The fully three dimensional governing equations in the electron magnetohydrodynamic (EMHD) regime for a plasma with inhomogeneous density is obtained. These equations in the two dimensional (2-D) limit can be cast in terms of the evolution of two coupled scalar fields. The nonlinear simulations for the two dimensional case are carried out to understand the propagation of EMHD magnetic structures in the presence of inhomogeneity. A novel effect related to trapping of dipolar magnetic structures in the high density plasma region in the EMHD regime is observed. The interpretation of this phenomena as well as its relevance to the problem of hot spot generation in the context of fast ignition is presented.
The magnetic connection theorem of ideal Magnetohydrodynamics by Newcomb [Newcomb W.A., Ann. Phys., 3, 347 (1958)] and its covariant formulation are rederived and reinterpreted in terms of a "time resetting" projection that accounts for the loss of simultaneity in different reference frames between spatially separated events.
Adopting the theoretical framework for the generalized fishbonelike dispersion relation, an extended hybrid magnetohydrodynamics gyrokinetic simulation model has been derived analytically by taking into account both thermal ion compressibility and diamagnetic effects in addition to energetic particle kinetic behaviors. The extended model has been used for implementing an eXtended version of Hybrid Magnetohydrodynamics Gyrokinetic Code (XHMGC) to study thermal ion kinetic effects on Alfvénic modes driven by energetic particles, such as kinetic beta induced Alfvén eigenmodes in tokamak fusion pl…
We report the first measurements of equations of state of a fully relaxed magnetohydrodynamic (MHD) laboratory plasma. Parcels of magnetized plasma, called Taylor states, are formed in a coaxial magnetized plasma gun, and are allowed to relax and drift into a closed flux conserving volume. Density, ion temperature, and magnetic field are measured as a function of time as the Taylor states compress and heat. The theoretically predicted MHD and double adiabatic equations of state are compared to experimental measurements. We find that the MHD equation of state is inconsistent with our data.
Parker's formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient alpha in the Hall MHD Beltrami condition turns out now to be proportional to the "potential vorticity." The Hall MHD Beltrami condition becomes equivalent to the "potential vorticity" conservation equation in two-dimensional (2D) hydrodynamics if the Hall MHD Lagrange multiplier beta is taken to be proportional to the "potential vorticity" as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as "po…
Axisymmetric relaxed states of a cylindrical plasma column are found analytically in both standard and Hall magnetohydrodynamics (MHD) by complete minimization of energy with constraints imposed by invariants inherent in corresponding models. It is shown that the relaxed state in Hall MHD is the force-free magnetic field with uniform axial flow and/or rigid azimuthal rotation. The relaxed states in standard MHD are more complex due to the coupling between velocity and magnetic field. Application of these states for reversed-field pinches (RFP) is discussed.
The possibility that the type of discontinuous flow changes as the conditions gradually (continuously) change is investigated in connection with the problems arising when the results of numerical simulations of magnetic reconnection in plasma are interpreted. The conservation laws at a discontinuity surface in magnetohydrodynamics admit such transitions, but the socalled transition solutions for the boundary conditions that simultaneously satisfy two types of discontinuities should exist in this case. The specific form of such solutions has been found, and a generalized scheme of permitted tra…
We investigate the propagation of electromagnetic waves in resistive pair plasmas using a onefluid theory derived from the relativistic two-fluid equations. When the resistivity normalized by the electron/positron inertia variable exceeds a critical value, the dispersion relation for electromagnetic waves shows that the group velocity is larger than the light speed in vacuum. However, in such a case, it also is found that the plasma parameter is less than unity: that is, the electron-positron pair medium no longer can be treated as plasma. Thus the simple two-fluid approximation is invalid. Th…
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes pressure anisotropy and general plasma flows. This anisotropic extension to our previous isotropic model is motivated by Sun and Finn's model of relaxed anisotropic magnetohydrodynamic equilibria. We prove that as the number of plasma regions becomes infinite, our anisotropic extension of MRxMHD reduces to anisotropic ideal MHD with flow. The continuously nested flux surface limit of our MRxMHD model is the first variational principle for anisotropic plasma equilibria with general …
We have explored the thermodynamics of compressed magnetized plasmas in laboratory experiments and we call these studies "magnetothermodynamics". The experiments are carried out in the Swarthmore Spheromak eXperiment device. In this device, a magnetized plasma source is located at one end and at the other end, a closed conducting can is installed. We generate parcels of magnetized plasma and observe their compression against the end wall of the conducting cylinder. The plasma parameters such as plasma density, temperature, and magnetic field are measured during compression using HeNe laser int…
Models of covariant linear electromagnetic constitutive relations are formulated that have wide applicability to the computation of susceptibility tensors for dispersive and inhomogeneous media. A perturbative framework is used to derive a linear constitutive relation for a globally neutral plasma enabling one to describe in this context a generalized Landau damping mechanism for non-stationary inhomogeneous plasma states.
