Plasma Depletion Layer Research Articles

Evolution of mirror structures in the magnetosheath of Saturn from the bow shock to the magnetopause

Mirror modes have been systematically observed by Voyagers 1 and 2 in wide portions of Jupiter's and Saturn's magnetosheaths. In particular, in one crossing of Saturn's subsolar magnetosheath, mirror waves are present almost continuously from the bow shock to the magnetopause. Therefore in this crossing, taking advantage also of relatively steady interplanetary conditions, we can track the evolution of mirror structures from a quasi‐perpendicular bow shock to a low‐shear magnetopause. We find that these structures evolve from quasi‐sinusoidal waves to nonperiodic structures, consisting of both magnetic field enhancements and wells, and, finally, to dips in the plasma depletion layer (PDL) close to the magnetopause. Both the amplitude and wavelength of the fluctuations tend to increase with increasing distance from the bow shock, except in the PDL, where they decrease toward the magnetopause. The waves are always compressional, and the direction of maximum variance forms an angle of ∼30° with B in the outer magnetosheath and a smaller angle in the inner magnetosheath. A comparison with the predictions of a nonlinear theory of the mirror instability shows some discrepancies, indicating that further theoretical studies are necessary.

MHD model of magnetosheath flow: comparison with AMPTE/IRM observations on 24 October, 1985

Abstract. We compare numerical results obtained from a steady-state MHD model of solar wind flow past the terrestrial magnetosphere with documented observations made by the AMPTE/IRM spacecraft on 24 October, 1985, during an inbound crossing of the magnetosheath. Observations indicate that steady conditions prevailed during this about 4 hour-long crossing. The magnetic shear at spacecraft entry into the magnetosphere was 15°. A steady density decrease and a concomitant magnetic field pile-up were observed during the 40 min interval just preceding the magnetopause crossing. In this plasma depletion layer (1) the plasma beta dropped to values below unity; (2) the flow speed tangential to the magnetopause was enhanced; and (3) the local magnetic field and velocity vectors became increasingly more orthogonal to each other as the magnetopause was approached (Phan et al., 1994). We model parameter variations along a spacecraft orbit approximating that of AMPTE/IRM, which was at slightly southern GSE latitudes and about 1.5 h post-noon Local Time. We model the magnetopause as a tangential discontinuity, as suggested by the observations, and take as input solar wind parameters those measured by AMPTE/IRM just prior to its bow shock crossing. We find that computed field and plasma profiles across the magnetosheath and plasma depletion layer match all observations closely. Theoretical predictions on stagnation line flow near this low-shear magnetopause are confirmed by the experimental findings. Our theory does not give, and the data on this pass do not show, any localized density enhancements in the inner magnetosheath region just outside the plasma depletion layer.Key words. Steady-state magnetosheath · Plasma depletion layer · Stagnation line flow

The effect of the magnetopause shapes of Jupiter and Saturn on magnetosheath parameters

The solar wind flow past nonaxisymmetric magnetospheres exhibits features which are absent in the case of axisymmetric magnetospheres such as that of Earth. We discuss results obtained by a numerical integration of the dissipationless MHD equations, under simplifying assumptions, and apply them to the two outer planets Jupiter and Saturn, both of whose magnetospheres depart substantially from axisymmetry. We model these magnetospheres as paraboloids with two different radii of curvature at the subsolar point, L 0 and L 1, where L 0 and L 1 refer to a magnetopause cut comtaining the rotational axis, and to the rotational equator, respectively ( L 0 < L 1). The degree of flattening is expressed by a parameter q:= L 0 L 1 , and, following earlier modelling and data analysis work, we set q = 0.35 for Jupiter and q = 0.64 for Saturn. We find here that the structure and behaviour of physical parameters in the magnetosheath of Saturn is intermediate to that at Earth and at Jupiter. For both planets, the thickness of the magnetosheath and the width and structure of the plasma depletion layer are found to be strong functions of the orientation of the interplanetary magnetic field (IMF). The effect of the IMF on the magnetosheath is strongest (weakest) when the IMF is directed perpendicular (parallel) to the rotational equator. For any intermediate orientation, a smooth rotation of the magnetosheath magnetic field towards the direction of the planet's rotational axis is superimposed on the field strength enhancement (and the density reduction) as the respective magnetopauses are approached. For Saturn, we study the dependence of magnetosheath parameters for various IMF orientations at two Alfvén Mach numbers. Throughout, we compare our results to similar calculations of solar wind flow past Earth.

