Ionospheric Plasma Clouds Research Articles

Nonlinear Three-Dimensional Simulations of the Gradient Drift and Secondary Kelvin–Helmholtz Instabilities in Ionospheric Plasma Clouds

A newly developed three-dimensional electrostatic fluid model solving continuity and current closure equations aims to study phenomena that generate ionospheric turbulence. The model is spatially discretized using a pseudo-spectral method with full Fourier basis functions and evolved in time using a four-stage, fourth-order Runge Kutta method. The 3D numerical model is used here to investigate the behavior and evolution of ionospheric plasma clouds. This problem has historically been used to study the processes governing the evolution of the irregularities in the F region of the ionosphere. It has been shown that these artificial clouds can become unstable and structure rapidly (i.e., cascade to smaller scales transverse to the ambient magnetic field). The primary mechanism which causes this structuring of ionospheric clouds is the E×B, or the gradient drift instability (GDI). The persistence and scale sizes of the resulting structures cannot be fully explained by a two-dimensional model. Therefore, we suggest here that the inclusion of three-dimensional effects is key to a successful interpretation of mid-latitude irregularities, as well as a prerequisite for a credible simulation of these processes. We investigate the results of 2D and 3D nonlinear simulations of the GDI and secondary Kelvin–Helmholtz instability (KHI) in plasma clouds for three different regimes: highly collisional (≈200 km), collisional (≈300 km), and inertial (≈450 km). The inclusion of inertial effects permits the growth of the secondary KHI. For the three different regimes, the overall evolution of structuring of plasma cloud occurs on longer timescales in 3D simulations. The inclusion of three-dimensional effects, in particular, the ambipolar potential in the current closure equation, introduces an azimuthal “twist“ about the axis of the cloud (i.e., the magnetic field B). This azimuthal “twist” is observed in the purely collisional regime, and it causes the perturbations to have a non-flute-like character (k‖≠0). However, for the 3D inertial simulations, the cloud rapidly diffuses to a state in which the sheared azimuthal flow is substantially reduced; subsequently, the cloud becomes unstable and structures, by retaining the flute-like character of the perturbations (k‖=0).

Non-thermal water loss of the early Mars: 3D multi-ion hybrid simulations

In this study we analyze the non-thermal loss rates of O +, O 2 + and CO 2 + ions over the last 4.5 billion years (Gyr) in the Martian history by using a 3D hybrid model. For this reason we derived the past solar wind conditions in detail. We take into account the intensified particle flux of the early Sun as well as an Martian atmosphere, which was exposed to a sun's extreme ultraviolet (EUV) radiation flux 4.5 Gyr ago that was 100 times stronger than today. Furthermore, we model the evolution of the interplanetary magnetic field by a Weber & Davis solar wind model. The ‘external’ influences of the Sun's radiation flux and solar wind flux lead to the formation of an ionospheric obstacle by photoionization, charge exchange and electron impact. For the early Martian conditions we could show that charge exchange was the dominant ionization mechanism. Several hybrid simulations for different stages in the evolution of the Martian atmosphere, at 1, 2, 5, 10, 30 and 100 EUV, were performed to analyze the non-thermal escape processes by ion pick-up, momentum transfer from the solar wind to the ionosphere and detached ionospheric plasma clouds. Our results show a non-linear evolution of the loss rates. Using mean solar wind parameters the simulations result in an oxygen loss equivalent to the depth of a global Martian ocean of about 2.6 m over the last 4.5 Gyr. The induced magnetic field strength could be increased up to about 2000 nT. A simulation run with high solar wind density results in an oxygen loss of a Martian ocean up to 205 m depth during 150 million years after the sun reached the zero age mean sequence (ZAMS).

