation energies corresponding
to 100,000 degrees with comparatively simple setups [3], I would judge it to
be highly probably that significant, detectable increases in the rates of T-T
and possibly D-T reactions should be possible using advanced cavitation
methods.  Details of such reactions will require further experimental and
(especially) numeric simulation work to be validated and studied in detail.


2.  FUNDAMENTALS OF VOID FORMATION

Cavitation consists of two major steps: void formation, and void collapse or
implosion.  This section looks at void formation.

2.1  VOIDS IN GASES AND LIQUIDS

The initial step in cavitation is the formation of a vacuum bubble (void)
within a gas or liquid.  Both gas and liquid voids are inherently unstable.
Gas voids will quickly be filled through simple diffusion, while liquid voids
will close because of surface tension in the void surface and (if present)
internal fluid pressure.

Of the two types, liquid voids are significantly more interesting due to the
special properties of well-defined void surfaces.  Sharply delineated void
surfaces that exhibit surface tension drastically alter the dynamics of void
collapse, generally by making them far more intense than gas void closures.
Apart from this key difference, the dynamics of gas voids should be largely a
subset of the dynamics liquid voids.  Thus in this paper gas voids will be
discussed only as they relate to the behavior of liquid voids.

2.2  INTRA-LIQUID BONDS

All liquids possess cohesive intra-liquid forces that hold the fluid together
even in the presence of a vacuum.  At the molecular level these cohesive
forces translate into inter-molecular and inter-atomic bonds that range over
many orders of magnitude in strength, from the exceedingly weak Van der Waals
forces that provide liquid helium with cohesion to the very strong ionic,
metallic, and covalent bonds that are characteristic of most high-temperature
fluids.  Hydrogen bonding, which allows the very light constituents of water
to exist in liquid form at room temperature, is an example of a intra-fluid
bonding mechanism of intermediate strength.  Intra-liquid bonds also vary
greatly in relative mobility, or the ease with which molecules or atoms can
"slip around" each other to form new bonds.  Van der Waals bonds and hydrogen
bonds in water are examples of highly mobile intra-fluid bonds, while the
largely covalent bonds of high-temperature liquids such as molten silica are
both highly directional and difficult to rearrange rapidly.

2.3  EXPLOSIVE VOID FORMATION

To form a void in liquid, it will be necessary to both to break and to
rapidly rearrange intra-fluid bonds to form a nanovoid, and to then expand
the nanovoid by rapidly accelerating its walls outward from the point of
origin.  There are two primary mechanisms for driving this outward
expansion:  explosive void formation, and decompressive void formation.  (A
third possibility of very rapid removal of an object from a fluid is similar
enough to decompressive void formation that it will not be treated separately
here.)

In explosive void formation, a void is created in a liquid (or gas) by a tiny
but intense explosion within the liquid.  Such an explosion drives away the
liquid with very high momentum gases (possibly the vaporized liquid itself),
thus leaving a region of relative vacuum.

Explosive void formation is limited in several ways.  Firstly, the energy
needed to enlarge the void increases rapidly with increasing void size, since
the explosion must "push" increasingly large volumes of fluid outward as the
radius of the void expands.  Secondly, the vacuum formed my such a explosive
methods will necessarily be imperfect for two reasons:  the early stages of
the micro-explosion are likely to vaporize much of the fluid around it, and
most micro-explosive mechanisms are likely to leave behind a residue of gases
or other products.

Ironically, the most practical approach to creating the necessary minuscule
explosions for explosive void formation is through implosion of decompression
voids.  That is, the rebound effect of void collapse can be energetic enough
and sufficiently point-like to lead to secondary (explosive) void formation.
Such secondary voids will in general be smaller than the voids that produced
them, but if the original implosion is exothermic (e.g., if it resulted in
the recombination of dissolved hydrogen and oxygen in the fluid), secondary
voids could in some cases be as large as or larger than the original voids.

This paper will in general assume that voids are created via decompression,
not explosion.  Explosive void formation will be discussed only as it is
relevant to the aftermath of decompressive void implosions.

2.4  DECOMPRESSIVE VOID FORMATION

In decompressive void formation, a void is formed literally by "stretching"
the liquid (that is, forcing it to increase in total volume) until nanovoids
present in the fluid undergo exponential expansion and become macroscopic.

In contrast to explosive void formation, decompressive void formation tends
to produce clean voids that can be expanded to arbitrarily large size,
without requiring the addition of large quantities of a foreign explosive
materials into the void region. Also, since the events surrounding the
rupture and subsequent rearrangement of intra-fluid bonds are relatively low
energy at the rupture point, less of the fluid is likely to be vaporized
during the early stages of void formation.  In fact, if the fluid possesses
sufficiently strong intra-fluid bonding, it should be possible to arrange
decompressive void formation so that extremely few (possibly zero) molecules
of liquid will enter into the void.

Voids of quite large size can be formed by decompression, since a
sufficiently rapid and symmetrical decompression cycle will allow them to
grow in size until the surrounding fluid either breaks up or physically can
no longer contain them.  However, once the dynamic forces of decompression
are removed, the resulting voids will necessarily become unstable due the
effects of surface tension at the void surface, even in the absence of
internal fluid pressure.  (The effects of surface tension are discussed
further in the Section 3.XX discussion of symmetry enhancement, and in the
Section 3.XX discussion of the early stages of void implosion.)

2.4.1  Impulse Decompression (and Void Formation in Nature)

Mechanically, decompressive voids can be created by something as simple as an
abrupt pull on a piston in a cylinder that contains a low-gas liquid. Note
that the liquid must "wet" or bond tightly to the piston and cylinder surface
if the void is to form in the interior of the fluid; weak bonding to the
surrounding surfaces will simply result in voiding formation at the junction
between the cylinder/piston and the fluid.

This concept of impulse decompression is sufficiently simple that it is quite
likely to occur naturally.  For example, one possible scenario for natural
formation of impulse decompression voids would be the sudden "snapping" of a
fluid-filled crack in a rock.  Because a sufficiently sudden break in the
rock would not allow enough time for fluid to fill the crack, void formation
would be a likely consequence.

2.4.2  "Flow Shadow" Decompression

Another mechanism that can be used to generate decompressive voids is the
very rapid flow of a fluid around a "shadow object."  If the flow is rapid
enough, and the if the trailing side of the object cuts off abruptly enough
to make laminar or even ordinary turbulent flow impossible, the result will
be the formation of a large "void shadow" that continually breaks up and
enters into the fluid flow voids of various sizes.  Using very-high-velocity
water, this technique has been studied as a method for drilling into solid
rock using the impact of the imploding voids [5].

Flow shadowing could perhaps exist in nature, but is less likely due the need
for very high fluid velocities in an environment free of gases. Nonetheless,
the existence of high-velocity "black smoker" vents at some mid oceanic
ridges provides a simple example of how surprisingly rapid velocities can
develop within natural fluids.  (To be of interest from a cavitation
perspective, such rapid flows would of course also need to meet the
additional requirement of having low dissolved contents, which is in general
not the case for such "black smokers" with their high hydrogen sulphide
content.)

2.4.3  Sonic Decompression

For general applications, the most common decompression void formation
technique is to use intense sound waves, generally (but not necessarily) in
the ultrasonic range.  Since sound waves are composed of traveling regions of
high and low pressure, sufficiently powerful sound waves provide a good
technique for rapidly and cyclically producing regions of sufficiently high
stress to cause fluid rupture around a transient defect or a point defect.
Sound has the additional advantage of providing compression cycles shortly
after the formation of a void.

Transient sonic cavitation in nature is clearly possible in any circumstances
where sharp, intense sounds are generated in fluids by natural phenomena.

Two major types of sonic decompression should be distinguished:

   1)  Traveling-wave decompression, and

   2)  Standing-wave decompression

Traveling waves are conventional sound waves in which the decompression
region moves at the speed of sound.  Although the can cause cavitation, they
are of secondary interest here because voids formed by this method will tend
to be "pulled along" by the traveling wave.  This "pulling" effect will tend
both to distort the shape of the void axially and cause the void to collapse
over an extended period of time, rather than as a single brief collapse event.

Standing wave decompression, which is usually achieve by reflecting the
initial traveling wave back on itself, is far more interesting from the
perspective of creating high-quality, high-symmetry voids.  In standing-wave
decompression the regions of decompression stay "in place", and furthermore
can be shaped to relatively high levels of symmetry by the use of complex
combinations of reflection and wave interference.  Finally, standing-wave
decompression permits the formation of "lattices" of similar decompression
regions that can be used to create large numbers of highly similar voids.