Charts of joint Kelvin‐Helmholtz and Rayleigh‐Taylor instabilites at the dayside magnetopause for strongly northward interplanetary magnetic field

We present maximum growth rate charts of the Kelvin‐Helmholtz (KH) and Rayleigh‐Taylor (RT) instabilities at the dayside magnetopause (MP), considering two orientations of the interplanetary magnetic field (IMF) (due north and 30° west of north). We input parameters in the plasma depletion layer calculated from an MHD code. We study both a sharp MP transition and an MP with an attached boundary layer (“thin” and “thick” approximations, respectively). Our analysis applies to wavelengths (λ) from ∼2 × 103 km to ≤9 RE. Thin model results are as follows: For a stationary MP and due north IMF, the off‐noon, low‐latitude MP is very low shear (≤10°) and is substantially KH active. With an IMF inclined to north, extremely low shear, KH‐active regions are confined to two strips, one in each hemisphere, where short λ perturbations are generated, which propagate as surface ripples on the high‐latitude, duskside MP. For a sunward accelerating magnetopause and IMF north, a large part of the MP is unstable. With an inclined IMF, the KH+RT unstable strips are broader and growth rates are higher. Thick model results are as follows: For IMF due north and a stationary MP, the middle‐ to high‐latitude MP is stable. At middle to low latitudes, the inner edge of the boundary layer (IEBL) is active, except for a 2‐hour local time band on either side of noon. For the inclined IMF, the MP is stable for long λ, with activity for short λ confined to two strips, as before, with slightly reduced growth rates. For the IEBL, a clear dawn‐dusk asymmetry in KH activity is evident. When the MP accelerates sunward and the IMF points north, we have to consider also the λ of the perturbation. For short λ, growth rates are enhanced with respect to stationarity at both the MP and the IEBL. While there are extensive regions of negligible growth at the MP, the entire IEBL is RT+KH unstable. We give an example of a long λ perturbation where both interfaces are coupled and oscillate together. Finally, for an inclined IMF, we have at the MP unstable strips which are wider and have higher growth rates. The IEBL, by contrast, is completely destabilized, with larger growth rates than under stationary conditions.

On the possible excitation of electromagnetic ion cyclotron waves in solar ejecta

We study the possibility of exciting electromagnetic ion cyclotron waves (EICWs) in solar ejecta (CMEs) by a kinetic instability driven by ion temperature anisotropies. Our approach is to vary key parameters about assumed baseline values. Since Tp,‖ &gt; Tp,⊥ in most solar ejecta, the polarization of the unstable waves is right‐handed. If the average proton beta is low (βp ≤ 0.3), the activity is negligible for moderate temperature ratios, Tp,‖/Tp,⊥. Increasing βp increases both the frequency range and the instability growth rate. Increasing the temperature anisotropy brings about qualitatively similar effects as increasing βp, with comparable growth rates. Increasing the relative alpha‐to‐proton density ratio η has two effects: the active frequency range is shifted toward lower frequencies and the growth rate increases. Between η = 0 and η = 0.15, the maximum growth rate increases by a factor of ∼20, highlighting the importance of the alphas for generating this instability. A case that may represent some magnetic clouds with exceptional parameters, βp = 0.2, Tp,‖/Tp,⊥ = 10, and η = 0.08 − 0.15, is considered. The maximum growth rate is found to be twice the reference CME case, while the active frequency range is 3 times wider. We conclude that EICWs should be present in some ejecta and possibly also in those magnetic clouds with relatively weak magnetic field, high He++ content, and large Tp,‖/Tp,⊥ ratios, and whose βp is high, for example, through interaction with a succeeding fast stream. We also suggest that substantial changes with respect to normal conditions should occur in the power spectrum of EICWs in the terrestrial plasma depletion layer when a CME, or a magnetic cloud, with negative anisotropy passes Earth.

