The UAH Spinning Terrella Accelerator Robert Sheldon
Over the past few decades, there has arisen a new realization that
plasma acceleration may be the dominant mechanism responsible for the
highest particle energies seen in space. Since increasingly
sophisticated computer simulations have shown that hydrodynamic shock
acceleration cannot explain the energetic particles observed, we
propose a novel kinetic plasma process, a dynamic 3-fluid, 3-D
mechanism responsible for the acceleration of highly collimated jets
observed in active galactic nuclei (AGN), young stellar objects (YSO),
Jupiter, and Earth. Such a theory would be a major undertaking
ab initio, but may prove to be a convincingly simple laboratory
experiment. We have developed a tabletop laboratory experiment that
can verify our acceleration theory, involving a spinning magnet in the
presence of a plasma source. As we explore the parameter regimes that
have a measurable effect, we provide experimental constraints crucial
for constructing a quantitative theory. And if the mechanism can be
shown to be relatively efficient, it could provide a new technique for
producing keV-MeV ion beams useful in accelerator and plasma fusion
physics. But most importantly, if these theories can be shown to scale
up to the size of our solar system, they provide an elegant solution
to the problem of generating astrophysical jets, a problem plaguing
astrophysicists since their discovery over 30 years ago.
The observations of astrophysical jets are as breathtaking in their
beauty as they are puzzling in their symmetry (see figure 1).
Although these objects have been known for over 30 years, there exist
no viable theory (Zhang99) to explain the two pencil thin jets
of plasma blasting in opposite directions from the center of active
galactic nuclei (AGN) or from young stellar objects (YSO).
FIGURE 1: Two examples of astrophysical jets, galactic (top panel)
and stellar (bottom panel).
- Previous Work
Despite many diagnostics on their composition, speed, origin,
distribution and the like, the driving mechanism that powers and
maintains this dynamic system is still unknown. Early work in the
1970's focussed on the properties of a jet of relativistic fluid
(e.g., Blandford82), but were found to be unconstrained and
perhaps unstable. The evidence that magnetic fields were an important
component of astrophysical jets came from two sources: the
observations of synchrotron radiation, and the exquisite symmetries in
the system which required a globally anisotropic medium. Thus work,
done in the 1980's added magnetic fields to stabilize and direct the
fluid flows, but inconsistently, for it did not allow the magnetofluid
to produce magnetic fields itself. The recognition that magnetic
fields are not just important components of astrophysical plasma jets,
but a driving force has led in the 1990's to the development of
magneto-hydrodynamic (MHD) 3-D models that self-consistently derive
the flows and the magnetic fields.
Such a progression has occurred also in space plasma physics, with
mature, large-scale, fully 3-D, non-dissipative MHD codes only now
returning quantitative results. Despite their many successes and
obvious future glory, one message is abundantly clear: they cannot
describe the energetic plasma in the high-beta, inhomogeneous,
large-gradient magnetic fields found at the centers of most
magnetospheres. For example, the Earth's ring current, a ~6
mega-ampere current that encircles the Earth at a distance of ~3
R_e and produces a 100--400 nT decrease in the surface magnetic
field during a major magnetic storm, is completely absent from all
such MHD codes. That is, a current system that can hold 1/2 of the
entire energy released in a magnetic storm is not itself derivable
from MHD. Thus the holy grail of self-consistency, of agreement
between particles and fields, slips through the mesh of all MHD models
in the presence of large-gradient fields, such as those in the core
engine of astrophysical jets.