3.  THE CAVITATION PROCESS

In this section the cavitation process is analyzed with the objective of
identifying parameters that are likely to influence peak implosion pressures
and temperatures.  Cavitation is described in terms of the following phases:

   1)  Void Initiation                 (Section 3.1)

   2)  Accelerated Expansion           (Section 3.2)

   3)  Inertial Overshoot              (Section 3.3)

   4)  Restructuring of Void Surface   (Section 3.4)

   5)  Implosion Initiation            (Section 3.5)

   6)  Early Implosion                 (Section 3.6)

   7)  Mid Implosion                   (Section 3.7)

   8)  Late Implosion                  (Section 3.8)

   9)  Implosion Termination           (Section 3.9)

   10)  Region of Maximum Energy       (Section 3.10)

   11)  Post-Implosion Rebound         (Section 3.11)


3.1  VOID INITIATION

The earliest identifiable stage in void formation is to create a macroscopic
region in a liquid for which the average intra-liquid bond length is somewhat
larger than normal.  This elastic stretching of molecule-to-molecule bonds in
the region then provides the necessary potential energy for the formation of
a void.

If the stretched bonds of the liquid region are viewed as an elastic
"fabric", then void formation is simply the release of their potential energy
through the rapid growth of a "hole" somewhere in the fabric.  Just as
pricking a balloon with a pin results in a (catastrophically) rapid expansion
of the hole to release energy in the stretched fabric of the balloon, a "pin
prick" in a (considerably less) stretched liquid will result in the rapid
formation of a void that permits intra-liquid bonding lengths to return to
normal.

(It should be noted that in the case of an extremely pure liquid, it may be
possible for such a stretched state to remain stable for long lengths of
time.  This "superstretched" liquid state would be a close analog of a liquid
superheated and supercooled states.  I do not know if this concept has ever
been explored experimentally.)

Borrowing the analogy of the balloon, what exactly would be the nature of the
"pin prick" (nanovoid) that would lead to rapid release of the potential
energy of intra-liquid bond stretching?

There are two possible answers:

   1)  Statistical Nanovoids.  Fluctuations at the molecular level should be
       capable of forming "nanovoids," or extremely tiny (Angstrom range),
       very short lived voids.  If the stress on the fabric of the liquid is
       very severe, amplification of these statistical nanovoids may be
       possible.

   2)  Void Seeds.  As implied by the name, void seeds are small to
       extremely small imperfections in the "fabric" of the stretched
       liquid.  They could be foreign bodies ranging in size from dust
       particles to single molecules, or the could be energy events such the
       passage of ionizing radiation.  A void seed forms a nanovoid when
       bonding of the fluid to the void seed fails and a vacuum region forms
       around the seed.

Except for extremely pure liquids preserved under careful conditions, the
most likely source of nanovoids will be void seeds, since the initial energy
required to expand around a statistical nanovoid will be so high that it will
tend to be self-equalizing -- that is, the pull of adjacent fluid molecules
on the surface of a statistical nanovoid will be near the limit of what the
fluid can handle, so that rather than expanding the nanovoid might simply
shift to or be recreated in a new position.  This means that the level of
strain on the intra-fluid bonds will be so high that amplification of a
statistical nanovoid will be more likely to cause a general explosion of the
liquid than it is to cause void formation.

Void seeding, however inadvertent, therefore will be assumed to be the normal
mechanism by which decompressive void formation is initiated.

3.2  ACCELERATED EXPANSION

3.2.1  Conversion of Bond Potential Energy into Void Potential Energy

The next phase of void formation is expansion, in which the potential energy
of the stretched intra-liquid bonds is rapidly converted into a general
acceleration away from the initial nanovoid.  This acceleration will be the
most rapid at the surface of he nanovoid, and will fall off linearly away
from the surface until at some point it reaches zero.  The closed surface
defined by all of these zero acceleration points will be called the Zero
Acceleration Surface (ZAS), and the volume of liquid enclosed by it will be
referred to as the ZAS cell for the void.

The ZAS cell contains the total volume of liquid that will contribute its
potential (tension) bond energy to the formation of the void.  Thus if the
size of the ZAS cell and the potential energy profile of the liquid within it
are both known, this information can be used to calculate the maximum total
energy available for forming the void.  There will be some loss of the bond
potential energy due to heating, but in general a high percentage of the
total bond energy in the ZAS cell should be converted into a new form of void
potential energy that will be released when the void collapses.

In a generally decompressed fluid in which multiple voids are formed at the
same time, a ZAS "cell structure" of zero acceleration surfaces will be
formed in the fluid, with a void at the center of each ZAS cell.  In the case
of sonic decompression the region that contributes to a single void will be
defined by the form of decompression regions of the standing waves, with ZAS
cells separated by distinct regions of sonic compression.

Although in this paper the ZAS cell will generally be discussed as if it were
a stable, unchanging volume in the fluid, a more realistic model must take
into account the fact that the ZAS cell may shrink or expand if the ambient
pressure changes during void expansion or collapse.

3.2.2  Release of Dissolved Gases Into Decompressive Voids

An important side effect of void expansion is the release of dissolved gases
into the growing void.  This is in part due simply to the natural tendency of
a liquid to de-gas into any hard vacuum with which it comes into contact, but
it is also due to the dynamic, non-equilibrium nature of the void surface
during expansion.  Because the void surface is rapidly "stretched" as it
expands, normal lateral surface bonding at the surface of the liquid will be
severely stressed.  This in turn means that the normally higher density of
the fluid surface may be largely or entirely lost, especially during the
early stages of decompression, and that this resulting "porous" surface will
not be able to inhibit the passage of dissolved gases as efficiently as a
normal fluid surface.  (This argument does not apply to explosively formed
voids, since during expansion their void surfaces will be compressed rather
than expanded.)

Also, the rapid expansion of the void during decompression will in effect
"sweep" a large volume of liquid into close proximity with the void surface.
This again will encourage release of dissolved gases into the void,
especially in combination with the increased porosity of the surface during
expansion.

The idea that decompression voids should act as effective gas "sweepers" is
demonstrated by the use of ultrasonic cavitation to degas liquids [6]. As
will be discussed later, the tendency for voids to sweep up dissolved gases
during expansion has considerable significance for the mid and late phases of
void implosion.

For a reasonably symmetrical void, the accelerated expansion phase of void
formation ends when average bond lengths in within the zero-acceleration
surface have returned to normal (non-stressed) lengths.  However, because the
particles near the void surface have appreciable mass, the void will continue
to grow for a short period after the zero-acceleration point.  This overshoot
effect is described in the next section.

3.3  INERTIAL OVERSHOOT

When the average bond length within the ZAS cell has reached normal values,
ZAS cell bond potential energy will have been converted primarily into three
new forms:

   1)  Kinetic energy (outward motion of liquid)

   2)  Tension in void surface

   3)  Dissipative heat

Dissipative heat during expansion should be relatively minor if the void is
highly symmetrical, and should impact void collapse only through the indirect
effect of possibly producing some heating of the liquid around the void.

The role of tension in the void surface can be best understood by realizing
that during the very early expansion of the nanovoid the dominant force that
must be overcome is not the inertia of the liquid, but the highly resistive
effects of surface tension in very small voids.  Just as blowing up a very
small balloon requires far more force than adding the same volume of air to a
balloon that has already been expanded to a large size, the energetic role of
this "stretching" of the nanovoid surface will be dominant while the void is
sufficiently small in size.  For a very large void the dominant force
resisting further expansion will become the inertial of the liquid, rather
than the surface tension of the void.  An accurate mathematical model of the
conversion of ZAS cell bond potential energy into void energy thus must take
the forces of surface tension carefully into account, especially for models
of the earliest stages of void expansion.

Kinetic energy will consist of an (ideally) linear outward-bound velocity
profile that has its highest value at the void surface, and reaches zero at
the ZAS.

It is the kinetic energy component of the newly formed void that will lead to
overshoot and further enlargement of the void.  This kinetic energy will be
converted rapidly into compression of (momentarily) normal-average-length
intra-fluid bonds within the ZAS cell.  For the ideally linear acceleration
profile of a line drawn from the void surface to the ZAS, this new
compressive potential energy should be stored uniformly throughout the fluid
of the ZAS cell.

The overshoot phase will end when all of the kinetic energy of the ZAS cell
has been converted over to compressive bond energy.  Since this is the point
at which all of the outward bound kinetic energy has been exhausted, it will
also be the same point at which the void encloses its maximum volume.

Another effect over overshoot compression is "closure" of void surface, which
was more porous than normal during the rapid expansion phase.  By the time
the void has reached its maximum volume, the void should have a fairly normal
(or actually compressed) liquid surface that exhibits higher density and
greater cohesiveness than the volume fluid.

