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It is argued that a simple model based on magnetic image arguments suffices to give a convincing insight into both the basic static as well as dynamic properties of the near-Earth’s magnetosphere. Qualitative results can be obtained for the heating due to the compression of the radiation belts. The properties of this simple dynamic model for the solar wind – magnetosphere interaction are discussed and compared to observations. In spite of its simplicity, the model gives convincing results concerning the magnitudes of the near-Earth’s magnetic and electric fields. The database contains ground based results for magnetic field variation in response to shocks in the solar wind. The observations also include satellite data, here from the two Van Allen satellites.

Analytical models for the statistical distribution of the gut content of fish larvae in a turbulent ocean environment are compared to data obtained in a field experiment. The proposed model allows the nutrition state and thereby the survival probability of plankton populations to be estimated for given conditions and parameters characterizing their environment, i.e., prey concentrations and turbulence levels. These parameters are all available in the field data. Other parameters such as the capture range and fields of view together with a characteristic time for digesting prey are assumed to be known. The analysis allows an estimate for the probability density of the gut content of plankton in terms of the number of nauplii in the gut. In particular, the analytical results give a basis for evaluating the average gut content of a given plankton population on the basis of basic information concerning the prey concentration and the turbulence intensity. Also analytical models for the prey capture rates are compared with results based on the field data. The analysis emphasizes the effects of turbulence.

To describe the lowest order nonlinear corrections to the basic linear wave analysis, it is an advantage to classify wave-types according to their dispersion relation. The important observation will be that many nonlinear wave phenomena can be “classified” into either Korteweg-deVries types or nonlinear Schrodinger types, as explained. There are many physically relevant phenomena which are described by this simple equation, but one would expect that in more general situations the pulses would be distorted and damped as they propagate. Physically, the wave steepening is due to harmonic generation by the nonlinearity being resonant since all harmonics are on the linear dispersion relation for the waves. For a boundary value problem with a harmonic wave excitation, we have at the point of excitation a well-defined frequency, and find higher harmonics develop at larger distances. This latter phenomenon is best illustrated by what is known as Fubini’s solution.

The stability analysis of collisionless plasma, electron plasma oscillations in particular, were based on a linearized model. In that description, amplitudes of unstable waves continue to grow exponentially, and the analysis eventually ceases to be valid when the assumption of linearization brakes down. Quasi-linear theory is one of the models which can answer that question, at least for some cases. Quasi-linear models for weakly dispersive waves are not well developed, although some weakly nonlinear models for wave-particle interactions have been proposed. Within the simple quasi-linear theory the fluctuations reach a stationary level since the growth is arrested and no damping is included in the analysis. Conservation of the average particle density demonstrated before ensures that the area under the distribution function is conserved; hence the final plateau is uniquely determined by the requirement that the two areas labeled 1 and 2 are equal.

In a fluid description of plasmas, as well as other media, we use space and time as independent variables in analyzing local densities and bulk velocities, for instance. The actual distribution of particle velocities in a small volume element is assumed a priori to be a Maxwellian locally. Due to the long range of the Coulomb interaction, a charged particle can interact with many other particles simultaneously. This can be true even if we allow for Debye shielding; for sub-thermal velocities any charged particle in plasma is interacting only with other charged particles within its local Debye sphere. Since a fluid description of the plasma in a number of cases reproduces many basic wave properties, the existence of wave-modes in particular, it seems intuitively reasonable to expect some sort of relation between descriptions based on a kinetic and a fluid model.

Magnetized inhomogeneous plasma can sustain a low frequency electrostatic wave type called “drift-waves” because they propagate in the direction of the electron diamagnetic drift. The driving mechanism is the pressure gradient perpendicular to the externally imposed magnetic field. Historically, the waves were identified as low frequency fluctuations, located near the edge of the plasma column in linear plasma devices. The basic features of electrostatic drift waves can be described by a simple model. The expense for this simplicity is that the result that the waves are linearly stable. This is in contradiction with observations where the waves are found to be spontaneously excited due to linear plasma instability. The use of a fluid model (rather than a kinetic model) imposes some self-evident limitations on the results. However, also the basic assumption of electrostatic waves limits the parameter range of the validity of the results.

