Effects of a kappa distribution function of electrons on incoherent scatter spectra

In usual incoherent scatter data analysis, the plasma distribution function is assumed to be Maxwellian. In space plasmas, however, distribution functions with a high energy tail which can be well modeled by a generalized Lorentzian distribution function with spectral index kappa (kappa distribution) have been observed. We have theoretically calculated incoherent scatter spectra for a plasma that consists of electrons with kappa distribution function and ions with Maxwellian neglecting the effects of the magnetic field and collisions. The ion line spectra have a double-humped shape similar to those from a Maxwellian plasma. The electron temperatures are underestimated, however, by up to 40% when interpreted assuming Maxwellian distribution. Ion temperatures and electron densities are affected little. Accordingly, actual electron temperatures might be underestimated when an energy input maintaining a high energy tail exists. We have also calculated plasma lines with the kappa distribution function. They are enhanced in total strength, and the peak frequencies appear to be slightly shifted to the transmitter frequency compared to the peak frequencies for a Maxwellian distribution. The damping rate depends on the electron temperature. For lower electron temperatures, plasma lines for electrons with a distribution function are more strongly damped than for a Maxwellian distribution. For higher electron temperatures, however, they have a relatively sharp peak.     

Enhanced ion acoustic fluctuations and ion outflows

A number of observations showing enhanced ion acoustic echoes observed by means of incoherent scatter radars have been reported in the literature. The Received power is extremely enhanced by up to 1 or 2 orders of magnitude above usual values, and it is mostly contained in one of the two ion acoustic lines. This spectral asymmetry and the intensity of the received signal cannot be resolved by the standard analysis procedure and often causes its failure. As a result, and in spite of a very clear spectral signature, the analysis is unable to fit the plasma parameters inside the regions of ion acoustic turbulence. We present European Incoherent Scatter radar (EISCAT) observations of large ion outflows associated with the simultaneous occurrence of enhanced ion acoustic echoes. The ion fluxes can reach 10¹⁴ m^–2 s^–1 at 800 km altitude. From the very clear spectral signatures of these echoes, a method is presented to extract estimates of the electron temperature and the ion drift within the turbulent regions. It is shown that the electron gas is strongly heated up to 11 000 K. Also electron temperature gradients of about 0.02 K/m exist. Finally, the estimates of the electron temperature and of the ion drift are used to study the possible implications for the plasma transport inside turbulent regions. It is shown that strong electron temperature gradients cause enhancement of the ambipolar electric field and can account for the observed ion outflows.     

First EISCAT measurement of electron-gas temperature in the artificially heated D-region ionosphere

The ionospheric electron gas can be heated artificially by a powerful radio wave. According to our modeling, the maximum effect of this heating occurs in the D-region where the electron temperature can increase by a factor of ten. Ionospheric plasma parameters such as N_e,T_e and T_i are measured by EISCAT incoherent scatter radar on a routine basis. However, in the D-region the incoherent scatter echo is very weak because of the low electron density. Moreover, the incoherent scatter spectrum from the D-region is of Lorentzian shape which gives less information than the spectrum from the E- and F-regions. These make EISCAT measurements in the D-region difficult. A combined EISCAT VHF-radar and heating experiment was carried out in November 1998 with the aim to measure the electron temperature increase due to heating. In the experiment the heater was switched on/off at 5 minute intervals and the integration time of the radar was chosen synchronously with the heating cycle. A systematic difference in the measured autocorrelation functions was found between heated and unheated periods.     

Transport of thermal plasma above the auroral ionosphere in the presence of electrostatic ion-cyclotron turbulence

The electron component of intensive electric currents flowing along the geomagnetic field lines excites turbulence in the thermal magnetospheric plasma. The protons are then scattered by the excited electromagnetic waves, and as a result the plasma is stable. As the electron and ion temperatures of the background plasma are approximately equal each other, here electrostatic ion-cyclotron (EIC) turbulence is considered. In the nonisothermal plasma the ion-acoustic turbulence may occur additionally. The anomalous resistivity of the plasma causes large-scale differences of the electrostatic potential along the magnetic field lines. The presence of these differences provides heating and acceleration of the thermal and energetic auroral plasma. The investigation of the energy and momentum balance of the plasma and waves in the turbulent region is performed numerically, taking the magnetospheric convection and thermal conductivity of the plasma into account. As shown for the quasi-steady state, EIC turbulence may provide differences of the electric potential of δ V ≈ 1–10 kV at altitudes of 500 < h < 10 000 km above the Earth’s surface. In the turbulent region, the temperatures of the electrons and protons increase only a few times in comparison with the background values.     