3.4  RESTRUCTURING OF VOID SURFACE

3.4.1  Surface Tension

Surface tension now begins to play a significant role in the maximum-volume
void.  Surface tension may be roughly understood as a lateral and downward
(into the fluid) "re-alignment" of intra-fluid bonds that otherwise would
have gone to bonding with the "missing" fluid.  A molecule at the surface of
a liquid thus will bond more tightly (and physically more closely) with the
fluid molecules around and below it, giving the net effect of an elastic
membrane that tends both to compress the underlying fluid and to resist
stretching.  This elastic-membrane analogy helps provide a general idea of
how such surfaces will behave.

It should be noted that if surface tension is a consequence of "re-alignment"
of intra-fluid bonds, the fluids that will tend to have the strongest surface
tensions will be those that have intra-fluid bonds that are both very strong
and easily re-aligned.  Many liquid metals provides examples of such strong
surface tension, since metallic bonding is both strong and generally easy to
re-align.  Hydrogen bonding also meets these criterion well, at least in the
case of water.

In general, the smaller the radius of a displacement of a liquid surface is,
the stronger the accelerating "displacement removal" force per molecule will
be.  A single molecule displaced slightly above the surface will be subject
to a very strong accelerating force consisting of its own bonding forces
trying to return it to body of the fluid, while for larger and larger
displacements of fluid this accelerating force will be distributed out over
increasingly large numbers of molecules.  Very large displacements thus will
be subject only to modest accelerations, and may be overcome by other forces
that could (for example) tend to break up the surface structure into droplets
or bubbles.

In general, these accelerating effects of surface tension thus will tend to
simplify the equations that describe the curvature of the liquid surface,
with very small radii of displacement being subject to very high, short-
duration accelerating forces, and large radii displacements being subject to
much lower accelerations over more extended periods of time.  This range of
accelerations over a wide scale of sizes helps produce the common liquid
effects of both bubble and droplet formation, and the tendency of a fluid in
a gravitational field to form a large-scale flat surface.

3.4.2  Surface Tension at Maximum Void Displacement

Once the kinetic energy of void overshoot has been expended, surface tension
will take over as the dominant force in the surface of voids in most fluids.
As described above, its major effect will be to rapidly "smooth out" the
surface of a the void and create a highly symmetrical spherical surface. Very
large voids may be subject to fragmentation, but relatively small ones are
far more likely to be "sphericized" than they are to fragment.  The most
likely remnants of asymmetry from the expansion phase will be comparatively
large-scale ones, such as the void being an ovoid instead of a sphere.

3.4.3  Void Formation and Entropy

The process of void formation is highly entropic in the sense that it cannot
be reversed in time.  Both the expansion phase and the restructuring of the
void surface by surface tension "lose" information needed to make the inverse
process of void collapse time-reversible.

This entropic process can be understood by imagining an orderly arrangement
of marbles at the bottom of a shallowly depressed, flexible sheet.  If this
sheet is very gently pushed upwards, the marbles will slowly begin to roll
outward along paths determined primarily by their initial positions on the
sheet.  This kind of outward expansion is non-entropic and time reversible in
the following sense:  If the sheet is again allowed to relax back to its
original shallowly depressed position, the marbles can in principle retrace
their paths and literally reassemble themselves back into the same positions
from which they originated.  The reversal process (collapse) is in this case
smooth and low in energy.  Each marble is enclosed by other marbles of
similar speed and direction, so that from the perspective of any individual
marble the surrounding environment is very "cool" (low in energy differences).

In contrast, if the marbles are allowed to expand over a sheet that is rough
and allowed to come to rest on a circular rim around the sheet, all of the
early time-reversible trajectory information that permitted each marble to
"remember" its original location relative to its neighbors will be lost.
Instead, when the sheet is flexed back down the marbles will all take on
trajectories that try to take them to the same location in space at the same
instant in time.  Time reversibility thus has been lost, and the gentle
return of the marbles to complementary positions has been replace with a
"race" that ensures that there will be relatively violent collisions between
the marbles as they attempt to occupy the same location in space and time.

In the case of voids, this same kind of entropic "forgetting" of original
positions occurs both as a result of rapid randomization of the trajectories
of individual molecules during the expansion phase, and as a result of the
strong coercing effect of surface tension, which tends to erase large-scale
differences in where the molecules would have been "targeted" to return.

All of this is relevant to the final intensity of void implosion in that a
void which is characterized by nearly total "forgetting" of the original
locations of all of the molecules on and near the void surface will result in
a far more intense collapse than one in which significant remnants of that
information can still be found in the detailed structure of the void.  In an
ideal "total position erasure" void, all of these molecules should be "aimed"
at a single very tiny target area at the center of the void, and all of them
should begin their inward trajectory at the same instant in time.  The result
is a highly time-asymmetric  collapse profile in which "competition" for the
interior target position of the void ensures much higher temperatures and
pressures than ever existed during the original formation of the void.

In contrast, a void in which there are severe long-range distortions of the
void surface, such as a long stretching along one axis (a thin tube) or two
axis (a thin sheet) will be far less severe (and far more time-symmetric) in
their collapse.

In summary, the degree of positional "forgetting" that is made possible both
by the void expansion process and surface tension at maximum void
displacement is a key initial condition for obtaining high intensity void
implosions.  The final intensity of that implosion process will of course be
determined by many other factors, also, but without this initial condition of
a past-erasing, highly spherical void form, very high final intensities are
unlikely.

3.5  IMPLOSION INITIATION

Another way of understanding the importance of spherical symmetry development
(or "sphering" as it will be referred to below) is to recognize that when it
is combined with a rapid, powerful inwardly directed acceleration of the void
surface it becomes the microscopic equivalent of a spherical explosive of
much higher quality and symmetry than can be obtained by large-scale
processing of explosive charges.  This micro-implosion analogy is useful in
understanding the subsequent evolution of the void as it collapses, because
it turns out that there are several forces which provide a substantial
initial impulse for the collapse of such spherical voids.

The three main forces working towards inward collapse of the void surface are:

   1)  Release of ZAS cell "overshoot" compressive potential energy

   2)  Ambient fluid pressure

   3)  Surface tension effects

Collectively, these three effects provide a sufficiently strong and rapid
inward acceleration of the void surface that the term "implosion" is used
instead of "collapse."  The use of the former term serves as a reminder that
the process of void closure is both forceful and highly energetic at the
physical scales involved.

3.5.1  Release of ZAS Cell Compressive Energy

As described earlier, the initial expansion of the void in a decompressed
fluid will normally lead to the conversion of the kinetic energy of void
formation into compressive potential energy that is stored evenly throughout
the ZAS cell.  At maximum void displacement this stored energy will lead to a
rapid rebound effect that begins accelerating the void cell surface inward.
The magnitude of this effect will depend on many factors such as the detailed
characteristics and compressibility of the fluid, but in general it should
lead to a rapid and strong initial inward acceleration of the void surface as
the compressive ZAS cell energy is converted back to kinetic motion.

As with the initial outward expansion, the ZAS cell should develop an overall
velocity profile in which the void surface is moving inward the fastest, with
the velocity (and acceleration) falling off in an ideally linear profile
until both reach zero at the ZAS boundary.  This gradual profile is important
not only because of the rapid and smooth acceleration of the void surface it
provides, but because the inertial of the fluid around the void will help
provide better containment (resistance to early rebound) as the process of
void implosion intensifies.

The release of compressive energy should nominally fall gradually to zero as
the void approaches the point of zero average intra-fluid bond distortion,
which (unless the pressure of the fluid is changing dynamically) will be well
before the collapse process is completed.  After that point the fluid will
again be under tension and should act as a drag against further implosion.

However, this profile can be modified by the use of dynamic pressure changes
in the fluid, such as can be provided by appropriately designed standing
sonic waves.  By causing the ambient pressure of the ZAS cell to increase at
or before the point where the void reaches its zero-ZAS-bond-distortion size,
it should be possible to effectively nullify or even reverse the slowing
effects of intra-fluid bond stretching.

Even in the presence of a rapidly increasing ambient fluid pressure profile,
however, the contribution of compression to the void collapse will eventually
fade due to entropic effects.  The fluid around the void cannot be compressed
in an exact time reversal of the way in which it was expanded, so that adding
high levels of external pressure will result more in heating of the fluid
around the collapsing void than it will contribute directly to the collapse
of the void.

