ABSTRACTThe theoretical and laboratory study of magnetically inhomo-geneous plasmas (MIP) aka dipole fields, is comparatively immature. The construction of the MIT/Cornell DPX machine has revealed that the theory describing even a simple dipole trapped plasma is not well developed. Millions are not needed to study these plasmas, however, since surprisingly good scientific data can be gathered from a device roughly 100,000 times less expensive, with important applications for space plasma physics and astrophysics. We describe several provocative images taken with a simple bell-jar experiment developed at UAH, NASA/ MSFC/ NSSTC, and Wheaton College with important contributions from WVU.

INTRODUCTION [A] Space charge can develop in MIP, Alfven 63. This occurs both in the dipole field of the earth, and in DC glow discharges in our simple laboratory experiment. We explore this space charge distribution with novel charged dust "probes", and found Saturn-like dust rings in a laboratory analog. [B] Such space charge plasma may also account for accelerated beams observed in Earth (Sheldon 98), Jupiter (Williams 96), [C] and the astrophysical jets seen by astronomers. [D] Also MIP support quadrupole trapping as well, both in the Earth's cusp and in double-dipole laboratory experiements. We compare space to laboratory experiments showing not only that full trapping occurs, but that quadrupole traps are ideal environments for particle acceleration. We postulate that much of the Earth's outer radiation belt electrons begin their life in the cusps as accelerated solar wind. [E] Another quadrupole geometry simulates x-line reconnection with some novel trapped orbits. In this example, laboratory data may complement computer simulations. [F] MIP can also explore the dynamics of a quadrupole trap with applied field-aligned potentials. The evolution of the trapped plasma appear amazingly similar to an auroral substorm.

[A] SPACE CHARGE & Saturn's rings

In this MSFC/NSSTC experiment, 3m SiO2 charged dust grains (green) acting as

tracer test particles were suspended against gravity by the space charge formed at the equator of a DC-glow discharge plasma (purple) surrounding a NdFeB disk magnet (black). The dust was illuminated from the left with a scanned 532nm diode laser. Tray with unsuspended dust is visible below the magnet, as well as an arc from tray to ground that charges the dust and scatters it upward. The neutral pressure was ~200mTorr, Ni-plated magnet with -500VDC applied. Since dust charges negative in a plasma environment, the space charge must be positive with respect to the ground plane roughly 12 cm below. Ignoring collective effects of the dusty plasma, we estimate that 10 electrons per dust grain will require a minimum of 30 kV/m to overcome gravity. Note that dust tracers accomplished what a Langmuir probe (inset) could not measure. What is producing the space charge? As Alfven pointed out, if trapped ion and electron pitchangle distributions are different, then parallel electric fields (aka space charge) is needed to achieve time-averaged neutrality (from a particle viewpoint). Whipple 77 calculates the potential resulting from a beam of ions in a Maxwellian plasma. A negatively biased magnet produces a “beam” of electrons, that attempts to neutralize a pancake “trapped” ion population at the equator. The production of ions by electron stripping of neutrals then proceeds via positive feedback to maintain this potential, which makes the magnetized DC glow discharge far more efficient than expected from a simple probe geometry.

[B] SPACE CHARGE & arcs

In this initial UAH experiment (Sheldon 01), a grounded magnet is spun at ~500 rpm on the left, or stationary on the right, while a nearby metal probe biassed to +600VDC injects plasma. A 40s exposure reveals many arcs (30 us discharge) emanating from the magnet preferentially on the injected plasma side, more uniformly when the magnet is spun. Arcs follow magnetic field lines, since the potential is field-aligned. Some arcs continue along the field line from top to bottom of Ni-plated magnet (inset), showing that the discharge is not generated by potentials on the magnet itself. Spinning the magnet causes the plasma to co-rotate, and makes the azimuthal plasma density more uniform, equivalent to biassing magnet directly. We see evidence for these arcs (beams) in space data as well:

POLAR/CEPPAD 30-150keV ions (Sheldon 98)

Maxwell 1880, Chapman 1932

Maxwell solved the double-dipole magnetic field in 1880, and Chapman used it to explain the repulsion of solar plasma by the Earth's magnetic field.

