(a) At the initial time t = 0, dense plasma occupies the region x < 0 and it expands into vacuum (x > 0) for t > 0. Ion density profiles are shown at times (units of ωpio −1) as indicated. The distance x from the plasma-vacuum interface is in units of λd = Vto/ωpio¸ where Vto is the H+ thermal velocity in the ambient plasma. (b) Potential and (c) ion velocity profiles for the density profiles in (a) at some selected times labeled on the curves. The inset in (a) shows the electric field profile for different times, revealing that the electric field produced by the expansion is a pulse, whose amplitude decreases and width increases with increasing time; (b) shows the acceleration of ions by the evolving electric field. For the O+, the velocity profile is shown only at t = 480 ωpio −1. Reproduced from N. Singh and R. W. Schunk, J. Geophys. Res. 87, 9154 (1982). Copyright 1982 American Geophysical Union.
Snapshot (t = 60 ωpio −1) of the potential profile associated with the expansion of a high-density plasma in region I into region II with a low density. The profiles are for different values of the density ratio R = nL/no , as labeled on the curves. Reproduced from N. Singh, H. Thiemann, and R. W. Schunk, Laser Part. Beams 5, 233 (1987). Copyright 1987, Cambridge University Press.
Properties of steady-state plasma expansion in a polar flux tube with the usual cold electrons with an additional minor hot electron population with density of 1% and temperature ratio η = Th/Tc as labeled in the panels. Left column shows nh/ni as a function of altitude r/Re on the vertical axis. Middle and right columns show the altitude profiles of density and drift velocity of H+ ions, respectively. Note the discontinuity in the outflow and sudden acceleration of ions at the discontinuity. Reproduced from A. R. Barakat and R. W. Schunk, J. Geophys. Res. 89, 9771 (1984). Copyright © 1984, American Geophysical Union.
(Color online) (a) Plasma density, (b) potential, and (c) electric field structures in an auroral flux tube in a steady-state model of DLs in an auroral flux tube in the upward current region. Note the abrupt transition in density (a), potential structure (b), and parallel electric field (c). The transition on the left is a TET-CFDL. The reduced density between the layers is the auroral density cavity. Reproduced from R. E. Ergun, C. W. Carlson, J. P. McFadden, E. S. Mozer, and R. J. Strangeway, Geophys. Res. Lett. 27, 4053 (2000). Copyright © 2000, American Geophysical Union.
Counter-streaming expansions of a high-density plasma prescribed at x = 0 and a low-density plasma at x = 2000λd; the former consists of 20% hot electrons with Th = 20 Tc. Stack plots of the evolving potential profiles from t = 2000 to 16 000 ωpe −1 are shown; the numbers labeled on the profiles show times in units of 1000 ωpe −1. Note the formation of a RFS at very early on at t ∼ 2000 ωpe −1 and its existence until t ∼ 16 000 ωpe −1, when it merges with the other DL in the simulated plasma. Reproduced from N. Singh and G. Khazanov, J. Geophys. Res. 108, 8007 (2003). Copyright © 2003, American Geophysical Union.
Same as Fig. 5, but density profiles are shown. Reproduced from N. Singh and G. Khazanov, J. Geophys. Res. 108, 8007 (2003). Copyright © 2003, American Geophysical Union.
(a) Temporal evolution of the density structure of a TET-CFDL. (b) Potential structure at t = 12 000 ωpo −1. The x-Vx phase space of (c) the cold ions accelerated by the RFS-CFDL, (d) cold electrons trapped below the RFS-CFDL, and (e) SBS and hot primary electrons. Times are in the units of ωpio −1 and distance in the units of Debye length with cold electron temperature and density no. Reproduced from N. Singh, C. Deverapalli, I. Khazanov, N. Puthumbakum, and A. Rajagiri, J. Geophys. Res. 110, A05205 (2005). Copyright © 2005, American Geophysical Union.
Plasma properties when the RFS-CFDL dissolves at t ∼ 32 000 ωpo −1: x-Vx phase space of (a) electrons, (b) cold ions, and (c) hot ions. Profiles of (d) potential φ(x) and (e) electric field E(x), both averaged over 20 units of time. (f) Total ion density n. The symbols “H” denote ion holes, generated by the persisting cold ion beam accelerated by the dissolved TET-CFDL. The ion holes generate fine structures in the high-altitude DL near the ion transition layer, where the hot ions are reflected as seen in (c). Reproduced from N. Singh, C. Deverapalli, I. Khazanov, N. Puthumbakum, and A. Rajagiri, J. Geophys. Res. 110, A05205 (2005). Copyright © 2005, American Geophysical Union.
Left panel is a schematic diagram of the triple plasma device, DOLII, at the University of Wisconsin (Diebold et al. 49). The panel on the right shows the potential profiles at z = 3.5 cm in the wake of the obstacle indicated in the left panel. Potential profiles are plotted as a function of x; x = 0 is at the top edge of the obstacle. The curve in rectangles is when only the plasma flows from the source camber while the curve in circles is when the plasma from both source and end chamber flow into the target chamber. The end chamber plasma consists of the hot electrons needed for the RFS. Reproduced from D. Diebold, N. Hershkowitz, T. Intrator, and A. Bailey, Phys. Fluids 30, 579 (1987). Copyright 1987, American Institute of Physics.