An important difference between early implosion in an explosively formed void
and a decompression void is that the fluid immediately behind the surface of
an explosive void will tend to "rebound" due to compression of that fluid
during the initial explosion.  This rebound effect will contribute to the
speed of the void collapse by reducing the "drag effect" that would normally
slow inward acceleration of the void surface.

3.5.2  Ambient Fluid Pressure

While high ambient fluid pressures will of course help close a void and add
to the initial implosion impulse, it must be recalled that for decompressive
voids the ambient pressure in the ZAS cell must initially be negative, or
else the void will never form in the first place.  Thus a high ambient
pressure amounts to the same case as using a rapidly increasing pressure
profile during the collapse of the void, as described above for extending the
useful length of ZAS cell compressive rebound.  A high ambient pressure will
be useful only if a decompression method that is sufficiently intense to
overcome the ambient pressure can be used.

On the positive side, the use of high ambient pressure provides a fairly
simple way to construct a rapidly increasing pressure profile during the
early stages of void collapse.  In the case of standing sonic waves, it may
be possible to further use the standing waves to shape the details of the
increasing pressure profile.

3.5.3  Surface Tension Effects

The effects of surface tension in driving the void collapse are especially
interesting.  Unlike compression of the liquid, surface tension will tend to
inwardly accelerate the surface of the void more rapidly as the void size
shrinks.  This is a consequence of the general principle described earlier
that surface tension tends to accelerate the molecules in small deformities
more quickly than it does the molecules of large deformities, primarily due
to surface forces being distributed over a smaller total numbers of molecules.

Thus while surface tension may or may not be a dominant force (compared to
compressive release) during the early stages of void collapse, it is likely
to play a highly significant role later in the collapse.  The constantly
increasing inward force of surface tension on the void surface will continue
until vaporization of the surface occurs and surface tension is thus lost.
The importance of surface tension acceleration and loss of surface tension
due to void surface vaporization will be discussed in more detail below,
since it is particularly relevant to trying to determine the total energy
that will be imparted during void implosion.  (These same surface tension
effects are also important for self-focusing.)

3.6  EARLY IMPLOSION

Early implosion is the period between maximum void displacement and the
vaporization (if any) of the void surface.  Early implosion is the energy
contribution phase, in which the void collapse process receives the majority
of the total energy that will be available to it during the final stages of
collapse.

As described above in Section 3.5, the drivers of early implosion are rebound
of the ZAS cell, ambient pressure, and surface tension.  While for very large
voids the ambient pressure would be the dominant effect, for small voids the
other two effects of rebound and surface tension will become increasingly
significant or dominant to the final energy contribution profile.

However, for intense void implosions in ordinary fluids the early implosion
phase must invariably end as a result of void surface heating.  This surface
heating is a direct consequence of the "competition" for the same location in
space and time that the molecules in the void surface must undergo in a
spherical collapse.  As the total void surface area decreases, molecules must
be "forced out" of the surface and outward into the surrounding fluid, an
effect which jostles the molecules and results in rapidly a rapidly
increasing temperature at the void surface.

Along with this heating effect there will also be an increase in void surface
pressure as too many molecules compete for the same space.  This increase in
pressure will in general reach a maximum very slightly outward from the void
surface, but for a very rapid implosion it may be present essentially at the
void surface due to inertial (acceleration) confinement of surface molecules.

The combination of void surface heating and void surface pressure increases
will complicate the behavior of the void collapse and make it dependent on
the particular properties of the fluid, but for ordinary fluids the effects
of heating will eventually win out and cause loss of surface tension (that
is, vaporization) at the implosion surface.  Despite this vaporization event,
the surface may remain rather sharply defined if collapse rate is very high. 
But the loss of surface tension has other important effects, such as loss of
the accelerating effects of surface tension, even if the surface itself
remains sharply defined.

The vaporization of the void surface will be referred to below as the
Vaporization Event, or VE.

3.6.1  Factors Affecting Early Implosion Energy Contribution

The main factors that affect the overall energy contribution during the early
implosion phase include:

   1)  Size of the void (the larger the better)

   2)  Available ZAS cell compression energy (the higher the better)

   3)  Increasing ambient pressure (best if "tuned" to collapse process)

   4)  High surface tension (the higher the better)

   5)  Delay of the vaporization event

Larger voids increase the total energy contribution simply by extending the
length of the acceleration phase.  However, larger void sizes involve factors
that tend to work against the benefits of a longer acceleration period. 
These include increased venting of gases into the void, increased turbulence,
and failure to make good use of surface tension acceleration prior to
vaporization of the void surface.  Thus the use of larger voids can be more
complex than it might at first appear.

The ZAS compression energy is most effective if the fluid is both elastic
under compression and capable of significant energy storage when under
decompressive tension.

Rapid increases in ambient pressure should be oriented towards adding energy
early in the collapse and preventing "drag" on surface tension acceleration
during later phases.  Additionally, it should help provide overall pressure
confinement during the final stages of collapse by preventing premature
rebound of the outer fluid layers around collapsing void.  Resonances and
standing wave methods provide the most direct approach to implementing such
detailed pressure increase profiles.

High surface tension comes into play not only as an accelerating force, but
also as a self-focusing mechanism (see below).

Delaying the vaporization event is particularly important if the void size
becomes small enough for surface tension acceleration to become significant.
The simplest approach is to pick a fluid with a high boiling point and to set
the ambient temperature of the fluid to be as low as possible.  Mixtures of
fluids often demonstrate higher boiling points than pure liquids, so this
point also argues for the use of such "antifreeze" style fluid mixtures.

3.6.2  Self-Focusing Effects

Until this point surface tension has been discussed primarily in the contexts
of initial shaping of the maximum displacement void surface, and acceleration
of the void surface during early implosion.  However, another important
effect of surface tension is that it provides "self-alignment" or focusing of
the collapse process itself.  The significance of this is that self-focusing
effects can significantly delay the onset of turbulence and thus increase the
intensity of the final stages of the collapse.

3.6.2.1  Radial Self-Focusing

Radial self-focusing refers to the tendency of surface tension to produce a
surface in which any line normal to the surface points to the exact center of
the void.  Because of the tendency of a liquid surface to suppress small
deviation more with greater force, this tendency may actually be grow
stronger as the void shrinks in size.

When combined with implosion, radial self-focusing due to surface tension has
the effect of "guiding" or correcting the trajectory of inward-bound
molecules so that they remain targeted towards the center of the void.

3.6.2.2  Temporal Self-Focusing

Temporal self-focusing refers to the tendency for surface tension to keep the
entire void surface collapsing at very nearly the same rate.  As with radial
self-focusing, this effect should increase in strength as the void collapses.
Temporal self-focusing has the net effect of keeping the molecules of the
void surface targeted to arrive at the center of the void at the same instant.


3.7  MID IMPLOSION

Although the vaporization event corresponds roughly to the end of external
energy contribution into the void collapse, it does not necessarily represent
the end of energy intensification.  In the next (mid implosion) phase the
emphasis shifts from mechanisms that contribute to the total energy of the
void collapse to a new set of mechanisms that serve to focus or collect the
energy of many inwardly moving molecules and transfer it to a smaller number
of correspondingly more energetic molecules.  It is this process, rather than
the initial implosion drivers, that is the most likely to make extremely high
densities and temperatures possible during a void collapse.

3.7.1  Wedge-Out Effect

The tendency for the void surface to increase in both pressure and
temperature as it implodes has already been mentioned, but these effects need
to be looked at in more detail to understand the details of the later stages
of implosion. In particular, the high spherical symmetry of an intense
collapse should lead to a tendency for these temperature and pressure effects
to be both selective and directional in nature.  In particular, faster or
more mobile molecules or ions should tend to be selectively given still
higher velocities that will be oriented primarily towards the center of the
void.  This _wedge-out effect_ is particularly important for estimating the
final energy intensity of the void collapse, since it presents a mechanism by
which the final stages of void collapse might reach almost arbitrarily high
densities and temperatures.

The term "wedge-out" intentionally has a mechanical connotation of forcing or
"popping out" an object under extreme mechanical pressure.  Figure 1 shows an
idealized wedge-out scenario.


                                   Pressure
                                   | | | |
                                   v v v v

                               --> ()()()|
                               --> ()()()|       ()  Slightly slower molecules
                      Pressure --> ()() <>|      <>  Slightly faster molecule
                               --> ()()()|        |  Void surface (gaseous)
                               --> ()()()|

                                   ^ ^ ^ ^
                                   | | | |
                                   Pressure

                                 ---------->
                              Overall Direction
                               of Acceleration
                               (All Molecules)


                       Figure 1 -- The Wedge-Out Effect


For elastic objects such as atoms, the scenario described in Figure 1 is
capable of transferring the kinetic energy of a number of (slower) molecules
into a lesser number of faster molecules that can then "escape" into the
interior of the void while carrying off most of the kinetic energy of that
originally belonged to the slower molecules.  The effect can be described
formally in terms of conversion of energy using two low-friction wedges to
rapidly accelerate an object between the wedges, but can perhaps be more
easily understood by the informal analogy of launching a slippery seed at
high speed by squeezing it tightly between two fingers.  Even though the
fingers never move at a high speed, they are capable of producing a rapid,
intensive acceleration of the seed and a commensurately large increase its
final momentum and energy.