Cusp-trapped electrons Sheldon 98

Sheldon recorded trapped MeV electrons in the cusp, and demonstrated that the quadrupole geometry of the cusp possesses three adiabatic invariants of the motion (proper trapping). What is the significance of cusp trapping? A quadrupole trap has very different topological and dynamical properties from a dipole trap, such that efficient stochastic acceleration is possible in the cusp. We surmise that this is the origin of the MeV electrons observed in the magnetospheres of Earth and Jupiter. Applying a simple scaling law, we test this theory for consistency

SCALING LAWS

This scaling law, normalized to Earth, does moderately well predicting the very high energies of Jupiter, the moderate energies of the other gas planets, and the absence of radiation belts at Mars and Venus. It is also the only estimate for the ~15keV ions observed at Mercury (Christon 89)

[E] X-LINE RECONNECTION

In this UAH/WVU experiment, two magnets were aligned anti-parallel (x-line configuration) and biassed identically with ~-400VDC. Top panel topview, lower panel sideview. Several novel plasma features appear in the trapped plasma, including a “halo” around the x-line in the “outflow” region. Note that no reconnection is occuring in these photographs, but that the collisional plasma can diffuse readily across field-lines and illuminate the geometry. What is significant is that there are trapped populations around an x-line topology that may contribute substantially to the inflow/outflow dynamics depending on the flow rates. Alternatively, this is just another version of a quadrupole trap with a different topology, so it is not surprising that there are trapped orbits of differing shape in this case.

Magnetically Inhomogeneous Plasmas & Space Charge Robert Sheldon NASA/MSFC/NSSTC

SPACE CHARGE Spectroscopically

In this UAH/WVU montage we show a negatively biassed magnet at varying neutral density. Lowest pressure is at the bottom center ~ 10mTorr with pressure increasing to ~200mTorr at clockwise to the right. Overhead view is shown in the center. Since a pink glow is generated when a single probe is biassed positively in air, whereas the blue glow is produced at negative bias, we interpret these pictures as indication that a dipole MIP is ion-dominated near the equatorial plane, and electron dominated over the poles. (White is actually bright pink saturating the 8-bit webcam.) From a pitch-angle perspective, the ions are pancake (oblate) trapped, while the electrons are beaming (prolate) from the surface of the magnet itself. The arcing observed in the bottom center panel is more common when the magnet is outgassing, and we attribute it to an avalanch breakdown of the parallel potential between the equator and the magnet, which occurs because the pressure is below the Paschen point, such that outgassing makes it more likely to discharge. Note that the magnet is negatively biassed in all these examples, so that pink glow is produced by positive feedback of the emitted electrons.

[C] SPACE CHARGE & Jets

In this Wheaton College experiment, we show a toroidal magnet, biassed at -500VDC at 50mTorr neutral pressure. In this weakly ionized plasma, the brightness of the discharge is proportional to the plasma density. The 8-bit color webcam saturates easily, so the discharge color at the center is still pink, corresponding to a ion-dominated plasma. Clearly the center of toroid corresponds to the highest density plasma which flows out along field lines. We argue that this is analogous to astrophysical jets observed with telescopes. In the case of young stellar jets such as Herbig-Haro objects, positive ion beams are accelerated in the jet. In microquasars or blazars the jet is produced when strong field-aligned potentials that attempt to contain electron beams and pancake ions become greater than 1MV, and e-p pairs are produced with subsequent acceleration of beaming positrons. Estimates of the saturation energy (Rothwell 95) are in good agreement with observations.

Hubble Space Telescope

HST HH30

On the left is a stellar jet in false color observed with Hubble, showing the central jet emerging from a star with an accretion disk around the center. Motion of knots in the jet have been used to estimate an energy of keV for the jet material. On the right is a picture of two jets emerging from a galaxy which has a bright accretion disk imaged by HST.

[D] Quadrupole Traps

In this UAH/WVU experiment montage, two magnets are aligned in parallel, with the rightmost biassed to -400VDC. Left panel shows view from above, right panel shows -100VDC and 0VDC applied to left magnet. Plasma produced on the right magnet crosses the separatrix (because it is a weakly ionized plasma) and flows into the “empty” magnetosphere through the cusps, which themselves are a quadrupole trap with sufficient trapped density to be observed. The “depth” of the quadrupole trap depends on the electric field, such that a grounded magnet produces the deepest trap. Note that double-dipole geometries have a long history in describing the Earth's magnetosphere, and a number of analogous processes can be identified from Earth.

1) N & e2) Saturated

3) - 400VDC4) 0.5Tesla5)10- 200mT

40keV B-field aligned O+

Trapped H+

–Brad ~ Bsurface= B0

–Bcusp ~ B0/Rstag3

–Erad= 5 MeV for Earth

–Ecusp ~ v2perp~ (Bcuspr)2 ~ [(B0/Rstag

3)Rstag]– =m E/B is constant

Erad-plnt~(Rstag-Earth/Rstag-plnt)(B0-plnt/B0-Earth)2Erad-Earth

PlanetMercuryEarthMarsJupiterSaturnUranusNeptune

ERAD

4 keV5 MeV< 1.5 eV150 MeV1.2 MeV1.4 MeV0.42 MeV

R STAG

1.410.41.2565202025

B0 (nT) 330 31,000 < 6430,000 21,000 23,000 14,000

[F] AURORAL SUBSTORM (the movie)

Dynamics of the double-dipole experiment simulate dynamics at Earth. In this experiment, we generated field-aligned potentials by making one magnet positive with respect to the other. Apparently electrons emitted from the righthand magnet migrate through the cusp and appear create “aurora” over the left hand magnet. As the field-aligned potential is increased, the separatrix barrier is gradually lowered until positive feedback generates a “westward” surge and draws enough current to trip the power supply.

