Download SPACE CHARGE & Jets

Magnetically Inhomogeneous Plasmas & Space Charge
Robert Sheldon
ABSTRACT
The 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.
NASA/MSFC/NSSTC
[F] AURORAL SUBSTORM (the movie)
SPACE CHARGE Spectroscopically
Maxwell 1880,
Chapman 1932
Aurora & Substorm
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 fieldaligned potentials. The evolution of the trapped plasma appear amazingly similar
to an auroral substorm.
[A] SPACE CHARGE & Saturn's rings
1) N & e
2) Saturated
3) -400VDC
4) 0.5Tesla
5)10 -200mT
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
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.
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!
[C] SPACE CHARGE & Jets
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
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
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
SCALING LAWS
–Brad ~ Bsurface= B0
–Bcusp ~ B0/Rstag3
–Erad= 5 MeV for Earth
–Ecusp ~ v2perp~ (Bcuspr)2 ~ [(B0/Rstag3)Rstag]
– m = E/B is constant
Erad-plnt~(Rstag-Earth/Rstag-plnt)(B0-plnt/B02E
)
Earth
rad-Earth
Planet
Mercury
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
R STAG
1.4
10.4
1.25
65
20
20
25
B0 (nT)
330
31,000
<6
430,000
21,000
23,000
14,000
ERAD
4 keV
5 MeV
< 1.5 eV
150 MeV
1.2 MeV
1.4 MeV
0.42 MeV
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)
HST
HH30
[E] X-LINE RECONNECTION
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)
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
Trapped
H+
40keV B-field
aligned O+
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.
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 ~$500
Unistrut 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.
CONCLUSIONS
The 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.
In this UAH/WVU experiment, two magnets were aligned anti-parallel (x-line
Sheldon, R, H. Spence and J. Fennell, "The Observation of 40 keV Oxygen
configuration) and biassed identically with ~-400VDC. Top panel topview,
Beams"`, Geophys. Res. Lett., 25, May 15, 1998.
lower panel sideview. Several novel plasma features appear in the trapped
Sheldon, R, H. Spence, J. Sullivan, T.Fritz, J.Chen, "The Discovery of Trapped
plasma, including a “halo” around the x-line in the “outflow” region. Note that Energetic Electrons in the Outer Cusp", Geophy. Res. Lett., 25, 1825, 1998.
no reconnection is occuring in these photographs, but that the collisional
Sheldon, R. and S. Spurrier, ``The Spinning Terrella Experiment: Initial Results'',
plasma can diffuse readily across field-lines and illuminate the geometry. What Physics of Plasmas, 8, 4, 1111-1118, 2001.
is significant is that there are trapped populations around an x-line topology
Sheldon, R, E.Thomas, Jr, M.Abbas, D.Gallagher, M.Adrian and P.Craven,
that may contribute substantially to the inflow/outflow dynamics depending on "Dynamic and Optical Characterization of Dusty Plasmas for Use as Solar Sails" in
the flow rates.
Space Technology and Applications International Forum-STAIF 2002 ed. M.S. ElAlternatively, this is just another version of a quadrupole trap with a different Genk, AIP 2002.
topology, so it is not surprising that there are trapped orbits of differing shape
Whipple, Jr, E.C. The signature of parallel electric fields in a collisionless plasma.
in this case.
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.