Statistical inversion theory is employed to estimate parameter uncertainties in incoherent scatter radar studies of non-Maxwellian ionospheric plasma. Measurement noise and the inexact nature of the plasma model are considered as potential sources of error. In most of the cases investigated here, it is not possible to determine electron density, line-of-sight ion and electron temperatures, ion composition and two non-Maxwellian shape factors simultaneously. However, if the molecular ion velocity distribution is highly non-Maxwellian, all these quantities can sometimes be retrieved from the data. This theoretical result supports the validity of the only successful non-Maxwellian, mixed-species fit discussed in the literature. A priori information on one of the parameters, e.g. the electron density, often reduces the parameter uncertainties significantly and makes composition fits possible even if the six-parameter fit cannot be performed. However, small ( < 0.5) non-Maxwellian shape factors remain difficult to distinguish. It is also found that a theory error of 0.7% can give rise to systematic errors of the same order as noiseinduced parameter uncertainties.

The contribution to the field‐aligned ionospheric ion momentum equation, due to coupling between pressure anisotropy and the inhomogeneous geomagnetic field, is investigated. We term this contribution the “hydrodynamic mirror force” and investigate its dependence on the ion drift and the resulting deformations of the ion velocity distribution function from an isotropic form. It is shown that this extra upforce increases rapidly with ion drift relative to the neutral gas but is not highly dependent on the ion‐neutral collision model employed. An example of a burst of flow observed by EISCAT, thought to be the ionospheric signature of a flux transfer event at the magnetopause, is studied in detail and it is shown that the nonthermal plasma which results is subject to a hydrodynamic mirror force which is roughly 10% of the gravitational downforce. In addition, predictions by the coupled University College London‐Sheffield University model of the ionosphere and thermosphere show that the hydrodynamic mirror force in the auroral oval is up to 3% of the gravitational force for Kp of about 3, rising to 10% following a sudden increase in cross‐cap potential. The spatial distribution of the upforce shows peaks in the cusp region and in the post‐midnight auroral oval, similar to that of observed low‐energy heavy ion flows from the ionosphere into the magnetosphere. We suggest the hydrodynamic mirror force may modulate these outflows by controlling the supply of heavy ions to regions of ion acceleration and that future simulations of the effects of Joule heating on ion outflows should make allowance for it.

The distorted ion velocity distribution associated with large ion drifts in the auroral F -region can drive ion cyclotron waves, as pointed out by Lakhina and Bhatia (1984, J. geophys. Res. 89 , 9845) in the case of cold electrons. We take into account the Landau damping of the waves by the electrons and show that the instability can be excited for all values of T ∗ T e , T ∗ being the field-parallel ion temperature and T e the electron temperature, and the threshold value of the drift parameter D ∗ is practically independent of the ion and electron temperatures for a plasma with a single ion species (D ∗ ≈ 1.3) , in contrast to the Post-Rosenbluth instability. A minimum value of T ∗ T e below which wave propagation would become impossible does not exist if a small deviation (∼ 1%) of the wave frequency from a multiple of the ion gyrofrequency is allowed for.

Incoherent scatter data from non-thermal F-region ionospheric plasma are analysed, using theoretical spectra predicted by Raman et al. It is found that values of the semi-empirical drift parameter D∗, associated with deviations of the ion velocity distribution from a Maxwellian, and the plasma temperatures can be rigorously deduced (the results being independent of the path of iteration) if the angle between the line-of-sight and the geomagnetic field is larger than about 15–20 degrees. For small aspect angles, the deduced value of the average (or 3-D) ion temperature remains ambiguous and the analysis is restricted to the determination of the line-of-sight temperature because the theoretical spectrum is insensitive to non-thermal effects when the plasma is viewed along directions almost parallel to the magnetic field. This limitation is expected to apply to any realistic model of the ion velocity distribution, and its consequences are discussed. Fit strategies which allow for mixed ion composition are also considered. Examples of fits to data from various EISCAT observing programmes are presented.

Data are presented from the EISCAT CP-3-E experiment which show the presence of non-thermal plasma over a range of latitudes. The O+ ion-velocity distribution function is almost toroidal when the electric field reaches values of 125 mV m−1. The ion temperature derived from such data assuming a Maxwellian distribution function will overestimate the true ion temperature when the observing angle is large with respect to the magnetic field, and underestimate the temperature when the aspect angle is small. When the expressions for the distribution function are extended to include mixed ion composition, an improvement is sometimes found in fitting the observed data, and estimates of the composition can be made. Such an analysis suggests that N2+ can ocassionally form a significant part of the total ion density in a narrow height region centred at 275 km.

