UCLA BPPL
Invited talk on whistlers in space and laboratory plasmas, IPELS 97

Fig. 1. Typical spectrogram of ionospheric whistler waves observed on the ground. The received waveform (top trace) is Fourier analyzed and displayed as an intensity plot vs. frequency and real time (bottom plot). The descending frequency produces falling tones which gave rise to the name "whistlers". [Courtesy of S. P. McGreevy].

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Fig. 2. Measured (solid line) and theoretical (dashed line) dispersion relation for whistler waves propagating along the magnetic field in a uniform plasma. Differences are due to the fact that theory applies to plane waves while in an experiment, antenna-launched whistlers contain a spectrum of k-modes which produce a diverging radiation pattern [from R. L. Stenzel, Whistler wave propagation in a large magnetoplasma (713 kB), Phys. Fluids 19, 857-864 (1976). (Link to original publication)].

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Fig. 3. Examples of interferometer traces in one and two dimensions. The upper trace displays amplitude and phase of the whistler wave electric field for propagation along the dc magnetic field. The lower plot shows the phase fronts (maxima and minima) of a whistler wave launched by a magnetic loop antenna at the origin. Note that the phase fronts are converging but the energy is diverging since group and phase velocities point in different directions with respect to the magnetic field.

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Fig. 4. Theoretical 2D dispersion surface (wavevector vs. angle) for low frequency whistlers. The group velocity is normal to the dispersion surface and, in general, differs both in magnitude and direction from the phase velocity. Special cases indicated are parallel whistlers, oblique whistler with parallel group velocity (Gendrin mode), and the resonance cone modes (quasi electrostatic whistlers).

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Fig. 5. 2-D phase front measurements of low frequency whistlers (a) in a laboratory plasma with field-aligned density crests and troughs (b). A variety of characteristic whistler modes are identified from their phase and group velocities [from R. L. Stenzel, Whistler wave propagation in a large magnetoplasma (713 kB), Phys. Fluids 19, 857-864 (1976). (Link to original publication)].

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Fig. 6. Example of 3D multipoint measurements of whistler wave fields. A wave packet is excited by a current pulse in a loop antenna. In repeated experiments the vector magnetic field is recorded with a movable probe at >10,000 positions vs time. Displayed is a snapshot of the wave magnetic field as isosurface with cut showing contours of constant field strength inside the packet [from Rousculp et al, Pulsed currents carried by whistlers. V. Detailed new results of magnetic antenna excitation (1.9 MB), Phys. Plasmas 2, 4083-4093 (1995). (Link to original publication)].

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Fig. 7. The eigenmodes of the wavepacket shown in Fig. 6 are obtained by Fourier transformation of the wavefields in 3D space and time. Displayed are an isosurface and contours of the wave magnetic field in 3D k-space at a fixed frequency. The gridded surface represents the theoretical dispersion surface of whistlers. The analysis demonstrates that the wave packet consists of oblique whistlers.

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Fig. 8. Resonance cone whistler modes are excited by a "point" source, e.g., a magnetic loop antenna small compared to the wavelength. The top picture shows the wave fields localized along an expanding cone, the bottom picture shows an angular scan of the wave electric field. Resonance cones are used for plasma diagnostics [from R. L. Stenzel, Antenna radiation patterns in the whistler wave regime measured in a large laboratory plasma, Radio Sci. 11, 1045-1056 (1976)].

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Fig. 9. Cherenkov instability of whistlers in a large electron beam-plasma system. The 1D interferometer trace of a test wave (top) indicates wave growth in the direction of the beam satisfying wave-particle resonance. The 2D phase fronts (bottom left) show that the unstable waves propagate oblique to the field-aligned beam close to the limiting phase velocity angle of whistlers. The 2D amplitude contours (bottom right) show that the wave grows oblique to the beam at the group velocity resonance cone angle. In the hemisphere opposite to the beam a decaying resonance cone is observed [from R. L. Stenzel, Observation of beam-generated VLF hiss in a large laboratory plasma, J. Geophys. Res. 82, 4805-4814 (1977)].

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Fig. 10. Broadband VLF hiss produced by a Cherenkov-type whistler instability in a large electron beam-plasma system. Whistlers grow spontaneously from thermal noise and are passively detected with a short electric antenna.

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Fig. 11. Spatial properties of the broadband VLF hiss shown in Fig. 10. (a) 1D cross correlation along the magnetic field for a selected frequency component showing several wavelengths within the coherence envelope. (b) Dispersion relation (frequency vs parallel wavelength) obtained from narrowband cross-correlation measurements. The parallel phase velocity matches the beam velocity in magnitude and direction, as expected for a Cherenkov instability.

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Fig. 12. 2D spatial properties of beam-generated VLF hiss. (a) Phase fronts of 2D narrowband cross correlations showing that the unstable waves propagate oblique to the field or beam. (b) The measured propagation angle vs frequency is close to the phase velocity resonance cone angle (solid line), demonstrating that VLF hiss consists mainly of slow electrostatic whistlers.

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Fig. 13. Whistler wave ducting and filamentation processes observed in a large laboratory plasma. Schematic sketch at top shows that antenna-launched whistlers in a uniform collisionless plasma exhibit an amplitude decay due to beam diverge. However, a field-aligned density depression guides (ducts) the whistler wave resulting in a constant amplitude with distance. The density depression is produced by the radiation pressure and thermal effects of a large amplitude whistler. Bottom traces show measured interferometer traces of linear and filamented whistlers [from R. L. Stenzel, Filamentation instability of a large amplitude whistler wave (669 kB), Phys. Fluids 19, 865-871 (1976). (Link to original publication).]