But no negative criticism should be taken seriously until there is a
positive and constructive solution offered. We therefore turn to the
requirements, the constraints put on any astrophysical jet theory by
The characteristics of YSO jets and blazar jets obviously vary by
orders of magnitude, but if we suppose that their similar
characteristics reflect a similar mechanism, we can draw some far
reaching conclusions. Such an assumption may be completely unwarranted
of course, but like the apocryphal story of Newton and the apple
unifying celestial mechanics with gravity, a unifying mechanism is
inherently satisfying and therefore theoretically compelling. Quoting
extensively from Pringle93 at the 1992 ``Astrophysical Jets
As I mentioned earlier, one point of this meeting is
to draw together the experts on extragalactic jets and protostellar
jets and to see if we can make common ground. The reason why one can
try to do this, is that one can say similar things about the jet
acceleration mechanism in both the extragalactic and the stellar
cases... For example one can argue that these jets are not driven by
radiation pressure, since in most instances the luminosities fall well
below the Eddington luminosity..., and one can also argue that the
jets are not pressure driven in view of the short cooling time for the
jet material in the protostellar case, and the lack of dense and hot
enough material to provide the jet-nozzle in the extragalactic
case. In view of this, jet theorists have taken refuge in magnetic
fields as the underlying acceleration and collimation mechanism for
both the protostellar and the extragalactic jets... The basic
ingredients of such a model are reasonably well agreed upon. They are:
first, a central potential well, provided by the star in the
protostellar case, and a massive black hole in the extragalactic case;
second, an accretion disc, in order to provide the energy to power the
jet and also the required symmetry for jet production; and third, a
well-ordered magnetic field threading the disc in the perpendicular
However, if we accept the hypothesis that both sets of jets are driven
by the same underlying mechanism, then by use of Occam's Razor we can
start to say things about what might or might not be required in the
theorists' black box. For example, since jets are produced just as
easily by protostars as by galactic nuclei, it is evident that neither
black holes, nor relativistic effects are necessary for jet formation
and any model which requires such effects can be discounted. Similarly
jet formation requires neither a central star spinning at break-up
speed...nor the existence of a boundary layer between disc and
star..., since black holes can provide analogies to neither of
these. Thus already we can start discarding some of the models that
are around in the literature--not because they are necessarily wrong,
but because they fail the test of simplicity (Occam's razor).
Pringle then goes on to make a list of characteristics which should be
addressed in any jet theory. We abbreviate his list as follows:
The ratio of the jet speed to the escape velocity of the
central object. Pringle derives a value of unity for YSO jets, and
gamma factors of ``a few'' for AGN jets, which, he argues ``has
significant implications for the magnetic model, the most important of
which is that the disc knows where its center is, for that is where it
produces the jet. Thus while self-similar models (e.g.,
Blandford82) are a valuable first step, they cannot be the full
answer...the preferred model must be one which is able to select the
central regions for jet production.''
The ratio of mass flux in the jet to disc accretion rate.
Pringle argues that this should be no more than 30%, which implies
again a central source, since if most of the mass in the accretion
disk is expelled in the jet, then ``this would make star formation a
remarkably inefficient process.''
The ratio of the radius at which collimation occurs to the
radius of the central object. Pringle argues for ratios < 10,000
for YSO, and <100 for AGN. He concludes ``thus it is important to
discover whether the mechanism which accelerates the jet material must
also do its own collimation, or whether it can rely on some
surrounding material to do the collimation for it.''
Variability. Pringle asks the question whether the
variability in YSO and AGN jets are alike, ``It will be important to
establish whether there are similarities, in timescales for
variability, or degree, between the two types of jet. The theorists
will need to ponder whether the variability is just due to variations
in the central accretion rate (due perhaps to some property of the
accretion disc) or whether it is due to some intrinsic property of the
acceleration or collimation mechanisms.''
One- or two-sidedness. Pringle asks whether a jet theory
should be symmetric (two-sided) or not (one-sided), and concludes that
the data is leaning toward symmetry.
How big a [magnetic] field do we need? Pringle calculates
the back pressure of a jet and compares it to the magnetic
pressure. From this calculation he concludes ``that in general the
poloidal field required to power the jet is insignificant as far as
the structure of the disc is concerned. Thus from the disc's point of
view, powering the jet requires only a weak magnetic field.''
Where does the [magnetic] field come from? Pringle
discusses two possibilities, that the magnetic field is some global
ambient field entrained in the disk and is advected inwards by
accretion, or that the accretion disk itself produces internal
magnetic fields through dynamo action. His calculations convince him
``that the disc itself is likely to contain fields with strengths much
greater than the strength of the poloidal field required to drive the
Do all jets have accretion discs, and/or do all accretion
discs have jets? Pringle argues that the data are ambiguous. ``In the
extragalactic case, the problem with deciding if all discs have jets
is obscured by the uncertainty of deciding whether all (active)
galactic nuclei have discs. In the protostellar case, complete and
unbiased surveys surveys are hard to come by, but it is beginning to
look as if one can make the case that all objects in the rapid
accretion phase, when they presumably have active accretion discs,
display phenomena associated with collimated molecular outflows.''
