Spacecraft observations in the strongly compressed subsolar magnetosheath show an inverse correlation between the proton temperature anisotropy (Wlp/•l p • 1 where _L and II denote directions perpendicular and parallel to the background magnetic field) and the parallel proton/• (/•llp)' This manuscript uses one-dimensional hybrid simulations of the proton cyclotron anisotropy instability in homogeneous electron-proton plasmas to study this correlation which may represent a limited closure relation for fluid theories of anisotropic space plasmas. The emphasis is on driven simulations which increase the temperature anisotropy by periodically reducing the magnetic-field-aligned velocities of the protons. The late-time states from ensembles of both initial value and driven simulations yield very similar expressions for the proton anisotropy//•ll p inverse correlation, and provide a basis for explaining differences between sheath observations from different spacecraft. The driven simulations also yield expressions for the maximum instability growth rate and the fluctuating field energy as functions of ]•llp and a parameter characterizing the anisotropy driver. Paper number 93JA03583. 0148-0227/94/93JA-03583505.00 number. These closure conditions often correspond to assumptions such as isotropicity and adiabaticity, conditions which may be useful for collision-dominated fluids but which are not necessarily appropriate for the collisionless plasmas of space. Spacecraft observations often demonstrate distribution functions that are dearly non-Maxwellian, implying that Vlasov theory may be an appropriate mechanism for determining closure under some circumstances [e.g., Feldman el al., 1973, 1976]. Tllp ]•llp with a linear correlation coefficient of R -0.996, a result very similar to equation (4) from the late-time initial 59•o GARY ET AL.. PROTON CYCLOTRON INSTABILITY _Lp ß . -1 T ß lip ß ß ß te ß ß 0.2

Distribution functions of ions heated in quasi‐perpendicular bow shocks have a large perpendicular temperature anisotropy that provides free energy for the growth of Alfvén ion cyclotron (AIC) waves and mirror waves. Both types of waves have been observed in the Earth's magnetosheath downstream of quasi‐perpendicular shocks. The question of whether these waves are produced at the shock and convected downstream or whether they are produced locally in the magnetosheath has not yet been answered. If the latter were true, then under most magnetosheath conditions AIC waves should dominate the wave activity, yet frequently mirror waves either dominate or are competitive with the AIC mode. We address this question by using two‐dimensional hybrid simulations to give a self‐consistent description of the evolution of the wave spectra downstream of quasi‐perpendicular shocks. Both mirror and AIC waves are identified in the simulated magnetosheath. They are generated at or near the shock front and convected away from it by the sheath plasma. Near the shock, the waves have a broad spectrum, but downstream of the shock, shorter‐wavelength modes are heavily damped and only longer‐wavelength modes persist. The characteristics of these surviving modes can be predicted with reasonable accuracy by linear kinetic theory appropriate for downstream conditions. Throughout the downstream region, the power in compressive magnetic oscillations is of the same order as the power in transverse oscillations. We also follow the evolution of the ion distribution function. The shocked ions that provide the free energy for wave growth have a two‐component distribution function: a core population of directly transmitted ions and a smaller halo of initially reflected ions that contains the bulk of the free energy. The halo is initially gyrophase‐bunched and extremely anisotropic. Within a relatively short distance downstream of the shock (of the order of 10 ion inertial lengths), wave‐particle interactions remove these features from the halo and reduce the anisotropy of the distribution to near‐threshhold levels for the mirror and AIC instabilities. A similar evolution has been observed for ions at the Earth's bow shock.

Ion populations with large perpendicular temperature anisotropies in the magnetosheath can excite both the mirror and proton cyclotron anisotropy instabilities. We compare kinetic aspects of these two instabilities using two‐dimensional hybrid simulations, expanding upon an earlier work using one‐dimensional simulations. Three simulation runs are examined: one in which the proton cyclotron instability has a higher linear growth rate, the second in which the mirror instability grows more rapidly, and the third in which the linear growth rates are identical. The last two runs include a large density of isotropic He++ ions to suppress the cyclotron instability. We find that initial growth occurs in all three runs at approximately the frequencies, wavenumbers, and obliquities expected by linear theory. As the system evolves, the power in both instabilities shifts to longer wavelength modes, and the characteristic frequency of the proton cyclotron instability decreases. In the first two runs, the instability with the larger linear growth rate dominates the wave energy at saturation, and in the third, the two instabilities contribute about equally. The proton cyclotron instability is relatively more important to wave‐particle energy exchange than the mirror instability; its importance to proton isotropization is generally greater than that suggested by its contribution to the total wave energy, and it is almost solely responsible for heating the helium ions.