A brief review of the existing kinetic-magnetohydrodynamic(MHD) hybrid models for the alpha particle physics in burning plasma demonstrates that the pressure-coupling scheme is equivalent to the current-coupling scheme only in a specific dynamic regime where the alpha particle density is much lower than the background ion and electron. A more comprehensive kinetic-multifluid model is proposed for a proper account of the dynamical regime of the burning plasma where both the energetic alpha and the helium ash particles are present. The Kinetic-multifluid model is further simplified into an exten…
We have carried out a 3D ideal-MHD (Magnetohydrodynamic) simulation to study the evolution of laser generated plasma plume in a moderate external magnetic field (0.13 T) oriented perpendicular to the flow direction of the plasma plume. The simulation shows that the plasma plume pushes the external magnetic field lines outward in the direction of the expansion. This leads to compression and bending of the magnetic field lines.The force resulting from the change in shape and the density of magnetic field lines opposes the expansion of the plume. An elliptic layer of shocked plasma is formed at t…
A 1D2V open boundary Vlasov-Ampere code has been implemented with the aim of making a detailed investigation of the propagation of finite amplitude electromagnetic disturbances in an inhomogeneous magnetized plasma. The code is being applied to study the propagation of an externally driven electromagnetic signal, localized at one boundary of the integration interval, through a given equilibrium plasma configuration with inhomogeneous plasma density and magnetic field.
The effect of electron temperature on the space-time evolution of nonlinear plasma oscillations in an inhomogeneous plasma is studied using a one-dimensional particle-in-cell (PIC) code. In contrast to the conventional wisdom, it is found that for an inhomogeneous plasma, there exists a critical value of electron temperature beyond which wave breaking does not occur. This novel result, which is of relevance to present day laser plasma experiments, has been explained on the basis of interplay between electron thermal pressure and background inhomogeneity.
A new neutrino magnetohydrodynamics (NMHD) model is formulated, where the effects of the charged weak current on the electron-ion magnetohydrodynamic fluid are taken into account. The model incorporates in a systematic way the role of the Fermi neutrino weak force in magnetized plasmas. A fast neutrino-driven short wavelengths instability associated with the magnetosonic wave is derived. Such an instability should play a central role in strongly magnetized plasma as occurs in supernovae, where dense neutrino beams also exist. In addition, in the case of nonlinear or high frequency waves, the n…
The effect of a narrow sub-Alfvenic shear flow layer near the minimum q_min of the tokamak safety factor profile in a configuration with reversed central shear is analyzed. Sufficiently strong velocity shear gives rise to a broad spectrum of fast growing Kelvin-Helmholtz (KH)-like ideal magnetohydrodynamic (MHD) modes with dominant mode numbers m,n ~ 10. Nonlinear simulations with finite resistivity show magnetic reconnection near ripples caused by KH-like vortices, the formation of turbulent structures, and a flattening of the flow profile. The KH modes are compared to double tearing modes (D…
The adiabatic limit of a recently proposed dynamical extension of Taylor relaxation, \emph{multi-region relaxed magnetohydrodynamics} (MRxMHD) is summarized, with special attention to the appropriate definition of relative magnetic helicity. The formalism is illustrated using a simple two-region, sheared-magnetic-field model similar to the Hahm--Kulsrud--Taylor (HKT) rippled-boundary slab model. In MRxMHD a linear Grad--Shafranov equation applies, even at finite ripple amplitude. The adiabatic switching on of boundary ripple excites a shielding current sheet opposing reconnection at a resonant…