Data are presented from the EISCAT (European Incoherent Scatter (Facility)) CP‐3‐E experiment which show large increases in the auroral zone convection velocities (>2 km s−1) over a wide range of latitudes. These are larger than the estimated neutral thermal speed and allow a study of the plasma in a nonthermal state over a range of observing angles. Spectra are presented which show a well‐defined central peak, consistent with an ion velocity distribution function which significantly departs from a Maxwellian form. As the aspect angle decreases, the central peak becomes less obvious. Simulated spectra, derived using theoretical expressions for the O+ ion velocity distribution function based on the generalized relaxation collision model, are compared with the observations and show good first‐order, qualitative agreement. It is shown that ion temperatures derived from the observations, with the assumption of a Maxwellian distribution function, are an overestimate of the true ion temperature at large aspect angles and an underestimate at low aspect angles. The theoretical distribution functions have been included in the “standard” incoherent scatter radar analysis procedure, and attempts have been made to derive realistic ionospheric parameters from nonthermal plasma observations. If the expressions for the distribution function are extended to include mixed ion composition, a significant improvement is found in fitting some of the observed spectra, and estimates of the ion composition can be made. The non‐Maxwellian analysis of the data revealed that the spectral shape distortion parameter, D*, was significantly higher in this case for molecular ions than for atomic ions in a thin height slab roughly 40 km thick. This would seem unlikely if the main molecular ions present were NO+. We therefore suggest that N2+ formed a significant proportion of the molecular ions present during these observations.

A procedure is presented for fitting incoherent scatter radar data from non-thermal F-region ionospheric plasma, using theoretical spectra previously predicted. It is found that values of the shape distortion factor D∗, associated with deviations of the ion velocity distribution from a Maxwellian distribution, and ion temperatures can be deduced (the results being independent of the path of iteration) if the angle between the line-of-sight and the geomagnetic field is larger than about 15–20°. The procedure can be used with one or both of two sets of assumptions. These concern the validity of the adopted model for the line-of-sight ion velocity distribution in the one case or for the full three-dimensional ion velocity distribution function in the other. The distribution function employed was developed to describe the line-of-sight velocity distribution for large aspect angles, but both experimental data and Monte Carlo simulations indicate that the form of the field-perpendicular distribution can also describe the distribution at more general aspect angles. The assumption of this form for the line-of-sight velocity distribution at a general aspect angle enables rigorous derivation of values of the one-dimensional, line-of-sight ion temperature. With some additional assumptions (principally that the field-parallel distribution is always Maxwellian and there is a simple relationship between the ion temperature anisotropy and the distortion of the field-perpendicular distribution from a Maxwellian), fits to data for large aspect angles enable determination of line-of-sight temperatures at all aspect angles and hence, of the average ion temperature and the ion temperature anisotropy. For small aspect angles, the analysis is restricted to the determination of the line-of-sight ion temperature because the theoretical spectrum is insensitive to non-thermal effects when the plasma is viewed along directions almost parallel to the magnetic field. This limitation is expected to apply to any realistic model of the ion velocity distribution function and its consequences are discussed. Fit strategies which allow for mixed ion composition are also considered. Examples of fits to data from various EISCAT observing programmes are presented.

Observations by the EISCAT experiments “POLAR” and Common Programme CP-3 reveal non-Maxwellian ion velocity distributions in the auroral F-region ionosphere. Analysis of data from three periods is presented. During the first period, convection velocities are large (≈2 km s-1) and constant over part of a CP-3 latitude scan; the second period is one of POLAR data containing a short-lived (<1 min.) burst of rapid (>1.5 km s-1) flow. We concentrate on these two periods as they allow the study of a great many features of the ion-neutral interactions which drive the plasma non-thermal and provide the best available experimental test for models of the 3-dimensional ion velocity distribution function. The third period is included to illustrate the fact that non-thermal plasma frequently exists in the auroral ionosphere: the data, also from the POLAR experiment, cover a three-hour period of typical auroral zone flow and analysis reveals that the ion distribution varies from Maxwellian to the threshold of a toroidal form.

Threshold conditions for the ion cyclotron instability, due to a distorted ion velocity distribution in the auroral F-region ionosphere, and the quasilinear evolution of the distribution function, are investigated. It is found that the critical value of the ion drift parameter D∗ for the resonant ion species is between 1.3 and 1.4 in most cases, becoming considerably larger only if the fractional concentration of the resonant species is less than about 20 % or if the field-parallel ion temperature for the non-resonant species is low compared with the resonant species. Also, the threshold is independent of the degree of distortion of the non-resonant ion velocity distribution. Velocity space diffusion driven by ion cyclotron waves becomes important if the ratio of the electrostatic energy and the ion thermal energy (the weak turbulence parameter) is of the order of 10−6 Δk| (m−1) or more, where Δk| is the width of the wave spectrum in k|. The steady state velocity distribution function for a given value of parallel velocity lies between two extremes: the Raman et al. -type distribution with a large positive slope in field-perpendicular velocity (ν⊥) and a distribution function with the positive slope replaced by a plateau of the size Δν⊥ ∼ 3.8 Ωik⊥, where Ωi is the resonant ion (angular) gyrofrequency and k⊥ the perpendicular wavenumber which dominates the spectrum.

