A Liquid Sodium Simulation of the α - Ω Dynamo
A Proposal to the NSF for Continuing Support of a
Laboratory Simulation of
The α - Ω Accretion Disk Dynamo that
Powers AGN
& Creates the Magnetic Fields of the Universe
STIRLING A. COLGATE, HOWARD F. BECKLEY, JAMES C.
WEATHERALL,
& VAN D. ROMERO,
Physics Dept., New Mexico Institute of Mining &
Technology,
Socorro, NM 87801
(Submitted to the National Science Foundation 22 September 2000)
A liquid sodium analog experiment is proposed as a
proof-of-principle of the α - Ω dynamo. The
successful demonstration of the α - Ω dynamo will
have important astrophysical significance. A substantial energy
component of the universe appears as magnetic energy filling the
walls and voids, and is particularly evident in AGN in galactic
clusters. The origin of this field is not explained. Assuming
that the major free energy of the universe progresses through
galaxy formation to massive galactic central black holes, the
black-hole accretion disk provides a natural α -
Ω dynamo which can process black-hole binding energy into
helical, force-free magnetic field. The experiment is designed to
simulate the type of field deformations produced by Keplerian
rotation and the collision of stars with the accretion disk. Other
applications of the α - Ω dynamo include the
generation of magnetic fields in stars from deep convection and in
neutron stars during supernova collapse.
With seed money from the NSF and LANL, the design and major
construction of the experiment for the Ω-Phase, and
two-thirds of the electronics have already been done. Initial flow
visualization experiments have been performed using water to
demonstrate the
Ω-flow field and the α-deformation required by the
dynamo. The expected positive gain in the experimental apparatus is
supported by a kinematic dynamo code at LANL. The proposed
new work is to use the apparatus to demonstrate the α -
Ω dynamo using a conducting fluid, liquid sodium, as the
fluid medium. The first phase of the experiment is designed to
show a multiplication of
~ × 20 of the toroidal field from an initial bias
poloidal field, and the second phase, a positive dynamo gain.
Confidence in the engineering feasibility and safety is gained from
recent successful liquid-sodium experiments at Riga and Karlsruhe
on a different class of α2-dynamo (not applicable to
accretion disks). However, the scale and cost of the proposed
α - Ω dynamo is much different from those experiments,
which were conducted in facilities left over from fast reactor
coolant work. For example, there is a vast difference between
using sodium at 600 C as a fast-reactor coolant and using sodium
at 110 C as in this experiment. Safety is a paramount concern in
this project. The experiment itself will be reviewed and
conducted at a major high explosive testing facility, the
Energetic Materials Research and Testing Center (EMRTC), located
at the New Mexico Institute of Mining and Technology.
The dynamo within the accretion disk forming the massive,
central black hole of nearly every galaxy almost certainly converts
this black hole binding energy, the major free energy of the
universe, into the previously unrecognized form of intergalactic
magnetic field. With equal conviction this ubiquitous massive
dynamo in all AGN must be an α - Ω dynamo. We propose
to demonstrate in the laboratory that such a dynamo works.
We plan to test first the now constructed Ω-Phase apparatus of a liquid sodium dynamo experiment.
Here, the differential winding, the Ω-flow, is
Keplerian flow in the disk, Ω ∝ R-3/2, meridional circulation in stars, Ω ∝ R-x, and Couette flow in the experiment, Ω ∝ R-2. We plan to measure first the
expected large multiplication, ~ × 20, of
an initial bias poloidal field, into toroidal field by Couette flow
alone in the liquid sodium. This multiplication is the first step of
the α - Ω dynamo (Parker 1955; Parker
1979). We plan to continue with constructing the driving
mechanism for the α-deformation in the same
apparatus, and test the α-Phase leading to dynamo
gain. We expect to achieve positive gain within the design limits of
the strength of the containment vessel and power of the
experiment.
The α - Ω dynamo is fundamental to most
astrophysical dynamos. We believe that this dynamo is formed because
of (1) the differential rotation within the Keplerian disk, the Ω-deformation, and (2) the plumes produced by star-disk
collisions. These plumes are ejected to large heights above the disk,
most probably give rise to the broad emission lines (Zurek et
al. 1994) and give rise to the α deformation.
Pop III stars are a small mass fraction, ~ 10-3 to -4, of the pre-galactic mass, but their predicted collisions with
the disk are frequent enough to drive the necessary helicity or α-deformation of the α - Ω
dynamo. In addition to this translation of matter and magnetic flux
to large heights above the disk, we have predicted, and now confirmed
with a laboratory water flow visualization experiment (Beckley &
Colgate 1998) how expanding plumes in a rotating frame, rotate (in
the same direction every time) differentially through a finite
angle, ~ π/2 radians, relative to the rotating
frame. This finite, coherent, rotation angle forms the basis for the
α-deformation, or helicity, of the α - Ω dynamo. The plumes are produced by driven pulsed jets in
the experiment. They occurs naturally within the postulated black
hole accretion disk dynamo by star-disk collisions, and similarly
from convective plumes in stars and planets and even in the
neutrino-heated halo of neutron stars during the supernova explosion.
The prior verification of plume rotation is central to the feasibility
of the experiment. The verification of the rotation of the toroidal
magnetic flux entrained within the plumes is similarly crucial to the
dynamo. We plan to measure this rotated flux in the experiment
under conditions less extreme than would predict positive dynamo
gain. Similarly, the differential rotation of the Ω-deformation is created in the laboratory experiment as
stable Couette flow between two rotating cylinders. The advantage of
stable Couette flow in the laboratory is the greatly reduced friction
and hence reduced power required for reaching a given velocity and
hence, a high value of magnetic Reynolds number, Rm,Ω ≅ 120 in the experiment. We plan to
measure this multiplication first.1
When all the above parameters of the experiment have been measured and
understood, we plan to increase the power, velocities, and
magnetic Reynolds numbers to the point of positive dynamo gain.
Finally we are interested in extending the theory of the α - Ω dynamo in the context of astrophysics. Already at Los
Alamos, in conjunction with the initiation of this experiment, we
are developing the theory of (1) the formation of the accretion
disk leading to the galactic black hole via Rossby vortices, (2)
the formation of the α - Ω dynamo within this disk,
and (3) the formation of the force-free helix that distributes the
magnetic energy and flux throughout the universe. However, this
experiment is hosted by NMIMT, where also the VLA and VLBA share
joint faculty appointments. It is fair to say that almost every
observation in the radio spectrum depends upon synchrotron
emission from some object with a magnetic field of unknown
origin. One of us, Prof. Weatherall shares a joint appointment
with NRAO. This offers the opportunity for a much needed link
between theory, observation, and experiment. We plan to
pursue calculations that apply the α - Ω dynamo to the
formation of the magnetic field of neutron stars during their
supernova phase of their formation. Supernova calculations are
unique for this endeavor in that the input of kinematic dynamo
calculations can come directly from supernova modeling
calculations where large-scale convective plumes have been shown
to be fundamental to the explosion mechanism (Herant et al. 1994).