MHD model of magnetosheath flow: comparison with AMPTE/IRM observations on 24 October, 1985

We compare numerical results obtained from a steady-state MHD model of solar wind flow past the terrestrial magnetosphere with documented observations made by the AMPTE/IRM spacecraft on 24 October, 1985, during an inbound crossing of the magnetosheath. Observations indicate that steady conditions prevailed during this about 4 hour-long crossing. The magnetic shear at spacecraft entry into the magnetosphere was 15°. A steady density decrease and a concomitant magnetic field pile-up were observed during the 40 min interval just preceding the magnetopause crossing. In this plasma depletion layer (1) the plasma beta dropped to values below unity; (2) the flow speed tangential to the magnetopause was enhanced; and (3) the local magnetic field and velocity vectors became increasingly more orthogonal to each other as the magnetopause was approached (Phan et al., 1994). We model parameter variations along a spacecraft orbit approximating that of AMPTE/IRM, which was at slightly southern GSE latitudes and about 1.5 h post-noon Local Time. We model the magnetopause as a tangential discontinuity, as suggested by the observations, and take as input solar wind parameters those measured by AMPTE/IRM just prior to its bow shock crossing. We find that computed field and plasma profiles across the magnetosheath and plasma depletion layer match all observations closely. Theoretical predictions on stagnation line flow near this low-shear magnetopause are confirmed by the experimental findings. Our theory does not give, and the data on this pass do not show, any localized density enhancements in the inner magnetosheath region just outside the plasma depletion layer.Key words. Steady-state magnetosheath · Plasma depletion layer · Stagnation line flow

A comparison of predictions of an MHD model solar wind flow past the magnetopause with AMPTE/IRM observations on 24 October, 1985

We compare numerical results of a steady-state MHD model for solar wind flow past the terrestrial magnetosphere with documented observations made by the AMPTE/IRM spacecraft on 24 October, 1985, during an inbound crossing of the magnetosheath. Observations indicate that steady conditions prevail during this ∼ 4 hour-long crossing. The magnetic shear at entry into the magnetosphere was 15 deg. A steady density decrease and a concomitant magnetic field pile-up were observed during the ∼ 40 min interval just preceding the magnetopause crossing. In this so-called plasma depletion layer (i) the plasma beta fell generally below unity; (ii) the flow speed tangential to the magnetopause was enhanced; and (iii) the local magnetic field and velocity vectors became increasingly more orthogonal to each other as the magnetopause was approached (Phan et al., 1994). We model parameter variations along a orbit similar to the AMPTE/IRM trajectory, which was at slightly southerly latitudes and ∼ 1.5 hours post-noon local time (GSE). In our model we consider the magnetopause to be a tangential discontinuity, as suggested by the observations, and take as input solar wind parameters those measured by AMPTE/IRM just prior to its bow shock crossing. We find that theoretical predictions match all observations closely.

Low‐latitude dusk flank magnetosheath, magnetopause, and boundary layer for low magnetic shear: Wind observations

We have studied in detail a Wind spacecraft crossing of the low‐latitude dusk flank magnetosheath, magnetopause (MP), and the low‐latitude boundary layer (LLBL) when the local magnetic shear across the MP was low (&lt;30°) and the interplanetary magnetic field (IMF) was northward. We find that the magnetosheath flow tangential to the MP slows down initially as one moves from the bow shock toward the MP. However, close to the MP this flow speeds up as the MP is approached. The source of flow acceleration is likely to be the magnetic force associated with draping of the field lines around the MP. Magnetic flux pile‐up and a plasma depletion layer are also observed next to the flank MP indicating that the level of magnetic flux transfer across the entire dayside low‐latitude MP via reconnection is low. The MP is characterized by changes in the plasma properties. The electron parallel temperature is enhanced across the MP and continues to increase across the LLBL, while the perpendicular temperature is constant across the MP. This constancy of the perpendicular temperature suggests that the transfer of plasma takes place across the local MP. In the LLBL, the ion and electron temperatures are well correlated with the density. In addition, the flow direction in a substantial portion of the LLBL is nearly aligned with that in the magnetosheath, and the flow speed tangential to the MP decreases gradually with decreasing LLBL density. The behavior of the particle distributions suggests that the entire LLBL was on closed field lines. In essence, our findings on the topology and on the LLBL plasma characteristics suggest that even in the absence of reconnection at the local low‐shear MP, the LLBL is locally coupled to the adjacent magnetosheath. The smooth variations of the plasma parameters with the density are consistent with the LLBL spatial profiles being gradual. This may suggest that diffusion processes play a role in the formation and dynamics of the LLBL. Finally, the magnetic field and the state of the plasma in the plasma sheet adjacent to the flank MP/LLBL appear to be functions of the IMF direction. Thus the IMF may control both the external (magnetosheath) and the internal (plasma sheet) boundary conditions for the flank MP processes.