Spacecraft-plasma interactions are studied with self-consistent numerical simulations of magnetized plasmas, where electrons are strongly magnetized whereas ions are weakly magnetized. It is found that for a spacecraft in such a magnetized plasma corresponding to a low Earth orbit, electrons can be reflected from a negatively charged spacecraft and then guided by geomagnetic field lines. The reflected electrons can leave a sharp trail like wings if the spacecraft size is greater than an average electron gyroradius of the environment. Such an electron wing-like structure is associated with propagating Langmuir waves. This results in nontrivial asymmetric electrostatic potentials close to the spacecraft and even farther than the Debye screening distance. The convective electric field also gives rise to a differential potential of the spacecraft with respect to the plasma, resulting in yet another asymmetry in the plasma dynamics and the potential distribution around the spacecraft. These asymmetries in the plasma dynamics can significantly influence in-situ measurements of space plasma. The results show a good qualitative agreement with actual measurements by a satellite in the polar regions.

The present studies address feeding of plankton in turbulent environments, discussed by a comparison of analytical results and field data. Various models for predator-prey encounters and capture probabilities are reviewed. Generalized forms for encounter rates and capture probabilities in turbulent environments are proposed. The analysis emphasizes ambush predators, exemplified by cod larvae Gadus morhua L. in the start-feeding phase (stage 7 larvae) collected in shallow waters near Lofoten, Norway. During this campaign, data were obtained at four sites with strongly turbulent conditions induced by tidal currents and long-wave swells, and one site where the turbulence had a lower level in comparison. The guts of the selected cod larvae were examined in order to determine the number of nauplii ingested. Analytically obtained probability densities for the gut content were compared with observations and the results used for estimating the rate of capture of the nauplii. This capture rate was then compared with analytical results using also data for the surroundings, such as measured prey densities and turbulence conditions, as quantified by the specific energy dissipation rate. Different from earlier studies, the presented data include conditions where the turbulence exceeds the level for optimal larval encounter-capture rates.

Anomalous transport due to large coherent structures, or coherent events, is studied experimentally in a magnetized toroidal discharge plasma. The present analysis emphasizes anomalous plasma losses as well as transport of electron thermal energy density across magnetic field lines. The experiment was carried out in the Blaamann device at the University of Tromsø. The diagnostics are based on data for potential, density and electron temperature variations as detected by Langmuir probes. Most of the data analysis uses conditional sampling. The flux of thermal energy density can be broken down into several components which are analyzed separately. Experimental means for obtaining the space-time variation of the complete polarization drifts are demonstrated, and the results compared with the fluctuating E × B0/B20-velocities. For the present conditions these polarization drifts contribute only little to the plasma losses, but for other discharge parameters in heavier gases they can be important. Our results show that while the density, the potential and the electric field variations are dominated by large scales, the vorticity of the E × B0/B20-flow as well as the ion polarization drifts are strongly intermittent.

Ion sound waves are studied in a plasma subject to gravitational field. Such systems are interesting by exhibiting a wave growth that is a result of energy flux conservation in inhomogeneous systems. The increasing wave amplitude gives rise to an enhanced interaction between waves and plasma particles that can be modeled by a modified Korteweg-de Vries equation. Analytical results are compared with numerical Particle-in-Cell simulations of the problem. Our code assumes isothermally Boltzmann distributed electrons while the ion component is treated as a collection of individual particles interacting through collective electric fields. Deviations from quasi neutrality are allowed for., 30 pages, 9 figures

Incoherent radar scatter from the ionosphere will, for equilibrium conditions, show two symmetric ion-acoustic lines, one for each direction of wave propagation. Many observation, from the EISCAT Svalbard Radar (ESR) for instance, demonstrate that the symmetry of this ion line can be broken, accompanied by an enhanced, nonthermal, level of fluctuations, i.e., Naturally Enhanced Ion-Acoustic Lines (NEIALs). Several models have been proposed for explaining these naturally enhanced lines. Here, we consider one of these, suggesting that decay of electron beam excited Langmuir waves gives rise to enhanced asymmetric ion lines in the ionosphere. We use a weak-turbulence approximation, and identify crucial parameters for Langmuir decay processes to be effective in generating the observed signals., 4 figures

Aquatic micro-organisms often depend on detecting signals caused by motions in the surrounding flow. The antennae and setae of plankton are considered as examples of small fibers that here serve to detect variations in the local fluid velocities. It is argued that the noise induced by the turbulent environment can disturb the signals originating from moving prey or predators. At times, the turbulent noise can be mistaken to represent a signal, motivating erratic attack or escape responses. The present review addresses the latter problem. The analysis is kept on a level sufficiently simple to let the results have practical applicability, while on the other hand, the basic elements of the problem are retained. More generally, the results can be applied for estimating some of the effects of turbulence on small rigid fibers being transported by a turbulent flow. Known results are supplemented by new findings, extending the parameter range.

