Three-dimensional images related to the Physics of Plasmas article, "The many faces of shear Alfvén waves," by W. Gekelman, S. Vincena, B. Van Compernolle, G. J. Morales, J. E. Maggs, P. Pribyl, and T. A. Carter, Phys. Plasmas 18, 055501 (2011).

Stereo Slide pairs to accompany "The many faces of shear Alfvén waves" by W. Gekelman et al.

They are split into left and right pairs and can be viewed with a variety of methods, which can be read about here and here.

Figure 1. View from above of the LAPD device at UCLA. The LAPD plasma column is 60 cm in diameter and 18 m long. The axial magnetic field is produced by 90 solenoidal magnets and may be varied over the range 300 G ≤ B_0z ≤ 2.5 kG. Ten power supplies generate current for the magnets therefore the axial magnetic field profile is variable. Possible magnetic field geometries are uniform, linearly increasing in z, mirror fields, multiple mirrors, and cusps. The plasma is produced by a DC discharge between a Barium oxide coated cathode and mesh anode. The bulk of the plasma carries no net current, therefore quiescent. The plasma parameters are: He, Ar, Ne, H, Xn, δn/n ≈ 3% , 10¹⁰ cm^-3 ≤ n_e ≤ 2 ×10¹² cm^-3, 0.05 ≤ T_e ≤ 10 eV, T_i ≤ 1 eV.

The plasma is pulsed at 1 Hz with typical plasma duration of 15 ms. The machine can run continuously for approximately four months before the cathode has to be cleaned and recoated. There are 450 access ports serviced by portable pump-down stations, which allow introduction of probes, antennas, additional cathodes, ion beams, electron beams, etc., while the machine is running. Probes go through specially designed ball valves that allow computer controlled probe drives to accurately move them on transverse planes throughout the device. In Fig 1, four pump down stations are visible on the top of the machine (the grey box is a residual gas analyzer). Also visible are magnets (purple and yellow along with their cooling lines). Several probes and probe drives are visible on the right. The probes may be introduced or removed from the machine while it is running using vacuum interlocks.

Figure 2. Another view of the LAPD device. Above and to the right are the water cooled copper bus bars used to deliver power to the magnets. A portable pump-down station is on the right and on the far right the power supplies and transistor switch used for the DC discharge. On the computer screen is an image of the plasma taken with a CCD camera and microsecond exposure. The RMF Alfvé́n wave antenna described in the text is also seen in the photograph.

Figure 3. Slide illustrating a theoretical calculation of the phase fronts of a shear Alfvé́n wave in the inertial (left) and kinetic (right) regime. When fluctuating narrow current filaments generate the waves they have a component of phase and group velocity across the field and move in cone-like patterns. In a typical experiment the waves spread across the background magnetic field by 0.3 degrees or about 11 cm over the 18-meter LAPD column.

Figure 4. Experimental data showing the Alfvén wave currents in a wave generated by a skin depth size current channel 0.5 cm in radius. The data were acquired in a plane with one axis (z-axis is horizontal) parallel to the background magnetic field. The figure is highly compressed, δz = 7m, δr = 9 cm. The blue "lines" are current field lines and the red arrows are current vectors. The pattern is symmetric about x=y=0. At this frequency the axial component of the magnetic field of the wave is negligible. The centers of the current vorticies are located 1.25 m apart in z.

Figure 5. Shear waves with a different morphology are launched by a rotating magnetic field antenna using two concentric multi-turn loops. Isosurfaces of current density at τ = 4.6 µs after the wave (ω/ω_ci = 0.54) is launched by the RMF antenna described in the text. The surfaces begin 33 cm to the right of the antenna and end approximately 8 m away. Two rotating counter-propagating helical current channels can be seen flowing in the z direction along _0z. As time advances the currents rotate in a left-handed sense. The outer surface represents a current density of 0.25 A/cm² and the inner surface a current density of 0.5 A/cm². The red surface denotes current flow in the positive z direction and the blue surfaces current in the negative z direction. Some representative magnetic field vectors are also shown.

Figure 6. Magnetic field data of a shear wave. The data are collected with the use of 3-axis magnetic pickup probes (1 mm cube). The magnetic field of the wave measured on a plane transverse to the background field 33 cm from the antenna. Data was acquired at 13,448 spatial locations and every 4th vector was drawn.