Plasma depletion layer model for low Alfvén Mach number: Comparison with ISEE observations

Together with the magnetic shear across the magnetopause, the solar wind Alfvén Mach number, MA∞ plays a central role in determining the structure of the magnetosheath. Recent theoretical modeling has shown, in particular, that as MA∞ decreases, the region adjacent to the sunward side of the magnetopause where the interplanetary magnetic field (IMF) exerts a strong influence on the flow (i.e., the so‐called “plasma depletion layer”), is no longer confined to a thin layer ∼ 0.3 Earth radii (RE) thick but occupies an increasingly larger fraction of the magnetosheath. Furthermore, the model predicts the possibility of a plasma depletion layer for low MA∞, irrespective of the size of the magnetic shear at the magnetopause. In this paper we study three examples of low latitude ISEE 2 passes through the dayside magnetosheath near noon: December 3, 1979; October 5, 1979; and November 11, 1979. In all three examples, MA∞ was lower than normal. During the December 3 pass (which we treat, qualitatively), we find evidence of a plasma depletion layer when the IMF was pointing south. On the other two passes (which we study quantitatively), the interplanetary magnetic field was strongly northward pointing, leading to low magnetic shear at the respective magnetopause crossings. The October 5 pass was under steady interplanetary conditions and we find good agreement between theory and data. Temporal variations of the interplanetary medium during the November 11 pass necessitated an extension of the steady state theory to encompass piecewise steady (on average) interplanetary conditions. Better agreement with the data results when the theory is extended further to correct the total pressure at the sunward side of the magnetopause by integrating the magnetic tension term across the layer. For wide plasma depletion layers, this correction can be substantial.

Relationships between plasma depletion and subsolar reconnection

Observations in the subsolar magnetosheath show that the plasma depletion layer (PDL) is less pronounced for southward than for northward IMF. Since subsolar plasma depletion indicates pile‐up of magnetic flux, the degree of plasma depletion should depend on the relative rates of flux transport via subsolar reconnection and flux advection by the solar wind flow. To identify the factors affecting plasma depletion, we consider the ratio D = Er/Esw where Er is the reconnection electric field and Esw is the imposed solar wind electric field. For a quasi‐perpendicular subsolar bow shock D can be expressed in terms of magnetosheath parameters. Since PDL formation is suppressed when the subsolar bow shock is quasi‐parallel, we restrict attention to quasi‐perpendicular conditions. We show that D increases with increasing reconnection efficiency, magnetic shear at the magnetopause, and the magnetosheath magnetic field but decreases with increasing total perpendicular pressure (particle plus magnetic field) in the magnetosheath. By combining observations of the subsolar quasi‐perpendicular magnetosheath from AMPTE/IRM and AMPTE/CCE we verify that the degree of plasma depletion is inversely correlated with D. Furthermore, we show that the greater prevalence of plasma depletion in the CCE data implies that the reconnection efficiency is lower for the CCE events and specifically that the reconnection efficiency depends roughly inversely on magnetosheath β, for β &gt; 1. Finally, the results show that all of the changes brought about by plasma depletion act to increase Er so that some subsolar reconnection is likely to occur even for low magnetic shear. Thus the percentage of the magnetosheath magnetic field that participates in reconnection near the subsolar region does not act as a rectifier but remains positive for all shear angles, decreasing monotonically as the magnetic shear at the subsolar magnetopause changes from high to low shear. This implies that the equatorward polar cap convection cells observed during northward IMF and conventionally thought to be driven by a viscous interaction may be due at least in part if not wholly to subsolar low shear reconnection.

