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Spectral gap of shear Alfvén waves in a periodic array of magnetic mirrors
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10.1063/1.2827518
/content/aip/journal/pop/15/1/10.1063/1.2827518
http://aip.metastore.ingenta.com/content/aip/journal/pop/15/1/10.1063/1.2827518

Figures

Image of FIG. 1.
FIG. 1.

Illustration of coupled shear Alfvén wave in an infinite magnetic mirror array configuration. Parameters used for calculation are: , , .

Image of FIG. 2.
FIG. 2.

Side view of the baseline mirror array configuration at the LAPD (lower half of the chamber is semitransparent). Red arrows illustrate the vectors (not to scale) of the mirror magnetic field. Circled numbers indicate port numbers of inserted instruments. Axial distance between two adjacent ports is . Port 23: Microwave interferometers for column integrated plasma density calibration; Port 13, 15, 19, 35: Triple probes for local , measurements; Port 51: SAW small disk antenna; Port 46–49: SAW blade antenna; Port 47: rectangular loop antenna; Port 14, 16, 18, 20, 36, 38: B-dot probes for local SAW magnetic field measurements.

Image of FIG. 3.
FIG. 3.

Radial profiles of (a) the plasma density , solid curve is a fit using ; (b) the Alfvén speed ; (c) the electron thermal speed ; and (d) , dashed line shows . All in the LAPD baseline mirror array configuration . Triple probe data including and are acquired with sampling rate of the digitizer, averaging 128 samples and 10 plasma shots. Random error .

Image of FIG. 4.
FIG. 4.

radial profiles at (port 14): (a) uniform magnetic field , average , ; (b) baseline mirror array configuration , , average , . [Field amplitude data acquired with sampling rate, averaging eight samples. (b) shows error bars calculated from five consecutive plasma shots.]

Image of FIG. 5.
FIG. 5.

SAW spectra with various numbers of mirror cells in the LAPD. (a) Magnetic mirror configurations including the uniform case, where the axial magnetic field is plotted against the LAPD port number. (Axial distance between two adjacent ports is .) (b) vs SAW frequency, curves labeled according to the mirror array configuration. (Field amplitude data acquired with sampling rate, averaging eight samples and 16 consecutive plasma shots. Maximum vertical error is less than 10% and horizontal .)

Image of FIG. 6.
FIG. 6.

Two different representations of the SAW spectrum at port 14 with the baseline mirror configuration . (a) Normalized vs ; antenna current rms value is also overplotted (error bars may be too small to be distinguished from the curve); (b) “disk energy density” normalized using a constant vs . . (All data acquired with sampling rate, averaging eight samples and five consecutive plasma shots. Maximum horizontal error is .)

Image of FIG. 7.
FIG. 7.

Four magnetic mirror array configurations with gradually increased mirror depth. ( calculated with field from port 20 to port 53; axial distance between two adjacent ports is .)

Image of FIG. 8.
FIG. 8.

SAW spectra for four magnetic mirror array configurations with different mirror depth at port 14: (a) maximum vs and (b) “disk energy density” normalized using a constant vs . Vertical error bars calculated from five consecutive plasma shots. Maximum horizontal error is .

Image of FIG. 9.
FIG. 9.

(a) Dependence of spectral gap width on mirror depth . Experiment: diamond with error bars; simulation: box; green dotted line: theoretical prediction of Mathieu’s equation [Eq. (14)] for an infinite system; blue dashed line: analytical prediction from TAE model (Ref. 44); (b) transmitted wave field amplitude and disk energy density vs mirror depth . (Vertical and horizontal error bars are random errors calculated from five consecutive plasma shots.)

Image of FIG. 10.
FIG. 10.

Time history of the running cross-covariance between the wave field and the antenna current with the baseline mirror array configuration at port 14. (a) Contour plot of wave field intensity vs frequency and time. The first white curve indicates the time that takes the wave to travel towards the probe one-way; the second white curve indicates the time that takes the wave to return to the probe after being reflected at the anode/cathode the first time. (b) Temporal plot of wave field intensity growth at three characteristic frequencies: , , and .

Image of FIG. 11.
FIG. 11.

Upper continuum spectra width with three different plasma densities. The upper continuum of each spectrum is centered at the horizontal origin. The inset shows the normalized spectra width vs plasma density. The error bars as well as the Gaussian fit of the peak are shown for the case. (All data acquired with sampling rate, averaging eight samples and five consecutive plasma shots. Maximum horizontal error is .)

Image of FIG. 12.
FIG. 12.

(a) Simulation of wave excitation as a function of and frequency. A sharp forbidden gap of wave excitation is evident between two branches of traveling waves. Here the wave amplitude is normalized by the antenna current. (b) The dispersion relation of excited waves from the simulation, in which corresponds to the maximum of each peak and .

Image of FIG. 13.
FIG. 13.

Computational setup used to simulate the mirror array in the LAPD shown in Fig. 2. (a) The computational domain. (b) The component of the external magnetic field (left) and the finite ion collision frequency in the beach area (right).

Image of FIG. 14.
FIG. 14.

The radial profiles of azimuthal field (rms) at three frequencies comparing simulation and experiment results. This simulation uses which is defined in Eq. (26).

Image of FIG. 15.
FIG. 15.

Comparison of : experiment vs the simulation at (a) port 14 and (b) port 36. The plots show the radial maximum of as a function of frequency. Three values represent possible estimates of effective collision frequencies for Landau damping [see Eq. (26)].

Image of FIG. 16.
FIG. 16.

The contour plots of wave energy density obtained from Eq. (27) for three frequencies. (a) below the gap; (b) in the gap; (c) above the gap.

Tables

Generic image for table
Table I.

Similarities between TAE and mirror array Alfvén experiment.

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/content/aip/journal/pop/15/1/10.1063/1.2827518
2008-01-08
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spectral gap of shear Alfvén waves in a periodic array of magnetic mirrors
http://aip.metastore.ingenta.com/content/aip/journal/pop/15/1/10.1063/1.2827518
10.1063/1.2827518
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