(Color) Theoretical patterns of one component, By, of the Alfvén wave in the kinetic and inertial regimes. The waves propagate from left to right.
From Lenhardt (1952). Liquid Sodium apparatus for studying Alfvén waves. The key elements are a heater on the bottom (21) and a stirrer, which, oscillated at 30 Hz (15) and a double probe that measured potential difference on the surface (20). The sodium was threaded by a uniform vertical magnetic field of 0.1-1T. The height of the sodium column was 10 cm.
From Lenhardt. The cylinder is the Na column. When the liquid is moved in the azimuthal direction the magnetic field entering the bottom is twisted sideways.
Theory and experimental predictions by Lenhardt (1952). The ordinate is the potential difference due to the wave electric field and the abscissa the inverse of the background magnetic field. The excellent agreement verified the existence of the shear wave.
Measurement by Borg et al. (Ref. 25) of the magnetic field of a shear Alfvén wave launched by an antenna at r = 5 cm. B = 0.8 T, f = 550 kHz, in a toroidal plasma. The solid lines are theory with N the number of times the wave circled the torus.
(Color) Plasma production in the LAPD device. An oxide-coated cathode heated to 900 °C is placed 55 cm from a molybdenum mesh anode. A transistor switch (Ref. 37) is used to apply a voltage between the cathode and anode, the current is supplied by a 4 F capacitor bank. A bank of 90 magnets supplies the axial DC magnetic field, B0z. The upper right insert is a photograph of a He plasma through an end window located radially near the wall of the machine.
(Color) The wave magnetic field of a shear Alfvén wave launched by a small mesh grid in a plane transverse to the background magnetic field B0z. An image of the grid antenna to scale is shown, although the grid is on a plane δz = 1.54 m (1 parallel wavelength) from the data plane shown. The background magnetic field is B0z = 1.1 kG, , Helium, T e = 10 eV, n = 2.0 × 1012 cm−3.
(Color) The measured current system of a shear Alfvén wave (in the kinetic regime, ). The current source has a 0.5 cm radius. The centers of the current vortices are located 1.25 m apart in z, which is . The pattern is invariant with rotation about its center along the x-axis. Note that the data is acquired on a plane in the LAPD device, the picture is highly compressed along z.
(Color) Magnetic fields shown as streamlines and background Ar ion drift (red arrows). In (a) the ions drift in the direction and in (b) taken 76μs later the ions are seen to close the current via the ion polarization drift. The experimental conditions: n = 1.3 × 1012cm-3, T e = 3.6 eV, T i = 0.8 eV, B 0z = 1200 G, f wave = 36 kHz. The experiment was in the kinetic regime.
(Color) (left) Schematic diagram of the Iowa University spatial waveform antenna for launching shear waves with fixed k ⊥ . The antenna has 48 elements that can be biased with individual waveforms for phase control in the x direction as shown in the left image. (right) Measured data for one component, (By), of the wave is shown on the right. The perpendicular wavelength for this case is 2.5 cm. For each launched value of k ⊥ the parallel wavelength can be measured and the dispersion relation plotted (Ref. 45). This is shown in Fig. 11 for a wave in the inertial regime.
(Color) Measured phase velocity and damping of a shear wave in the inertial regime where k ⊥ δ e is the relevant scale length. Here δ e = 0.61cm, B0z = 2.3 kG. The wave frequency was 380 kHz (). The theoretical dispersion relation, including damping, is drawn as a solid black line. The dash curves are theory bounds reflecting uncertainty in plasma parameters.
(Color) Experimental setup (a). The RMF antenna is aligned so the rotation axis of the induced magnetic field at the center of the antenna is parallel to the direction of the background magnetic field B0. The data are collected with the use of 3-axis magnetic pickup probes (1mm cube). (b) 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 in figure (b) every 4th vector was drawn.
(Color) Isosurfaces of current density at τ = 4.6μs after the wave () 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 . 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. Red 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.
Distribution of oscillation frequencies obtained from the estimation of magnetopause motion by spline interpolation (Plaschlke et al., 2009).
(Color) (left) Spectrum of frequencies in the exciter pulse (dotted line), and observed spectrum measured by an in-situ magnetic pickup probe. (right) Measured magnetic field for the lowest order mode n = 1, showing the FLR is confined to the center of the device.
Side view of the original LaPD showing the magnitude of the confining axial magnetic field (at r = 0) for the magnetic beach experiments. Also indicated is the region in which detailed measurements were obtained. The wave travels from a region of high electron Landau damping to a region of ion cyclotron absorption.
(Color) Comparison of measured to theoretical wave magnetic field as the shear Alfvén wave propagates into a decreasing magnetic filed. Lower axis is in cm and upper is the ratio of wave frequency to local helium ion cyclotron frequency. The red curve shows on ion cyclotron damping in the model while the blue further incorporates electron Landau damping and electron-ion Coulomb collisions. The electron damping channels are equally effective. The antenna is located at z = 0 cm.
(Color) Shear Alfvén wave currents (streamlines) and magnetic field magnitude (colored plane) 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 (see also Fig. 16). 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 × B drifts near the cyclotron frequency.