Magnetospheric lion roars

The Equator-S magnetometer is very sensitive and has a sampling rate normally of 128 Hz. The high sampling rate for the first time allows detection of ELF waves between the ion cyclotron and the lower hybrid frequencies in the equatorial dawnside magnetosphere. The characteristics of these waves are virtually identical to the lion roars typically seen at the bottom of the magnetic troughs of magnetosheath mirror waves. The magnetospheric lion roars are near-monochromatic packets of electron whistler waves lasting for a few wave cycles only, typically 0.2 s. They are right-hand circularly polarized waves with typical amplitudes of 0.5 nT at around one tenth of the electron gyrofrequency. The cone angle between wave vector and ambient field is nearly always smaller than 1°.     

Heating of beam ions by ion acoustic waves

Satellite measurements show that ion beams above the auroral acceleration region are heated to hundreds of eV in a direction perpendicular to the magnetic field. We show that ion acoustic waves may be responsible for much of this heating. Even in the absence of a positive slope in the velocity distribution of the beam ions, ion acoustic waves can be generated by a fan instability. We present analytical estimates of the wave growth rate and ion beam heating rate. These estimates, which are confirmed by particle simulations, indicate that the perpendicular temperature of the beam ions will increase by 30 eV/s, or by 1 eV in 20–25 km. From the simulations we also conclude that the heating saturates at a perpendicular temperature around 200 eV, which is consistent with observations.     

Stability of stationary and time-varying nongyrotropic particle distributions

The ubiquity of nongyrotropic particle populations in space plasmas warrants the study of their characteristics, in particular their stability. The unperturbed nongyrotropic distribution functions in homogeneous media without sources and sinks (closed phase space) must be rotating and time-varying (TNG), whereas consideration of open phase spaces allows for the occurrence of homogeneous and stationary distributions (SNG). The free energy brought about by the introduction of gyrophase organization in a particle population can destabilize otherwise thoroughly stable magnetoplasmas (or, a fortiori, enhance pre-existing gyrotropic instabilities) and feed intense wave growth both in TNG and SNG environments: The nongyrotropic (electron or ion) species can originate unstable coupling among the gyrotropic characteristic waves. The stability properties of these two types of homogeneous nongyrotropy shall be contrasted for parallel (with respect to the ambient magnetic field) and perpendicular propagation, and their potential role as wave activity sources shall be illustrated resorting to solutions of the appropriate dispersion equations and numerical simulations.     

The role played by thermal feedback in heated Farley-Buneman waves at high latitudes

It is becoming increasingly clear that electron thermal effects have to be taken into account when dealing with the theory of ionospheric instabilities in the high-latitude ionosphere. Unfortunately, the mathematical complexity often hides the physical processes at work. We follow the limiting cases of a complex but systematic generalized fluid approach to get to the heart of the thermal processes that affect the stability of E region waves during electron heating events. We try to show as simply as possible under what conditions thermal effects contribute to the destabilization of strongly field-aligned (zero aspect angle) Farley-Buneman modes. We show that destabilization can arise from a combination of (1) a reduction in pressure gradients associated with temperature fluctuations that are out of phase with density fluctuations, and (2) thermal diffusion, which takes the electrons from regions of enhanced temperatures to regions of negative temperature fluctuations, and therefore enhanced densities. However, we also show that, contrary to what has been suggested in the past, for modes excited along the E₀ × B direction thermal feedback decreases the growth rate and raises the threshold speed of the Farley-Buneman instability. The increase in threshold speed appears to be important enough to explain the generation of Type IV waves in the high-latitude ionosphere.     