WHEATON COLLEGE HARDWARE ~$500Unistrut frame (new, ~$600) Sargent-Welsh oil piston vacuum pump

(available, ~$500-1000),KF-25 quickflange fittings (new, ~$1000), Vacuum valves (used, ~$500)3/4” aluminum baseplate (new, ~$100)L-gaskets (new, ~50$), glass bell jar and matching collar

(used, ~$1000, *lucky*), thermocouple gauge (available ~$100?), 1000VDC power supply & 19” rack

(available, ~$500), Lexan box blast shield (new, ~$100), webcam & PC (available, ~ $500) NIB magnets (new, ~$100)

(low Curie point = short life!)Optical baseplate w/1” spaced holes

(new, ~$1000)We were fortunate to have some expensive items, such as the pump and power supply, on hand, but we made good use of the web, both finding used equipment sellers and seasoned advice. We splurged on the Unistrut frame, the optical baseplates, and the KF-25 flanges, which could have been done more cheaply, but made for a pretty setup. We also purchased a 40-year old diffusion pumpstand from e-Bay that turned out not to be useful. A pump suspension made from bungee cords worked very effectively to eliminate vibrations. Future upgrades intended were: 700mW 532nm laser, a 10-12bit color camera (to avoid the saturation problems), and dust tracers.

CONCLUSIONSThe DC glow discharge in the presence of a strong magnet is a remarkably simple tool for exploring magnetically inhomogeneous plasmas. Negatively biassed magnets produce positive space charge that forms a robust positive feedback plasma source, which is a powerful tool for imaging magnetospheric geometries with simple cameras. We explore X-lines, quadrupole cusp trapping, field-aligned beams, astrophysical jets, and auroral substorms with this simple geometry. The space charge can also levitate charged dust grains, providing another tool for the understanding of dusty plasmas and Saturn's rings. (It may even be possible to use electrostatically confined dust as a gossamer solar sail!) With so much good physics in such simple experiments, we expect the theory to rapidly catch up with the flood of remarkable photographs. One limitation that may have hindered understanding is the need for kinetic (rather than MHD) codes to describe the inhomogeneous equilibria (e.g. space charge). A current project is to model the annular magnetic geometry with hybrid code and apply it to relativistic jets observed by astrophysics..

REFERENCES Alfven, H. and C.-G. Falthammar. Cosmical Electrodynamics, Fundamental Principles. Clarendon, Oxford, 1963. Chapman, S. and V. C. A. Ferraro. A new theory of magnetic storms. J. Geophys. Res., 37, 147--156, 1932. Christon, S, Plasma and energetic electron flux variations in the Mercury1C event: Evidence for a magnetospheric boundary layer, J. Geophys. Res., 94, 6481, 1989. Rothwell, P, M. Silevitch, L. Block, and C.-G. Fälthammer. Single ion dynamics and multiscale phenomena. In J. Horwitz, N. Singh, and J. Burch, ed, Cross-Scale Coupling in Space Plasmas, Geophysical Monograph 93, pp 151-154. AGU, 1995. Sheldon, R, H. Spence and J. Fennell, "The Observation of 40 keV Oxygen Beams"`, Geophys. Res. Lett., 25, May 15, 1998. Sheldon, R, H. Spence, J. Sullivan, T.Fritz, J.Chen, "The Discovery of Trapped Energetic Electrons in the Outer Cusp", Geophy. Res. Lett., 25, 1825, 1998. Sheldon, R. and S. Spurrier, ``The Spinning Terrella Experiment: Initial Results'', Physics of Plasmas, 8, 4, 1111-1118, 2001. Sheldon, R, E.Thomas, Jr, M.Abbas, D.Gallagher, M.Adrian and P.Craven, "Dynamic and Optical Characterization of Dusty Plasmas for Use as Solar Sails" in Space Technology and Applications International Forum-STAIF 2002 ed. M.S. El-Genk, AIP 2002. Whipple, Jr, E.C. The signature of parallel electric fields in a collisionless plasma. J. Geophys. Res., 82, 1525, 1977. Williams, D, B Mauk, R McEntire, E Roelof, T Armstrong, B.Wilken, J. Roederer, S. Krimigis, T. Fritz, and L. Lanzerotti. Electron beams and ion composition measured at Io and in its torus. Science, 274, 401--403, 1996.

Aurora & Substorm

UAH/WVU experiment, B// with left magnet biassed +10-60VDC in steps, right magnet ~-400VDC.-Aurora appears 1mm above magnet, and with ion colors-Sideview camera had slower framerate than topview camera, causing aliasing in last frame.-Assymetric aurora with local brightening and “westward” surge.-Substorm!