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Fig. 14. Measured vector magnetic field of a whistler wave packet showing a 3D vortex topology as emphasized by the linked solenoidal and toroidal field lines [from Urrutia et al, Pulsed currents carried by whistlers. III. Magnetic fields and currents excited by an electrode (2.8 MB), Phy. Plasmas 2, 1100-1113 (1995). (Link to original publication).]

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Fig. 15. Ideal spherical vortex (e.g., Hill's vortex, spheromak) to which the observed whistler pulse of Fig. 14 resembles. Whistler wave vortices exhibit right-handed linkage (positive helicity) when propagating along the dc magnetic field and left-handed linkage for the opposite direction of propagation.

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Fig. 16. Schematic picture describing the directionality of whistler wave antennas based on helicity injection and conservation. A simple field-aligned loop antenna (top figure) possessing no helicity, excites two equal whistler vortices of opposite helicity propagating in opposite directions, hence zero helicity is maintained. An antenna consisting of a loop along the axis of a torus (bottom figure) exhibits helical fields. For positive helicity injection a vortex of positive helicity is excited which propagates along the field (and vice versa for negative helicity). As a receiving antenna its directionality is reversed. Transmission between two identical antennas is unidirectional, i.e., non-reciprocal. These concepts were first tested in computer simulations [Rousculp and Stenzel, Helicity injection by knotted antennas into electron magnetohydrodynamical plasmas (425 kB), Phys. Rev. Lett. 79, 837-840 (1997). (Link to original publication)].

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Fig. 17. Sketch of a whistler wave antenna which exhibits directionality by matching the helicity of antenna and wave fields. It consists of a loop on the axis of a low aspect-ratio torus such that the resultant fields are helical. The direction of currents in the loop and torus determines the sign of helicity, hence direction of preferred radiation. The radiation properties of the antenna have been measured in a large uniform magnetoplasma (see Figs. 18,19).

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Fig. 18. Snapshot of the magnetic field components of a whistler wave packet excited by a current pulse to a loop-torus antenna of positive helicity. Top panels show the transverse (toroidal) fields in a vector plot and the axial (solenoidal) field component in a contour plot. Bottom panel shows the axial field component in the central y-z plane on both sides of the antenna. The amplitude asymmetry demonstrates the directionality of the helicity antenna.

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Fig. 19. Axial field component in a z-t diagram demonstrating the propagation of whistlers excited by a directional loop-torus antenna located at z=0 and driven by a sinusoidal current (central trace).

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Fig. 20. Properties of a thin current sheet with parameters in the electron MHD regime (magnetized electrons, unmagnetized ions, thickness of electron inertial length). Left hand diagram shows the experimental setup. A long flat electrode is biased so as to draw a current pulse in a uniformly magnetized background plasma. With probes the perturbed magnetic field is measured and from its curl the current density obtained in space and time. The right hand contour plots show the axial current density in two orthogonal planes after the current sheet has been established. There are no tearing instabilities due to the force-free fields (J || B).

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Fig. 21. Space-time evolution of an EMHD current sheet. Three sets of current density contours show the growth, steady state and decay of the sheet. During the growth localized return currents are induced, during the decay the current collapses to a filament near the center of the electrode. These are linear features of transient whistler currents from the axial wire which feeds the current pulse to the sheet electrode.

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Fig. 22. Propagation of an EMHD current sheet. Top trace shows the applied current pulse. Bottom contour plot shows the perturbed magnetic field component in a z-t diagram. The slope dz/dt represents the propagation speed of the current sheet along the dc magnetic field. The enhancement of the field after turn-off is due to the collapse of the current on axis (see Fig. 21).

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Fig. 23. Characteristics of EMHD currents to a pulsed electrode in a uniform magnetoplasma. The current density lines form right-handed spirals due to the presence of both field-aligned currents and azimuthal electron Hall currents. The J-lines from the electrode penetrate a finite distance into the plasma before spiraling back to the return electrode in the back of the disk electrode. A current tube has been constructed from the measured data. It's enclosed current is conserved and the J-lines lie on its surface.

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Fig. 24. Propagating whistler wave packet emitted from tethered electrodes in a uniform magnetoplasma. Three snapshots display isosurfaces of the wave magnetic field excited by a short current pulse applied at the tether center. An electrodynamic tether in space also excites whistler wave packets since its motion across field lines creates transient currents. The superposition of such transient currents produces a whistler wing as demonstrated in laboratory measurements [Urrutia et al, Three-dimensional currents of electrodynamic tethers obtained from laboratory models, Geophys. Res. Lett. 21, 413-416 (1994)].

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Fig. 25. Snapshot of measured current density lines in 3-D space, excited by tethered electrodes in a laboratory magnetoplasma. An applied current pulse generates helical plasma currents at each electrode which are closed by electron Hall currents induced by the insulated tether wire. Multiple current loops are excited which propagate in the whistler mode along the dc magnetic field. A second current system (not shown here) propagates in the direction opposite to the field.

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Fig. 26. Whistler wings in the perturbed magnetic field of a current loop moving across the magnetic field. The wing is constructed by Huygens principle from a superposition of delayed whistler wavelets from displaced loop positions [Urrutia et al, Magnetic dipole antennas in moving plasmas: A laboratory simulation, in "Solar System Plasmas in Space and Time," J. L. Burch and J. H. Waite, Jr., editors, Geophysical Monograph 84, AGU, Washington, DC, 129-133, 1994]. Similar structures have been observed behind magnetized asteroids in the solar wind [Kivelson et al, Magnetic signatures near Galileo's closest approach to Gaspra, Science 261, 331, 1993].

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