1 We believe it is feasible with this
multiplication to look for the predicted Balbus-Hawley
(Chandrasekar-Velikhov) instability due to the toroidal field alone
and in intrinsically stable Couette flow (Chandrasekhar 1960;
Chandrasekhar 1981; Balbus & Hawley 1998; Balbus & Hawley
1991; Hawley & Balbus 1991; Hawley & Balbus 1992).
With $100k initial seed money from NSF and $30k from
LANL, a full mechanical design of the Liquid Sodium α - Ω Dynamo experiment has been completed, Fig. 1, as well as
the construction of the rotating parts, Fig. 3. This system,
designated the
Ω-Phase, is designed to produce the critical magnetic
Reynolds number Rm,Ω ≅ 120 in Couette flow in
liquid sodium.
Figure 1: Figure 1 shows a detailed design
drawing of the rotating components of the the Ω-Phase of the Liquid Sodium α - Ω
Dynamo experiment. By comparing Figs. 1 & 2 the labeling of
the various components can be compared and identified in the two
drawings. The main cylinder of radius, R0 = 30.5 cm
rotates between two bearing mounts with three bearings. In the Ω-Phase no plume piston, or hydraulic drive is shown,
even though the constructed aluminum parts of Fig. 2 show the
port plate and two ported reservoir plenum cylinders. These parts are
necessary to define the plume end of the Couette flow annular
space.
Figure 2: Figure 2 shows shows the design
drawing of both the rotating components as well as the plume drive
mechanism of both the α- and Ω-Phases of the Liquid Sodium α - Ω Dynamo experiment. The primary drive shaft, belt pulleys,
and electric motor are not shown, but have been designed, components
purchased, and partially constructed.
Figure 3: Figure 3 shows the constructed
parts the Ω-Phase of the Liquid Sodium α - Ω Dynamo experiment mounted on the bearings and
supporting pedestals. Also shown is the port plate and two ported
reservoir plenum cylinders and the inlet & outlet recirculating
oil rotary unions. The primary drive shaft, belt pulleys, and
electric motor have yet to be added.
Figure 1 shows a detailed design drawing of the Ω-Phase of
the Liquid Sodium α - Ω Dynamo experiment. The
functions of the components of Fig. 1 can be recognized from the
sub-captions of Fig. 2. These describe the design of the entire
apparatus including the main rotating cylinder, the internal
construction of the rotating components, the plume drive piston,
the port plate, and ported reservoir plenum cylinders. The
oscillating hydraulic drive for the jet- plume production is a
hydraulic cylinder driven by a secondary source of power.
Figure 3 shows the constructed rotating components of the Liquid
Sodium α - Ω Dynamo. The plume port plate and reservoir
plenum cylinders are shown yet to be mounted internally. The plume
drive piston is not constructed in this phase. The plume port
plate is supported by both reservoir plenum cylinders for greater
rigidity. The rotating drive components of the experiment are not
yet mounted on the bearing supports. The massive bearing supports
and base plate are surplus materials. Their their large mass,
~ two tons, is designed to reduce the rotating vibration
amplitude. The oscillating hydraulic drive mechanism for the jet-
plume production is not constructed, awaiting the α-Phase
of the experiment.
The α-Phase, Fig. 2 with the addition of the drive mechanism
has been designed to produce the pulsed plumes for the α-
deformation. The helicity produced by the plumes in a rotating
frame then permits the measurements of dynamo gain. The
centrifugal stress in the vessel walls is designed to be 1/3 of
the yield strength of the rotating chamber. (The total running
time of the apparatus at modest speed should be no more than
several hours and at extreme high speed only tens of minutes.) The
equipment for the rotating power has been identified and reserved
from surplus. The HTD belt-drives, bearings and bearing mounts
for both the low-speed drive tube and high-speed drive shaft for
power transmission have been purchased, constructed and
assembled. The principle components of the hydraulic system
necessary to produce the plumes have been designed, identified and
reserved. Similarly the recirculating heated-oil system used to
liquefy the sodium through heat transfer in the inner cylinder and
possibly cooling has also been designed. We have designed the
high-pressure oil lubrication system used for the dynamo
main-support bearings and for the hydraulic ram thrust bearing
assembly. All components for this system have been reserved from
surplus.
Due in part to in-kind contributions from the Research
Division of NMIMT, a new laboratory space for the design,
development and construction of the experimental dynamo and its
electronic instrumentation has been set up. A new computer for
instrumentation control and data acquisition has been purchased
and set up. Los Alamos National Laboratory has contributed funding
to complete the construction of the Ω-Phase. This will
particularly help in validating the kinematic vector potential
dynamo code for use with astrophysical dynamos. A web site has
been established. (Please see http://physics.nmt.edu/~dynamo/.)
The electronic instrumentation has been designed and constructed with
the help of undergraduate students, Clint Ayler and Manuel Jaramillo.
It has been designed to measure the pressures, temperatures and
magnetic fields at various locations of the rotating fluid and to be
converted for digital transmission to the computer. In total 128
sensors are designed to be monitored at ~10 MHz data
rate from a rotating system with a centrifugal acceleration of ~1000 g at the sensors and ~200 g at the
electronics. The sensors have been identified, purchased and
verified. The data aquisition, transmission, and interconnection with
the computer has been designed, and bread-boarded as well. The design
of the circular printed circuit is now in fabrication.
The magnetic instrumentation uses small, single-axis Hall effect
detectors without internal gain (18 Hall sensors in the Ω-Phase and 108 in the α-Phase). These magnetic sensors have
sufficient dynamic range to measure from the earth's field, 0.2 G
to the expected transient, back-reaction saturation field, 15 kG,
if positive gain is achieved. These miniaturized detectors are
assembled into three-axis packages and arranged in linear and
matrix arrays. Included with the Hall detectors are the associated
multiplexers for power distribution and signal collection, linear
and log operational amplifiers, analog to digital converters, and
digital transmission through capacitative slip-rings to the
computer, now tested and bread boarded. This instrumentation
configuration will allow for trouble shooting, diagnostics, and
calibration procedures to be established prior to the sodium
experiments. This instrumentation system has been designed to
ensure that the following can be observe in the rotating frame:
1) The temperature of the oil and of the sodium at several
locations to ensure that the sodium is
liquefied and not overheated by friction.