Wedge-out is relevant in void collapse only because the extreme inward
compression of the void surface and lateral compression due to shrinking void
surface area create a very difficult "competition" among void surface
molecules.  Essentially all "escape routes" except inward ones are blocked
for nearly all of the surface molecules, and even those paths are severely
limited by rapid shrinking of the void surface.  By "wedging out" any
molecule that has moved slightly farther into the interior due either to
chance or a higher average velocity, the slower molecules are able to expend
some of their inward kinetic energy while simultaneously reducing the total
number of molecules in the surface.  Slightly faster molecules or ions thus
will be preferred for this "launching" into the void interior, since they
will be the ones that are more likely to protrude slightly towards the
interior.

Wedge-out thus can be thought of a "directed" temperature rise, in which the
kinetic energy of the molecules increases as in a normal temperature rise,
but the direction in which the rise in kinetic energy occurs will be strongly
biased towards the interior of the void.

Two key requirements for an effective wedge-out effect are that:

   1)   the interior of the void be as empty of gases as possible, and

   2)   the surface of the void remain as sharply defined as possible.

The first of these requirements simply reflects the need for a clear, well-
defined "exit path" to keep the wedge-out effect directional.  Gases in the
interior of the void will make alternative energy release paths (primarily
random-motion heating of the void surface) more attractive and rapidly reduce
the acceleration affect provided by wedge-out.

The second requirement for a well defined void surface reflects the need to
keep a very high pressure profile as close to the void surface as possible. 
If the point of maximum pressure falls too far behind the collapsing void
surface, the result will again be to make alternative random-heat energy
release paths more attractive than wedge-out.

In short, the wedge-out effect will be most effective when the sharpest
possible contrast between void surface pressure and interior void pressure
can be maintained.  A very sharp, very well-defined transition from extremely
high pressure to a hard vacuum should allow the wedge-out effect to produce
quite phenomenal accelerations of some subset of the void surface molecules.

It is worth noting that wedge-out is primarily a gaseous effect, and that for
single-molecular fluids it is unlikely to become a significant factor until
after the vaporization event.  The reason is that surface tension will tend
to resist allowing any of the fluid molecules to "get ahead" enough to permit
wedge-out to dominate until after vaporization of the surface.

However, for multi-molecular fluid wedge-out may become a significant effect
even in the pre-vaporization early acceleration phase, since the dominant
fluid may permit other components to "leak out" into the leading edge of the
void surface.

3.7.2  Wedge-Out Cascades

Wedge-out becomes even more interesting when it is note that it can (at least
in principle) be cascaded.  That is, the highly accelerated molecules
resulting from the first major wedge-out event may, if sufficiently even in
both radial and temporal distribution, come together to cause a second wedge-
out event in which another component is "launched" at even higher velocity. 
Just as a multi-stage rocket permit small payloads to reach phenomenally high
velocities, such wedge-out cascades could in principle result in phenomenally
high final velocities of a (generally very small) "payload" of lightweight,
fast particles that have been "distilled" out of the liquid by repeated
applications of the wedge-out effect.

Due to the self-focusing effects of surface tension, it appears quite likely
that first-order wedge-out effects can almost certainly be obtained by high-
quality cavitation experiments.  An interesting experimental question is then
whether second and higher-order wedge-out cascades can be constructed to
provided even higher final accelerations and energies.  One clear requirement
for obtaining higher-order wedge-out events will be a very high level of
initial symmetry, since otherwise the growth of turbulence will rapidly make
the formation of a sharp pressure/vacuum interface impossible.

Speculations concerning the limits of compression in sonoluminescence would
tend to support the idea that some sort of unusual acceleration phenomenon
exists in highly symmetrical cavitation phenomena [7].  Wedge-out and wedge-
out cascades could well provide just such a mechanism.

3.7.3  Wedge-Out Shells

Because the wedge-out process will favor lighter, faster molecules and ions,
there should be a natural tendency for components of the fluid to separate
and form shells of distinct chemical composition during the last stages of
the collapse.  These wedge-out shells are of interest because formation of
"clean" shells of a uniform composition may encourage the development of
wedge-out cascades (and thus much higher final temperatures and pressures).

The formation of wedge-out shells could also result in new (very short-lived)
liquid surfaces, since the newly separated components may behave differently
under the extreme pressures of the void implosion.  Whether these new liquid
surfaces would have time to influence (in particular, to re-focus) the inward
motion of the void surface is difficult to say without explicit simulation or
experimental modeling.

3.7.4  Ionization of Wedge-Out Shells

It should be noted that because the wedge-out process is primarily mechanical
in nature, it should be capable of accelerating not just whole molecules, but
also charged (ionic) fluid components.  Thus is should be possible for highly
charged wedge-out shells for form during the collapse process, owing to the
preferential separation of any charged ions whose average velocity in the
fluid is greater than that of the majority fluid molecules.  The formation of
such charged shells will of course be an energy-consuming event, and would in
general reduce the final intensity of the collapse.

However, the formation of charged wedge-out shells would be extremely
interesting from both a theoretical viewpoint and an exploratory,
experimental viewpoint.  Recombination of the charges after rebound would
lead to various forms of electromagnetic radiation, whose overall features
would tend to be complex due to the details of the recombination currents in
the type of highly dynamic environment that should exist during the final
stages of the void collapse.

It is entirely possible that sono-luminescence [8], an effect that has
already been observed in cavitation research, is an example of one of the
electromagnetic radiation effects stemming from wedge-out shell ionization of
the inner layers of a void collapse.  Further examination of such
luminescence effects as possible evidence for the formation of wedge-out
shells would be most interesting, since it would tend to confirm that
cavitation possesses an acceleration mechanism (wedge-out) by which
exceptionally high energies could be obtained by void collapse phenomena.

One of the most important "side-effects" of the formation of ionized wedge-
out shells would be its potential as an effective tool for exploring the
details of the final void collapse.  Radiation released by recombination
should be rich in information about both the formation of such shells and
their subsequent development.  It should also provide important information
on how various experimental parameters may result in higher or lower final
pressures.  Appropriate ions could also be "seeded" at low levels to act as
tracers for higher intensity void implosions, since in general the energy-
draining formation of high levels of charge in the shells will need to be
avoided to reach the highest possible final pressures and temperatures.

3.7.5  Plasma Event

For highly symmetrical, highly energetic void collapses, the mechanisms of
wedge-out and (possibly) wedge-out cascades should be capable of producing 
late implosion energies that are easily capable of ionizing the imploding
gas.  (This tends to be confirmed also by the presence of ultraviolet light
in sono-luminescence [9], which implies a significant level of ionization.) 
This ionization process may be assisted or quickened by the formation of
charged shells when the liquid contains ionic components, but should also be
capable of occurring as a result of inward acceleration effects alone.

The mid implosion phase is arbitrarily defined as ending when the void
surface becomes primarily a plasma in composition (the Plasma Event, or PE). 
It should be noted that the plasma formed at the time of this event should
for a very symmetrical collapse consist of very high velocity ionized
particles whose velocity vectors are still directed inward toward the void
center.  As long as this inward velocity of the plasma remains largely
intact, the maximum implosion temperature and pressure will not yet have been
reached.


3.8  LATE IMPLOSION

3.8.1  Initial Conditions for Late Implosion

The late implosion phase extends from the plasma event until termination of
the implosion by one or more rebound effects, which are discussed in the next
section.

Ideally, late implosion should begin as a set of inwardly directed plasma
ions that are still focused on a shared central point.  Wedge-out effects are
still conceivable during the late implosion if the radial and temporal
symmetry of these inwardly directed plasma components remain high enough.

3.8.2  Micro Ion Fusion (MIF) Analogy

One way of viewing the potential intensity of the late implosion is to note
its similarity to a microscopic version of what is known as "ion fusion," in
which very fast ions are directed inwards to a single target point in order
to induce light-element fusion.  Although constructed in a very different
fashion, the "machinery" of early and mid implosion of a well-formed void may
very well be capable of producing a final scenario that is essentially the
same as that of ion fusion -- that is, a set of roughly synchronized ions
moving radially inwards at a very high velocity towards a common target.