Low-frequency electrostatic drift wave turbulence has been studied in both laboratory plasmas and in space. The present review describes a number of such laboratory experiments together with results obtained by instrumented spacecraft in the Earth's near and distant ionospheres. The summary emphasizes readily measurable quantities, such as the turbulent power spectra for the fluctuations in plasma density, potential and electric fields. The agreement between power spectra measured in the laboratory and in space seems to be acceptable, but there are sufficiently frequent counterexamples to justify a future dedicated analysis, for instance by numerical tools, to explain deviations. When interpreting spectra at low ionospheric altitudes, it is necessary to give attention to the DC ionospheric electric fields and the differences in the physics of electron–ion collisions and collisions of charged particles with neutrals for cases with significant Hall drifts. These effects modify the drift wave spectra. A dedicated laboratory experiment accounted for some of these differences.

Published version. Source at http://doi.org/10.5194/angeo-33-257-2015. Analytical models are presented for currents along vertical magnetic field lines due to slow bulk electron motion in plasmas subject to a gravitational force. It is demonstrated that a general feature of this problem is a singularity in the plasma pressure force that develops at some finite altitude when a plasma that is initially in static equilibrium is set into slow motion. Classical fluid models thus do not allow general steady-state solutions for field-aligned currents. General solutions have to be non-stationary, varying on time scales of many periods of a plasma equivalent to the Brunt–Väisälä frequency. Except for very special choices of parameters, a steady-state solution exists only in an average sense. The conditions at large altitudes turn out to be extremely sensitive to even small changes in parameters at low altitudes. Low frequency fluctuations detected at large altitudes in the polar regions need not be caused by local low frequency instabilities, but merely reflect small fluctuations in conditions at low altitudes.

Analytical models for weakly nonlinear electron plasma waves are considered in order to obtain dynamic equations for the space-time evolution of their local power spectra. The model contains the wave kinetic equation as a limiting case for slow, long wavelength modulations. It is demonstrated that a finite spectral width in wavenumbers has a stabilizing effect on the modulational instability. The results invite a simple heuristic relation between the spectral width and the root-mean-square amplitude of stable stationary turbulent Langmuir wave spectra. A non-local average dispersion relation is derived as a limiting form by using the formalism developed for the spectral dynamics.

Predator-prey encounter and capture rates are key drivers of population dynamics of planktonic organisms. Turbulent mixing gives rise to enhanced encounter rates, but high turbulence levels may reduce capture rates. We present an estimate for the optimum turbulence level for a predator that is characterized by a number of parameters, such as its range of interception. A limit at small spatial scales is recovered where classical diffusion competes with turbulent motions. Particular attention is given to the question of turbulence-induced noise signals, which a predator can misinterpret as indicators of prey. Analytical expressions are obtained for the occurrence of these "error signals" in terms of the basic parameters of the problem. The basic hypothesis rests on the assumption that if several such error signals are received within a time needed for the predator to capture prey, then its capacity for cap- turing prey is reduced or even made impossible. The aim of the study is to present closed general analytical expressions for the capture rate in turbulent environments, where the results contain free parameters that can be used for modeling selected species. Statistical descriptions of the velocity fluctuations on spatial scales in the viscous subrange of turbulence are determined and placed in the context of predator-prey encounter and capture rates. The relevant probability densities are obtained by direct numerical solutions of the Navier-Stokes equation for turbulent conditions. The analysis is given a compact formulation in terms of scaled dimensionless variables.