A comparison of magnetohydrodynamic instabilities at the Martian ionopause

It is known from Pioneer Venus measurements that at the Venusian ionopause wave-like structures develop, which can detach in the form of ionospheric plasma clouds. This phenomenon is assumed to occur due to the Kelvin–Helmholtz instability, which can appear in large regions of the Venusian ionopause. Recent studies of Mars Global Surveyor measurements indicate that wave–like structures and plasma clouds also detach from the Martian ionopause. Therefore, these features seem to be common for the solar wind interaction of non-magnetized planets. We study the conditions at the Martian ionopause with respect to the occurrence of several MHD instabilities. The conditions in the magnetosheath are modeled by a semi-analytical MHD simulation that includes mass loading. The ionospheric parameter needed for the model calculations are taken from a global hybrid model. The stability of the Martian ionopause against the Kelvin–Helmholtz, the Rayleigh–Taylor, and the interchange instability is analyzed. Further, we suggest that including the Hall term in the description of the Kelvin–Helmholtz instability gives a current in the planetary boundary layer resulting in a shear flow compared with the ionospheric plasma, which can lead to an unstable boundary layer near the subsolar point. Since the interchange instability depends on the curvature of the magnetic field lines, we additionally study the influence of the strong curvature of the Martian ionopause due to the localized, remnant, crustal magnetism appearing mainly in the southern hemisphere of Mars.

Ion loss on Mars caused by the Kelvin–Helmholtz instability

Mars Global Surveyor detected cold electrons above the Martian ionopause, which can be interpreted as detached ionospheric plasma clouds. Similar observations by the Pioneer Venus Orbiter electron temperature probe showed also extreme spatial irregularities of electrons in the form of plasma clouds on Venus, which were explained by the occurrence of the Kelvin–Helmholtz instability. Therefore, we suggest that the Kelvin–Helmholtz instability may also detach ionospheric plasma clouds on Mars. We investigate the instability growth rate at the Martian ionopause resulting from the flow of the solar wind for the case where the interplanetary magnetic field is oriented normal to the flow direction. Since the velocity shear near the subsolar point is very small, this area is stable with respect to the Kelvin–Helmholtz instability. We found that the highest flow velocities are reached at the equatorial flanks near the terminator plane, while the maximum plasma density in the terminator plane appears at the polar areas. By comparing the instability growth rate with the magnetic barrier formation time, we found that the instability can evolve into a non-linear stage at the whole terminator plane but preferably at the equatorial flanks. Escape rates of O + ions due to detached plasma clouds in the order of about 2 × 10 23 – 3 × 10 24 s - 1 are found. Thus, atmospheric loss caused by the Kelvin–Helmholtz instability should be comparable with other non-thermal loss processes. Further, we discuss our results in view of the expected observations of heavy ion loss rates by ASPERA-3 on board of Mars Express.

Acceleration of ionospheric plasma clouds in the Venus ionosheath

A discussion is presented to examine the acceleration and distribution of ionospheric plasma clouds around Venus. It is argued that magnetic forces may not be sufficient to accelerate those features and that their motion should also be influenced by the momentum of the solar wind around the flanks of the ionosheath. Plasma data obtained from selected Pioneer Venus Orbiter (PVO) passes show ionospheric clouds that have been displaced downstream from the planet, with a component directed away from the Venus plasma tail axis. The position and speed of these features suggests that they may not have been only accelerated by magnetic forces, but that most likely were also subject to effects produced by the kinetic energy of the solar wind. This suggestion derives from the observation of plasma tail rays with velocities comparable to the escape speed from the planet and also measurements of superalfvenic solar wind conditions around the flanks of the Venus ionosheath. While plasma clouds can be accelerated by magnetic forces near the subsolar region, where there is a strong accumulation of interplanetary magnetic field fluxes, the available experimental evidence shows that the Venus upper ionospheric plasma is accelerated mostly near the terminator, but not around the subsolar region. These views suggest that the ionospheric plasma clouds could be mostly accelerated around the flanks of the Venus ionosheath.

Polar expansion fan in the Venus ionosheath

Magnetic field data of the Pioneer Venus Orbiter (PVO) are used to examine the configuration of the intermediate transition around the Venus wake. The intermediate transition is a plasma boundary characterized by a sudden decrease of the magnetic field intensity to low values in the inner ionosheath and a strong rotation of the magnetic field orientation to a direction closer to the Sun‐Venus axis. Measurements show that the intermediate transition is not seen across the entire Venus wake but in an expansion fan that is formed around the solar wind‐induced magnetic polar regions of the Venus ionosheath. The magnetic field geometry within the expansion fan is produced by ionosheath magnetic field lines that are draped around those regions and that are then converted by the shocked solar wind. Examples are shown where the intermediate transition is seen at positions different from those of ionospheric plasma clouds. Across both features the magnetic field may also exhibit a different rotation including changes in the polarity of its component along the Sun‐Venus axis. A schematic of the magnetic field geometry within and in the vicinity of the expansion fan is presented. It is argued that the expansion fan flares away from the Venus tail and that the local orientation of the magnetic field is different from that observed around the Venus dayside ionosphere.

