Weak Alfvénic turbulence in relativistic plasmas. Part 1. Dynamical equations and basic dynamics of interacting resonant triads

Alfvén wave collisions are the primary building blocks of the non-relativistic turbulence that permeates the heliosphere and low- to moderate-energy astrophysical systems. However, many astrophysical systems such as gamma-ray bursts, pulsar and magnetar magnetospheres and active galactic nuclei have relativistic flows or energy densities. To better understand these high-energy systems, we derive reduced relativistic magnetohydrodynamics equations and employ them to examine weak Alfvénic turbulence, dominated by three-wave interactions, in reduced relativistic magnetohydrodynamics, including the force-free, infinitely magnetized limit. We compare both numerical and analytical solutions to demonstrate that many of the findings from non-relativistic weak turbulence are retained in relativistic systems. But, an important distinction in the relativistic limit is the inapplicability of a formally incompressible limit, i.e. there exists finite coupling to the compressible fast mode regardless of the strength of the magnetic field. Since fast modes can propagate across field lines, this mechanism provides a route for energy to escape strongly magnetized systems, e.g. magnetar magnetospheres. However, we find that the fast-Alfvén coupling is diminished in the limit of oblique propagation.

Effect of ionization waves on dust chain formation in a DC discharge

An interesting aspect of complex plasma is its ability to self-organize into a variety of structural configurations and undergo transitions between these states. A striking phenomenon is the isotropic-to-string transition observed in electrorheological complex plasma under the influence of a symmetric ion wake field. Such transitions have been investigated using the Plasma Kristall-4 (PK-4) microgravity laboratory on the International Space Station. Recent experiments and numerical simulations have shown that, under PK-4-relevant discharge conditions, the seemingly homogeneous direct current discharge column is highly inhomogeneous, with large axial electric field oscillations associated with ionization waves occurring on microsecond time scales. A multi-scale numerical model of the dust–plasma interactions is employed to investigate the role of the electric field in the charge of individual dust grains, the ion wake field and the order of string-like structures. Results are compared with those for dust strings formed in similar conditions in the PK-4 experiment.

Characteristics of collisional damping of surface ion-acoustic mode in Divertor Plasma Simulator-2 (DiPS-2)

The dissipation of ion-acoustic surface waves propagating in a semi-bounded and collisional plasma which has a boundary with vacuum is theoretically investigated and this result is used for the analysis of edge-relevant plasma simulated by Divertor Plasma Simulator-2 (DiPS-2). The collisional damping of the surface wave is investigated for weakly ionized plasmas by comparing the collisionless Landau damping with the collisional damping as follows: (1) the ratio of ion temperature $({T_i})$ to electron temperature $({T_e})$ should be very small for the weak collisionality $({T_i}/{T_e} \ll 1)$ ; (2) the effect of collisionless Landau damping is dominant for the small parallel wavenumber, and the decay constant is given as $\gamma \approx{-} \sqrt {\mathrm{\pi }/2} {k_\parallel }{\lambda _{De}}\omega _{pi}^2/{\omega _{pe}}$ ; and (3) the collisional damping dominates for the large parallel wavenumber, and the decay constant is given as $\gamma \approx{-} {\nu _{in}}/16$ , where ${\nu _{in}}$ is the ion–neutral collisional frequency. An experimental simulation of the above theoretical prediction has been done in the argon plasma of DiPS-2, which has the following parameters: plasma density ${n_e} = (\textrm{2--9)} \times \textrm{1}{\textrm{0}^{11}}\;\textrm{c}{\textrm{m}^{ - 3}}$ , ${T_e} = 3.7- 3.8\;\textrm{eV}$ , ${T_i} = 0.2- 0.3\;\textrm{eV}$ and collision frequency ${\nu _{in}} = 23- 127\;\textrm{kHz}$ . Although the wavelength should be specified with the given parameters of DiPS-2, the collisional damping is found to be $\gamma = ( - 0.9\;\textrm{to}\; - 5) \times {10^4}\;\textrm{rad}\;{\textrm{s}^{ - 1}}$ for ${k_\parallel }{\lambda _{De}} = 10$ , while the Landau damping is found to be $\gamma = ( - 4\;\textrm{to}\; - 9) \times {10^4}\;\textrm{rad}\;{\textrm{s}^{ - 1}}$ for ${k_\parallel }{\lambda _{De}} = 0.1$ .

Phase transition to blob-hole coherent structure in the Hasegawa–Mima model for plasmas

An equilibrium statistical mechanics theory for the Hasegawa–Mima equations of toroidal plasmas, with canonical constraint on energy and microcanonical constraint on potential enstrophy, is solved exactly as a spherical model. The use of a canonical energy constraint instead of a fixed-energy microcanonical approach is justified by the preference for viewing real plasmas as an open system. A significant consequence of the results obtained from the partition function, free energy and critical temperature, is the condensation into a ground state exhibiting a blob-hole-like structure observed in real plasmas.