[1] Drift waves with vertical magnetic fields in gravitational ionospheres are considered where the unperturbed plasma density is enhanced in a magnetic flux tube. The gravitational field gives rise to an overall decrease of plasma density for increasing altitude. Simple models predict that drift waves with finite vertical wave vector components can increase in amplitude merely due to a conservation of energy density flux of the waves. Field-aligned currents are some of the mechanisms that can give rise to fluctuations that are truly unstable. We suggest a self-consistent generator or “battery” mechanism that in the polar ionospheres can give rise to magnetic field-aligned currents even in the absence of electron precipitation. The free energy here is supplied by steady state electric fields imposed in the direction perpendicular to the magnetic field in the collisional lower parts of the ionosphere or by neutral winds that have similar effects.

Low Frequency Waves and Turbulence in Magnetized Laboratory Plasmas and in the Ionosphere was developed from courses taught by the author at the universities of Oslo and Tromso in Norway. Suitable for undergraduates, graduate students and researchers, the first part of the book is devoted to discussing some relevant plasma instabilities and the free energy that drives them. In the second part, the more advanced topics of nonlinear models and the interactions of many modes are discussed. Theoretical tools available for turbulence modelling are also outlined. The book summarizes a number of studies of low-frequency plasma waves, drift waves in particular, from laboratory and space experiments. Part of the IOP Plasma Physics Series

Link to publishers version: 10.1088/0741-3335/58/10/104002 A simple analytically solvable model for blobs in magnetized plasmas is proposed. The model gives results for a scaling of the blob velocity with the amplitude of the density perturbation. Limiting cases are considered: one where the plasma motion is strictly perpendicular to an externally imposed toroidal magnetic field, and one where the electrons can move along magnetic field lines to compensate partly the collective electric fields. For these limiting cases, the model predicts scaling laws for the dependence of the blob velocities and accelerations with varying cross section, plasma density and temperature. Also the scaling with the dominant ion mass is derived. The analysis is completed by including the effects of collisions between ions and neutrals.

Source: doi: 10.1063/1.4951016 A stochastic model is presented for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas. The fluctuations in the plasma density are modeled by a super-position of uncorrelated pulses with fixed shape and duration, describing radial motion of blob-like structures. In the case of an exponential pulse shape and exponentially distributed pulse amplitudes, predictions are given for the lowest order moments, probability density function, auto-correlation function, level crossings, and average times for periods spent above and below a given threshold level. Also, the mean squared errors on estimators of sample mean and variance for realizations of the process by finite time series are obtained. These results are discussed in the context of single-point measurements of fluctuations in the scrape-off layer, broad density profiles, and implications for plasma–wall interactions due to the transient transport events in fusion grade plasmas. The results may also have wide applications for modelling fluctuations in other magnetized plasmas such as basic laboratory experiments and ionospheric irregularities.

The existence of low-frequency waveguide modes of electrostatic ion acoustic waves is demonstrated in magnetized plasmas for cases where the electron temperature is striated along magnetic field lines. For low frequencies, the temperature striation acts as waveguide that supports a trapped mode. For conditions where the ion cyclotron frequency is below the ion plasma frequency we find a dispersion relation having also a radiative frequency band, where waves can escape from the striation. Arguments for the formation and propagation of an equivalent of electrostatic shocks are presented and demonstrated numerically for these conditions. The shock represents here a balance between an external energy input maintained by ion injection and a dissipation mechanism in the form of energy leakage of the harmonics generated by nonlinear wave steepening. This is a reversible form for energy loss that can replace the time-irreversible losses in a standard Burgers equation.

Turbulence plays an important role for predator–prey interactions in aquatic environments. In one sense turbulence benefits the predator by increasing its encounter rate with prey, but on the other hand it can benefit the prey by making them more difficult to catch. In the present study of this problem, a turbulent flow field is obtained by direct numerical solution of the Navier–Stokes equation. The analysis includes the effects of the turbulence on the encounter rate between passively moving predators and prey, and at the same time also models the capture probability depending on the relative turbulent motions of predator and prey. Analytical results for scaling laws for planktonic encounter and capture rates in turbulent environments are obtained in terms of the basic parameters for the problem, and the results are compared with related findings reported in the literature. For large values of the specific energy dissipation rates ϵ the turbulence reduces the capture probability significantly, in part also because the effective capture range reduces for increasing turbulence intensity. The results presented here predict the parameters for an optimum turbulence level for the predator capture rate. For enhanced turbulence levels sudden bursts in the space–time varying velocity field contribute to a noise level that can reduce the probability for capturing prey. We consider cases where the capture range of an organism is comparable to or smaller than the effective Kolmogorov length scale, as well as the opposite limit of larger capture ranges in the inertial range of the turbulence. The reference model assumes spherical interception volumes, but it is demonstrated that the results remain basically valid also for the case where these volumes are hemispherical or conical: the consequences of having a shape of the interception surface deviating from a sphere can be accounted for by an empirical scaling factor, which depends solely on the opening angle of the cone.

