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Register a new userLocal and global properties of energy transfer in models of plasma turbulence
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Christian V\\'asconez
Publication date
2020
fields
Physics
and research's language is
English
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The nature of the turbulent energy transfer rate is studied using direct numerical simulations of weakly collisional space plasmas. This is done comparing results obtained from hybrid Vlasov-Maxwell simulations of colissionless plasmas, Hall-magnetohydrodynamics, and Landau fluid models reproducing low-frequency kinetic effects, such as the Landau damping. In this partially developed turbulent scenario, estimates of the local and global scaling properties of different energy channels are obtained using a proxy of the local energy transfer (LET). This approach provides information on the structure of energy fluxes, under the assumption that the turbulent cascade transfers most of the energy that is then dissipated at small scales by various kinetic processes in this kind of plasmas.
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In weakly collisional space plasmas, the turbulent cascade provides most of the energy that is dissipated at small scales by various kinetic processes. Understanding the characteristics of such dissipative mechanisms requires the accurate knowledge of the fluctuations that make energy available for conversion at small scales, as different dissipation processes are triggered by fluctuations of a different nature. The scaling properties of different energy channels are estimated here using a proxy of the local energy transfer, based on the third-order moment scaling law for magnetohydrodynamic turbulence. In particular, the sign-singularity analysis was used to explore the scaling properties of the alternating positive-negative energy fluxes, thus providing information on the structure and topology of such fluxes for each of the different type of fluctuations. The results show the highly complex geometrical nature of the flux, and that the local contributions associated with energy and cross-helicity nonlinear transfer have similar scaling properties. Consequently, the fractal properties of current and vorticity structures are similar to those of the Alfvenic fluctuations.
The fundamental assumptions of the adiabatic theory do not apply in presence of sharp field gradients as well as in presence of well developed magnetohydrodynamic turbulence. For this reason in such conditions the magnetic moment $mu$ is no longer expected to be constant. This can influence particle acceleration and have considerable implications in many astrophysical problems. Starting with the resonant interaction between ions and a single parallel propagating electromagnetic wave, we derive expressions for the magnetic moment trapping width $Delta mu$ (defined as the half peak-to-peak difference in the particle magnetic moment) and the bounce frequency $omega_b$. We perform test-particle simulations to investigate magnetic moment behavior when resonances overlapping occurs and during the interaction of a ring-beam particle distribution with a broad-band slab spectrum. We find that magnetic moment dynamics is strictly related to pitch angle $alpha$ for a low level of magnetic fluctuation, $delta B/B_0 = (10^{-3}, , 10^{-2})$, where $B_0$ is the constant and uniform background magnetic field. Stochasticity arises for intermediate fluctuation values and its effect on pitch angle is the isotropization of the distribution function $f(alpha)$. This is a transient regime during which magnetic moment distribution $f(mu)$ exhibits a characteristic one-sided long tail and starts to be influenced by the onset of spatial parallel diffusion, i.e., the variance $<(Delta z)^2 >$ grows linearly in time as in normal diffusion. With strong fluctuations $f(alpha)$ isotropizes completely, spatial diffusion sets in and $f(mu)$ behavior is closely related to the sampling of the varying magnetic field associated with that spatial diffusion.
In the context of space and astrophysical plasma turbulence and particle heating, several vocabularies emerge for estimating turbulent energy dissipation rate, including Kolmogorov-Yaglom third-order law and, in its various forms, $boldsymbol{j}cdotboldsymbol{E}$ (work done by the electromagnetic field on particles), and $-left( boldsymbol{P} cdot abla right) cdot boldsymbol{u}$ (pressure-strain interaction), to name a couple. It is now understood that these energy transfer channels, to some extent, are correlated with coherent structures. In particular, we find that different energy dissipation proxies, although not point-wise correlated, are concentrated in proximity to each other, for which they decorrelate in a few $d_i$(s). However, the energy dissipation proxies dominate at different scales. For example, there is an inertial range over which the third-order law is meaningful. Contributions from scale bands stemming from scale-dependent spatial filtering show that, the energy exchange through $boldsymbol{j}cdotboldsymbol{E}$ mainly results from large scales, while the energy conversion from fluid flow to internal through $-left( boldsymbol{P} cdot abla right) cdot boldsymbol{u}$ dominates at small scales.
Using kinetic particle-in-cell (PIC) simulations, we simulate reconnection conditions appropriate for the magnetosheath and solar wind, i.e., plasma beta (ratio of gas pressure to magnetic pressure) greater than 1 and low magnetic shear (strong guide field). Changing the simulation domain size, we find that the ion response varies greatly. For reconnecting regions with scales comparable to the ion Larmor radius, the ions do not respond to the reconnection dynamics leading to electron-only reconnection with very large quasi-steady reconnection rates. The transition to more traditional ion-coupled reconnection is gradual as the reconnection domain size increases, with the ions becoming frozen-in in the exhaust when the magnetic island width in the normal direction reaches many ion inertial lengths. During this transition, the quasi-steady reconnection rate decreases until the ions are fully coupled, ultimately reaching an asymptotic value. The scaling of the ion outflow velocity with exhaust width during this electron-only to ion-coupled transition is found to be consistent with a theoretical model of a newly reconnected field line. In order to have a fully frozen-in ion exhaust with ion flows comparable to the reconnection Alfven speed, an exhaust width of at least several ion inertial lengths is needed. In turbulent systems with reconnection occurring between magnetic bubbles associated with fluctuations, using geometric arguments we estimate that fully ion-coupled reconnection requires magnetic bubble length scales of at least several tens of ion inertial lengths.
In this study we present an inversion method which provides thermal plasma population parameters from characteristics of chorus emissions only. Our ultimate goal is to apply this method to ground based data in order to derive the lower energy boundary condition for many radiation belt models. The first step is to test the chorus-inversion method on in-situ data of Van Allen Probes in the generation region. Density and thermal velocity of energetic electrons (few keV - 100 keV) are derived from frequency sweep rate and starting frequencies of chorus emissions through analysis of wave data from Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) onboard the Van Allen Probes. Nonlinear wave growth theory of citet{omura2011triggering} serves as the basis for our inversion method, assuming that the triggering wave is originated by the linear cyclotron instability. We present sixteen, consecutive rising-tone emissions recorded in the generation region between 11-12UT on 14 November 2012. The results of the inversion are compared with density and thermal velocities (parallel and perpendicular) of energetic electrons derived from unidirectional flux data of Helium Oxygen Proton Electron (HOPE) instrument, showing a good agreement: the normalized root-mean-square deviation between the measured and predicted values are $sim13%, sim6%$, and $sim10%$, respectively. We found that the theoretical amplitudes are consistent with the measured ones. The relation between linear and nonlinear wave growth agrees with our basic assumption, namely, linear growth is a preceding process of nonlinear wave growth. We analyze electron distributions at the relativistic resonant energy ranges.
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