The UAH Spinning Terrella Accelerator

Robert Sheldon
Scott Spurrier


  1. Summary

    2. 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 propose to develop a tabletop laboratory experiment that can verify our acceleration theory, involving a spinning magnet in the presence of a plasma source. We will explore the parameter regimes that affect the results, which would provide experimental constraints crucial for constructing a quantitative theory. And if the mechanism were shown to be relatively efficient, it could provide a new technique for producing keV-MeV ion beams useful in accelerator and plasma fusion physics.

  2. Introduction

    3. The observations of astrophysical jets are as breathtaking in their beauty as they are puzzling in their symmetry (see figure \ref{herbig-haro}). Although these objects have been known for over 30 years, yet there remains no viable theory (\cite{Zhang98}) 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). Three things seem to be necessary for an object to display such behavior: they must be magnetized, they must have an accretion disk, and they must be spinning.



    Two examples of astrophysical jets, galactic (top panel) and stellar (bottom panel).

    The requirement of a magnetic field implies that plasmas must be involved, but accretion disks are mostly unionized. Fortunately, the inner edge of the accretion disk is thought to be ionized and therefore a key to the acceleration process. We have no accretion disks around our spinning Sun, but the Earth both spins and has a magnetic field, as well as half of an accretion disk: the plasmasheet. That is, the inner edge of the plasmasheet functions in an identical manner as the inner edge of an accretion disk, supplying plasma to the rotating magnetic field. Can we observe something related to this jet engine operating in the vicinity of the Earth?

    We assert that the POLAR satellite has seen exactly this sort of mechanism operating at the Earth. During magnetic storms, a strong electric field appears across the plasmasheet that brings in the inner edge very close to the Earth (\cite{Sheldon98a}). Suddenly beams of collimated ions appear, rising from the Earth's ionosphere and accelerated to thousands of volts. In our analysis of this phenomenon (\cite{Sheldon98b}), it appears that a plasma source inside the spinning Earth's magnetic field is required to generate these collimated beams. The coincidences with astrophysical constraints were just too great for this to be an accident. We scaled this effect upward for the conditions occurring at an AGN and, amazingly, it reproduced the GeV energies observed to occur in these highly relativistic jets.

    Before any new theory should be accepted, it either should build on well accepted results, or have conclusive experimental evidence. If this mechanism is truly robust, it should scale down as well as up, so that a laboratory experiment might produce the evidence needed. Furthermore, the experiment could be exceedingly simple. A ``bell jar'' sized vacuum chamber pumped to a pressure of 1 micro-torr would provide the collisionless plasma environment; a strong permanent magnet cemented to the end of a spinning rod would provide the spinning magnetic field; and a simple ``plasma gun'' such as a carbon arc would provide the plasma source. The result should be a measurable voltage appearing along the support rod. In order to explore the maximum range of parameters corresponding to AGN's, YSO's and Earth, we could adjust the pressure from micro- to milli-torr; the carbon arc could be given a variable voltage from -1 to +1 kV, and placed a variable distance from the magnet; the magnet itself could be coated with either a non-conductor or a conductor; and the speed of the rotation could be adjusted from 0 - 10,000 rpm. The outcome of the experiment, once constructed, should easily provide the high quality data that can prove or disprove the hypothesis.


    The laboratory setup.

  3. Theory

    4. The theory is based on the kinematic effect of $\nabla B$-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 technical terms, which we use here for brevity, the $\nabla B$-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 $\nabla B$-drift with ExB-drift frustrates the ability of the plasma to find a low energy neutral equilibrium leading directly to space charge formation. This produces parallel potentials and currents from the ``ionosphere'', 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.

    Obviously, this situation cannot continue unchecked, so we need to identify the timescale or spatial scale on 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 (\cite{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 velocities.

    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 AGN (black hole?) and as they rise 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 all the focussing is done early on, in the vicinity of their acceleration by the AGN magnetic dipole field.

    At a fundamental level, the physics of trapped, non-neutral plasmas has only been recently explored in the context of positron traps (\cite{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.

  4. Experiment

    5. 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 envision either a Co-Sm or Al-B disk-shaped 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, with either sliding contacts or AC coupling for the volt sensors. 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 ionosphere.

    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 would provide excellent service for this application.

  5. Future Work

    6. 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.

  6. Equipment Budget (no salaries)

    7. Vacuum Chamber (redeemable from surplus) 0
    Cryopump . . . . . . . . . . . . . . . . 6000
    Pressure Gauges (redeemable from surplus). . . 0
    Ceramic Magnet . . . . . . . . . .. . . . . . 300
    Voltage Probes, Pickup Loops (can be constructed) . . . . 50
    High rpm motor . . . . . . . . . . . . . . . . 100
    Digital PC Volt/Ammeter . . . . . . . . . . . . 350
    Voltage sources (available through surplus) . . . . . 0
    PC (available) . . . . . . . . . . . . . . . . . . 0
    Controller board w/software . . . . . . . . . . . . 500
    Plasma sources (can be constructed) . . . . . . . . 500
    UV light source (available) . . . . . . . . . . . . 0
    Misc vacuum fittings and seals . . . . . . . . . . 1000


  7. Bibliography

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