The generation of non aspect sensitive plasma density irregularities by field aligned drifts in the lower ionosphere

A theory of the generation of plasma density irregularities with virtually no aspect sensitivity, in the lower ionosphere at high latitudes, by electron drifts aligned with the geomagnetic field, is presented. The theory is developed through fluid equations in which the destabilising mechanism involves positive feedback from electron collisional heating. When field aligned electron drift speeds exceed a few km s^–1, this effect destabilises waves with wavelengths in excess of a few tens of metres in the lower E-region, where collisional effects are sufficiently large. Furthermore, the threshold conditions are almost independent of the wave propagation direction and the unstable waves propagate at speeds well below the ion acoustic speed. The role that this new instability may play in recent radar backscatter observations of short scale irregularities propagating in directions close to that of the geomagnetic field, in the lower E-region is also considered.     

A mode filter for plasma waves in the Hall-MHD approximation

A filter method is presented which allows a qualitative and quantitative identification of wave modes observed with plasma experiments on satellites. Hitherto existing mode filters are based on the MHD theory and thus they are restricted to low frequencies well below the ion cyclotron frequency. The present method is generalized to cover wave modes up to the characteristic ion frequencies. The spectral density matrix determined by the observations is decomposed using the eigenvectors of the linearized Hall-MHD equations. As the wave modes are dispersive in this formalism, a precise determination of the κ-vectors requires the use of multi-point measurements. Therefore the method is particularly relevant to multi-satellite missions. The method is tested using simulated plasma data. The Hall-MHD filter is able to identify the modes excited in the model plasma and to assign the correct energetic contributions. By comparison with the former method it is shown that the simple MHD filter leads to large errors if the frequency is not well below the ion cyclotron frequency. Further the range of validity of the linear theory is examined rising the simulated wave amplitudes.     

On the dispersion of two coexisting nongyrotropic ion species

Space observations in the solar wind and simulations of high Mach number bow-shocks have detected particle populations with two coexisting nongyrotropic ion species. We investigate the influence of these two sources of free energy on the stability of parallel (with respect to the ambient magnetic field) and perpendicular propagation. For parallel modes, we derive their dispersion equation in a magnetoplasma with protons and alpha particles that may exhibit stationary nongyrotropy (SNG) and discuss the characteristics of its solutions. Kinetic simulations study the behaviour of perpendicular electrostatic (Bernstein-like) waves in a plasma whose ion populations (positrons and fictitious singly-charged particles with twice the electron mass, for the sake of simulation feasability) can be time-varying nongyrotropic (TNG). The results show that the coexistence of two gyrophase bunched species does not significantly enhance the parallel SNG instability already found for media with only one nongyrotropic species, whereas it strongly intensifies the growth of Bernstein-like modes in TNG plasmas.     

Auroral E-region electron density gradients measured with EISCAT

In the theory of E-region plasma instabilities, the ambient electric field and electron density gradient are both included in the same dispersion relation as the key parameters that provide the energy for the generation and growth of electrostatic plasma waves. While there exist numerous measurements of ionospheric electric fields, there are very few measurements and limited knowledge about the ambient electron density gradients, N_e, in the E-region plasma. In this work, we took advantage of the EISCAT CP1 data base and studied statistically the vertical electron density gradient length, L_z = N_e/(dN_e/d_z), at auroral E-region heights during both eastward and westward electrojet conditions and different ambient electric field levels. Overall, the prevailing electron density gradients, with L_z ranging from 4 to 7 km, are found to be located below 100 km, but to move steadily up in altitude as the electric field level increases. The steepest density gradients, with L_z possibly less than 3 km, occur near 110 km mostly in the eastward electrojet during times of strong electric fields. The results and their implications are examined and discussed in the frame of the linear gradient drift instability theory. Finally, it would be interesting to test the implications of the present results with a vertical radar interferometer.     

A generation mechanism for chorus emission

A chorus generation mechanism is discussed, which is based on interrelation of ELF/VLF noise-like and discrete emissions under the cyclotron wave-particle interactions. A natural ELF/VLF noise radiation is excited by the cyclotron instability mechanism in ducts with enhanced cold plasma density or at the plasmapause. This process is accompanied by a step-like deformation of the energetic electron distribution function in the velocity space, which is situated at the boundary between resonant and nonresonant particles. The step leads to the strong phase correlation of interacting particles and waves and to a new backward wave oscillator (BWO) regime of wave generation, when an absolute cyclotron instability arises at the central cross section of the geomagnetic trap, in the form of a succession of discrete signals with growing frequency inside each element. The dynamical spectrum of a separate element is formed similar to triggered ELF/VLF emission, when the strong wavelet starts from the equatorial plane. The comparison is given of the model developed using some satellite and ground-based data. In particular, the appearance of separate groups of chorus signals with a duration 2–10 s can be connected with the preliminary stage of the step formation. BWO regime gives a succession period smaller than the bounce period of energetic electrons between the magnetic mirrors and can explain the observed intervals between chorus elements.     