Possible plasma depletion layer ahead of an interplanetary ejecta

We present observations of a plasma depletion layer in front of an interplanetary magnetic cloud and analyze them quantitatively using a recent magnetohydrodynamic (MHD) theory of flow around magnetic clouds driving shocks. The magnetic field and plasma measurements were made by the ISEE 3 and IMP 8 on September 28–29, 1978. The magnetic cloud is expanding, and with a frontside boundary speed of ≈ 900 km s−1 it is one of the fastest ever seen at Earth orbit. We find a simple variation of field and plasma parameters in the sheath region behind the shock. Along the spacecraft trajectory the sum of the gas and plasma pressures is approximately constant, with a plasma beta less than unity. As the frontside boundary of the magnetic cloud is approached, the magnetic field strength increases while the density and temperature simultaneously decrease. These are defining characteristics of a plasma depletion layer, similar to that often seen in the terrestrial magnetosheath adjacent to the magnetopause. This suggests that the underlying cause is the same: the stretching of interplanetary magnetic field lines around the ejecta. The plasma depletion layer extends throughout the sheath region for which data are available, that is, for approximately 3 out of 5.7 hours. The sheath terminates at a clear discontinuity at the cloud's surface. To compare the observations with MHD theory, we model the ejecta as a magnetic flux rope of locally straight cylindrical geometry. We consider two limiting cases separately: (1) bulk motion relative to the surrounding medium but without expansion and (2) expansion into the ambient medium but without bulk motion. The predictions of both these limiting theories yield good agreement with observed variations of plasma parameters and magnetic field strength across the sheath. This paper is intended as a first attempt at modeling plasma depletion layers associated with interplanetary magnetic clouds.

Numerical modelling of solar wind flow about nonaxisymmetric magnetospheres: Planets Jupiter and Saturn

We discuss results on the solar wind flow past the non-axisymmetric magnetospheres of planets Jupiter and Saturn obtained by integrating numerically the dissipationless MHD equations under simplifying assumptions. We model these equatorially broadened magnetospheres as paraboloids with two different radii of curvature at the subsolar point. The thickness of the magnetosheath and the width and structure of the plasma depletion layer are found to be strong functions of the orientation of the interplanetary magnetic field (IMF). The effect of the IMF on the magnetosheath is strongest (weakest) when the IMF is directed perpendicular (parallel) to the rotational equator. For any intermediate IMF orientation, a smooth rotation of the magnetosheath magnetic field towards the direction of the planet's rotational axis is superimposed on the field strength enhancement (and the density reduction) as the respective magnetopauses are approached. These effects are more pronounced at Jupiter than at Saturn.

Electromagnetic ion cyclotron waves in the terrestrial plasma depletion layer: Effects of possible differential speeds between thermal H+ and He2+ ions

The terrestrial plasma depletion layer (PDL) is characterized by electromagnetic ion cyclotron waves (EICWs) [Anderson et al., 1991, 1994; Anderson and Fuselier, 1993]. These are of two types, continuous (CON), where the wave power transverse to the local mean field decreases continuously with frequency, and bifurcated (BIF), where a diminution in wave activity occurs between two activity peaks [Anderson et al., 1994]. Linear kinetic theory of plasma waves has been applied successfully to explain many features of the observed spectra [Denton et al., 1993; Gary et al., 1993]. In this paper we complement these theoretical studies by examining the effects a possible relative motion between the thermal H+ and He2+ populations has on the ion cyclotron activity, illustrating theoretical predictions by comparison with observed CON and BIF spectra. We find that even a modest differential speed (Uα ≡ | vα| − | vp |∼ 0.1 vA, where vA is the local Alfvén speed) can regulate the presence, location, and strength of the diminution in wave power often observed between the upper (∼ 0.55fp &lt; f &lt; fp) and lower (0.2 fp &lt; f &lt;∼ 0.40 fp) local maxima in wave activity. Using parameters appropriate to the CON spectrum, we find that when Uα = 0, there is a frequency interval centered around 0.45 fp, where the waves are damped, in disagreement with CON observations. With Uα, negative (i.e., the alpha particles are slower), the damping is enhanced and the damped frequency interval broadens, accentuating the discrepancy with the observations. When, however, Uα is small but positive, the previously damped frequency interval becomes an unstable region where wave growth rates are smaller with respect to peak values. Thus, although the activity is reduced there, it is not fully damped. By raising the positive values of Uα further, the bifurcation disappears and the spectrum becomes continuous. This may thus explain CON observations. For the BIF observation we find that a linear theory which does not incorporate inter‐ion species drift predicts a frequency gap (i. e., a region where there are no waves, damped or otherwise) centered at ∼ 0.45 fp, in addition to further intervals where the waves are damped. A small positive Uα (∼ 0. 07 vA) eliminates the frequency gap. A further, small increase in Uα eliminates the damped frequency intervals. We also compare the effects of the relative positive drift between H+ and He2+ ions with those obtained by raising the proton beta. In summary, we suggest that an H+ – He2+ relative drift may further help explain features of the bifurcated and continuous wave spectra observed by the CCE spacecraft in the PDL.