2) The pressure at 5 radii at the end wall to derive and
interpret the Couette flow rotation profile.
3) The magnetic field in 3-axes at 6 locations radially
within the rotating fluid in order to measure the
poloidal and toroidal field, the Ω-Phase.
The toroidal multiplication, Btoroidal/Bpoloidal ~ 10 to 30, is the Ω-effect.
4) The magnetic field in 3-axes in a 5 × 6 = 30 matrix array located opposite one plume at the end-wall. This
allows a reconstruction of the field topology (rotation) produced by
the plumes. The poloidal component of this field distribution,
derived from the plumes is the helicity or α-effect. This instrumentation is to be constructed
just for the α-Phase.
In addition, in the stationary frame there are provisions to
monitor 15 additional detectors of temperatures, pressures, and
the quadrupole bias field while the rotating experiment is in
progress. In total, the instrumentation was designed to determine:
1) The separate partial toroidal and poloidal
multiplications.
2) The combined partial dynamo gain.
3) The positive exponentiating gain.
4) The saturated dynamo field configuration if positive
gain is achieved.
In summary, the mechanical design of the experiment is
completed. A working laboratory for the experiment is established.
The major fraction of the mechanical equipment has been
constructed and purchased. We have designed, tested,
bread-boarded, and initiated construction of the diagnostic
sensors and electronics to instrument the experiment. The
experiment has been modeled with realistic experimental values of
magnetic Reynolds number. The plume rotation has been
experimentally verified. These allow the prediction of:
1) a large measurable signal of the Ω- and
α-effects separately at well below 10% of the design stress
and power.
2) partial, (negative) dynamo gain at 10% of design stress
and power.
3) positive gain at ~1/3 the yield stress of the
vessel and less than the limiting power.
The following paper has been submitted for publication.
- Beckley, H.F., Colgate, S.A, Romero, V.D., &
Ferrel, R., "The Flow Field for a Liquid Sodium α - Ω Dynamo Experiment, I: The Plume Rotation Experiment" 2000, Physics of
Fluids, submitted.
The following talks have been given:
- Beckley, H.F. & Colgate, S.A., "Fluid Flow
for an Experimental α - Ω Dynamo: Plume Rotation"
1998, APS, DFD., Abst. 5253.
- Colgate, S.A. & Beckley, H.F., 1998, "Flow
Field for an Experimental α - Ω Dynamo: Plume
Rotation" APS, DFD., Abst. 5252.
In addition talks have been given at: The New Mexico Symposium,
NRAO, 10/99; NMIMT colloquium, 12/1999; Aspen Center For Physics,
winter work shop 1/31/2000; Cornell Univ. colloquium, 3/10/2000;
SLAC, colloquium, 4/18/2000; APS Meeeting, LongBeach, 4/29/2000;
Aspen Center For Physics; 6/2000.
In addition the theory and astrophysical motivation for the experiment
has been substantially advanced supported by Los Alamos National
Lab. We, (Colgate, Hui Li, Vladimir Pariev of LANL and R. Lovelace of
Cornell ) believe we have solved five major problems that when linked
create a causal picture of the flow of the major free energy in the
universe. The α - Ω dynamo is only one, but
crucial step in this sequence. Starting with the collapse of a
galactic mass Lyman-α cloud, the baryonic fraction
forms, with cooling, a flat, co-rotating disk. We are presently
calculating how tidal torquing separates angular momentum and mass to
produce the "flat" rotation curve mass distribution, Minterior ∝ 1/R. We believe we have solved a long
standing problem of the hydrodynamic transport of angular momentum in
accretion disks, the α-viscosity problem, by the
excitation by radial pressure gradients of co-rotating Rossby
vortices. The excitation of Rossby vortices depends upon entropy
conservation and hence thickness, which in turn with the
"flat" rotation mass distribution predicts the previously
enigmatic 108 Mʘ black hole. With the theory
and experiment of this proposal we have predicted the α - Ω dynamo in this disk, which, when saturated, converts all the
free binding energy of the black hole to magnetic energy. We have
calculated how this magnetic energy naturally forms a large,
force-free helix, filling the inter-galactic space in the walls with
evidently, stable, force-free magnetic flux. Because of this
stability we predict that the configuration lasts a Hubble time in the
walls and voids. We are now calculating how this force-free flux
partially reconnects and slowly over a Hubble time, converts the
magnetic energy to the extragalactic cosmic ray spectrum. The short
loss time of the CRs from the walls to the voids avoids the GZK
cut-off, and the energy required is supplied by the magnetic field
energy from the BH binding energy through the α - Ω dynamo of every forming galaxy. Papers that have been
written or submitted on these topics are: Lovelace et al. 1999;
Colgate & Buchler 1999; Li 2000; Colgate & Li 1997.
The constraint of the conservation of energy and momentum are the
final tyrannies in astrophysical theories. Dark matter has allowed
us to tinker with gravity, and the universe is an infinite sink for
angular momentum. Entropy can always be dispersed at 3 deg K in
the BB radiation or at 2 deg K in the neutrino background (good
luck). Finally magnetic flux can be dissipated by reconnection,
but it can only be generated astrophysically by a dynamo (with
caveats).
There have been hundreds of papers and dozens of reviews on the origin
of galactic and extragalactic magnetic fields, but almost universally
the magnitude of the energy and of the flux required has not been
emphasized; yet a dynamo produces only magnetic flux and magnetic
energy (see Kulsrud 1999; Zweibel & Heiles 1997; Parker 1979;
Ruzmaikin 1989; Moffatt 1978; Krause & Beck 1998; Weilebinski
1993).
In addition, flux and energy are seldom emphasized in the observations
(see reviews by Miley 1980; Bridle & Perley 1984, Kronberg 1994
and the observations themselves, e.g. Perley et al. 1984; Taylor et
al. 1990; Taylor & Perley 1993; Taylor et al. 1994; Eilek et
al. 1984; Kronberg 1994). However, the magnitude of the implied fluxes
and energies, ~1060 erg, in galactic cluster sources
as well as ~1061 erg in field AGN outside clusters
in the radio lobes, are so large, ×104 and
×106 respectively compared to these quantities within
standard galaxies, that their origin requires a different source of
energy and a different form of the dynamo than a galactic one. The
difficulties associated with a primordial origin of the field is
recently augmented and reviewed by the analysis of Blasi et al. 1999,
leaving only an α - Ω dynamo in a BH accretion disk
dynamo as the plausible explanation. Figure 4 shows the rotation
measure maps of the AGN in the Hydra Cluster, (Taylor & Perley
1993) and of the cluster 3C75 (Eilek et al. 1999). These maps show the
immense dimensions, 50 to 100 kpc, over which the fields are coherent
in field direction and the underlying polarization in the case of
3C75. The absolute value of the fields, 33 μG in
the case of hydra and 10 to 20 μG in the case of
3C75 throughout the volume of these dimensions leads to the
extraordinarily large total energies.