WIND observations of coherent electrostatic waves in the solar wind

The time domain sampler (TDS) experiment on WIND measures electric and magnetic wave forms with a sampling rate which reaches 120 000 points per second. We analyse here observations made in the solar wind near the Lagrange point L1. In the range of frequencies above the proton plasma frequency f_pi and smaller than or of the order of the electron plasma frequency f_pe, TDS observed three kinds of electrostatic (e.s.) waves: coherent wave packets of Langmuir waves with frequencies f ≃ f_pe, coherent wave packets with frequencies in the ion acoustic range f_pi ≥ f ≥ f_pe, and more or less isolated non-sinusoidal spikes lasting less than 1 ms. We confirm that the observed frequency of the low frequency (LF) ion acoustic wave packets is dominated by the Doppler effect: the wavelengths are short, 10 to 50 electron Debye lengths λ_D. The electric field in the isolated electrostatic structures (IES) and in the LF wave packets is more or less aligned with the solar wind magnetic field. Across the IES, which have a spatial width of the order of ≃25_D, there is a small but finite electric potential drop, implying an average electric field generally directed away from the Sun. The IES wave forms, which have not been previously reported in the solar wind, are similar, although with a smaller amplitude, to the weak double layers observed in the auroral regions, and to the electrostatic solitary waves observed in other regions in the magnetosphere. We have also studied the solar wind conditions which favour the occurrence of the three kinds of waves: all these e.s. waves are observed more or less continuously in the whole solar wind (except in the densest regions where a parasite prevents the TDS observations). The type (wave packet or IES) of the observed LF waves is mainly determined by the proton temperature and by the direction of the magnetic field, which themselves depend on the latitude of WIND with respect to the heliospheric current sheet.     

Letter to the editor The ionospheric response during an interval of Pc5 ULF wave activity

A preliminary analysis of Pc5, ULF wave activity observed with the IMAGE magnetometer array and the EISCAT UHF radar in the post midnight sector indicates that such waves can be caused by the modulation of the ionospheric conductivity as well as the wave electric field. An observed Pc5 pulsation is divided into three separate intervals based upon the EISCAT data. In the first and third, the Pc5 waves are observed only in the measured electron density between 90 and 112 km and maxima in the electron density at these altitudes are attributed to pulsed precipitation of electrons with energies up to 40 keV which result in the height integrated Hall conductivity being pulsed between 10 and 50 S. In the second interval, the Pc5 wave is observed in the F-region ion temperature, electron density and electron temperature but not in the D and E region electron densities. The analysis suggests that the wave during this interval is a coupled Alfven and compressional mode.     

Nongyrotropic particle distributions in space plasmas

In nonstationary, strong inhomogeneous or open plasmas particle orbits are rather complicated. If the nonstationary time scale is smaller than the gyration period, if the inhomogeneity scale is smaller than the gyration radius, i.e. at magnetic plasma boundaries, or if the plasma has sources and sinks in phase space, then nongyrotropic distribution functions occur. The stability of such plasma configurations is studied in the framework of linear dispersion theory. In an open plasma nongyrotropy drives unstable waves parallel and perpendicular to the background magnetic field, whereas in the gyrotropic limit the plasma is stable. In nonstationary plasmas nongyrotropy drives perpendicular unstable waves only. Temporal modulation couples a seed mode with its side lobes and thus it renders unstable wave growth more difficult. As an example of an inhomogeneous plasma a magnetic halfspace is discussed. In a layer with thickness of the thermal proton gyroradius a nongyrotropic distribution is formed which may excite unstable parallel and perpendicular propagating waves.     