Statistical description of coalescing magnetic islands via magnetic reconnection

The physical picture of interacting magnetic islands provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath and the Earth's magnetosphere. In this work, we derive an island kinetic equation to describe the evolution of the island distribution function (in area and in flux of islands) subject to a collisional integral designed to account for the role of magnetic reconnection during island mergers. This equation is used to study the inverse transfer of magnetic energy through the coalescence of magnetic islands in two dimensions. We solve our island kinetic equation numerically for three different types of initial distribution: Dirac delta, Gaussian and power-law distributions. The time evolution of several key quantities is found to agree well with our analytical predictions: magnetic energy decays as $\tilde {t}^{-1}$ , the number of islands decreases as $\tilde {t}^{-1}$ and the averaged area of islands grows as $\tilde {t}$ , where $\tilde {t}$ is the time normalised to the characteristic reconnection time scale of islands. General properties of the distribution function and the magnetic energy spectrum are also studied. Finally, we discuss the underlying connection of our island-merger models to the (self-similar) decay of magnetohydrodynamic turbulence.

Exact nonlinear solutions for three-dimensional Alfvén-wave packets in relativistic magnetohydrodynamics

We show that large-amplitude, non-planar, Alfvén-wave (AW) packets are exact nonlinear solutions of the relativistic magnetohydrodynamic equations when the total magnetic-field strength in the local fluid rest frame ( $b$ ) is a constant. We derive analytic expressions relating the components of the fluctuating velocity and magnetic field. We also show that these constant- $b$ AWs propagate without distortion at the relativistic Alfvén velocity and never steepen into shocks. These findings and the observed abundance of large-amplitude, constant- $b$ AWs in the solar wind suggest that such waves may be present in relativistic outflows around compact astrophysical objects.

The fast transit-time limit of magnetic pumping with trapped electrons

Recently, the energization of superthermal electrons at the Earth's bow shock was found to be consistent with a new magnetic pumping model derived in the limit where the electron transit time is much shorter than any time scale governing the evolution of the magnetic fields. The new model breaks with the common approach of integrating the kinetic equations along unperturbed orbits. Rather, the fast transit-time limit allows the electron dynamics to be characterized by adiabatic invariants (action variables) accurately capturing the nonlinear effects of electrons becoming trapped in magnetic perturbations. Without trapping, fast parallel streaming along magnetic field lines causes the electron pressure to be isotropized and homogeneous along the magnetic field lines. In contrast, trapping permits spatially varying pressure anisotropy to form along the magnetic field lines, and through a Fermi process this pressure anisotropy in turn becomes the main ingredient that renders magnetic pumping efficient for energizing superthermal electrons. We here present a detailed mathematical derivation of the model.

Interaction of radio frequency waves with cylindrical density filaments: scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas, vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci., vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

Test particle acceleration in resistive torsional fan magnetic reconnection using laboratory plasma parameters

Particle acceleration via magnetic reconnection is a fundamental process in astrophysical plasmas. Experimental architectures are able to confirm a wide variety of particle dynamics following the two-dimensional Sweet–Parker model, but are limited in their reproduction of the fan-spine magnetic field topology about three-dimensional (3-D) null points. Specifically, there is not yet an experiment featuring driven 3-D torsional magnetic reconnection. To move in this direction, this paper expands on recent work toward the design of an experimental infrastructure for inducing 3-D torsional fan reconnection by predicting feasible particle acceleration profiles. Solutions to the steady-state, kinematic, resistive magnetohydrodynamic equations are used to numerically calculate particle trajectories from a localized resistivity profile using well-understood laboratory plasma parameters. We confine a thin, 10 eV helium sheath following the snowplough model into the region of this localized resistivity and find that it is accelerated to energies of ${\approx }2$ keV. This sheath is rapidly accelerated and focused along the spine axis propagating a few centimetres from the reconnection region. These dynamics suggest a novel architecture that may hold promise for future experiments studying solar coronal particle acceleration and for technology applications such as spacecraft propulsion.

Evolution of an arched magnetized laboratory plasma in a sheared magnetic field

Arched magnetized structures are a common occurrence in space and laboratory plasmas. Results from a laboratory experiment on spatio-temporal evolution of an arched magnetized plasma ( $\beta \approx 10^{-3}$ , Lundquist number $\approx 10^{4}$ , plasma radius/ion gyroradius $\approx 20$ ) in a sheared magnetic configuration are presented. The experiment is designed to model conditions relevant to the formation and destabilization of similar structures in the solar atmosphere. The magnitude of a nearly horizontal overlying magnetic field was varied to study its effects on the writhe and twist of the arched plasma. In addition, the direction of the guiding magnetic field along the arch was varied to investigate its role in the formation of either forward- or reverse-S shaped plasma structures. The electrical current in the arched plasma was well below the current required to make it kink unstable. A significant increase in the writhe of the arched plasma was observed with larger magnitudes of overlying magnetic field. A forward-S shaped arched plasma was observed for a guiding magnetic field oriented nearly antiparallel to the initial arched plasma current, while the parallel orientation yielded the reverse-S shaped arched plasma.