Figure 4: Figure 4(a) shows the Faraday
Rotation map in color overlaid upon the emission contour map of the
Hydra Cluster (Taylor & Perley 1993). Figure 4(b) shows the
polarization of the emission ,Fig. 4(c), resulting in the Faraday
rotation map, Fig. 4(d), of the AGN in cluster 3C75 (Eilek et
al. 1999). The total emission from minimum energy arguments leads to
× 10 to 30 greater field energy than the Faraday
rotation measure. Figure 4(e) shows the force-free helix produced by
the boundary condition of the Rossby vortex accretion disk,
Fig. 4(f) (Colgate & Li 1998).
These energies are much larger than the binding energy of galaxies
×102 (including the dark matter) and the fluxes are
×103 greater than the magnetic flux of the galaxy
times the winding number of the galaxy in a Hubble time, ~50 turns. However, the free binding energy of the black
hole, ~1062 erg, and the winding number of
the disk forming the BH of nearly every galaxy is the feasible source
of both this flux and energy. The conversion of nearly all this
energy, ~90% to 95%, into a form of
magnetic energy that is not rapidly (in an Alfv'en time) dissipated
into an observational form is the challenge of the physics of the
accretion disk α - Ω saturated dynamo. Furthermore,
the distribution of this magnetic flux and energy throughout the
universe is an equal challenge. We believe this requirement can only
be met by the dynamo creating a cylindrically symmetric force-free
magnetic field, a helix. The dissipation of this extragalactic field
and the remaining 5% to 10% of the magnetic
energy in the form of the AGN spectra is the challenge of
understanding the plasma physics of reconnection and the consequential
acceleration in force-free fields. The discovery of this missing
magnetic energy is the challenge to observations. Together this would
explain the missing BH luminosity (Richstone 1998; Krolik 1998), the
fraction we do observe as the AGN phenomena, and the magnetic fields
of the universe. Finally the reconnection of these extragalactic
force-free fields during a Hubble time is the reasonable explanation
of the extragalactic cosmic ray spectrum. Only the α - Ω dynamo, when saturated, has the potential for transforming
the accretion disk kinetic energy into an axisymmetric force-free
field configuration. Finally the winding number or number of turns of
the inner most orbits of the accretion disk is so large in the
lifetime of the disk, ~1012 turns in
108 years, that the smallest dynamo gain per turn, a small
fraction of 1012, leads to saturation in a short time.
This high, near infinite gain avoids the question of the origin of the
seed field. This view of the dominant role of magnetic energy in the
universe is presented in Colgate & Li 1997; Colgate & Li 1998.
Figure 5: Figure 5(a) shows the sodium
dynamo experiment in comparison to the accretion disk dynamo of
Fig. 5(b). In both cases differential rotation in a conducting
fluid wraps up an initial radial field component into a much stronger
toroidal field. Then either liquid sodium plumes driven by a pulsed
jet or star-disk collisions eject and rotate a loop of toroidal flux
into the poloidal plane. Resistivity or reconnection merges this new
or additional poloidal flux with the original poloidal flux leading to
dynamo gain.
Figure 5(a) shows how the α - Ω dynamo works in the
Liquid Sodium Dynamo experiment and Fig. 5(b) shows how the
α - Ω dynamo works [in the accretion disk forming the
galactic black hole]. Differential rotation is established in the
liquid sodium, [ionized accreting matter], between two rotating
cylinders as Couette flow, Ω ∝ 1/R2, by driving
Ω1 = 4Ω0 where R0 = 2 R1 [and
Keplerian, Ω ∝ 1/R-3/2, around a central mass,
the black hole]. This differential rotation wraps up the radial
component of an initial poloidal, quadrupole bias
~100 G field made with coils [or Fig. 5(b(A)) an
infinitesimally small, < 10-19 G field from density
structure at decoupling]. The resulting toroidal field is stronger
than the initial poloidal field by Btoroidal/Bpoloidal = nΩBpoloidal is the number of
turns. This multiplication factor becomes nΩ ≅ Rm,Ω/2π where the magnetic Reynolds number Rm,Ω = Ω0R02/ηNa and
ηNa is the resistivity of liquid sodium or [for the disk,
ionized plasma, Rm,Ω = Ω0Hdisk2/ηplasma where the height of the disk, H0 >>
R0]. Then a driven pulsed jet [or a collision with the disk by
a star, Fig. 5(b(C))] causes a plume to rise towards the end plate
[or above the disk] with displaced toroidal flux forming a loop of
toroidal flux. The radial expansion of the plume material causes
the plane of this loop to untwist or rotate differentially about
its own axis relative to the rotating frame so that the initial
toroidal orientation of the loop is transformed to a poloidal one,
Fig. 5(b(D)).
Resistive diffusion in liquid sodium metal [or reconnection in ionized
plasma] allows this now poloidal loop to merge with the original
poloidal field. For positive dynamo gain, the rate of addition of
poloidal flux must be greater than its decay. It is only because the
toroidal multiplication can be so large or that Rm,Ω can be so large that the helicity of the α - Ω dynamo can be more rare and episodic. This
is different from the α2 dynamos of the Rädler
(Rädler et al. 1988) and Busse (Busse et al. 1996) experiment and
the Gailitis experiment (Gailitis et al. 2000) where the helical flow
must be steady and leads to positive dynamo gain at Rm,α ≅ 17. However, despite this low
Rm, this steady helical flow must be driven
and maintained by rigid vanes and walls so that the turbulent friction
with the walls is relatively large. The Ω flow on the
other hand is maintained in our experiment by Couette flow where,
because of stability, the friction loss is very much less, ~1/10. As a final thought, the α - Ω dynamo has episodic periods of turbulance, the plumes,
separated by relatively long periods of laminar flow. This may be
important if turbulence indeed interferes with dynamo gain as in the
Dudley James type flows. (pvt. com. J. Finn, J Laythrup).