The subsolar magnetosheath and magnetopause for high solar wind ram pressure: WIND observations

On a rapid inward pass through the subsolar magnetosheath (MSH) and magnetopause (MP), the WIND spacecraft initially encountered a moderately‐compressed low‐magnetic shear MP (at a radial distance of 8.6 RE), followed by multiple crossings of a high‐shear MP (at 8.2 RE). The large shear resulted from a southward turning of the external MSH field. Strong magnetic field pile‐up, a plasma depletion layer (PDL), and plasma flow acceleration and rotation to become more perpendicular to the local magnetic field were observed in the MSH on approach to the low‐shear MP. At the high‐shear MP, magnetic reconnection flows were detected, and there are some indications that plasma depletion effects were weak or absent in the adjacent MSH. We attribute the changes in the MP and MSH properties to the sudden rotation of the MSH field direction. In essence, the structure of the MP regions under the unusually high solar wind ram pressure condition in this case does not seem to be qualitatively different from that observed under more typical (less compressed) conditions. Also similar to previous observations, the mirror mode is marginally unstable in the MSH proper, but is stable in the PDL. In this region, the proton temperature anisotropy is inversely correlated with βp∥. Finally, the electron distributions are observed to be anisotropic (Te⟂/Te∥ ∼1.3) throughout the entire MSH.

Correction to “Observations of mirror waves and plasma depletion layer upstream of Saturn's magnetopause”

Correction to “Observations of mirror waves and plasma depletion layer upstream of Saturn's magnetopause”

Observations of mirror waves and plasma depletion layer upstream of Saturn's magnetopause

The two inbound traversals of the Saturn's magnetosheath by Voyagers 1 and 2 have been studied using plasma and magnetic field data. In a great portion of the subsolar magnetosheath, large‐amplitude compressional waves are observed at low frequency (∼0.1 fp) in a high‐β plasma regime. The fluctuations of the magnetic field magnitude and ion density are anticorrelated, as are those of the magnetic and thermal pressures. The normals to the structures are almost orthogonal to the background field, and the Doppler ratio is on the average small. Even though the data do not allow the determination of the ion thermal anisotropy, the observations are consistent with values of T⊥/T∥ &gt; 1, producing the onset of the mirror instability. All the above features indicate that the waves should be most probably identified with mirror modes. One of the two magnetopause crossings is of the high‐shear type and the above described waves are seen until the magnetopause. The other crossing is of the low‐shear type and, similarly to what has been observed at Earth, a plasma depletion occurs close to the magnetopause. In this layer, waves with smaller amplitude, presumably of the mirror mode, are present together with higher‐frequency waves showing a transverse component.