Plasma clouds and the intermediate transition in the Venus ionosheath

Plasma and magnetic field PVO measurements are described to examine the relative position of the intermediate transition and ionospheric plasma clouds in the Venus ionosheath. Examples show that both features occur as different events and that plasma clouds are observed at altitudes lower than that of the intermediate transition. In a set of PVO passes in which there is evidence of both events it is found that the intermediate transition represents the outer boundary of the region where plasma clouds are observed. The magnetic field of the solar wind experiences different changes in both cases. Across the intermediate transition there is a strong rotation of the magnetic field direction and also a decrease of the magnetic field intensity to low values which extend throughout most of the inner ionosheath. Different values of the intensity and orientation of the magnetic field are observed mostly in the vicinity of plasma clouds.

Three‐dimensional simulation study of ionospheric plasma clouds

We present the results of fully three‐dimensional numerical simulations of ionospheric plasma cloud evolution. We first consider the evolution of the plasma cloud considered by Drake and Huba [1987] in the limit of vanishingly small ion compressibility. The simulations support the results of the analytical theory: finite plasma temperature, combined with fully three‐dimensional plasma dynamics, is a stabilizing influence on plasma cloud evolution. This stability is associated with sheared azimuthal ion flows in the vicinity of the cloud surface. We then consider cloud evolution using realistic values of ion compressibility. We find that the cloud rapidly diffuses to a state in which the sheared azimuthal flow is substantially reduced; subsequently, the cloud becomes unstable and structures.

Three-dimensional equilibrium and stability of ionospheric plasma clouds

The equilibrium and stability of three-dimensional (3-D) ionospheric plasma clouds is investigated. The equilibrium density profile is assumed to be a 3-D water bag with a circular cross section transverse to B, and an ellipsoidal cross section parallel to B. The equilibrium potential consists of two parts: a polarization potential driven by a uniform neutral wind, and an ambipolar potential driven by parallel electron pressure. The latter potential is shown to cause sheared azimuthal plasma flows perpendicular to B. A stability analysis of this equilibrium is carried out. It is found that the E×B instability, which causes the structuring of ionospheric plasma clouds, can be stabilized by the shear in the azimuthal flow. A marginal stability criterion is derived. On the basis of this stability criteria, striations of barium clouds in the ionospheric F region should be stable to further bifurcation, as is observed

Dynamics of three‐dimensional ionospheric plasma clouds

In this paper we will present the first fully three‐dimensional analytic study of plasma cloud dynamics, as well as computational results based upon a recently developed three‐dimensional electrostatic code. We derive a stability criterion for the large‐scale structuring of an ionospheric cloud based on a water bag model for the special case Lz = rc(σ‖/σ⊥)1/2 (here, Lz is the half length of the cloud along the magnetic field, rc is the radius of the cloud, and σ‖,⊥ are the parallel and perpendicular cloud conductivities, respectively). We also present preliminary numerical results of three‐dimensional plasma cloud behavior. We examine the self‐consistent pressure‐induced plasma flow that results from a realistic plasma cloud in a realistic atmosphere in two‐dimensional cylindrical geometry, and the evolution of fully three‐dimensional perturbations of such a cloud.

The influence of ionization and recombination processes on the dynamics of ionospheric plasma clouds

The dynamics of a one-dimensional ionospheric irregularity interacting with the magnetosphere is studied by numerical simulation. The polarization electric field produced by charge separation within the irregularity propagates along magnetic field lines with the Alfvén velocity V A and drives polarizational and field-aligned currents in the magnetosphere. Their values and localization are controlled by motion and deformation of the irregularity resulting from its electrostatic coupling to the background ionosphere. The pattern of the field-aligned currents varies with time and depends primarily on gradients of the polarization electric field. The latter is controlled by the ambient electric field, diffusion, recombination process, intensity of the initial perturbation, etc. Feedback effect of the magnetospheric conductance on the development of the irregularity is examined.

