Further Investigation of Electrostatic Electron Cyclotron Waves Observed by the Plasma Wave Instrument on the Polar Spacecraft

J. D. Menietti, O. Santolik, J. D. Scudder, J. S. Pickett, D. A. Gurnett

We report the results of an investigation of waves observed by the Polar spacecraft at high altitudes and latitudes and at frequencies just above the cyclotron frequency. These observations are made frequently when the spacecraft is over the polar cap as well as near the dayside cusp and near the nightside auroral region, and for ratios of gyrofrequency to plasma frequency, f_p/f_ce ~ 1. We investigate the role of electron beams with E <~ 1 keV in the generation of these waves. Observed plasma parameters are used as input to the WHAMP computer code to place contstraints on the free energy source and growth of these waves.


WHAMP, Waves in Homogeneous, Anisotropic Multicomponent Plasmas by Kjell Ronnmark [1982]

WHAMP is a computer program which solves the dispersion relation of waves in a magnetized plasma. The dielectric tensor is derived using the kinetic theory of homogeneous plasmas with Maxwellian velocity distributions. Up to six different plasma components can be included (we use up to 3 in this work), and each component is specified by its density, temperature, particle mass, anisotropy and drift velocity along the magnetic field.


CLICK ON THE IMAGE FOR A FULL RESOLUTION (1024x768) GIF PLOT.



The following figures are f-vs-time spectrograms showing the intense electrostatic emissions just above the electron cyclotron frequeny

EEC 97/07/20

EEC 97/07/20


The following image is a higher resolution plot of electric field only for the time period where low-energy electron beams are observed.

EEC 97/07/20


Following are high-resolution measurements of the electric field components (field-aligned coordinates) obtained during the emissions.

E-field 97/07/20


Following are contours of the velocity-space electron distribution function (Hydra) observed during a time period when electrostatic electron cyclotron waves were observed. Note the low-energy beams coming up the field line. The blue dots are the actual data points.

contour 97/07/20

contour 97/07/20


Contours of the velocity-space electron distribution function resulting from a model of drifting Maxwellians.

fit 97/07/20


Results of the solution of the dispersion equation: The coordinate of the plot is wave number (m^-1) and the three panels display the real frequency (bottom), cB/E (middle), and the ratio of imaginery to real frequency (top). In the bottom panel we display the non-growing whistler mode and the electrostatic beam mode (f_ce < f < f_uh), which does have a small but measurable imaginery frequency and thus growth rate.

growth 97/07/20


Following is a plot of the calculated ratio of Ex/Ez showing the nearly linear polarization of the waves.

Ex/Ez 97/07/20


We have performed the calculations for a number of wave normal angles as shown in the following plot. The wave growth is confined to angles between about 50 degrees and 85 degrees.

Psi 97/07/20


Following shows calculations of real and imaginery f for an electron distribution function containing a beam with a parallel temperature about 10 times greater than used above (similar to the observed distribution within the dayside auroral region). Note the positive growth of the waves.

growth 97/07/20


SUMMARY

Electrostatic electron cyclotron waves are observed frequently just above the cyclotron frequency, f_ce, for northern hemisphere passes of Polar and are present along with low-energy (< 1 keV) electron beams. At Polar altitudes we often find that f_p > f_ce.

Electron beam plasma distributions are modeled based on observations. These distributions are input to the WHAMP dispersion solver. The calculations indicate that at least some of the distributions are modestly unstable to growth of electrostatic electron cyclotron waves on the beam mode. The waves typically lie between f_ce and f_uh for a plasma with f_p >~ f_ce. A preliminary search of parameter space indicates reasonable agreement with observed plasma distributions for wave normal angles close to 75 degrees.


ACKNOWLEDGEMENTS

This research was supported by NASA through grants NAG5-7943 and NAG5-9561 with NASA/Goddard Space Flight Center.