Laboratory Observation of Ion Conies by Velocity-Space Tomography of a Plasma

Laboratory experiments have examined particular elements of proposed mechanisms for ion conic for-mation seen in the Earth's auroral-zone magnetosphere. A laser-induced fluorescence diagnostic mea-sured the ion distribution function at many angles in velocity space, allotting tomographic techniques to reconstruct the multidimensional ion distribution function. Ion conies, as well as drifting Maxwellians, were observed. lower hybrid

Ion conies are observed in the Earth's auroral-zone magnetosphere through the use of ion-energy analyzers on satellites. ' These conical distributions in velocity space are seen in conjunction with double layers, electrostatic ion-cyclotron waves, and lower hybrid waves.
One suggested mechanism of ion conic formation is perpendicular (to the geomagnetic field) ion heating due to waves, followed by pVB forces folding the distribution into a conic. Laboratory experiments at the University of California, Irvine, are simulating aspects of the magnetosphere to examine the processes which may be responsible for the satellite data. In this Letter we report observations of drifting undisturbed Maxwellian velocity distributions and the first laboratory observations of ion conic production in the presence of radio frequency waves. These measurements were made by a new technique of optical tomography in velocity space. Previously, a direct measure of multidimensional ionvelocity distribution functions was difficult to achieve. Typically, laboratory ion-energy analyzers have a wide particle-acceptance angle and therefore good angular resolution is difficult to obtain. Also, the distribution function usually can be inferred only by the taking of the derivative of a signal, a risky process. Lastly, the presence of an energy analyzer in a laboratory plasma may be a significant perturbation to the system. With these difficulties in mind, experiments can still benefit substantially from analyzer data, both in space' and in the laboratory.
Laser-induced fluorescence' ' has been used in the laboratory to measure one-dimensional ion distribution functions. A single-frequency (col ) laser beam characterized by a wave vector kL is sent through a plasma. Ions at velocity v; having an electronic transition frequency cop may undergo a transition and emit a photon upon relaxing to another state when the required Doppler shift dimensional velocity distribution function. The onedimensional nature of the distribution function is arrived at because of the scalar product in Eq. (1) which, in essence, means that the measuring technique integrates over the two dimensions perpendicular to kL, e.g. , It is important to note that this method of measuring ion distributions is nonperturbing to the plasma, has good spatial resolution (1 mm ) and good speed resolution (3X10 cm/s or about 3X10 v" for this experiment), and does not require substantial inference. Having obtained a one-dimensional distribution, one may now expand to two and three dimensions by the use of a new technique we shall call optical tomography in velocity space. At constant position I, one may take a set of distributions (typically distributed uniformly in two or three dimensions), at arbitrary angles, 'Pt, by causing kL to change direction when the laser beam is rotated through the angles of interest (see Fig. 1). Given the difficulty of presentation of four-dimensional plots, we will use only two velocity dimensions in this Letter. permits the use of tomographic methods by the use of the Radon transform' and filtered back projection ' A more detailed description of the equipment and techniques may be obtained in Ref. 8.
The magnetospheric simulation experiments reported here were performed in a single-ended Q machine' (see Fig. 1) which provided a low-density (n =10' cm ), low-temperature (T; = T, = 0.2 eV), nearly completely ionized barium plasma 1.0 m long and 5 cm in diameter. The confining magnetic field was 6 kG.
An undisturbed plasma formed at the hot plate will drift axially to the opposite end of the machine where it is lost. One might expect the ion distribution function to be approximately a drifting Maxwellian. A set of laser scans at many (8-16) angles in the x -z plane was taken and unfolded to give f;( x, "t,v" t). As discussed in Ref.  Fig. 2, two ways to view f;(xv", t"t) are displayed. Ten sampling angles were used to obtain this graph. Figure  was produced ' by our drawing an axial electron current to a biased button in a 6-mm channel down the axis of the machine. Such a configuration creates electron flow and dc potential profilesz (see Fig. 3, provided by Lang ) similar in shape to those observed in the magnetosphere.  Lang,Ref. 24. Note that the experiment has a linear magnetic field while the Earth's lower magnetosphere has the flaring field lines of a dipole. Several experiments' ' have used laser-induced fluorescence to diagnose particulars of this instability such as density fluctuations, but none have reported multidimensional distribution measurements and hence such structures as ion conies have not been observed previously. A recent paper discusses ion-energy-analyzer measurements of parallel and perpendicular heating for a similar experiment in a flaring magnetic field configuration. When large-amplitude waves, ep/T~1, were excited, substantial changes in the distribution function occurred, as shown in Fig. 4 (sixteen sampling angles were used to obtain this graph). An ion conic may be characterized as a distribution function where the contours of constant f; form a conical shape in velocity space, rather than the circular shapes of Fig. 2, commonly having the vertex near v=0 and axis of the cone along the v, axis. In Fig. 4 one sees an ion conic distribution quite similar in shape to magnetospheric observations. ' The conic nature is discernible up through the fortieth percentile contour while the instrumental and reconstruction resolution is about 4% here. The location of the tomographic measurement was radially at the current-channel center and axially at about the equivalent Fig. 3 position of z =80 cm. The ion distribution function is stretched in the perpendicular direction as ions are heated by the instability in their transit down the machine. We speculate that the ion conic is formed as a result of the heated distribution interacting with the dc potential structure. To see this, consider two ions with the same v11 and different v& values. The ions must suffer a deceleration to reach the measurement location. The ion with the larger pitch angle will give up less 6v11 in doing work against the dc electric field than the smaller-pitch-angle ion to reach the measurement position (note also that their paths to this position are not identical). Hence, a perpendicularly heated ion distribution interacting with such a potential structure could form an ion conic.
Lower hybrid waves have been proposed as a mechanism for perpendicular ion heating in the auroral magnetosphere. In fact, perpendicular ion heating from waves generated near cuz, was a suggested energy channel for the electron-slideaway-regime operation of the Alcator tokamak.
Additionally, ion-energy-analyzer measurements showed increases in perpendicular ion temperature when the cross-field-current driven lower hybrid instability was driven by an electron current.
In the laboratory, lower hybrid waves were launched from a 12-cm axial extent cylindrical antenna which was coaxial with the plasma column. The waves were broad band in frequency with the center frequency about twice the ion plasma frequency. The waves were detected throughout the plasma by means of small, radially moveable coaxial rf probes with 3-mm tips oriented along the magnetic field lines. We have reported a study of such wave effects on perpendicular distributions. ' Figure 5 shows the ion response to large-amplitude (ep/T~1) lower hybrid waves launched from the antenna. Eight sampling angles were used in this figure, yielding resolution of only (8-10)%, which shows mostly in the incoherent structure of the lowest-level contour.
Substantial heating is seen in the perpendicular direction while the parallel ion distribution remains nearly unchanged as is expected for k = k & in the waves. For the figure T;~/T;~~= 2.1. There is only a hint of an ion conic, but it is not substantial, and is at the level of resolution for this figure which is consistent with the conic of Fig. 4 being produced by heating plus the potential structure (not found for the lower hybrid experiment). Up to a factor of 6 increase in T;& has been observed with less than a 25% change in T;11. Clearly, the next step would be to perform these experiments in a dipole magnetic field geometry, where pVB forces might produce a conic.
In summary, a direct, nonperturbing optical tomography diagnostic has been developed which measures multidimensional ion velocity-space distribution functions. In laboratory experiments, large-amplitude waves can modify a drifting Maxwellian plasma to form ion conic distributions similar to those observed by satellite measurements.