Schematic of the UCLA experimental set up. The source plasma is generated by ionizing argon gas between the cathode and anode. There is an axial magnetic field along the z direction. The source plasma expands along the magnetic field as indicated by a broad arrow. The source plasma contains a Maxwellian electron population and an energetic population as needed for the formation of a TET-CFDL. Reproduced from G. Hairapetian and R. L. Stenzel, Phys. Fluids B 3, 899 (1991). Copyright © 1991, American Institute of Physics.
Top panel: Two-dimensional (r-z) structure of TET-CFDL for a weak magnetic field B = 3 Gauss. Note that the equipotential contours imply outward pointing radial (diverging from the axis r = 0) electric field all along the length of the plasma chamber; a shallow U-shaped DL forms. Bottom panel: TET-CFDL for a strong magnetic field B = 30 Gauss. Note that the equipotential contours show outward pointing radial electric fields for z < 22 cm while for z > 22 cm, E⊥ point inward toward the axis of the plasma column, resulting in to a back-to-back TET-USDL (). Reproduced from G. Hairapetian and R. L. Stenzel, Phys. Fluids B 3, 899 (1991). Copyright © 1991, American Institute of Physics.
TET-CFDL for a strong magnetic field B = 45 Gauss. Note that equipotentials show outward pointing radial electric fields for z < 27 cm, while for z > 27 cm, E⊥ point inward toward the axis (r = 0) of the plasma chamber forming the back-to-back USDL(). Reproduced from G. Hairapetian and R. L. Stenzel, Phys. Fluids B 3, 899 (1991). Copyright © 1991, American Institute of Physics.
(a) Axial profiles of potential along the line r = 0 and (b) corresponding density profiles for different values of the density ration ntai/nM in the plasma source. Note that the DL shifts outward into the expanding plasma as ntail decreases. Reproduced from G. Hairapetian and R. L. Stenzel, Phys. Fluids B 3, 899 (1991). Copyright © 1991, American Institute of Physics.
Schematic diagram showing HPD at ANU:74 The narrow Pyrex tube on the left, for z < 30 cm and |x| < 7 cm, is the plasma source; x denotes radial distance from the z axis. The plasma is generated by an RF discharge by a RF helical antenna. Magnetic fields shown by thin solid lines are created by the axial solenoids placed around the source tube. The magnetic field diverges in the diffusion chamber of radius 15 cm and it occupies the axial distance 30 cm < z < 60 cm. The diffusion chamber wall is made of aluminum. The approximate location of the DL is shown by the thick parabolic shape near the throat at z = 15 cm, where the sudden transition between the source and the diffusion chamber occurs. Reproduced from C. Charles, R. W. Boswell, and R. Hawkins, Phys. Rev. Lett. 103, 095001 (2009). Copyright © 2009, American Physical Society.
Measured results on CFDLs from Charles61,62 and Musso et al.:83 Top row: axial density (left) and potential (right) profiles. Bottom row: magnetic field profiles (left) and corresponding ion energy distribution functions (right) measured at z = 40 cm showing two peaks for the stronger magnetic fields.
(Color online) (a) Reproduced Fig. 2 in Charles:74 Equipotential contours are shown in the x-z (r-z) plane. Note the densely packed nearly horizontal equipotentials near the throat at z = 30 cm; such equipotentials imply large perpendicular electric fields (radial, E⊥s) supporting a perpendicular potential drop φ⊥0 ≈ 47–20 = 27 V. A major part of the horizontal equipotentials close in the region |x| < 7 cm directly downstream of the source plasma generating a U-shaped DL as highlighted by the red line (smooth bowl shaped curve in print version) curve. The other part of the equipotentials give parallel potential drops for |x| > 7 cm and the resulting parallel electric fields have polarity Ez < 0, opposite to the parallel field in the USDL with Ez > 0. (b) Reproduced Fig. 3 in Charles:74 The density structure in the diffusion region associated with the equipotentials in (a). Note the largest density gradients, the transition from dark red (dark grey scale) to dark blue (light grey scale), near the throat where E⊥ s exists. Reproduced from C. Charles., Appl. Phys. Lett. 96, 051502 (2010). Copyright (c) 2010, American Institute of Physics.
Reproduced Figs. 4(e) and 4(f) from Charles et al. 73 Radial profiles of electric potential (top) and the transverse electric field E⊥(bottom) derived from the measured potential in (e). Note the large E⊥ near x = ±5 cm. Reproduced from C. Charles, R. W. Boswell, and R. Hawkins, Phys. Rev. Lett. 103, 095001 (2009). Copyright (c) 2009, American Physical Society.
The top panels show different types of termination of the source Pyrex source tube as described in the text and the bottom panel shows the ion energy distribution function in the diffusion chamber. Note that ion beam, the peak in the 40-50 eV range, is measured for all the terminations indicating formation of a DL even in case (a), which allows current in the HPD. Reproduced from N. Plihon, P. Chabert, and C. S. Corr, Phys. Plasmas. 14, 013506 (2007). Copyright © 2007, American Institute of Physics.
(Color online) Variation of the (a) plasma densities and (b) ion beam velocities in the source (squares) and diffusion (circles) chambers as function of the RF (antenna) frequency: Note the critical frequency near f ∼ 11.5 MHz where the plasma density in the source chamber suddenly drops and the ion beam in the diffusion chamber disappears as the frequency decreases from a high value of 14 GHz. Reproduced from S. C. Thakur, M. Galante, A. Hansen, S. Houshmandyar, A. M. Keesee, D. McCarren, S. Sears, C. Biloiu, and X. Sun, Phys Plasmas 17, 055701 (2010). Copyright © 2010, American Institute of Physics.
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