More recent observations
Since that meeting, observations have poured in from recently opened
observatories that have extended the multifrequency spectral range of
blazars as well as improved the resolution of previously observed
spectral ranges. At the International Workshop on Blazar Continuum
Variability in 1996, a number of these new observations were reported
that put tighter constraints on blazar models. R. Blandford
(Blandford96) summarized the conference by making the points:
Hydrodynamic Jets The distance a hypersonic jet propagates
in a constant homogeneous gas is the product of Mach number and jet
diameter. However extragalactic jets are much longer than this, which
Blandford attributes to possible power-law density variations in the
ambient pressure away from the galaxy. However in the case of M87, he
acknowleges that the jet must be collimated within 300 Schwarzschild
radii, a task that only magnetic confinement can manage. He doesn't
say whether that magnetic confinement contributes to the pressure
gradient needed for extended jets.
Variability Much progress has been made in correlating
multi-spectral data of variability, from radio to gamma-rays. In
some cases strong correlations were found, such as visible and
gamma-ray in other cases little correlation was found, such as
radio and gamma-ray. But at least in some cases, there is strong
evidence that travelling shocks within the relativistic jet are
responsible for this cross-scale variability
(Marscher96). There is also evidence from the inverse Compton
models that the different frequency photons all derive from the same
relativistic energy electrons (Ghisellini96). This suggests
that the variability is not due to compositional changes in the jet
(different energies, or species), rather it is due to inhomogeneities
in the density and magnetic field of the jet (e.g., in shocks).
Accretion Disks Blandford says that there is general
agreement that disks are essential to jet formation. "However we do
not often have direct evidence of this at the radii where the jets are
supposed to be formed, although there are more and more examples of
rotating gas at larger radii." From which we infer that the data are
hard to get, but support the hypothesis that all jets have disks.
Fundamental properties Blandford writes "If we reduce
everything to fundamentals then a plausible set would be the mass of
the [black] hole, the spin of the hole and the mass accretion rate. To
this set of `intrinsic' parameters, I would add the extrinsic factors,
the viewing angle and the nuclear star and gas densities."
Summary of Observations
From the reports, we can see that the new data of 1996 have confirmed
and deepened the observational constraints known in 1992. The data all
point to a relativistic jet arising from a system that includes an
accretion disk, arising from the center of the system and collimated
by magnetic forces. Recent studies by Zhang also imply that the core
must be spinning at rather high rates.
The theory is based on the kinematic effect of grad-B-drift, which
occurs wherever the magnetic field is not uniform. A dipole magnetic
field is just such a magnetic field which, because of the lack of
magnetic monopoles in nature, is also the simplest configuration of
any magnetic field. Thus wherever or whatever forms magnetic fields in
nature, at sufficient distances from the source it will acquire a
dipolar configuration. This universal toplogy is a crucial requirement
if the mechanism is to work on length scales from centimeters in the
laboratory to millions of kilometers in AGNs.
In such a dipole field, the grad-B-drift causes not just opposite
charges to separate, but different energies to separate when in the
presence of an additional drift. Thus the combination of
grad-B-drift (from dipole fields) with ExB-drift (from rapidly rotating
magnetosphere) frustrates the ability of newly injected hot plasma
(near the equatorial plane) to find a low energy neutral equilibrium,
which leads directly to space charge formation Alfven63. Space
charge produces parallel potentials and draws currents from the
``ionosphere'', currents which are still unable to neutralize the
space charge because the hot ions or electrons have a different
perpendicular energy from the parallel accelerated plasma, and thus
follow different paths. Only scattering events can neutralize these
species, which occur on a much longer timescale in this collisionless
plasma than the above drifts. Even the growth of instabilities,
apparently, occurs on too long a timescale to affect the scattering
rate and neutralize the plasma.