We have simulated the α and Ω
flow fields in water (Beckley & Colgate 1998). Figure 6(a) is the
schematic showing the two differentially rotating cylinders and the
pulsed plumes. Figure 6(b) shows a side view of the pulsed, rising
and expanding plume outlined by a line of bubbles (like an entrained
line of force). Figure 6(c) is a plot of plume rotation angle vs
frame rotation angle from solid-body and differential frame rotation
data and plume rotation theory. Figures 6(d) and 6(e) are a time
sequence of the top view of a rising plume in a rotating frame
showing the progressive rotation of the plume angle as needed for the
generation of the coherent helicity.
Figure 6: Figure 6 shows a composite of the
flow visualization experiment where a rising plume in a rotating
frame, Fig. 6(a), is viewed from the side, Fig. 6(b), and
top, Figs. 6(d) & 6(e). The resulting angle of differential
plume rotation is measured and plotted as a function of frame
rotation, Fig. 6(c). (see http://physics.nmt.edu/~dynamo/)
Pariev et al. 2000 have performed kinematic dynamo calculations
using a 3-D vector potential code for the evolution of the magnetic
field as a function of time by a time-dependent velocity flow field.
The α - Ω dynamo, by its nature, is 3-D
and non axisymmetric, but the primary flow is circular, Couette or
Keplerian, with occasional non-axisymmetric flows or plumes. Thus the
code is written in cylindrical coordinates, analogous to both the
astrophysical or experimental geometries. We use the vector potential
for the calculated quantity, because then ∇ · B = 0 at all times and no periodic calculational "cleaning"
of ∇ · B has to be performed. The
boundary condition is perfectly conducting so that the flux through
the boundary must be constant in time. This allows for an initial
poloidal bias field, but thereafter the flux through the boundary must
remain constant. Therefore all the flux generated by a dynamo
solution must remain within the box. Since this is not the case for
either the experiment or the astrophysical circumstance, we must
simulate problems with the walls as far removed from the region of
action as possible. A non-conduction boundary condition requires the
solution of the external potential field at each time step and is
planned for the future.
Figure 7: Figure 7 shows the dynamo
calculations of Pariev et al. 2000 with an initial bias poloidal
field, Fig. 7(a), with radial and axial components. This field
is wrapped up by the differential rotation in the liquid sodium,
Fig. 7(b). A pair of plumes every N revolutions gives
rise to a gain Fig. 7(c) that shows marginal gain at a pair of
plumes each 6 revolutions. The exponentiating field energy is shown in
Fig. 7(d) where N=3 and the pulsed increase in field
energy is seen for each plume.
Figure 7(a) shows the cylindrical geometry with a radial initial
poloidal field, a potential field as will be imposed by external
coils. Differential rotation, Couette flow, Ω ∝ 1/R2, is imposed with a value of resistivity such that Rm,Ω = (R0 - R1)ν0/ηNa = 120. Figure 7(b) shows the
poloidal field wrapped up into a toroidal field with a ratio shown
in Fig. 7(c) as a function of radius. We expect to measure these
same quantities in the Ω-Phase experiment. Simulations show
the fields when a pair of symmetric, cylindrical plumes are
injected vertically of initial radius, rplume,0 = R0 / 6 or
2rplume,0 = dplume,0 = ( 2/3)(R0 - R1 ). For
positive dynamo gain, ≅0.12 per revolution, this pair of
plumes is pulsed once every 3 turns with a vertical velocity of
vplume,z = 0.5 v0. The simulated plumes are cylinders of
constant radius that untwist or rotate relative to the frame such
that their change in angle is π/2 radians when the background
fluid at the plume radius has rotated π radians. A marginal
positive dynamo gain of 0.01 per turn is observed for a pair of
plumes per 4 revolutions. In the experiment we expect the plumes
to diverge as they rise and rotate more rapidly when they strike
the end wall as observed in the fluid visualization experiment. As
a consequence of both these effects, the experimental plumes
should create greater helicity than in the simulations. Other
(unknown) effects will surely decrease the dynamo gain. We are
therefore planning the experiment to meet these conditions.
This section is more detailed than would be of general interest,
but our last proposal was firmly criticized for lack of detailed
engineering calculations of the strength of the vessel and the
power to drive it to the necessary magnetic Reynolds number.
Consequently we calculate the pressure and power as a function of
Rm,α &
Rm,Ω and then use an engineering stress analysis to
demonstrate that our constructed experiment, Figs. 3, meets the
criteria of the kinematic dynamo calculations above. These
criteria are Rm,α = 20 and Rm,Ω = 120 with
one pair of plumes per three turns. The size, power and cost of
the experiment are are related to these desired values of Rm.
We have chosen cylindrical geometry as the closest approximation to
the black hole accretion disk geometry and the most convenient for
construction. Spherical geometry would simulate stellar dynamos and
make easier the calculation of resistive boundary conditions. We
have also chosen Couette flow to minimize the fluid flow
dissipation rate and maximize the shear or differential rotation
for the Ω flow. For a given desired Rm we will
calculate how the pressure and power varies as a function of
R0, namely the choice of a size.
The centrifugal pressure in the fluid sodium determines the
required strength of the vessel wall. For Couette flow,
Ω ∝ 1/R2 or ν ∝ 1/R and the fluid pressure
becomes:
| |
(1) |
when R1 / R0 = 1/2. This ratio is chosen to
maximize the annular space, R0 - R1 for the dynamo and
hence maximize
Rm,Ω = (R0 - R1)ν0/ηNa, yet minimize
the acceleration and hence the wall stress at R1. For
rigid-body rotation and the thin-wall approximation, the inner
wall stress becomes
| τ1 = α1ρ1 = ρ1ν12/R1 = ρ1(ν02/R0)(R0/R1)3. |
(2) |
Therefore for the ratio R1 / R0 = 1/2, the inner
wall stress will be ×8 the outer wall stress without fluid
pressure. This then allows the outer wall to support primarily the
fluid centrifugal pressure rather than its own centrifugal stress,
whereas the inner cylinder supports just its own centrifugal
stress. Thus for a limiting wall stress or pressure and a desired
Rm,Ω, the stress decreases as 1/R02 and so there
is a large advantage to size. With this in mind we chose the
largest size for which there exists standard bearings, drive
belts, mounts, surplus materials, materials handling, and local
machine tools for finishing. This size is R0 = 30 cm, and
Z0 = R0 = 30 cm. We next calculate the achievable
Rm,Ω and Rm,α within the envelope of wall
stress and power and compare the results with dynamo calculations.