This "Micro Ion Fusion" (MIF) analogy also helps emphasize the need for more
experimentation to determine what, exactly, is the final densities and
temperatures possible through cavitation collapse.  Because of the extreme
simplicity of "building" liquid void "mechanisms" in comparison to large-
scale ion fusion machinery, an experimental verification that inwardly
directed plasma streams actually do exist in some forms of cavitation would
be of considerable interest theoretically and experimentally.


3.9  IMPLOSION TERMINATION

In this section the various mechanisms that lead to termination of inward
motion of the void surface are discussed.

3.9.1  Implosion Termination Due to Pressure of Void Gas

The single most detrimental to achieving high-intensity void implosions is
the presence of a low-quality vacuum in the void -- that is, the presence of
significant levels of void gases.

The negative impact of void gases can be imagined in part by recognizing that
in the extreme case they result in a stable, non-collapsing gas-filled bubble
instead of an unstable void.  In less extreme cases the void gases will
result in a very rapidly increasing pressure profile as the void shrinks in
size, so that at some point the outward pressure of the void gases will cause
the collapse process to stall.  Such a scenario will result in moderately
high pressures and temperatures through simple compression, but is unlikely
to result in exceptional pressure or temperatures for three reasons:

   1)  the collapse energy will be spread out over too many gas molecules,

   2)  wedge-out acceleration mechanisms will be "shut down" prematurely, and

   3)  gas impinging on the void surface may damage its symmetry and cohesion.

The first effect of excessive spreading of energy is unavoidable because the
central gases retain their "information" on their relative position and thus
behave in a simple spring-like compressive fashion.  As mentioned earlier in
the discussion of void formation and entropy, achieving very high pressures
and temperatures depends critically on getting as much of the system as
possible to "forget" the original comparatively orderly arrangement of
molecules, and instead have them "compete" for a single position in space and
time.  Void gases fail to meet this criterion, and thus act as a serious
"drag" to increasing the final collapse intensity.

The second effect of premature shut down of the wedge-out acceleration
mechanism is a consequence of the fact that wedge-out requires a very sharp
pressure/vacuum transition at the void surface, a condition that is not
possible if the gas pressure within the void rises rapidly.

Finally, the presence of gases will also negatively impact the void surface
by encouraging small-scale turbulent behavior and lessening surface tension
through the impact of the gas molecules.  These are comparatively minor
effects, but still may need to be taken into account in some cases.

Termination of implosion due to void gases is significant not only because of
its negative effects on final intensity, but also because it is very easy for
voids to acquire such gases.  Voids naturally tend to "scoop up" gases as
they form, so that initially the voids that form in a fluid are unlikely to
be capable of significant implosion intensities.  On the other hand, the void
mechanism itself can be used to help rid the fluid of dissolved gases, so
that a similar experimental arrangement can be used both to "clean" the fluid
and subsequently produce more intense collapses.

Another key factor is fluid vaporization, since some level of fluid molecules
will almost certainly end up in the void.  The use of cooled fluids and fluid
mixtures with very low vapor pressures can help greatly in this area.  (An
added benefit is that these same characteristics will also tend to help in
the formation and preservation of surface tension during the early stages of
the void collapse.)

3.9.2  Implosion Termination Due to Void Surface Turbulence

Prior to the vaporization event, a fluid with strong surface tension is
likely to be highly effective at minimizing turbulence in the void surface. 
This again emphasizes the importance of maintaining a liquid surface for as
long as possible during the void collapse, since even a small delay in the
onset of turbulence can provide a significant improvement in the orderliness
of the final collapse.

However, after the vaporization event the radial and temporal self-focusing
effects of surface tension will be lost and turbulence will begin to grow
much more rapidly.  Compression will lead to a limited form of radial self-
focusing after the VE, since each void surface molecule will be constrained
into a largely radial path by the pressure of the molecules around it.

However, this limited form of compression-induced radial alignment is
unstable with respect to temporal alignment.  That is, the pressure effects
will also increasingly encourage some parts of the surface either to fall
behind or race ahead of the average void surface.  (Wedge-out acceleration is
in fact a "favorable" form of this temporal instability effect, provided that
the inward wedge-out of fluid occurs in a sufficiently symmetrical fashion.) 
After a time, the instability of the surface with respect to time will cause
a general loss of order and cause the "directed heat" of the imploding
molecules to become ordinary (non-directed) heat.

Again, the presence of a very hard vacuum in the void interior can help delay
the onset of temporal instabilities by providing a clear "direction" in which
some fraction of the faster molecules can head.  This "race effect" can in
effect "filter out" initial levels of turbulence by allowing a subset of the
molecules to enter an energetically favorable region of (empty) space.

Another factor that can help delay turbulence is a high particle momentum.  A
heavy-mass molecule should tend to be affected by turbulence at a somewhat
lower rate than a light, easily disturbed molecule.

3.9.3  Implosion Termination Due to Loss of Confinement Layers

Another mechanism by which implosion maybe terminated is loss of one or more
of the outer "confinement layers" surrounding the collapsing void.  These are
layers of fluid that should (ideally) display a pressure profile that during
the final stages of collapse increases monotonically in towards the central
collapse.

Stated in a somewhat different form, it is important that all the layers of
fluid around the collapse retain either a slight inward velocity or no
velocity at all during the period of the final collapse.  If any of these
outer layers "rebounds" and loses its pressure prematurely, the net effect
will be a "peeling back" of layers until the central void collapse is
reached.  As the decompression reaches the central void it will rapidly
become turbulent and then rebound back into the surrounding fluid.

A qualification to this is that if the lost confinement layer is far enough
out from the central collapse, it may not influence that collapse until after
the central void has reached its maximum intensity.

To avoid termination due to the loss of confinement layers, the overall
pressure profile around the central void should at least be taken into
account in modeling the final collapse.  Modification of the decompression
and compression cycles for the void should then be able to limit or avoid
premature rebound of such confinement layers.

3.9.4  Implosion Termination Due to Charge Build-Up

As mentioned earlier, the wedge-out effect should be capable of producing
some separation of ionized fluid components, leading to the build-up of
layers of charge around the collapsing void.  The formation of significantly
charged shells would be a significant drain on the energy available to the
collapse process, and in some cases may be sufficient to halt the implosion.


3.10  REGION OF MAXIMUM ENERGY (ROME)

The late implosion phase ends with termination of directed inward motion, and
results in a (generally turbulent and roughly isotropic) region of maximum
energy density.  Due to turbulence, this Region Of Maximum Energy (ROME) will
in most cases be a ragged-edged region in space-time, and will contain a
(generally very small) quantity of very high temperature gases.

The duration of the ROME will depend largely on how smoothly the confinement
pressure profile around the ROME falls back to zero.  If the profile falls in
an orderly, uniform fashion the ROME may persist considerably longer than for
the case of an irregular breakup of the pressure confinement profile (which
will in turn lead to earlier loss of one or more confinement layers).  As in
ion fusion devices, the use of high-mass particles for the fluid may also
help extend the duration of the ROME through simple inertial effects in both
the ROME itself and in the surrounding confinement pressure profile.

As described earlier, experimental evidence for ROMEs that contain high-
temperature plasmas already exists for some cooled water-based cavitation
systems [3] [9].  Thus it appears likely that even more intense ROMEs can be
created in future generations of cavitation systems.  Given reports of
effective temperatures in the tens of thousands of degrees for existing
cavitation systems and the existence of many currently poorly controlled
parameters in such systems, it appears likely that ROMEs with temperatures in
the million degree range are at least plausible.  The combination of possible
accelerating mechanisms such the wedge-out effect and existing reports of
very high temperatures would certainly appear to make the effort to at least
try for such high temperatures plausible.

Obviously, on of the most interesting experiments to try if high-intensity
ROMEs can be created and verified would be fusion of light hydrogen isotopes
such as tritium and deuterium, possibly in combination with lithium.  Indeed,
in some cases such materials might even act as important experimental probes
for testing and gaining a better understanding of ROME properties.


3.11  POST-IMPLOSION REBOUND

Post-implosion rebound is most notable here in that it may help generate a
second-generation (explosively formed) void.  Such effects will be increased
if the implosion produces a net release of energy.  Cyclic void formation
processes, such as those provided by sonic standing waves, will need to take
rebound into account to accurately model and "tune" the cyclic void formation
process.