The characteristics of the magnetopause reconnection X‐line deduced from low‐altitude satellite observations of cusp ions

We present an analysis of a “quasi‐steady” cusp ion dispersion signature observed at low altitudes. We reconstruct the field‐parallel part of the Cowley‐D ion distribution function, injected into the open LLBL in the vicinity of the reconnection X‐line. From this we find the field‐parallel magnetosheath flow at the X‐line was only 20 ± 60 km s−1, placing the reconnection site close to the flow streamline which is perpendicular to the magnetosheath field. Using interplanetary data and assuming the subsolar magnetopause is in pressure balance, we derive a wealth of information about the X‐line, including: the density, flow, magnetic field and Alfvén speed of the magnetosheath; the magnetic shear across the X‐line; the de‐Hoffman Teller speed with which field lines emerge from the X‐line; the magnetospheric field; and the ion transmission factor across the magnetopause. The results indicate that some heating takes place near the X‐line as the ions cross the magnetopause, and that sheath densities may be reduced in a plasma depletion layer. We also compute the reconnection rate. Despite its quasi‐steady appearance on an ion spectrogram, this cusp is found to reveal a large pulse of enhanced reconnection rate.

Bounded anisotropy fluid model for ion temperatures

A bounded anisotropy fluid model is developed which describes the temperature evolution of a collisionless plasma including the effect of pitch angle scattering due to ion cyclotron waves. The model equations accurately describe the proton temperature evolution in the plasma depletion layer, a magnetosheath regime of decreasing plasma density near the magnetopause. As in double adiabatic theory, changes in T⊥ are driven by changes in flux tube area A (∝ 1/B), while changes in T∥ are driven by changes in field line scale length L. In the bounded anisotropy model, if the proton temperature ratio T⊥/T∥ rises above the value 1 + 0.85 β∥p−0.48 (Anderson et al., 1994), where β∥p is the proton parallel beta, energy is transferred from the perpendicular to parallel temperature until this equation is satisfied. This energy exchange represents the effect of ion cyclotron wave pitch angle scattering, which keeps the plasma state near to marginal stability. Equations of the same form, employing bounded anisotropy expressions appropriate to different species, are also applied to He2+ and to electrons. These equations well describe the evolution of the He2+ but do not describe the evolution of the electron temperature, apparently due to the high electron thermal conduction which the model does not include. These results indicate that an energy exchange term may be incorporated into anisotropic fluid equations to simulate the effect of ion cyclotron wave pitch angle scattering in global fluid equations.

A comparison of energetic ions in the plasma depletion layer and the quasi‐parallel magnetosheath

Energetic ion spectra measured by the Active Magnetospheric Particle Tracer Explorers/Charge Composition Explorer (AMPTE/CCE) downstream from the Earth's quasi‐parallel bow shock (in the quasi‐parallel magnetosheath) and in the plasma depletion layer are compared. In the latter region, energetic ions are from a single source, leakage of magnetospheric ions across the magnetopause and into the plasma depletion layer. In the former region, both the magnetospheric source and shock acceleration of the thermal solar wind population at the quasi‐parallel shock can contribute to the energetic ion spectra. The relative strengths of these two energetic ion sources are determined through the comparison of spectra from the two regions. It is found that magnetospheric leakage can provide an upper limit of 35% of the total energetic H+ population in the quasi‐parallel magnetosheath near the magnetopause in the energy range from ∼10 to ∼80 keV/e and substantially less than this limit for the energetic He2+ population. The rest of the energetic H+ population and nearly all of the energetic He2+ population are accelerated out of the thermal solar wind population through shock acceleration processes. By comparing the energetic and thermal He2+ and H+ populations in the quasi‐parallel magnetosheath, it is found that the quasi‐parallel bow shock is 2‐3 times more efficient at accelerating He2+ than H+. This result is consistent with previous estimates from shock acceleration theory and simulations.

Low‐frequency magnetic fluctuation spectra in the magnetosheath and plasma depletion layer

Recent observations have delineated several different kinds of enhanced magnetic fluctuation spectra below the proton cyclotron frequency in the terrestrial magnetosheath. A model is presented that represents the variation of plasma parameters across the plasma depletion layer and into the magnetosheath proper. Using this model, we find that many of the properties of the observed spectra follow directly from the predictions of linear Vlasov instability theory. The observed progression of spectral features is a natural progression from mirror mode to merged (in frequency range) proton and He2+ cyclotron modes to bifurcated (in frequency range) cyclotron modes as plasma convects earthward in the magnetosheath. The necessary change in dispersion surface topology from separated proton and He2+ cyclotron surfaces at low beta to merged surfaces at high beta is described.