The power required to drive the Ω flow is more
complicated to estimate because the process of fluid dissipation is
less well known in the particular limits of this experiment. We
assume the Couette flow is absolutely stable and so the dissipation
within the bulk of the fluid depends only on departures from ideal
Couette flow. The primary departure is at the end walls where an
Eckman layer forms (Batchelor 1999) of thickness ΔZ ≅ Z0Rfluid,Ω-1/2. In our experiment the fluid
Reynolds number is Rfluid,Ω = (R0 - R1)νCouette/μNa = Rm,Ω(ηNa/μNa) = 9 × 106, where Rm,Ω = 120, ηNa = 750 cm2s-1 and μNa = 10-2 cm2s-1. With
Z0 = R0, the thickness of an
Eckman layer becomes ΔEckman=(R0/2)Rfluid,Ω-1/2≅7×10-4. The radial
flow velocity within the Eckman layers will be νEckman ≅ νΩ/2 because the flow is
dissipative. Thus the Reynolds number of the flow within the Eckman
layer becomes Rfluid,Eckman = Rfluid,Ω1/2/2 ≅ 1.4 × 103. The flow at this Reynolds number is
within the transition to turbulence and so we expect a larger
effective viscosity than μNa = 0.01 and thus a
larger thickness, Rturbulent,Eckman
> Rfluid,Eckman. Recognizing this
uncertainty, the power becomes the kinetic energy dissipated in the
fluid flow in a cross-sectional area of 2πRΔEckman. The change in specific kinetic energy occurs
between the Couette flow,
vCouette2 /2 and the wall at
v02(R/R0)2/
2. Then the energy loss in two layers becomes
| |
(3) |
This power is unrealistically small. It implies a
spin-down time of
| |
(4) |
Thus the spin down time corresponds to a number of turns
of
| |
(5) |
The power predicted is unrealistically small and the
number of turns for spin down is similarly unrealistically large.
The Eckman flow will be broken up in a complicated fashion by the
jet ports in one of the end plates, and so a more realistic
estimate of the power required is times ten larger, or 12 kW,
which in turn is modest. The scaling with Rm,Ω of
Eq. (3) becomes power so that again for minimizing power there is a significant
advantage in large size.
Similarly the plume power is small. The area of two plumes is
Aplume = 2πrplume,02 = 2πR02(rplume,02/R02), and so the plume power becomes
| |
(6) |
For vplume = v0/2, nplumes/turn = 1/3, and rplume,0 / R0 = 1/6, we have kW.
This too is modest and well within a feasible design limit of 50
kW. We expect the plumes and the Ω flow to interact adding
to the dissipation of the Ω flow, but this should be
proportional to the volume ratio, well within the factor of ten
additional dissipation allowed for. Thus we don't see power as
the limitation, but instead pressure and the strength of the
vessel.
The actual design parameters are: an outer cylinder of R0 =
30.5 cm (12 in) with a wall thickness of ΔR0 = 3.2 cm
(1.25 in) and test-space length of Z0 = 30.5 cm (28 in).
Since Rm,Ω = 120 and ηNa = 750 cm2 s-1,
ν0 = 6 × 103 cm s-1. Consequently the pressure of
the liquid sodium at the wall from Eq. (1) is P0 = 54 atm or
P0 ≅ 800 psi.
The thin wall cylindrical vessel under pressure is the simplest stress
analysis, σhoop,Al = PNa(R0/ΔR0) = 8000 psi, (Formula (1b), Table (29), p. 448, ``Formulas for
Stress and Strain'', Roark and Young 1975). Similarly there is an
additional stress due to the centrifugal acceleration of the
cylindrical vessel itself. In this case for aluminum with density 2.7
and again in the thin wall limit σhoop,Al ≅ ρAlν02((R0 + ΔR0)/R0) = 107 atm = 1570 psi (p. 566, ``Formulas for Stress and Strain'', Roark
and Young 1975). Since this stress is also a hoop stress, it can be
directly added to that from the liquid sodium to give a total hoop
stress in the aluminum cylinder of 9,570 psi. The aluminum of the
cylinder is 5083H3 which at a temperature of 110C has a yield strength
of 32 ksi. Thus we feel that the wall stress at the maximum conditions
will be 1/3 the yield strength. As an additional safety measure we
expect to band the vessel with stainless steel or
KevlarTM, pre-compressing the vessel by 2000 psi at
an internal stress of the banding of half the yield strength of the
banding.
The axial stress in the cylinder is determined by the integral of
the end wall pressure, Eq. (1), the force Fend divided by the
circumference and the thickness,
| |
(7) |
For ρNa = 1 and R1/R0 = 1/2, the axial
stress becomes
| |
(8) |
For the desired value v0 = 6000 cm/s, the axial
stress becomes 220 atm = 3,300 psi. This adds vectorally to the
hoop stress a small ≅10% addition. We will initially
perform the tests with the thrust end-plate welded and the driven
end-plate bolted using 40 grade 316SS 3/4 - 10 × 3 bolts on
a 32 cm (12.62 in) bolt circle. The resulting bolt stress becomes
40 ksi, an acceptable value.
The thrust end-plate is 6061T651 aluminum of thickness ΔZend = 3.2 cm (1.25 in), 61 cm (24 in) o.d. with an i.d. of
20.3 cm (8 in), Fig. 3(a). The driven end-plate is 5083H3
aluminum of thickness of ΔZend = 3.2 cm (1.25 in), 70
cm (27.5 in) o.d. with an i.d. of 17.8 cm (7 in), Fig. 3(b).
The maximum centrifugal stress in these annular plates is given by
(Formula (6), p. 567, ``Formulas for Stress and Strain'', Roark
and Young 1975) as
| |
(9) |
for the conditions Rhole/Router = 1/4 and the
desired velocity of v0 = 6000 cm/s. Thus the centrifugal
stress in the end plates is is negligible.
The bending stress due to the fluid pressure is more significant. We
must consider a circular plate of outer radius
Rend,outer, fixed by the cylinder and
loaded with the pressure distribution of Eq. (1) from
R0 to just inside R1 with the
inner edge guided. The bolting or welding to the cylinder serves the
purpose of "fixing" the outer radius with the inner radius
guided by the flanges and no axial confinement by the bearings.