4.  EXPERIMENTAL

4.1  MATERIALS

4.1.1  General Materials Characteristics

The following is a list of general characteristics that should be favorable
towards the production of intense cavitation events:

   1)  Resistance to void formation

   2)  Low vapor pressure

   3)  Simple, highly stable molecular composition

   4)  Small molecule size (atomic being ideal)

   5)  High molecular weight

In general, the harder a liquid is to cavitate, the more likely it will be to
produce highly intense void collapses.  Resistance to cavitation tends to
indicate both very strong intra-fluid bonding and a low vapor pressure, both
of which should be highly advantageous to void formation and collapse.

The need for a low vapor pressure is a direct consequence of the need to keep
a very hard vacuum in the void interior.

Simple, highly stable molecules are needed to prevent non-collapse mechanisms
paths from draining energy from the void collapse.  Molecules that are easily
broken apart may both absorb energy and complicate surface mechanics during
the early collapse.

Molecules that are too large will be hard to accelerate during and rearrange
during the final stages of collapse, and in extreme cases could lead to an
"arch effect" in which the void surface briefly locks up into a highly
resistant, semi-solid structure.  Additionally, large "floppy" molecules are
more likely to convert the energy of rearrangement into wasted (premature)
heat.  From this perspective the ideal molecule for cavitation are those
whose molecules consist of single atoms, which are both highly mobile and
highly elastic under collision.

Finally, a high molecular weight is helpful (but not critical), since it can
extend the duration of the ROME and possibly make the ROME significantly more
intense.  The analogy here is a simple one:  Hitting two sledge hammers
together tends to be a more energetic event than hitting two ordinary hammers
together.

Where mixtures of fluids meet some of these criteria better than individual
fluids (e.g., by reducing vapor pressure), those mixtures may also provide
good cavitation candidates.

4.1.2  Specific Possibilities for Materials

When combined, these recommended characteristics point to two particularly
interesting classes of fluids for cavitation experiments:

   1)  Water, small-molecule water-like, and mixtures of these

   2)  Mercury, liquid metals, and mixtures of these

Mercury in particular is an exceedingly interesting candidate because of its
very high surface tension, low vapor pressure, single-atom composition, and
high molecular (atomic) weight.  However, it has the disadvantage of being
impermeable to nearly all forms of electromagnetic radiation, making it
difficult to verify the consequences of cavitation.  Indeed, in the case of
mercury it may be necessary to use an isotope such as tritium simply to
permit "fusion tracing" of the radiation results of cavitation events that
are (presumably) intense enough to fuse such materials.

There are many other metals (e.g, gallium, lead, tin, and the alkaline metal
of Li, Na, P, and Cs) that melt at low temperatures and are also relatively
easy to work with (and in the case of tin, far less toxic) than mercury.  For
such metals the term "cold" can be used relatively, since the key issues are
low vapor pressure and enduring surface tension, rather than low temperatures
per se.  Metals and other substances that maintain these characteristics at
high temperature should be quite usable, even if the absolute temperatures at
which they become fluids are well above room temperature.

Metal mixtures and mercury amalgams are also interesting candidates for
cascaded wedge-out effects, since it may be possible for distinct wedge-out
shells of different atomic masses to form more readily from such a medium.

Water and mixtures of low-mass, water-like molecules (e.g., the (CHOH)nH2
family that includes methanol, glycol, and glycerin) are also interesting
candidates due to their small sizes and strong, easily rearranged hydrogen
bonding.  Moreover, these media are much easier to work with experimentally
because of their transparency to most forms of electromagnetic radiation. 
Finally, water and related hydrogen-bonded liquids are capable of dissolving
a wide variety of ionic substances that could prove useful in both modifying
and experimentally tracing cavitation properties in such fluids.

Mixing such hydrogen-bonded fluids can drastically lower freezing point of
the fluids, so that very cold initial fluids can be used both to greatly
reduce vapor pressure during void expansion, and to increase the period of
time for which surface tension will provides self-focusing and acceleration
of the void surface.

4.1.3  Purity of Materials

As noted before, "ready to use" materials should have extremely low levels of
dissolved gases to prevent premature implosion termination.  Salts and other
soluble materials are less likely to interfere, but the possibility that they
could enhance the formation of charged layers and thus reduce the energy of
the final collapse should at least be taken into account.

A more complex issue is that of particulate impurities.  In general some
degree of particular impurities are likely to be needed to provide seeds for
nanovoid formation, but too many particles (especially too many large
particles) is likely to degrade the ability to form high-quality voids.

Ideally, particles in the fluid should be as small as possible while still
permitting formation of nanovoids at reasonable decompression intensities,
and common enough to be readily available at the void formation site.

4.1.4  Gas and Particulate Doping

Both gases and particulate material may be intentionally introduced into a
fluid for the explicit purpose of providing "targets" for the final implosion
of cavitation voids.

In the case of gases the idea would be to add a very low lever of dissolved
"target" gas, such that a very small quantity of the gas will be swept up by
the void during expansion.  A disadvantage of such an approach is that even a
very small increase in the total gas in the void may greatly reduce the final
intensity of the collapse.

A potentially superior approach is to intentionally introduce very small,
solid particles that will act both as seeds for initial void formation and as
"targets" during the final collapse.  The solid state of the target keeps it
from interfering with the collapse process, and potentially could allow a
sharp pressure/vacuum transition to exist in the void surface until the very
last instant of the collapse.

While a solid target in a vacuum void will fall somewhat due to gravity, the
generally very short time between expansion and collapse (e.g., half of an
ultrasound cycle) should keep the target particle near the needed location. 
The intentional introduction of a slight vertical asymmetry into the initial
expansion of the void might also provide a mechanism by which the target
could be "tossed upwards" and subsequently fall back to the position where
the implosion will reach its maximum.  Finally, the high pressure of the
implosion surface should provide a strong sweeping effect on a solid
particle, moving it towards the center (but at the cost of some of the
spherical symmetry of the final collapse).

In general, seed/target particles should have surfaces that are not easily
wet (adhered to) by the fluid selected.  Thus a seed/target in liquid metal
should not mix with the metal, and a seed/target in water and water-like
fluids should have a hydrophobic (oil-like) surface.  The importance of this
is that it provides a natural base for the formation of a nanovoid.

One interesting long-term class of seed/targets for water like-fluids and
possibly liquid metal fluids) would be graphite-jacketed "fullerene" spheres
of large size.


4.2  INITIAL TEMPERATURE

In general, the absolute temperature of a cavitation fluid should be less
significant than how temperature effects vapor pressure and the duration of
surface tension during collapse.  Thus a relatively high temperature for a
liquid metal such as lead might prove to be just as effective as a much lower
temperature for a mix of hydrogen-bonded, water-like liquids.

Thus temperatures should be selected primarily on the basis of how they
affect the particular fluid selected.  In general, the lower range of
temperatures at which the fluid remains free-flowing should give better
results than the higher temperature ranges for that same fluid.


4.3  INITIAL PRESSURE

In general a high initial pressure should help contribute to both the initial
implosion impulse and subsequent confinement of the implosion layers around
the collapsing void.  However, it should be noted that the decompression
method used will always have to "fight against" this initial pressure, so
that substantially more energetic decompression mechanisms may be required. 
This added energy then contributes to the void collapse once it is formed,
and so falls under the general rule of "the harder to cavitate, the better."


4.4  PHYSICAL SET-UP AND TECHNIQUES

4.4.1  Single-Node Sonic Decompression Methods

The most powerful and symmetrical decompression generators are spherical-
symmetry, single-void ultrasonic generators, such as those described by
Steven Jones for ongoing work at BYU [4].  It is likely that if interesting
collapse phenomena can be found that these types of generators will be the
best for initial identification and exploration of such effects.

A somewhat less exact form of single-node decompression would be to use
either a long parabolic reflector and a plane wave generator, or two "end to
end" parabolic reflectors with a small, point-like sonic generator at the
focus of one of the generators [10].

4.4.2  Multi-Node Sonic Decompression Methods

Another class of sonic based generators are "lattice" generators that create
a three-dimensional field of alternating compression and decompression
regions, each of which has a reasonably high (e.g., cubic) initial level of
symmetry.  The simplest way to construct an example of such a cavitation
lattice is to direct a plane sound wave into a corner-cube reflector. 
Reflections within the corner-cube will then result in the formation of a
field of compression/decompression regions with roughly cubic symmetry.

Since lattice methods provide only modest radial symmetry during expansion,
it is likely that a high surface-tension liquid and careful timing of the
decompression/compression cycle would be needed to allow surface tension to
thoroughly restructure the void surface at peak void displacement.  In
particular, a pressure cycle that would tend to extend the period of peak
displacement would provide more time for reshaping of the void surface.