Magnetosheath plasmas are typically characterized by a proton/• > 1 and a proton temperature anisotropy V.l_/T]l > 1. Such a plasma is unstable to both the ion cyclotron anisotropy and mirror instabilities, and evidence for both of these growing modes has been found in the magnetosheath. In this paper, we use one-dimensional hybrid simulations to investi•[ate the kinetic properties of these two instabilities. We find that, for moderate values of ion/• and temperature anisotropy, the two instabilities produce similar levels of turbulence, but that the cyclotron instability apparently produces higher fluctuation levels than the mirror instability for high /• or anisotropy. Although both instabilities saturate by reducing the ion temperature anisotropy, mirror waves accomplish this through the use of the wave magnetic fields, whereas cyclotron waves do so by using the wave electric fields in resonant interactions with the ions. Consequently, mirror waves preferentially affect those ions with large magnetic moment, while cyclotron waves affect a broader range of ions and thereby dominate the isotropization process even when the mirror mode is somewhat stronger. We also investigate the utility of transport ratios as mode identifiers, and find that the Alfv6n ratio in particular can be useful in distinguishing between the two modes. than the ion temperature 2ql parallel to Bo [Gary et al., 1976, 1992]. These conditions are achieved by the heating and reflection of ions at the bow shock and persist downstream in the magnetosheath [Sckopke et al., 1983, 1990; Thomsen et al., 1985], and are also achieved by the draping and compression of the magnetic field in the magnetosheath [Zwan and Wolf, 1976; Crooker and Siscoe, 1977].The characteristics and properties of both the ion cyclotron anisotropy and mirror instabilities have been studied in detail. The mirror instability can be described by fluid theory in the long wavelength limit, has zero real frequency in the plasma rest frame, and has a maximum growth rate at a direction of the wave vector k that is at a_. large angle with respect to the background magnetic field Bo. Consequently, the magnetic perturbations caused by the mirror waves are approximately parMid to Bo. The ion cyclotron anisotropy instability can only be described by kinetic theory and has a maximum growth rate at a nonzero frequency below the ion gyrofrequency with k parallel to Bo. Hence, the magnetic perturbations associated with the ion cyclotron waves are oriented approximately perpendicular to Bo. In terms of polarization, linear theory and numerical simulations show that parallel-propagating ion cyclotron waves are left-hand circularly polarized [Tajima et al., 1977; Ambrosiano and Brecht, 1987; Brinca et al., 1990]. Linear anMyses of the two instabilities in electron-proton plasmas have found that, for •3ill < 6.0 (where •3ill is the proton beta associated with Tll), the cyclotron instability should grow more quickly, and be excited at a lower anisotropy threshold, than the mirror instability [Gar...

Recent observations and theoretical studies have established the importance of the tenuous helium ion component in determining instability growth and low‐frequency magnetic fluctuation properties in the terrestrial magnetosheath. Under low‐β, high‐ion‐anisotropy sheath conditions, enhanced fluctuations observed below the proton cyclotron frequency have been attributed to the proton and helium cyclotron anisotropy instabilities. This paper uses second‐order theory and one‐dimensional hybrid computer simulations to examine the nonlinear properties of these two instabilities at relatively weak fluctuation levels and at propagation parallel to the background magnetic field. The simulations confirm the second‐order predictions that both instabilities yield efficient wave‐particle interactions; the rate at which the driving species anisotropy is reduced is much greater than the rate at which that species loses kinetic energy. This result suggests that these instabilities should saturate at relatively low levels; we derive an approximate expression for the fluctuating field energy at saturation of the fastest growing modes and find that it is in fair agreement with three computer simulations. In addition, second‐order theory and simulations concur that the helium component enhances the wave‐particle exchange rate for proton anisotropy reduction by the proton cyclotron instability; theory predicts and simulations confirm that the saturation energy of this mode is substantially lower than it is in the absence of helium.