Dynamics of three dimensional ionospheric plasma clouds.

The first self-consistent, three-dimensional analysis of plasma cloud evolution in the ionosphere is presented. It is demonstrated that there is a preferred perpendicular scale size associated with 3D plasma clouds given by ${\mathrm{r}}_{\mathrm{c}}$\ensuremath{\sim}c(${\mathrm{T}}_{\mathrm{e}}$+${\mathrm{T}}_{\mathrm{i}}$)/${\mathrm{eB}}_{\mathrm{z}}$${\mathrm{V}}_{\mathrm{n}}$${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{c}}$, where ${\mathrm{r}}_{\mathrm{c}}$ is the cloud radius, ${\mathrm{T}}_{\mathrm{\ensuremath{\alpha}}}$ is the temperature of the \ensuremath{\alpha} species, ${\mathrm{B}}_{\mathrm{z}}$ is the ambient magnetic field, and ${\mathrm{V}}_{\mathrm{n}}$ is the neutral wind speed, and ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{c}}$1/ \ensuremath{\surd}2 .

Convective stabilization of ionospheric plasma clouds

We derive a stability criterion for the large‐scale structuring of ionospheric plasma clouds due to the E × B gradient drift instability. For the equilibrium we consider a cylindrical two‐dimensional water bag cloud aligned along a uniform magnetic field that is polarized by a uniform neutral wind. We perform a stability analysis that allows three‐dimensional perturbations (in r, θ, and z), and we consider both local and global modes. We find that when the parallel wave number kz exceeds a threshold value, exponentially growing poloidal eigenmodes form which are localized on the “backside” of the cloud. This is in contrast to the kz = 0 limit in which there are no exponential solutions. As kz is increased further, the unstable modes localize at a finite angle away from the backside, at a point where the diamagnetic propagation velocity Vd balances the convective flow velocity of the background plasma around the cloud, Vb. We find that the E × B gradient drift instability is stable when Vd > Vb so that the cloud is no longer susceptible to large‐scale structuring. We apply these results to ionospheric barium clouds and estimate that they will cease structuring when L⊥ < (cT/eB)(M + 2)/2Vn where L⊥ is the transverse size of the cloud, T = Te + Ti is the total temperature, M = nc/nb (nc is the cloud density, and nb is the background density), and Vn is the neutral wind velocity. For mid‐latitude barium releases at ∼180 km we estimate L⊥ ∼ 160–480 m, which is consistent with observations.

The role of finite parallel length on the stability of barium clouds

A simple model is used to show that the finite parallel length of ionospheric plasma clouds can affect the growth rate of striation instabilities (e.g., gradient drift). The finite parallel length of plasma clouds tends to favor the growth of striations with short perpendicular wavelengths.

Quasi steady state multiple‐plasma‐cloud configurations in the F region ionosphere

The morphology of a finite array of plasma density enhancements (multiple plasma clouds) in the ionosphere is studied in order to determine the condition under which the system undergoes a quasi steady state E × B drift. In such a system the polarization‐induced self‐electric field inside all the plasma clouds must be essentially equal and uniform. The method of image dipoles previously developed for multiple equatorial spread F bubbles is used to calculate the instantaneous electric field exactly. It is found that even for small separation distances for which the intercloud interaction is significant, the electric field remains nearly uniform both internally and from cloud to cloud for typical ionospheric plasma cloud parameters, so that the multiple plasma clouds drift in unison without changing their geometrical shapes. This constitutes a quasi steady state configuration. The implications to the behavior of late time plasma cloud striations are discussed.

Contour dynamics—An interface method for studying the evolution of large density gradient ionospheric plasma clouds

A 2-D model is introduced of an ionospheric plasma cloud with a piecewise-constant density gradient and a diffusive-regularized boundary. Using contour dynamics (a boundary integral method) only the boundary between the regions of different densities need to be followed so that the 2-D model reduces to the 1-D motion of closed curves. Numerical results are shown including a comparison of the finite-difference and contour dynamics models.