4.4.3  Impulse Decompression Methods

Impulse generators could be constructed in the lab by techniques as simple as
tapping a piston that has been arranged to decompress a fluid within a
cylinder.  Such simple methods would have difficulty competing with
ultrasonic generation, but impulse decompression has the advantage of being
able to generate unusually severe decompressions.

For example, the same cylinder just described could be severely decompressed
by firing a high-speed projectile at the piston, instead of simply tapping it
with a hammer.  For very pure, very low-gas fluids such explosively rapid
decompressions could make intense cavitation possible in fluids that might
not respond to ultrasound or other milder techniques.


4.5  SONIC FREQUENCY AND INTENSITY

A final point about experimental setups is simply to note the importance of
scanning a broad range of both frequency and intensity for sonic (and
impulse) generation methods.  Because the number of variables that could
potentially affect final cavitation intensity, it may, for example, not
always be the case that "more intense is better."  Subtler effects such as
loss of confinement layers around a void may in some cases mean that lower
intensities or frequencies will work better.

Eventually, detailed shaping of sonic pressure cycles to match the particular
characteristics of a fluid would probably provide the best results.


5.  Ultra Cavitation in Nature

Perhaps one of the most interesting aspect of the idea of ultra cavitation is
that if it exists at all, it may quite possibly also exist as a natural
effect.  This is particularly interesting in light of earlier proposals by
Jones et al [11] that the heat output of large planets may in part be due to
some form of very-low-level natural fusion.  Natural ultra cavitation could
quite possibly provide both a plausible mechanism by which such very-low-
level fusion might occur.  Perhaps more importantly, the specificity of the
conditions needed for ultra cavitation to occur should make such hypotheses
empirically testable through simulations of relevant natural conditions.

5.1  CANDIDATE FLUIDS FOR NATURAL ULTRA CAVITATION

The major natural fluids in which some form of cavitation could (at least in
principle) occur include:

   1)  Surface and free-flowing water

   2)  Ocean bed and thermal vent water

   3)  Hydro fluids associated with deep faults

   4)  Hydro fluids associated with subduction

   5)  Volcanic magmas

   6)  Liquid iron alloys at the mantle/outer-core interface

   7)  Liquid iron alloys at the inner-core/outer-core interface

5.2  EARTHQUAKES, SUBDUCTION, AND IMPULSE DECOMPRESSION

With possible exception of free-flowing surface water, the best candidate
mechanism for void formation in all of these fluids would be some form of
impulse decompression.  The likelihood of successful void formation by this
method will fall drastically for very deep, very high-pressure fluids such as
the liquid iron alloys of earth's outer core, but cannot be excluded even
here for sufficiently energetic impulse decompressions.  If cavitation does
occur at such depths, it would inherently be very high in available energy. 
The question would be more one of whether the very rapid collapse of a void
at such a depth would permit the development of a high degree of symmetry in
the void.

The simplest model for natural impulse decompression is the "snapping" of a
rock that already contains a fluid-filled crack.  Such a scenario places
sever stress of the fluid near the center of the crack, and should be capable
of forming significant voids even deep within the earth.

The "snapping" idea is particularly interesting in conjunction with hydro
fluids that are associated with both deep faults and subduction zones, where
often extremely vigorous fracturing of rock is a commonplace occurrence.  It
seems likely that in such regions the basic requirements for cavitation of
some sort are not only available, but highly likely.

The question then becomes one of whether the fluids involved are capable of
meeting the criteria for ultra cavitation -- that is, cavitation in which the
void contains a vacuum of exceptionally high quality, and the spherical
symmetry of the void is high.  Both hydro fluids and (perhaps) highly fluid
magmas could be worth considering in this regard.

A question of this type cannot easily be answered without detailed estimates
of the nature of such fluids, their gas contents, how they will evolve over
time (e.g., will they tend to degass?), and other features relevant to the
formation of high-quality voids.  A positive feature of such questions is
that they should be amenable to experimental testing and simulation.

As a research issue, perhaps the best approach to resolving whether a natural
form of ultra cavitation could lead to very-low-level fusion within the earth
would be to first verify whether or not significant levels of fusion can be
achieved with cavitation in a controlled laboratory environment.  If the
answer to that question should turn out to be "yes," then it would seem
highly appropriate for the question of natural ultra cavitation fusion to be
pursued with great vigor through a combination of theory, speculation,
numerical simulation, and direct testing of simulated deep-earth environment.


6.  NUMERICAL SIMULATION OF ULTRA CAVITATION

Ultra cavitation is a problem that fairly well begs for detailed numerical
simulation, since many of the details of how and whether certain intensities
can be reached will be dependent on behaviors that cannot be accurately
estimated by manual methods.

One interesting possibility for speeding the development of ultra-cavitation
simulation programs could be to "borrow" features from simulations of other
larger collapse phenomena, such as ion and laser confinement fusion, or
possibly even supernova collapse simulations.  However, highly tailored
software would clearly be needed to accurately model this special class of
collapses in which the final stages may involve a small number of atoms.

Numeric simulation would also help wade through the potentially vast number
of chemical and mechanical parameters that could be modified for ultra
cavitation experiments, particularly in combination with experiments to
identify interesting or unexpected regions of behavior.


7.  SUMMARY

In summary, it seems likely that the full range of temperatures and pressures
available through the simple, well-known phenomenon of cavitation has yet to
be fully explored.  This paper has presented the premise that when cavitation
is combined with a very hard void vacuum and a very high level of spherical
symmetry, a significantly enhanced process that is referred to in this paper
simply as "ultra cavitation" may extend obtainable pressures and temperatures
into ranges normally reserved for intense plasma phenomena.

Experimental verification of this very-high-end range of cavitation effects
would be of great interest scientifically and perhaps practically, since it
would mean that such very high pressures and temperatures could be obtained
far more easily, and with far less complex equipment, than was previously
thought possible.

Finally, the possibility of naturally occurring ultra cavitation provides an
intriguing possibility for experimental examination of the Jones et al
hypothesis that planetary heating is in part the result of very-low-level
fusion deep within the earth.


8.  REFERENCES

    [1] Terry B. Bollinger (terry@asl.dl.nec.com), "In defense of Steven
        Jones."  Newsgroups: sci.physics.fusion, Message-ID:
        <1992Dec15.233802.16896@asl.dl.nec.com>, Date:  Tue, 15 Dec 1992
        23:38:02 GMT.

    [1] Terry B. Bollinger (terry@asl.dl.nec.com), "HICCUP Fusion."
        Newsgroups: sci.physics.fusion, Message-ID:
        <1992Dec16.201708.26730@asl.dl.nec.com>, Date: Wed, 16 Dec 1992
        20:17:08 GMT.

    [3] Steven E. Jones (jonesse@physc1.byu.edu), "Sonofusion at BYU."
        Newsgroups: sci.physics.fusion, Message-ID:
        <1992Dec16.113342.285@physc1.byu.edu>, Date: 16 Dec 92 11:33:42 -0700.

    [4] Steven E. Jones (jonesse@physc1.byu.edu), "Sonoluminescence
        References."  Newsgroups: sci.physics.fusion, Message-ID:
        <1992Dec18.111410.294@physc1.byu.edu>, Date: 18 Dec 92 11:14:10 -0700

    [5] Private conversations with Jay Yow regarding his research work at UMR.

    [6] Private email from Tom Droege regarding ultrasound equipment.

    [7] B.P. Barber, S.J. Putterman, "Observation of synchronous picosecond
        SL," Nature, 352:318, 25 July 1991.  [Reference provided by S. Jones.]

    [8] D.F. Gaitan, L.A. Crum, C.C. Church, R.A. Roy, "Sonoluminescence and
        bubble dynamics for a single, stable, cavitation bubble," J. Acoust.
        Soc. Am. 91(6): 3166 (June 1992).  [Reference provided by S. Jones.]

    [9] R. Hiller, S.J. Putterman, B.P. Barber, "Spectrum of Synchronous
        Picosecond SL", Physical Rev. Letters, 69:1182 (24 Aug. 1992).
        [Reference provided by S. Jones.]

   [10] Tom Droege (DROEGE@FNALD.FNAL.GOV), "Misc." Newsgroups:
        sci.physics.fusion, Message-ID:<921221133431.20c01220@FNALD.FNAL.GOV>,
        Date: Mon, 21 Dec 1992 21:02:37 GMT

   [11] Steven E. Jones (jonesse@physc1.byu.ed), "Natural Fusion in Earth
        Hypothesis." Newsgroups: sci.physics.fusion, Message-ID:
        <1992Dec28.121139.306@physc1.byu.edu>, Date: 28 Dec 92 12:11:39 -0700.


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