Abstract Nearly incompressible magnetohydrodynamic (NI MHD) theory for β ∼ 1 (or β ≪ 1) plasma has been developed and applied to the study of solar wind turbulence. The leading-order term in β ∼ 1 or β ≪ 1 plasma describes the majority of 2D turbulence, while the higher-order term describes the minority of slab turbulence. Here, we develop new NI MHD turbulence transport model equations in the high plasma beta regime. The leading-order term in a β ≫ 1 plasma is fully incompressible and admits both structures (flux ropes or magnetic islands) and slab (Alfvén waves) fluctuations. This paper couples the NI MHD turbulence transport equations with three fluid (proton, electron, and pickup ion) equations, and solves the 1D steady-state equations from 1–75 au. The model is tested against 27 yr of Voyager 2 data, and Ulysses and NH SWAP data. The results agree remarkably well, with some scatter, about the theoretical predictions.
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On the Conservation of Turbulence Energy in Turbulence Transport Models
Abstract Zank et al. developed models describing the transport of low-frequency incompressible and nearly incompressible turbulence in inhomogeneous flows. The formalism was based on expressing the fluctuating variables in terms of the Elsässar variables and then taking “moments” subject to various closure hypotheses. The turbulence transport models are different according to whether the plasma beta regime is large, of order unity, or small. Here, we show explicitly that the three sets of turbulence transport models admit a conservation representation that resembles the well-known WKB transport equation for Alfvén wave energy density after introducing appropriate definitions of the “pressure” associated with the turbulent fluctuations. This includes introducing a distinct turbulent pressure tensor for 3D incompressible turbulence (the large plasma beta limit) and pressure tensors for quasi-2D and slab turbulence (the plasma beta order-unity or small regimes) that generalize the form of the WKB pressure tensor. Various limits of the different turbulent pressure tensors are discussed. However, the analogy between the conservation form of the turbulence transport models and the WKB model is not close for multiple reasons, including that the turbulence models express fully nonlinear physical processes unlike the strictly linear WKB description. The analysis presented here both serves as a check on the validity and correctness of the turbulence transport models and also provides greater transparency of the energy dissipation term and the “turbulent pressure” in our models, which is important for many practical applications.
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- Award ID(s):
- 1655280
- PAR ID:
- 10356041
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 928
- Issue:
- 2
- ISSN:
- 0004-637X
- Page Range / eLocation ID:
- 176
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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In a recent paper [P. H. Yoon and G. Choe, Phys. Plasmas 28, 082306 (2021)], the weak turbulence theory for incompressible magnetohydrodynamics is formulated by employing the method customarily applied in the context of kinetic weak plasma turbulence theory. Such an approach simplified certain mathematical procedures including achieving the closure relationship. The formulation in the above-cited paper starts from the equations of incompressible magnetohydrodynamic (MHD) theory expressed via Elsasser variables. The derivation of nonlinear wave kinetic equation therein is obtained via a truncated solution at the second-order of iteration following the standard practice. In the present paper, the weak MHD turbulence theory is alternatively formulated by employing the pristine form of incompressible MHD equation rather than that expressed in terms of Elsasser fields. The perturbative expansion of the nonlinear momentum equation is carried out up to the third-order iteration rather than imposing the truncation at the second order. It is found that while the resulting wave kinetic equation is identical to that obtained in the previous paper cited above, the third-order nonlinear correction plays an essential role for properly calculating derived quantities such as the total and residual energies.
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Pressure anisotropy can strongly influence the dynamics of weakly collisional, high-beta plasmas, but its effects are missed by standard magnetohydrodynamics (MHD). Small changes to the magnetic-field strength generate large pressure-anisotropy forces, heating the plasma, driving instabilities and rearranging flows, even on scales far above the particles’ gyroscales where kinetic effects are traditionally considered most important. Here, we study the influence of pressure anisotropy on turbulent plasmas threaded by a mean magnetic field (Alfvénic turbulence). Extending previous results that were concerned with Braginskii MHD, we consider a wide range of regimes and parameters using a simplified fluid model based on drift kinetics with heat fluxes calculated using a Landau-fluid closure. We show that viscous (pressure-anisotropy) heating dissipates between a quarter (in collisionless regimes) and half (in collisional regimes) of the turbulent-cascade power injected at large scales; this does not depend strongly on either plasma beta or the ion-to-electron temperature ratio. This will in turn influence the plasma's thermodynamics by regulating energy partition between different dissipation channels (e.g. electron and ion heat). Due to the pressure anisotropy's rapid dynamic feedback onto the flows that create it – an effect we term ‘magneto-immutability’ – the viscous heating is confined to a narrow range of scales near the forcing scale, supporting a nearly conservative, MHD-like inertial-range cascade, via which the rest of the energy is transferred to small scales. Despite the simplified model, our results – including the viscous heating rate, distributions and turbulent spectra – compare favourably with recent hybrid-kinetic simulations. This is promising for the more general use of extended-fluid (or even MHD) approaches to model weakly collisional plasmas such as the intracluster medium, hot accretion flows and the solar wind.
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We discuss the phenomenon of energization of relativistic charged particles in three-dimensional incompressible MHD turbulence and the diffusive properties of the motion of the same particles. We show that the random electric field induced by turbulent plasma motion leads test particles moving in a simulated box to be accelerated in a stochastic way, a second-order Fermi process. A small fraction of these particles happen to be trapped in large scale structures, most likely formed due to the interaction of islands in the turbulence. Such particles get accelerated exponentially, provided their pitch angle satisfies some conditions. We discuss at length the characterization of the accelerating structure and the physical processes responsible for rapid acceleration. We also comment on the applicability of the results to realistic astrophysical turbulence.more » « less
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ABSTRACT The nature of cosmic ray (CR) transport in the Milky Way remains elusive. The predictions of current microphysical CR transport models in magnetohydrodynamic (MHD) turbulence are drastically different from what is observed. These models usually focus on MHD turbulence with a strong guide field and ignore the impact of turbulent intermittency on particle propagation. This motivates our studying the alternative regime of large-amplitude turbulence with δB/B0 ≫ 1, in which intermittent small-scale magnetic field reversals are ubiquitous. We study particle transport in such turbulence by integrating trajectories in stationary snapshots. To quantify spatial diffusion, we use a set-up with continuous particle injection and escape, which we term the turbulent leaky box. We find that particle transport is very different from the strong guide-field case. Low-energy particles are better confined than high-energy particles, despite less efficient pitch-angle isotropization at small energies. In the limit of weak guide field, energy-dependent confinement is driven by the energy-dependent (in)ability to follow reversing magnetic field lines exactly and by the scattering in regions of ‘resonant curvature’, where the field line bends on a scale that is of the order of the local particle gyro-radius. We derive a heuristic model of particle transport in magnetic folds that approximately reproduces the energy dependence of transport found numerically. We speculate that CR propagation in the Galaxy is regulated by the intermittent field reversals highlighted here and discuss the implications of our findings for CR transport in the Milky Way.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3847/1538-4357/ac596e
