High‐β theory of low‐frequency magnetic pulsations

184

141

The generation of nonoscillatory mirror waves is studied using a one‐dimensional periodic hybrid electromagnetic simulation. The ion dynamics are treated exactly; the electrons are approximated as a finite pressure, massless fluid. Compression of the flux tubes in the magnetosheath causes a large pressure anisotropy, and it has been proposed that this anisotropy drives a mirror instability. The mirror waves have been identified by large amplitude fluctuations of the magnetic field, anticorrelated with pressure fluctuations. The simulations are initiated in a homogeneous high beta (beta = 2.5) plasma with the ambient magnetic field at various angles to the simulation axis. It is found that ion cyclotron waves are also driven by the pressure anisotropy, in competition with the nonoscillatory mirror waves. Simulations indicate that in a pure ¹H+ plasma the much faster growing ion cyclotron waves absorb the free energy in the anisotropy to the extent that mirror waves should not be observed. Analysis of the dispersion relations of mirror waves and ion cyclotron waves in the multi‐component plasma indicates that 4He2+ and 16O6+ ions in the solar wind should stabilize the ion cyclotron waves sufficiently that the mirror waves become the dominant instability.

Section: Instabilitiesmentioning

confidence: 85%

Numerical simulation of nonoscillatory mirror waves at the Earth's magnetosheath

Price¹,

Swift²,

Lee³

1986

184

141

“…A more complete study of the wave turbulence, which we leave for the future, would involve the possible coupling of the wave modes by solving a complete 3 x 3 dispersion equation including the density and magnetic field gradients, the anisotropy of the ions, and finite beta effects. This kind of analysis ['e.g., Migliuolo, 1983] show the interaction of drift mirror, drift compressional, and shear Alfven waves. The shock situation is complicated by the fact that the density and magnetic field gradients are not held in equilibrium by a simple force balance (Vn opposite to VB), but instead by the inflowing solar wind (so that Vn is parallel to VB), as well as the aforementioned nonlinearities.…”

Section: Dominatementioning

confidence: 99%

Magnetic field and density fluctuations at perpendicular supercritical collisionless shocks

Winske¹,

Quest²

1988

196

189

Perpendicular collisionless shocks are studied by means of two‐dimensional hybrid (particle ion, fluid electron) simulations, with emphasis on the relaxation of the highly anisotropic ion distribution that arises primarily from reflection of some of the incident ions but also adiabatic compression of the other, directly transmitted ions and the related growth of low frequency electromagnetic waves. It is commonly assumed that the waves are due to the Alfven ion cyclotron instability that propagate parallel to the ambient magnetic field (k⊥ = 0) and that the isotropization of the ions due to pitch angle scattering by the waves and the corresponding modification of the wave spectrum is quasi‐linear. It is shown that this is indeed a reasonably good description downstream of the shock front, behind the magnetic overshoot. However, at the shock ramp there is a large discrepancy between the wavelengths measured in the simulations and those predicted by linear theory, and large density and magnetic field oscillations parallel to the ambient magnetic field are also seen. By comparing results for both high and low ion beta cases, it is shown that these effects can be understood in terms of obliquely propagating (k⊥ ≠ 0) modes, more likely due to the Alfven ion cyclotron instability instead of the (drift) mirror instability, although a more complete explanation awaits the derivation and analysis of an appropriate dispersion relation describing the growth and coupling of low‐frequency modes in the inhomogeneous high beta environment of the shock. The observational consequences of these results and their application to improving nonlocal leakage models for the ion foreshock are also discussed.