So although the ``ionosphere'' is a plentiful source of cold plasma,
the distances involved in bringing it to the equatorial plane mean
that pure inertia will generate large space charge potentials. The
evolution of that space charge in a dipole magnet field generates an
electrostatic quadrupole. It is this quadrupole effect that may
precipitate electrons in both hemispheres to generate the aurora, and
it is this quadrupole that accelerates ions up from both hemispheres
to generate the ring current. If this quadrupolar charge separation
mechanism is a robust instability of two-fluid models, as we argue
below, then it may be the mechanism that taps the accretion disk
energy and directs it out the axis of the jet.
Obviously, this growth of the separation electric fields cannot
continue unchecked, so we need to identify the timescale or spatial
scale at which the mechanism saturates. Since the inability of first
order ExB drift to neutralize the charge separation led to the space
charge in the first place, it requires the second order drift,
(ExB)xB, to short out the growing electric field (Rothwell95).
Calculations for a typical AGN magnetic field gave an upper limit of 1
GeV for this mechanism, which is almost precisely the observed jet
So in summary, the quadrupolar electric field grows stronger as long
as fresh plasma is injected into the equatorial plane of a spinning
dipole, until the field saturates by second order drifts. This
quadrupolar field accelerates positive charges, either positrons or
protons, up over the poles in opposite directions, thereby forming the
two jet structure observed in nature. Further collimation may occur as
the magnetic field deforms in the presence of this plasma, requiring
an MHD treatment outside the dipolar field region.
Clearly extraordinary claims must have extraordinary evidence, so we
collect the evidence that point to the feasibility of the mechanism
outlined above. In the first subsection, we ask whether any examples
of such a jet have been analyzed. In the section subsection we ask
whether we can support a dipole field for these exotic astrophysical
objects. In the third subsection we ask whether the energy of these
jets can be explained by this mechanism. In the fourth subsection we
address the collimation of the jets. In the last subsection we address
whether space charge of these proportions is consistent with plasma
The crucial aspect of the experiment is scaling. Unlike astrophysical
plasmas, our experiment has a fixed wall that limits the size of the
trapped plasma. Thus the plasma must be highly magnetized in order
that the gyroradius fit within the vacuum containment
vessel. Likewise, the vacuum must be sufficiently good that the
scattering time is much less than the gyroperiod, which is true for
p<10-6 Torr. This means that the highest strength permanent
magnet be used for the rotating dipole, and a high-vac pump such as a
cryopump be installed. We have built a disk-shaped Fe-Nd-B ceramic
magnet, with a surface field approaching 1 T, and a diameter of
several centimeters, cemented to a hollow but rigid non-magnetic
rod. Copper wires threading the rod can sample the plasma potential at
several radial positions, in addition to wire probes used elsewhere in
the chamber. The rod is attached to a variable speed DC motor that is
capable of at least 10,000 rpm. Clearly some effort must be expended
in balancing the spinning magnet assembly, with one possibility being
a thin coat of spin-balanced epoxy. The surface of the magnet can then
be made conducting or non-conducting by the application of a graphite
(Aerodag) coating. An adjustable UV light source such as a hydrogen
lamp could also be used to simulate the presence (or absence) of an
- Example: Earth Jets
At the Earth, the magnetosphere is drawn into a long comet tail by the
flow of magnetized solar wind. As reconnection occurs along the
flanks, a non-axisymmetric electric field is generated that moves
~1 keV plasma sunward by ExB drift from the tail. When this
neutral plasma reaches the more dipolar region of the magnetosphere,
within 8 R_e of the Earth, the magnetic gradients of the dipole
itself cause the positive ions to move clockwise, and the negative
electrons to move counter-clockwise around the Earth. This
counter-streaming flow generates a current that almost forms a ring
around the Earth. If some mechanism of nonadiabatic Earthward
transport exists, then the ring is completed and the plasma is
trapped. Both diffusion and time-dependent electric fields have been
invoked to explain the growth in this trapped ring current during
magnetic storms (Sheldon93a).
Note that charge separation occurs as soon as the dipole gradients are
seen by the sunward convecting neutral plasma. It is generally assumed
that the high conductivity of the cold plasma (assumed to be zero
temperature, and therefore oblivious to magnetic gradients) allows the
electrons to be redistributed in a way to maintain quasi-neutrality.