Formula (3f) of Table (24), p. 345 of
``Formulas for Stress and Strain'', Roark and Young 1975 best fits
this circumstance of outer edge fixed and inner edge guided with a
linearly increasing pressure distribution extending from
R1 to R0. This approximation is
conservative relative to the quadratic distribution. The actual case
is between these limits. The maximum stress in the plate then becomes
| |
(10) |
for both the driven and thrust plates where R0/ΔZend ≅ 10. Then for R0/R1 = 2, Formula (3f)
gives KM<<596>>R<<439>>0 = 0.025 and KM<<597>>R<<440>>1 = 0.011. The
corresponding stresses become σend,R0 = 15P0 and
σend,R1 = 6.6P0. At our desired velocity of 6000
cm/s, these become σend,R0 = 8000 psi and
σend,R1 = 3500 psi. Both of these stresses are
modest compared to the strength of 6061T651 Al at 110 C of 32
ksi. The deflection of the plates under this load is given by
| |
(11) |
Where the plate constant, D = EAlΔZend3/(12(1 - ν2)) = 1.8 × 106. Then for Ky,R1 = 7 × 10-4, the deflection on axis δZend = 3 × 10-3 in. This is a negligible axial deflection considering
the end play in the thrust bearing and the much larger thermal
expansion of ΔZthermal = ΔTL0Kthermal ≅ 0.04 cm. We recognize that this
analysis is not exact, but plan to hydrostatically test the vessel,
measure the deflections, and compare to these estimates. Additional
strength can be added to weak points in the design later if
necessary, but the major fraction of the physics is accessible at
one half the planned maximum velocity and therefore at 1/4 the
stress.
The rotating mass of the vessel and shafts is Mrotating,R0 ≅ 300 kg. We have designed the bearings of nominal size 5
in, to operate for a "normal" lifetime of 108 revolutions (4
months at 30 Hz) with a load of ×100 the rotating mass.
Since the acceleration at R0 is a(R0) = 103 g, then we
can expect the bearings to support an out-of-balance rotating load
of 1/10 the static mass at R = R0. This is absurdly large.
The mass of the base and mounts is ≅×5 the mass of
the rotating apparatus or 1500 kg, so that without additional
restraint, the static support and mounts will restrain an
out-of-balance mass of ≅1.5 kg at R = R0. This also
is an absurdly large balance error. Our electronic sensors weigh
≅100 g and we expect to balance the rotating mass to
≅10 g corresponding to an out-of-balance load of 10 kg at
R = R0. Automotive crank shafts are routinely balanced to
0.01 g at R = 5 cm.
For Couette flow the inner cylinder rotates at Ω1 = 4Ω0 and so the acceleration becomes a(R1) = 8 × 103 g. This larger acceleration requires a more careful
balancing, but since the inner cylinder is a single part whose
mass Mrotating,R1 ≅ 20 kg or ≅ 0.06 Mrotating,R0, the degree of balance, 0.1 g at R = R1,
is also feasible on an automotive crank shaft balance system.
With this degree of out-of-balance mass of 10 and 0.1 g
respectively and thus with an out-of-balance load of
Mload = 10 kg, we expect a vibration amplitude of ΔR = 2Mloadg/(MmountΩ0,12) ≅ 2 × 10-4 cm. Since this is much smaller than the bearing clearances, we
expect the vibration amplitude to be that of the rotating mass
itself resulting in an amplitude of ×10 larger or ΔR = 2 × 10-3 cm. Again this amplitude of vibration is minor.
We next consider the rotating seals. We plan to operate the experiment
with a small quantity of mineral oil, ~ 10 to 100 cm3 in contact and floating above the liquid sodium. The density
of oil is ρoil ≅ 0.96 ρNa and
consequently floats above liquid sodium. We have performed MHD
experiments in the past taking advantage of this small density
difference (Colgate et al. 1960) and the oil coating avoids the
requirement for using an inert gas in the handling of liquid sodium.
Thus, in the rotating frame of the the experiment, the oil
"floats" to the axis. We expect to adjust the quantity of
oil such that the shaft seals are always bathed in oil, not sodium.
This ensures that the industrial problem of seals and liquid sodium is
avoided.
Solid sodium is an excellent thermal conductor, ≅ 1/2 that
of copper. Hence, the thermal time constant of the entire mass,
heated or cooled from inside the inner cylinder by hot oil is
theat = R02/Dthermal ≅ 600 s. Once the sodium
is hot enough to liquefy, at 100 C, convection is rapid and the
experimental mass becomes isothermal For example, the heating of
20 kW of heat or power dissipation is theat = (heat mass)/power = 2000 s or 1/2 hour. Similarly an experimental run
lasting 10 seconds at high power, e.g. 40 kW, will heat the whole
apparatus by 1 deg C without cooling, an acceptable small value.
Cooling by windage will be comparable.
Along with the proof-of-principle of the α - Ω dynamo, the project also seeks to connect the dynamo to the
physical universe. Besides the black hole accretion disk dynamo,
we see a natural way to produce an astrophysical dynamo during a
core collapse supernova. We propose to simulate such a dynamo
using an available numerical code.
Present type II supernova theory (Herant et al. 1994) predicts that a
robust explosion occurs only above the forming degenerate core because
of neutrino-driven large scale convection in the supernova. This
large scale convection in a rotating frame is exactly the conditions
necessary for the α - Ω dynamo. In fact, such a dynamo may be necessary for
the following reason: Ultra strong magnetic fields ~1012 G are a fundamentally accepted part of neutron star/pulsar
theory, but their origin and extraordinary uniformity among pulsars is
hard to explain. The standard explanation requires an initial field
of 108 G in the core of the supernova progenitor star for
every case, which seems unrealistic.
We believe that a natural way to arrive at the ubiquitous field of
~1012 G inferred from the
spin-down in radio pulsars is to create a dynamo during the supernova
event that naturally leads to a much stronger initial field and
subsequent crustal relaxation leads to the upper limiting field of
~3 × 1012 G (Flowers & Ruderman).
An additional consequence of the dynamo is to generate field with
high-order multipole moments at the neutron star's surface. Such
multipoles could facilitate the modeling of emission profiles which
don't fit the simple dipole model (Eilek et al. 2000).
The simulations of the supernova core collapse dynamo will use the
existing code, described in Section 4.4 Pariev et al. 2000. The
current version of the code assumes a boundary which is perfectly
conducting. A necessary modification of the code, to include
non-conducting boundary conditions, requires solution of the external
potential field, which is simpler in spherical geometry and will be
undertaken as part of the proposed work.
The fear of sodium may have been fueled by youthful indiscretions in
the chemistry lab, yet metallic sodium is a major industrial
chemical. Industry has used millions of tons of metallic sodium,
shipped in thousands of railroad tank cars of greater than 50 tons
each. These tank cars are surrounded by an oil jacket for heating.