“…This will, in general, produce a destabilizing effect, since the (6) modes of interest need finite • to be unstable. Given bi = 0.1, Te = Ti, nc = 100nh, k•Ln = 10, in Migliuolo's [1983] dispersion relation (for clarity, we momentarily adopt the notation (7) of that paper, thus subscript i(e) of that paper corresponds to our subscripts 0 (2)), the drift-compressional mode (% = 0, kll/k•_ = 0.001) is stable for fi• •< 0.1, while the drift-mirror mode (% = 1.5, kll/kl = 0.004) is stable for/• •< 0.6 (remember that using the dispersion relation given in this report will yield stabilization for slightly larger values of fi because of the small difference in the contribution of the cold component to 033 ) . tend to destabilize it (this occurs for both the driftcompressional and drift-mirror modes).…”

Section: -(To/kllc)a•z When Compared To (Oo/kllc)a•z and (K•t•_o/mentioning

confidence: 99%

“…Since such plasmas are not confined to the plasma pause but are of common occurrence in space (e.g., the boundaries of solar coronal holes and the interfaces between cool prominences and the hot plasma of the solar corona), one might be tempted to conclude that such pulsations are present, though yet unobserved, in many if not all space plasmas Before such a conclusion can be drawn, however, one must show that these low-frequency waves can be destabilized under many different parameter regimes. Past work Parks, 1978, 1982;Migliuolo, 1983;Ng and Patel, 1983a, b] has shown that the basic process operates under greatly varying parameter regimes, for finite-/• plasmas (/• •> 10-3 for the hot component). One dependency that has not yet been examined is that on the ratio of temperatures between components.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Drift waves in high‐β two‐temperature plasmas

Migliuolo¹

1984

Self Cite

The linear stability of low-frequency drift-compressional and drift-mirror modes is examined in twocomponent (hot and cold) plasmas. A full-/• dispersion relation is derived that retains finite temperature effects for the cold component. The effect of a nonzero ratio T c/T• is examined, and the critical value of this parameter (that produces stabilization of the modes) is determined. The main result of this work shows that very small temperature ratios (Tc/T • less than 1%, in some cases) are sufficient to completely stabilize these modes at certain wave numbers. INTRODUCTIONLow-frequency hydromagnetic waves (i.e., waves with frequencies much smaller than an ion cyclotron frequency that are composed of both electric and magnetic perturbations of an equilibrium) have long been observed in the plasma magnetosphere of the earth [-Barfield and Coleman, 1970; Barfield and McPherron, 1972, 1978' Kokubun et al., 1976; Sin•]er and Kivelson, 1979]. Pioneering theoretical work dealt with longitudinal instabilities of the drift-mirror and drift-compressional modes [Hasegawa, 1969, 1971a, and references therein; Lanzerotti et al., 1969' Lanzerotti and Hasegawa, 1975]. It was recognized, in those papers, that instability characteristics were strongly dependent on the longitudinal component of the perturbed magnetic field. An improvement on this theory occurred with subsequent work [Lin and Parks, 1978, 1982; Miqliuolo, 1983, and references therein; Patel and Miqliuolo, 1980] which considered coupling of longitudinal and transverse components of the perturbation, a feature observed for many magnetospheric events. These latter authors mostly considered models applicable to low-fl situations, though high-fl dispersion relations were given by Lin and Parks [1982] and Miqliuolo [1983]. Still, Lin and Parks [1982] sacrificed selfconsistency in exchange for physical intuition' finite-fl corrections were not calculated for all elements of the matrix dispersion relation (they were omitted, in particular, from the offdiagonal terms that couple longitudinal and transverse modes). Hence their results, though qualitatively and physically correct, do not yield precise estimates for the eigenfrequency and polarization of unstable modes. Miqliuolo [1983] presented the correct high-fl dispersion relation in the absence of temperature gradients, but unfortunately, an error (subsequently corrected) in the numerical code that solved the dispersion relation yielded results that, again, were qualitatively correct but quantitatively untrustworthy. To date, the only quantitatively correct estimates of mode eigenfrequencies, in high-fl plasmas, are given by Ng and Patel [1983a, b] and Patel et al. [1983], who derived the high-fl dispersion relation with temperature gradients. The aforementioned papers have established that such hydromagnetic waves, known as Pc 5 pulsations, can be destabilized (quite generally) by sources of free energy internal to two-component (hot and cold) plasmas, in systems with axial magnetic field (B = dxB(x)). Among such sou...