Pressure-anisotropy-driven microturbulence and magnetic-field evolution in shearing, collisionless plasma

Abstract

The nonlinear state of a high-beta collisionless plasma is investigated in which an externally imposed linear shear amplifies or diminishes a uniform mean magnetic field, driving pressure anisotropies and, therefore, firehose or mirror instabilities. The evolution of the resulting microscale turbulence is considered when the external shear changes, mimicking the local behaviour of a macroscopic turbulent plasma flow, viz., the shear is either switched off or reversed after one shear time, so that a new macroscale configuration is superimposed on the microscale state left behind by the previous one. It is shown that there is a threshold value of plasma beta: when β ≪ Ω/S (ion cyclotron frequency/shear rate), the emergence of firehose or mirror fluctuations when they are driven unstable by shear and their disappearance when the shear is removed or reversed are quasi-instantaneous compared to the macroscopic (shear) timescale. This is because the free-decay time scale of these fluctuations is ∼ β/Ω ≪ S −1 , a result that arises from the free decay of both types of fluctuations turning out to be constrained by the same marginal-stability thresholds as their growth and saturation in the driven regime. In contrast, when β Ω/S ("ultra-high" beta), the old microscale state can only be removed on the macroscopic (shear) timescale. Furthermore, it is found that in this ultra-high-beta regime, when the firehose fluctuations are driven, they grow secularly to order-unity amplitudes (relative to the mean field), this growth compensating for the decay of the mean field, with pressure anisotropy pinned at marginal stability purely by the increase in the fluctuation energy, with no appreciable scattering of particles (which is unlike what happens at moderate β). When the shear reverses, the shearing away of this firehose turbulence compensates for the increase in the mean field and thus prevents growth of the pressure anisotropy, stopping the system from going mirror-unstable. Therefore, at ultra-high β, the system stays close to the firehose threshold, the mirror instability is almost completely suppressed, while the mean magnitude of the magnetic field barely changes at all. Implications of the properties of both ultra-high-and moderate-beta regimes for the operation of plasma dynamo and thus the origin of cosmic magnetism are discussed, suggesting that collisionless effects are broadly beneficial to fast magnetic-field generation.

Fluctuation Dynamo in a Collisionless, Weakly Magnetized Plasma

“…Since the viscous-scale rate of strain increases as Re 1/2 eff , the dynamo in this intermediate second regime should, at some point, be self-accelerating, with the field-stretching eddies becoming smaller and faster as the magnetic field is amplified. Similar scenarios have previously formed the basis for theories of explosive dynamo in collisionless plasmas (Schekochihin & Cowley 2006a,b;Melville et al 2016;Mogavero & Schekochihin 2014), a topic that will be the subject of a separate publication.…”

“…Following the reasoning presented in § 4.2.2 of Melville et al (2016), we estimate the effective parallel viscosity µ eff .…”

“…where d i is the (field-strength-independent) ion inertial scale. (Equation (1.14a) is referred to as the 'ultra-high-β' limit in Melville et al 2016. ) For characteristic parameters of the ICM, equation (1.14a) implies For magnetic-field strengths satisfying (1.14b), the hard-wall limiters are unsuitable and the parallel Reynolds number is smaller than that given by (1.10).…”

Kinetic Simulations of the Interruption of Large-Amplitude Shear-Alfvén Waves in a High- β Plasma

“…The firehose modes' evolution is governed by Δp [12], which varies in space. Near the wave nodes, where S ¼ j∇uj ≈ 0 and δB z ≈ 0, Δp is not driven by a large-scale dB=dt and can freely decay [29,32,34,35]. Near the wave antinodes, where S ∼ β −1=2 ω A ≈ 6 × 10 −5 Ω i [10] and δB z ≠ 0, Δp is continuously driven by the decreasing field [29,31,[36][37][38].…”

A Stringent Limit on the Amplitude of Alfvénic Perturbations in High-Beta Low-Collisionality Plasmas

“…The reader may wonder about the imposition of a mirror (but no firehose) limit in Figures 1(b)-(c). This is required because our model cannot capture the mirror instability, which gives rise to growing modes at (Melville et al 2016). This implies that SA waves cannot circumvent the limit (11) by starting from B=0 or D > 0 (see Figure 1(b)).…”