Oscillations with periods on the order of 5–10 min have been observed by instrumented spacecrafts in the Earth's magnetosphere. These oscillations often follow sudden impacts related to coronal mass ejections. It is demonstrated that a simple model is capable of explaining these oscillations and give a scaling law for their basic characteristics in terms of the basic parameters of the problem. The period of the oscillations and their anharmonic nature, in particular, are accounted for. The model has no free adjustable numerical parameters. The results agree well with observations. The analysis is supported by numerical simulations solving the Magneto-Hydro-Dynamic (MHD) equations in two spatial dimensions, where we let a solar wind interact with a magnetic dipole representing a magnetized Earth. We consider two tilt-angles of the magnetic dipole axis. We find the formation of a magnetosheath with the magnetopause at a distance corresponding well to the analytical results. Sudden pulses in the model solar wind sets the model magnetosphere into damped oscillatory motions and quantitatively good agreement with the analytical results is achieved.

This is an author-created, un-copyedited version of the article, Fredriksen, Å., Pécseli, H.L. & Trulsen, J.K. (2018). A solvable model for the basic properties of a simple magnetized plasma torus. Plasma Physics and Controlled Fusion, 60(085021). https://doi.org/10.1088/1361-6587/aacd2a, which has been accepted for publication/published in Plasma Physics and Controlled Fusion. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6587/aacd2a. A simple magnetized plasma torus is modeled by using a 'top-hat' density variation. The benefit of this simplification is an exactly solvable model, allowing for a few additions, such as an externally maintained parabolic steady state potential variation imposed on the plasma. The combined effects of the resulting plasma rotation and the plasma polarization due to magnetic field gradient particle drifts can be described. The stabilizing and confining effects of plasma rotation are explicitly demonstrated. In a special high plasma density limit the results are confirmed by a more general model, indicating that the results of the top-hat model can be used with confidence in more general cases. A small vertical magnetic field component can be included for a plasma with neutral collisions and its influence on the electron dynamics studied. The effects of ion–neutral collisions are also included. The rotation and polarization of the plasma has different effects on the time variations of the plasma density and potential. As a reference we use data from the Blaamann device at the University of Tromsø obtained by a movable multi-probe, measuring variations in density, floating potential and an electric field component. The fluctuations in the plasma are characterized by auto-correlations and by cross-correlations between the signal from a fixed reference probe and data. The model accounts adequately for the phase variations of the signals for varying spatial multi-probe positions.

In aquatic environments the encounter rates between small predators and their prey are increased by turbulence. We present an expression for the flux of prey into the detective sphere of a small self-propelled predator. We then test this model by direct comparison of theoretical encounter rates with predictions from a numerical experiment where the Navier–Stokes equation is solved explicitly. This allows us to estimate encounter rates numerically under realistic small-scale flow environments, and to explore the accuracy of a simple theoretical formulation of this process. Our analysis includes results for cruising and spiralling motions, as well as pause-travel search behaviour. We find that the analytical model yield surprisingly accurate predictions for models including also the shape of the predator’s perceptive sphere and turbulence conditions. This adds confidence to such simple approximations in applied models of predator–prey encounter rates for a wide range of scale sizes of the predator’s reactive volumes, their motility patterns and turbulence levels.

Small solid metallic objects in relative motion to thermal plasmas are studied by numerical simulations. We analyze supersonic motions, where a distinctive ion wake is formed behind obstacles. At these plasma drift velocities, ions enter the wake predominantly due to deflections by the electric field in the sheath around the obstacle. By irradiating the back side of the object by ultraviolet (UV) light, we can induce also an enhanced photo-electron population there. The resulting charge distribution gives rise to a pronounced local potential and plasma density well behind the object. This potential variation has the form of a three-dimensional ion acoustic double layer, containing also an ion phase space vortex. The analysis is supported also by one-dimensional numerical simulations to illustrate the importance of boundary conditions, Dirichlet and von Neumann conditions in particular.