Figure 7. Electrons, which move along the magnetic field, carry the parallel wave current but as the electrons are highly magnetized (r_ce≈100 µm), the cross-field current is carried by ions via the ion polarization drift. The ion motion in the wave field was measured using laser induced fluorescence. Magnetic fields shown as streamlines and background Ar ion drift (red arrows). Here the ions drift in the direction {v_ExB = cE/[B₀(1 - ϖ²)]}.

Figure 8. Magnetic field (measured with a probe) and the ion motion measured at the instant of time that the cross field current is carried by the ion polarization drift v_pol = {c/[ω_ci(1-ϖ²)]}dE_⊥/dt.

Figure 9. A shear Alfvén wave can propagate into a magnetic beach, a region of decreasing magnetic field This was studied in the LAPD device. Here shear Alfvén wave currents (streamlines) and magnetic field magnitude (colored plane) are shown at one instant of time. The wave propagates from left to right until it encounters the magenta surface at the right where the wave frequency equals the local ion cyclotron frequency. Parallel currents are carried by electrons, radial currents are due to ion polarization drifts, and azimuthal currents result from the slippage of the electron and ion E x B drifts near the cyclotron frequency.

Figure 10. Experimental setup to study the collision of two dense laser produced plasmas in a background magnetoplasma. Two laser beams (shown in red although they are 1 micron wavelength and not visible, δt = 8 ns, 1.5 J) strike a pair of carbon targets in the LAPD device which contains the LAPD background plasma (not shown), 60 cm in diameter. The port spacing along the background magnetic field is 32 cm.

Figure 11. Measurement of the currents and magnetic fields of a "diamagnetic bubble" close to a carbon target which is struck by a laser (10¹¹W/cm²). The data is acquired at 6000 spatial locations, 470 ns after the target is struck. The target (rendered in perspective) is 1 cm in diameter. The currents shown as blue-green lines are helical and as high as 1100 A/cm². The magnetic field associated with the current is shown as red arrows and an isosurface (also red) of 200 G. The background field points in the opposite direction.

Figure 12. Superposition of a fast photograph (δt_exp= 3ns) of the colliding laser produced plasma in the foreground with the two carbon targets rendered to scale. Shown are measured magnetic field lines (see also Fig. 14) of shear Alfvén wave produced in the interaction.

Figure 13. Three-dimensional currents in the two-target lpp experiment derived from the volumetric magnetic field data set (16,000 spatial locations). The targets are drawn in the background for reference. The dominant Alfvén is λ_|| = 2.62 m. The current closes by ion polarization drift every half wavelength, the currents close at δz=1.31 meters from the targets at τ = 5.34 µs after the targets are struck.

Figure 14. Three-dimensional magnetic field lines generated during the collision of the two laser produced plasmas. The 600 Gauss background field is not included in the calculation. Twisting vortex-like structures near the targets eventually merge and settle down to the relatively simple patterns of torsional (shear) Alfvén waves. Between the two current channels seen as "O" points in the magnetic field is a magnetic "X" point.

Figure 15. The 'X' point shown in Fig. 14 is not static because the current channels move toward and away from each other in time. Magnetic field line reconnection occurs when this happens. Shown is a close up of a bundle of field lines near the reconnection region. The reconnection does not occur in a plane but is fully three-dimensional.

Figure 16. A magnetic flux rope is a bundle of magnetic field lines with pitch varying with radius. One may alternatively consider a rope as a spiraling current system. An experiment at UCLA on colliding flux ropes was done on the LAPD device. The QSL region has a simple interpretation. Two closely spaced field lines, which enter the QSL, wind up at very different spatial separations at finite distances along the current channel. Outside the QSL neighboring field lines remain close to each other. In this experiment the Quasi Seperatrix Layer (QSL) was measured for the first time. Representative field lines from the two flux ropes are shown in yellow and blue along with the Q=1000 surface in blue threading between them. The axial dimension is compressed 30 times.

Figure 17. Three flux ropes are studied and mapped in three dimensions. The field lines of three flux ropes (background field of 300 G included) are colored red green and blue to distinguish them. Note the scale difference between the transverse (Δx = 13.2 cm) and axial distances (Δz = 4.79 m). The flux ropes twist around one another and collide in space and time. When the flux ropes collide in this instance one or two QSL's are formed. These are shown as colored surfaces.