Recent observations show that this assumption of sufficient cold
plasma fails during a magnetic storm, and real charge separation may
occur. Under these conditions, cold plasma from distant regions is
required, and indeed accelerated to shield the space charge. POLAR
made recent measurements of a 30 keV field-aligned potential drop
during a small storm, that populated the ring current with accelerated
ionospheric plasma (Sheldon98a). Thus the ring current can be
explosively driven on timescales of minutes by upward ionospheric
jets, as is evident in high time resolution magnetograms.
- The Dipole Field
The theory depends crucially on the existence of a dipole magnetic
field for all these astrophysical jets. For YSO, this is easy to
invoke by analogy with our own Sun, but what about blazars? Why should
they have any field at all, much less a dipole field? Certainly there
is a great desire to invoke magnetic fields to solve the collimation
and acceleration problems, as Pringle argues in the introduction, but
there may be other reasons as well.
The physics of black holes is still an area of active research, with
recent publications on the stability of magnetic fields in the
vicinity of static black holes. But more importantly, recent work on
black hole binaries, show that the black hole is probably spinning
very rapidly, close to breakup speed Zhang99. We know that a
black hole posesses three characteristics: mass, spin and charge.
These rapidly spinning Kerr black holes may also be charged. Such a
Kerr-Newman black hole will have a magnetic field that up to now, has
never been calculated. Our expectation is that this will turn out to
be the mechanism by which a blazar black hole minimizes its internal
Regardless of speculations in general relativity, we know that the
convective motion of plasma within a star produces magnetic fields by
dynamo action. A similar process is occurring in the molten core of
the Earth, which, surprisingly, is also a good approximation to MHD.
In all these dynamo models, the dominant term in the magnetic field
turns out to be the dipole term. Since the higher multipole moments in
all such dynamo fields decay with distance more rapidly than the
lowest, dipole term, there is emminently good reasons for arguing that
a dipole field is generated wherever dynamo theory is applicable. It
is our suspicion that independent of whether a black hole produces a
dipolar field, dynamo theory should be applicable to the accretion
disk, and should produce a dipolar field. Even a simple toroidal
current at the inner edge of the accretion disk would appear as a
dipole field from a sufficient distance. Thus we argue that several
plausible mechanisms exist that can explain the ubiquitous nature of a
dipole magnetic field in the vicinity of AGNs and YSOs.
- The Jet Velocity
We see two processes limiting the charge separation electric field, a
parallel and perpendicular limit. As the space charge builds up, the
ions are repelled and mirror deeper down the field line. In the case
of a protostellar object, this brings the ions closer to the dense
plasma of the star itself, and eventually cold electrons or
recombination destroy the space charge. In the case of a blazar black
hole, the mirror force is exceptionally strong because the compact
size of the hole permits a large convergence of field lines, so we
would expect a much large space charge to develop. Eventually Hawking
radiation or loss to the Schwarzschild boundary would destroy the
space charge. This is the parallel limit.
The perpendicular limit occurs when second order effects become
important in the drift of the charged particles. Adjacent to the space
charge will be flux tubes with no space charge, yet they will ``see''
this space charge and hence collect plasma attempting to provide a
``Debye'' shielding to the space charge. Electrons will be
preferentially collecting at the equator of this neighboring flux tube
as they find a potential well generated by the adjacent space
charge. Physically this produces a large perpendicular electric field
and electric field gradient, which itself causes drifts. This is
analogous to Pedersen and Hall conductivities in the ionosphere. The
electric field causes a Hall conductivity, but the gradient in
electric field generates a Pedersen conductivity, which can discharge
the space charge.