The recent identification of non-thermal plasmas using EISCAT data has been made possible by their occurrence during large, short-lived flow bursts. For steady, yet rapid, ion convection the only available signature is the shape of the spectrum, which is unreliable because it is open to distortion by noise and sampling uncertainty and can be mimicked by other phenomena. Nevertheless, spectral shape does give an indication of the presence of non-thermal plasma, and the characteristic shape has been observed for long periods (of the order of an hour or more) in some experiments. To evaluate this type of event properly one needs to compare it to what would be expected theoretically. Predictions have been made using the coupled thermosphere-ionosphere model developed at University College London and the University of Sheffield to show where and when non-Maxwellian plasmas would be expected in the auroral zone. Geometrical and other factors then govern whether these are detectable by radar. The results are applicable to any incoherent scatter radar in this area, but the work presented here concentrates on predictions with regard to experiments on the EISCAT facility.

Three rapid, poleward bursts of plasma flow, observed by the U.K.-POLAR EISCAT experiment, are studied in detail. In all three cases the large ion velocities (> 1 kms−1) are shown to drive the ion velocity distribution into a non-Maxwellian form, identified by the characteristic shape of the observed spectra and the fact that analysis of the spectra with the assumption of a Maxwellian distribution leads to excessive rises in apparent ion temperature, and an anticorrelation of apparent electron and ion temperatures. For all three periods the total scattered power is shown to rise with apparent ion temperature by up to 6 dB more than is expected for an isotropic Maxwellian plasma of constant density and by an even larger factor than that expected for non-thermal plasma. The anomalous increases in power are only observed at the lower altitudes (< 300 km). At greater altitudes the rise in power is roughly consistent with that simulated numerically for homogeneous, anisotropic, non-Maxwellian plasma of constant density, viewed using the U.K.-POLAR aspect angle. The spectra at times of anomalously high power are found to be asymmetric, showing an enhancement near the downward Doppler-shifted ion-acoustic frequency. Although it is not possible to eliminate completely rapid plasma density fluctuations as a cause of these power increases, such effects cannot explain the observed spectra and the correlation of power and apparent ion temperature without an unlikely set of coincidences. The observations are made along a beam direction which is as much as 16.5° from orthogonality with the geomagnetic field. Nevertheless, some form of coherent-like echo contamination of the incoherent scatter spectrum is the most satisfactory explanation of these data.

A new method is presented of computing the theoretical spectrum of the incoherent scatter signal from nonthermal ionospheric F region plasma. An expression for the ion line‐of‐sight velocity distribution function is derived analytically and the evaluation of the Cauchy principal value integral, part of the longitudinal dielectric function, is discussed. Spectra revealing the presence of nonthermal plasma have recently been observed by the European Incoherent Scatter (EISCAT) radar during periods of rapid plasma flow, and the incorrect assumption of Maxwellian plasma at such times will cause errors in the plasma density and temperatures derived. The new procedure is tailored to satisfy the needs of non‐Maxwellian spectral analysis of data from EISCAT and other incoherent radar systems.

In the auroral zone, ionospheric plasma often moves horizontally at more than 1 km s−1, driven by magnetospheric electric fields, but it has usually been assumed that vertical velocities are much smaller. On occasions, however, plasma has been seen to move upwards along the magnetic field line at several hundred m s−1. These upward velocities are associated with electric fields strong enough to heat the ion population and drive it into a non-thermal state1,2. Here we report observations of substantial upwards acceleration of plasma, to velocities as high as 500 m s−1. An initial upthrust was provided by a combined upwelling of the neutral atmosphere and ionosphere but the continued acceleration at greater heights is explained by a combination of enhanced plasma pressure and the 'hydrodynamic mirror force'3. This acceleration marks an important stage in the transport of plasma from the ionosphere into the magnetosphere.

A procedure is presented for deriving the ion velocity distribution function in the auroral F-region ionosphere allowing for large ion drifts relative to the neutral atmosphere and linearly unstable electrostatic waves. The ions are considered as magnetized and the ion-neutral collision frequency is assumed to be much less than the ion gyrofrequency so that the distribution is gyrotropic.

Observations by the EISCAT experiments “POLAR” and Common Programme CP-3 reveal non-Maxwellian ion velocity distributions in the auroral F—region ionosphere. Analysis of data from three periods is presented. During the first period, convection velocities are large k2 km S ~) and constant over part of a CP-3 latitude scan; the second period is one of POLAR data containing a short—lived (<1 mm,) burst of rapid (>1.5 km ~_1) flow. We concentrate on these two periods as they allow the study of a great many features of the ion-neutral interactions which drive the plasma non—thermal and provide the best available experimental test for models of the 3— dimensional ion velocity distribution function. The third period is included to illustrate the fact that non—thermal plasma frequently exists in the auroral ionosphere: the data, also from the POLAR experiment, cover a three—hour period of typical auroral zone flow and analysis reveals that the ion distribution varies from Maxwellian to the threshold of a toroidal form.