Nonlinear theory of the E × B instability with an inhomogeneous electric field

Using analytical and numerical simulation techniques, the nonlinear evolution of the E × B instability with an inhomogeneous electric field has been studied. For the case where the electric field component parallel to the density gradient is inhomogeneous, we find that the inhomogeneous E × B instability in the nonlinear regime (1) evolves into large‐scale anisotropic fingerlike structures, (2) can be described by power laws P(kx) ∝ kx−nx, nx ≃ 2, P(ky) ∝ ky−ny, ny ≃ 2–3, where P(kx) and P(ky) are the one‐dimensional power spectra parallel and perpendicular to the initial density gradient, and (3) can be stabilized by quasi‐linear mechanisms in which the initial density gradient is modified by a finite‐amplitude wave spectrum. Application is made to naturally occurring plasma density fluctuations in the auroral ionosphere, but the results are applicable to plasma jet and striation formation in artificially produced ionospheric plasma clouds.

Ion‐Pedersen drift and parallel electric field effects on plasma jetting

The combination of ion‐Pedersen currents and parallel electric fields are shown to affect significantly both the jetting of ionospheric plasma clouds transverse to the geomagnetic field and the Alfven waves generated by the moving plasma. Ion‐Pedersen currents and parallel electric fields invalidate the “frozen‐in” field approximation and cause Alfven waves to decay. They also imply an eigenvalue condition on the size of the plasma cloud transverse to the geomagnetic field and the direction of cloud motion. The attenuation of Alfven waves reduces the likelihood that the waves can cause an electromagnetic pulse on the ground and implies that the initial directed energy in the plasma jet is coupled, over great distances, to ions and electrons. It is suggested that two phenomena are more likely to occur at higher altitudes (e.g., > 500 km), where neutral and ambient densities become smaller. First, there is the substantial displacement of plasma clouds with an accompanying temporary change in the geomagnetic field. Second, the Alfven waves created in response to the motion of plasma clouds are less subject to attenuation and more likely to cause an electromagnetic pulse on the ground.

Ionospheric plasma cloud dynamics via regularized contour dynamics. I. Stability and nonlinear evolution of one-contour models

The linear stability and nonlinear evolution of a regularized contour dynamical model of an ionospheric plasma cloud (or deformable dielectric) is examined. That is, the cloud is modeled by piecewise-constant ion density regions; and the regularization is accomplished with a tangential diffusion operator that models aspects of the diffusion operator in two dimensions. A complete linear stability analysis of a circular cloud shows that a single-mode excitation ‘‘cascades downward’’ in wavenumber as it grows in amplitude, a process that results from the symmetry-breaking electric field. Approximate formulas are derived for the amplitude growth and cascade-down phenomena and verified with precise numerical calculations. A simple rescaling shows that clouds with large λ (=cloud-ion density/ambient-ion density) evolve more slowly and appear more dissipative. The regularized contour-dynamical algorithm for computations in the nonlinear regime is validated against the linear analysis and truncation errors are assessed by using different spatial resolutions. Calculations in the nonlinear regime show the experimentally observed ‘‘backside’’ striations. Furthermore, at long times, a secondary structure arises on the sides of the primary striations. A comparison of simulations with different λ shows that nonlinear effects arise sooner in normalized time (but longer in real time) if λ is larger.

Influence of velocity shear on the Rayleigh‐Taylor instability

The influence of a transverse velocity shear on the Rayleigh‐Taylor instability is investigated. It is found that a sheared velocity flow can substantially reduce the growth rate of the Rayleigh‐Taylor instability in the short wavelength regime (i.e., kL > 1 where L is the scale length of the density inhomogeneity), and causes the growth rate to maximize at kL < 1.0. Applications of this result to ionospheric phenomena [equatorial spread F (ESF) and ionospheric plasma clouds] are discussed. In particular, the effect of shear could account for, at times, the 100’s of km modulation observed on the bottomside of the ESF ionosphere and the km scale size wavelengths observed in barium cloud prompt striation phenomena.