dV_x/dt = e/M (E_x(x(t)) + V_y B)
dV_y/dt = -e/M V_x B
which can be combined,
d2V_x/dt2 + (omega2 - e/M dE_x/dx)V_x = 0
where we define,
Omega2 = omega2 - e/M dE_x/dx
Rothwell writes, ``The main effect of a spatial gradient in E_x is
to modify the gyrofrequency, where the symbol omega=eB/M denotes
the gyrofrequency. It is immediately seen that if
V_x has an exponential rather than an oscillatory solution. That
is, if the electric field gradient is too steep the ions become
If space charge can be made large enough, we will have available MeV
to GeV potentials. Thus the ability for this positive space charge to
accelerate GeV protons (Lorentz factors of a few) and GeV electrons
(Lorentz factors of 103) depends on the discharge or recombination
mechanisms available. From this equation, we can see that if our
space charge is limited by this electric-field-gradient conductivity,
then a 1017 cm magnetosphere (Mkn421) with a field of 0.04 G
will support a potential of 1 GeV, giving nearly the Lorentz factors
required. This happy coincidence lends support to the validity of this
- The Jet Formation
How would such a magnetic field-aligned beam of particles become so
pencil thin? Well we need to know more about the mechanism before we
understand fully what is happening, but here is our best guess. The
more massive ions near the equator of the dipole field arising from
the accretion disk will generate a positive space charge, which the
rapidly moving electrons cannot quite compensate, so that a negative
charge accumulates near the poles of the AGN. This situation forms a
quadrupolar electric field of MV to GV intensity. Now beams of
positive charges (protons? positrons?) are quickly accelerated from
near the center of the system at the ``ionosphere'' and as they
accelerate upward the magnetic field weakens to the point that they
are no longer magnetically confined. Their momentum carries them up
over the pole where they are both magnetically and electrically
focussed to a narrow beam. Presumably they become neutralized at some
point by scattering electrons from the ambient medium and ``dragging''
them along with the beam. The key point is that most of the focussing
is done early on, in the vicinity of their acceleration by the AGN
magnetic dipole field.
A second factor is the bending of the magnetic field by this jet. This
requires self-consistency between the particles and the field, and is
best modelled with MHD. So at some distance from the dipole center,
MHD becomes a valid approximation and can simulate the self-focussing
that occurs as charged plasma ``drag'' the field lines and produce a
- Non-neutral Plasma
One of the major obstacles in this theory is the predication of a
non-neutral space charge. At a fundamental level, the physics of
trapped, non-neutral plasmas has only been recently explored in the
context of positron traps (Hansen95), and no one has postulated
it for space plasmas. Thus it is very important to demonstrate that a
dipole magnetic field has the capability to trap non-neutral plasmas.
In the Malmberg trap used by Hansen and Fajans, a strong cylindrical
magnetic field ``bottle'', with endcaps held at high voltage, is made
to circulate via a time-dependent azimuthal field. In principle, this
has a striking similarity to a rotating magnetic dipole field, where
the surface charge on the dipole acts as a endcap field. The
difference is that Fajans is using the electric potential to confine
the space charge, whereas our application uses the space charge to
produce the encap fields. As a very suggestive corollary, Carl
McIlwain (private communication, 1995) found that the electric
potential model, E5W, that best fit his ATS-5 satellite data included
a monopole term for the Earth. Thus the missing link in this theory
appears to be a conclusive test of the ``dipole charging'' of a
spinning magnet in the presence of a plasma source, a laboratory
FIGURE 2: The laboratory setup, and a high voltage plasma discharge in a tenuous,
1 Torr atmosphere.
The plasma source must produce a reliable source of ions and electrons
at eV energies up to keV energies. The eV plasma may not produce much
voltage, but will be more magnetized and at a higher density than the
keV plasma. Several sources can be tried, including a hot filament, a
sharp needle, a duoplasmatron, and a carbon arc. The source should
have an adjustable potential (up to a few kilovolts) as well as a
mechanical positioner. Since most plasma sources are also gas sources,
the pump should be capable of pumping at a sufficient rate to hold the
pressure below a micro-Torr. A few liter/second cryopump will provide
excellent service for this application.
We expect that this experiment, if successful, will be of great value
to NASA's astrophysics and magnetospheric physics disciplines, with
good opportunities of future funding. In addition, it may provide
insight into fusion plasmas, which would provide opportunities for
funding through NSF's basic plasma research program. Since the
principle investigator is presently lacking in laboratory support,
this grant would provide essential seed money for growing an
experimental laboratory. In short, it would provide the kernel of a
research program with five to seven years of fruitful investigation.
We want to acknowlege the support from the
University of Alabama in Huntsville and the surplus equipment donated
by M. Zukic, M. Abushagar and J. Dimmock that enabled us to build this
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