Theory and simulation experiment are presented for a wide variety of transverse electromagnetic instabilities in plasmas with different sources and degrees of anisotropy. In each of the electron bi-Maxwellian, electron-pinch, and ion-pinch experiments, the bulk response of the system during the initial stages of instability is in good agreement with the predictions of quasilinear theory. Furthermore, the two independent energy constants which derive from the fully nonlinear Vlasov-Maxwell equations are found to remain constant to very good accuracy, even when the magnetic field energy reaches a substantial fraction of the total system energy. In each simulation experiment it is found that the magnetic energy saturates once the magnetic bounce frequency has increased to a value comparable to the linear growth rate prior to saturation, i.e., when ω¯B∼γ¯k. It is concluded that amplitude limitation for Weibel instabilities is a result of magnetic trapping for a broad range of system parameters. In many experiments a large remnant anisotropy in kinetic energy persists long after saturation.
The local dispersion relation for the lower-hybrid-drift isntability is derived in a fully self-consistent manner including the finite-beta effects associated with (a) transverse electromagnetic perturbations (δB≠0), and (b) resonant and nonresonant h/B0 electron orbit modifications. Moreover, the analysis is carried out for arbitrary values of local β=8πn (Te+Ti)/B02, Te/Ti, ω2pe/ω2ce, and VE/vi. (Here, VE is the cross-field E×B velocity, and vi is the ion thermal speed.) For all parameter regimes studied, the net effect of finite plasma beta is to reduce the maximum growth rate γm of the lower-hybrid-drift instability. The details, however, vary, depending on plasma parameters. For example, if Te≪Ti and VE<vi, then the maximum growth rate is reduced by a factor (1+βi/2)−1/2, relative to the value obtained when βi=8πnTi/B20→0. On the other hand, for Te≈Ti, there exists a critical value of plasma beta (βcr) such that the lower-hybrid-drift instability is completely stabilized (γ<0) for β≳βcr.
This article examines the consequence of the ionization (e.g., photoionization) of a small population of neutral atoms (hydrogen or helium) in interplanetary space. It is found that, even if the density of the newly ionized particles is only a very small fraction of that of the solar wind, these particles can efficiently excite electromagnetic waves by means of a new collective instability. The instability is driven by an anisotropy in kinetic energy of the newly ionized particles. The typical linear growth rate is γ ≃ (ωin/2½) (υ0⊥/c) where ωin is the plasma frequency of the newly ionized ions, and υ0⊥ is the characteristic speed of the newly ionized ions perpendicular to the ambient magnetic field in the frame of the solar wind.
The linear stability behavior and anomalous transport properties associated with the lower-hybrid-drift instability are studied assuming flute-like perturbations with k⋅B0=0. Primary emphasis is placed on the low-drift-velocity regime with VE≲vThi (here, VE is the cross-field electron E×B drift velocity), which pertains to the late stages of implosion and the post-implosion phase of high-density pinch experiments. Nonlinear estimates of the instantaneous heating rates and rate of momentum transfer are made, and the results are studied numerically to determine the parametric dependence on VE/vThi and the level of turbulent field fluctuation energy ℰF. It is shown that the lower-hybrid-drift instability can result in substantial resistivity and plasma heating for VE≲vThi, as well as for the large-drift-velocity regime (VE≳vThi). For example, when Ti/Te≫1 and ω2pe/ω2ce≫1, the bound on anomalous resistivity for VE≲vThi is [nan]max≃4π√π/2(VE/vThi)2 ωLH/ω2ce, where ωLH = (ωciωce)1/2 is the lower-hybrid frequency. This large value of resistivity is consistent with observations made during the post-implosion phase of the ZT-1 experiment.
Low frequency (ω≈ωci=eiB0/mic) transverse electromagnetic perturbations propagating parallel to a confining magnetic field B0êz are shown to exhibit instability in the presence of ion energy anisotropy with Ti⊥≳Ti∥. The characteristic maximum growth rate for Ti⊥≫Ti∥ is γM≈(βi⊥/2)1/2ωci, where βi⊥=8πniTi⊥/B20, and the wavelengths corresponding to instability are of order c/ωpi, where ωpi is the ion plasma frequency. Within the context of a quasi-linear model, it is shown that the characteristic time scale for energy isotropization through nonlinear response of the ions to the instability is several γ−1M. Since γ−1M≪τii (the ion-ion binary collision time) in typical high-density pinch experiments, this instablity appears to provide a viable collective mechanism for ion energy isotropization during the implosion or post-implosion phases of these experiments. It is also shown that the instability persists in the limit of weakly magnetized ions (‖ω+iγ‖≫‖ωci‖, k2zr2Li≫1) and strongly magnetized electrons (‖ω+iγ‖≪‖ωce‖, k2zr2Le≪1) provided βi⊥≫1. The instability also has applications to astrophysical plasmas with Ti⊥≳Ti∥ as well as laboratory plasmas heated by neutral-particle injection perpendicular to B0.
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