Sausage mode instability of thin current sheets as a cause of magnetospheric substorms

Observations have shown that, prior to substorm explosions, thin current sheets are formed in the plasma sheet of the Earth’s magnetotail. This provokes the question, to what extent current-sheet thinning and substorm onsets are physically, maybe even causally, related. To answer this question, one has to understand the plasma stability of thin current sheets. Kinetic effects must be taken into account since particle scales are reached in the course of tail current-sheet thinning. We present the results of theoretical investigations of the stability of thin current sheets and about the most unstable mode of their decay. Our conclusions are based upon a non-local linear dispersion analysis of a cross-magnetic field instability of Harris-type current sheets. We found that a sausage-mode bulk current instability starts after a sheet has thinned down to the ion inertial length. We also present the results of three-dimensional electromagnetic PIC-code simulations carried out for mass ratios up to M_i/m_e = 64. They verify the linearly predicted properties of the sausage mode decay of thin current sheets in the parameter range of interest.     

Non-magnetic aspect sensitive auroral echoes from the lower E region observed at 50 MHz

Backscatter from E-region irregularities was observed at aspect angles close to 90° (almost parallel to the direction of the magnetic field) using the ALOMAR SOUSY radar at Andoya/Norway. Strong electric fields and increased E-region electron temperatures simultaneously measured with the incoherent scatter facility EISCAT proved that the Farley-Buneman plasma instability was excited. In addition, strong particle precipitation was present as inferred from EISCAT electron densities indicating that the gradient drift instability may have been active, too. Backscatter at such large aspect angles was not expected and has not been observed before. The characteristics of the observed echoes, however, are in many aspects completely different from usual auroral radar results: the Doppler velocities are only of the order of 10 m/s, the half-width of the spectra is around 5 m/s, the echoes originate at altitudes well below 100 km, and they seem to be not aspect-sensitive with respect to the magnetic field direction. We, therefore, conclude that the corresponding irregularities are not caused by the mentioned instabilities and that other mechanism have to be invoked.     

Effect of suprathermal electrons on the intensity and Doppler frequency of electron plasma lines

In an incoherent scattering radar experiment, the spectral measurement of the so-called up- and downshifted electron plasma lines provides information about their intensity and their Doppler frequency. These two spectral lines correspond, in the backscatter geometry, to two Langmuir waves travelling towards and away from the radar. In the daytime ionosphere, the presence of a small percentage of photoelectrons produced by the solar EUV of the total electron population can excite or damp these Langmuir waves above the thermal equilibrium, resulting in an enhancement of the intensity of the lines above the thermal level. The presence of photo-electrons also modifies the dielectric response function of the plasma from the Maxwellian and thus influences the Doppler frequency of the plasma lines. In this paper, we present a high time-resolution plasma-line data set collected on the EISCAT VHF radar. The analysed data are compared with a model that includes the effect of a suprathermal electron population calculated by a transport code. By comparing the intensity of the analysed plasma lines data to our model, we show that two sharp peaks in the electron suprathermal distribution in the energy range 20–30 eV causes an increased Landau damping around 24.25 eV and 26.25 eV. We have identified these two sharp peaks as the effect of the photoionisation of N2 and O by the intense flux of monochromatic HeII radiation of wavelength 30.378 nm (40.812 eV) created in the chromospheric network and coronal holes. Furthermore, we see that what would have been interpreted as a mean Doppler drift veloCity for a Maxwellian plasma is actually a shift of the Doppler frequency of the plasma lines due to suprathermal electrons.     

Low frequency waves in plasmas with spatially varying electron temperature

Low frequency electrostatic waves are studied in magnetized plasmas with an electron temperature which varies with position in a direction perpendicular to the magnetic field. For wave frequencies below the ion cyclotron frequency, the waves need not follow any definite dispersion relation. Instead a band of phase velocities is allowed, with a range of variation depending on the maximum and minimum values of the electron temperature. Simple model equations are obtained for the general case which can be solved to give the spatial variation of a harmonically time varying potential. A simple analytical model for the phenomenon is presented and the results are supported by numerical simulations carried out in a 2.5-dimensional particle-in-cell numerical simulation. We find that when the electron temperature is striated along B₀ and low frequency waves (_ci) are excited in this environment, then the intensity of these low frequency waves will be striated in a manner following the electron temperature striations. High frequency ion acoustic waves (_ci) will on the other hand have a spatially more uniform intensity distribution.