This is accomplished with negligible risk to the public as determined
by DOT. The mass of sodium in each tank car is more than several
hundred times the mass of sodium used in our experiment. Sodium is
also shipped in barrel size containers where the container is
non-returnable. Liquid sodium is the lowest density, high
conductivity fluid that is biologically benign. There is a vast
difference between using sodium at 600 deg C as a fast reactor coolant
and using sodium at 110 C as in this experiment. Much of the high end
technology of liquid sodium was developed for the high temperature
coolant purpose. Those facilities, built on a massive scale and now
surplus, have been used for two recent successful sodium dynamo
experiments in East Germany and Latvia (Gailitis et al. 2000; Busse et
al. 1996; Rädler et al. 1988). These experiments were performed
in immense halls for full containment of a liquid sodium equipment
failure. We believe that this scale, cost, and the equipment is an
unnecessary burden. We expect to test a different dynamo flow field in
more modern and modest equipment, developed in the laboratory and
easily moved periodically to and from an adjacent, proven testing
facility for high-energy materials (whenever testing with liquid
sodium). These tests will be performed in a safety test cell and
remotely. This facility, the Energetic Material Research and Testing
Center (EMRTC) has a 60 year history of tens of thousands of accident
free high explosive tests. Sodium is very safe compared to HE; it
cannot detonate. Finally one of us (Colgate 1955) has had extensive
hands-on use of liquid sodium in laboratory experiments for
determining MHD stability for fusion confinement.
The experiment will be perfomed in compliance with Federal, State,
Industry and Institutional safety practices and procedures
involving the receipt, storage, handling, disposition and use of
sodium metal. Because of length, the Safety Practices,
Procedures and Compliance are presented in our web-site
http://physics.nmt.edu/~dynamo/.
A removable, electrically heated, safety shield will surround the
cylindrical vessel and will be useed whenever the apparatus is
rotated and filled with either oil or sodium. This will
confine any dynamic sodium loss and absorb the kinetic energy and
containment of disrupted parts should a mechanical failure occur.
Operating procedures will include: safety training, balancing,
hydrostatic pressure testing with oil, pressure deflection checks,
calibration of pressure sensors, relief-valve testing and setting,
and thermal controls. Because of length, these Operating
Procedures are also presented in our web-site for the project:
http://physics.nmt.edu/~dynamo/
1) The sodium experiments will be performed at the Energetic
Materials Research and Testing Center (EMRTC), a division of
NMIMT, Socorro, NM, where explosives and armaments have been
tested and developed since WWII. Many students, graduate and
undergraduate, work at EMRTC, so that strong student participation
has been a tradition for 58 years. Thus education, safety, and
health are fundamental to the operation as well as the basic
engineering and experimental expertise.
2) The VLA and VLBA operations center of NRAO is located
on the NMIMT campus. Several Physics Department faculty positions
are jointly held at NRAO (e.g. Prof. J. Weatherall, Co-PI). Thus,
astrophysics plays a major role in the Physics Department where the
principal investigator is an adjunct professor.
3) The calculational simulation work has been initially
performed at Los Alamos National Laboratory in the Theoretical
Division. Recently three year funding has been obtained from
within the lab, "LDRD" (S.A. Colgate, coPI at Los Alamos), that is
supporting kinematic dynamo calculations, vortex accretion disk
theory, calculations of the helix-jet formation of AGN resulting
from the saturated dynamo, and general relativistic effects close
to the black hole. This work is done in both T-15, plasmas, and
T-6, astrophysics. The PI holds an associate position in
astrophysics at Los Alamos.
4) It is reasonable to expect a future expansion of this
computational work and theoretical support both at New Mexico Tech
and at other universities. Particularly we hope to interest the
University of Chicago with its strong magnetohydrodynamics and
dynamo physics program and funding under ASCI to participate in
the modeling and analysis.
5) Initial financial support for the fluid flow
visualization experiments has been given by both NMIMT through
EMRTC, (~$13k), and the IGPP University program of Los
Alamos National Lab (~$7k per year for three years). This
support has lead to the flow visualization experiments that have
defined the fluid flow field for the sodium dynamo experiment and
serendipitously initiated the Rossby vortex accretion disk
mechanism. It is reasonable to expect modest future support.
Stirling Colgate is an astrophysicist. He holds an associate
position (retired) at LANL and is an Adjunct Professor of Physics
at NMIMT. He has had extensive past experience as an
experimentalist in the plasma physics of fusion and sodium MHD
experiments. His experience with liquid and solid sodium
experiments include four MHD experiments performed by Colgate
(1954, 1955) and Colgate, Furth, & Halliday (1960). He also has
an extensive reputation in theoretical astrophysics. Funding
request is for travel only.
Howard Beckley is a Ph.D. graduate student in
experimental astrophysics at NMIMT. He has over 16 years
experience in prototype and development machining with
approximately 10 years of design engineering experience embedded
within that. The Phase I development and operation of this
project is his Ph.D. dissertation. Funding requested is for
salary, publication costs and travel.
James Weatherall is a Associate Professor of Physics at
NMIMT. He specializes in theoretical astrophysics, and is a
Collaborating Scientist at NRAO. Funding request is for summer
salary and travel.
Van Romero is an Adjunct Professor of Physics and Vice
President for Research at NMIMT. He is a past director of the
Energetic Materials research and Testing Center (EMRTC) at NMIMT.
His specialty is elementary particle physics, and has worked
jointly on the flow visualization experiments. Funding request is
for travel only.
The following LANL staff are partially supported for
theoretical work on the galactic dynamo and its consequences for
AGN and quasars. (LDRD, 3 y)
John Finn is a staff member in T-15, theoretical plasma
physics at LANL. He has published in dynamo theory, written
kinematic dynamo codes, and helped direct Pariev in writing the
kinematic dynamo code. (LANL support)
Vladimir Pariev is a graduate student at Univ. of Arizona (Jokipii and
Levy professor) who has spent summers at LANL, published in GR of
black holes, and written and tested the α - Ω
code. This fall he will continue with his theoretical dissertation on
the experimental and galactic dynamos under the direction of Finn and
Colgate. (LANL support)
Hui Li is a member of group X-6 who has specialized in
x-ray and gamma ray emission mechanisms and spectra. He will be
instrumental in the astrophysical interpretation of the saturated
dynamo and AGN. He has also led the effort on the Rossby vortex
mechanism of accretion disks and thus the hydrodynamic basis of
the galactic dynamo. (LANL support)
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