Low frequency electrostatic turbulence in the io- nospheric E-region is studied by means of numerical and ex- perimental methods. We use the structure functions of the electrostatic potential as a diagnostics of the fluctuations. We demonstrate the inherently intermittent nature of the low level turbulence in the collisional ionospheric plasma by us- ing results for the space-time varying electrostatic potential from two dimensional numerical simulations. An instrumen- ted rocket can not directly detect the one-point potential va- riation, and most measurements rely on records of potential differences between two probes. With reference to the space observations we demonstrate that the results obtained by po- tential difference measurements can differ significantly from the one-point results. It was found, in particular, that the in- termittency signatures become much weaker, when the pro- per rocket-probe configuration is implemented. We analyze also signals from an actual ionospheric rocket experiment, and find a reasonably good agreement with the appropriate simulation results, demonstrating again that rocket data, ob- tained as those analyzed here, are unlikely to give an ade- quate representation of intermittent features of the low fre- quency ionospheric plasma turbulence for the given condi- tions. (Chandrasekhar, 1957) that the second order structure func- tion, as a function of spatial separations, can be obtained by simple dimensional arguments, apart from a numeri- cal constant. For the longitudinal second order velocity structure function in the universal Kolmogorov-Oubokhov range of homogeneous isotropic turbulence we thus find 92(r)

Every day billions of meteoroids impact and disintegrate in the Earth’s atmosphere. Current estimates for this global meteor flux vary from 2000 to 200,000 tons per year, and estimates for the average velocity range between 10 km/s and 70 km/s. The basic properties of this global meteor flux, such as the average mass, velocity, and chemical composition remain poorly constrained. We believe much of the mystery surrounding the basic parameters of the interplanetary meteor flux exists for the following reason, the unknown sampling characteristics of different radar meteor observation techniques, which are used to derive or constrain most models. We believe this arises due to poorly understood radio scattering characteristics of the meteor plasma, especially in light of recent work showing that plasma turbulence and instability greatly influences meteor trail properties at every stage of evolution. We present our results on meteor plasmas simulations of head echoes using particle in cell (PIC) ions, which show that electric fields strongly influence early stage meteor plasma evolution, by accelerating ions away from the meteoroid body. We also present the results of finite difference time domain electromagnetic simulations (FDTD), which can calculate the radar cross section of the simulated meteor plasmas. These simulations have shown that the radar cross section depends in a complex manner on a number of parameters. These include the angle between radar and meteor entry, a large dependence on radar frequency, which shows that for a given meteor plasma size and density, the reflectivity as a function of probing radar frequency varies, but typically peaks below 100 MHz.

Recently, meteor head echo detections from high powered large aperture radars (HPLA) have brought new measurements to bear on the study of sporadic interplanetary meteors. These same observations have demonstrated an ability to observe smaller meteoroids without some of the geometrical restrictions of specular radar techniques. Yet incorporating data from various radar reflection types and from different radars into a single consistent model has proven challenging. We believe this arises due to poorly understood radio scattering characteristics of the meteor plasma, especially in light of recent work showing that plasma turbulence and instability greatly influences meteor trail properties at every stage of evolution. In order to overcome some of the unknown relationships between meteoroid characteristics (such as mass and velocity) and the resulting head echo radar cross-sections (RCS), we present our results on meteor plasma simulations of head echo plasmas using particle in cell (PIC) ions, which show that electric fields strongly influence early stage meteor plasma evolution, by accelerating ions away from the meteoroid body at speeds as large as several kilometers per second. We also present the results of finite difference time domain electromagnetic simulations (FDTD), which can calculate the radar cross-section of the simulated meteor plasma electron distributions. These simulations have shown that the radar cross-section depends in a complex manner on a number of parameters. In this paper we demonstrate that for a given head echo plasma the RCS as a function of radar frequency peaks at sqrt (2*peak plasma frequency) and then decays linearly on a dB scale with increasing radar frequency. We also demonstrate that for a fixed radar frequency, the RCS increases linearly on a dB scale with increasing head echo plasma frequency. These simulations and resulting characterization of the head echo radar cross-section will both help relate HPLA radar observations to meteoroid properties and aid in determining a particular radar facility’s ability to observe various meteoroid populations.