Alfvén wave maser signal near threshold shows bursty behavior. Inset: blow up of a single shot trace of Bx is highly coherent. Above threshold the maser signal reaches steady state.
(Color) Experimental magnetic field setup of the magnetic mirrors in the LAPD. Here η = 0.26 and L m = 3.5 m. The plasma parameters: n = 1 × 1012 cm−3, T e = 6 eV, T i = 1 eV, He. The waves were launched at 50kHz ≤ f ≤ 180kHz.
(left) The wave energy density as a function of f/f Bragg . The width of the dip at 1.05 agrees well with the prediction for Δf. (right) Time history of the running cross-covariance between the wave field and the current of the antenna that launched the wave at η = 0.25. The grey and white contours show the wave magnetic field. The first white curve indicates the time it takes for the wave to travel towards the detector probe one-way, the second curve the time it takes for the wave to return to the probe after being reflected from the anode/cathode for the first time. The standing wave and “gap” mode appears after this.
A schematic of the experimental setup used in creating and studying the temperature filament showing the location of the electron beam and the probes used to diagnose the experiment.
(Color) (top panel) Contours of fluctuations in ion saturation current show a steady progression in wave number of the drift-Alfvén waves driven by the pressure gradient. (bottom panel) The temporal signal obtained at the location marked in the first contour plot indicates that the frequency of the signal is nearly constant even though the m-number of the mode is changing dramatically, indicating that the eigen-frequencies of this system are nearly degenerate.
(Color) (top panel) Contours of temperature produced by convection in the presence of two drift waves shows the development of structure from the initially Maxwellian temperature distribution. (middle panel) Lorentzian-shaped decreases in temperature produce near the center of the filament (r = 1.85 mm) produced by inward transport. (bottom panel) Lorentzian-shaped increases in temperature produced in the outer regions of the filament (r = 3.85 mm) due to outward transport.
(Color) (top) Measured magnetic fluctuation spectrum during weak multimode emission (dominant m = 1 mode). To the right is a line plot of the power spectrum at t = 8 ms. (bottom) Measured magnetic and density (ion saturation current) fluctuation spectrum during strong multimode emission.
(Color) Two laser beams (shown in red although they are 1 micron wavelength and not visible, τ= 8 ns, 1.5 J) strike a pair of carbon targets in the LAPD device which contains the LAPD background plasma (diameter indicated), 60 cm in diameter. The port spacing along the background magnetic field is 32 cm.
(Color) Magnetic field data at t = 390 ns after the target is struck. Solid planes are current density obtained from . Red/blue represents electrons going in the –z/+z direction. Vector plot shows the perpendicular magnetic field. The target is shown to scale at its appropriate location relative to the z = −6 cm plane. The laser is incident along the x axis.
(Color) Magnetic field measured 400 ns after the targets are struck by two 1-J lasers. The data plane is 5 cm away from the targets. The spatial extent of the data is Δx = 22 cm, Δy = 23 cm. (a) Transverse magnetic field from a head-on perspective. A magnetic X point is clearly visible in the center. The bubbles are moving towards each other and flux is annihilated in the center. (b) Another view of the same data showing that most of the magnetic field is in the z direction. The background magnetic field points downwards.
(Color) Three-dimensional currents in the two-target lpp experiment derived from the volumetric magnetic field data set. The targets are drawn in the background for reference. The dominant Alfvén wavelength is λ P = 2.62m. The current closes by ion polarization drift every half wavelength, the currents close at δz = 1.31 meters from the targets at τ = 5.25 μs after the targets are struck.
(Color) Magnetic field lines of a shear Alfvén waves produced 1.6 μs after the collision of two laser-produced plasmas. The targets are several meters in the back of the picture. At this instant of time there are two strong and two weak current channels. The background magnetic field (not shown) is out of the plane of the image. The inductive electric field is calculated from the time varying magnetic field and rendered as sparkles on the field lines (the brighter the sparkle the higher the field). The largest induced fields, parallel to B0z, are of order 2.5 V/m. The reconnection region is in the center.
(Color) (a) Magnetic field lines started at the edge of the two, 2.5 cm diameter flux ropes. The current in each rope is 30A. The 270 G guide field is included in the calculation. The grid lines occur at δx = 2 cm, δz = 30 cm. Note the field lines twist about themselves, and rotate about one another. The magenta surface is the QSL = 200 surface which is also a flux tube. The yellow lines are the transverse magnetic field of the ropes δz = 1.3 meters from their source. Careful inspection of transverse field lines shows there are “X” type structures in the center. The blue arrows are electron current density. Note that at the right current is flowing backwards, i.e., electrons are going towards the source of the ropes. (b) Lower right corner X point topology δz = 6.6 m from start of flux ropes. t = 2.5 ms after the flux ropes are switched on.
(Color) Magnetic field lines of three flux ropes (background field of 300 G included). 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. The reflective surface is placed on the bottom to aid in perspective.
(Color) Three-dimensional picture (anaglyph) of three flux ropes and the resultant QSLs formed (Q = 20). To view this requires red/blue 3D glasses, which can be purchased in a host of specialty shops. The speckled pattern in the back provides a reference at infinity.
(Color) Shear wave Hydra.
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