We investigate the nonlinear propagation of multidimensional magnetosonic shock waves (MSWs) in a dissipative quantum magnetoplasma. A macroscopic quantum magnetohydrodynamic (QMHD) model is used to include the quantum force associated with the Bohm potential, the pressure-like spin force, the exchange and correlation force of electrons, as well as the dissipative force due to the kinematic viscosity of ions and the magnetic diffusivity. The effects of these forces on the properties of arbitrary amplitude MSWs are examined numerically. It is found that the contribution from the exchange-correl…
Using direct numerical simulations of three-dimensional magnetohydrodynamic (MHD) turbulence the spatio-temporal behavior of magnetic field fluctuations is analyzed. Cases with relatively small, medium and large values of a mean background magnetic field are considered. The (wavenumber) scale dependent time correlation function is directly computed for different simulations, varying the mean magnetic field value. From this correlation function the time decorrelation is computed and compared with different theoretical times, namely, the local non-linear time, the random sweeping time, and the A…
Relativistic electron beam propagation in plasma is fraught with several micro instabilities like two stream, filamentation etc., in plasma. This results in severe limitation of the electron transport through a plasma medium. Recently, however, there has been an experimental demonstration of improved transport of Mega Ampere of electron currents (generated by the interaction of intense laser with solid target) in a carbon nanotube structured solid target [Phys. Rev Letts. 108, 235005 (2012)]. This then suggests that the inhomogeneous plasma (created by the ionization of carbon nano tube struct…
The cat-eyes steady state solution in the framework of hydrodynamics describing an infinite row of identical vortices is extended to the magnetohydrodynamic equilibrium equation with incompressible flow of arbitrary direction. The extended solution covers a variety of equilibria including one- and two-dimensional generalized force-free and Harris-sheet configurations which are preferable from those usually employed as initial states in reconnection studies. Although the vortex shape is not affected by the magnetic field, the flow in conjunction with the equilibrium nonlinearity has a strong im…
Equations describing the linear evolution of a non-dissipative Langmuir wave in inhomogeneous nonstationary anisotropic plasma without magnetic field are derived in the geometrical optics approximation. A continuity equation is obtained for the wave action density, and the conditions for the action conservation are formulated. In homogeneous plasma, the wave field E universally scales with the electron density N as E ~ N^{3/4}, whereas the wavevector evolution varies depending on the wave geometry.
It is proved that (a) the solutions of the ideal magnetohydrodynamic equation, which describe the equlibrium states of a cylindrical plasma with purely poloidal flow and arbitrary cross sectional shape [G. N. Throumoulopoulos and G. Pantis, Plasma Phys. and Contr. Fusion 38, 1817 (1996)] are also valid for incompressible equlibrium flows with the axial velocity component being a free surface quantity and (b) for the case of isothermal incompressible equilibria the magnetic surfaces have necessarily circular cross section.
Temporal evolution of the inhomogeneous energy density driven instability (IEDDI) is examined in presence of a nonuniform transverse dc electric field in collisional magnetized plasma cylinder. Using experimentally known parameters relevant to IEDDI, we have estimated the growth rate for $ν$=1, 2 and 3 nonlocal eigenmodes.
The theory of the ion cyclotron (IC) electrostatic parametric instabilities of the inhomogeneous plasma which are driven by the inhomogeneous electric field of the fast wave (FW) in front of FW antenna is developed. It is found that the spatial inhomogeneity of the parametric IC turbulence and of the drift turbulence is at the origin of the flows which transport a large part of FW power, deposited to the pedestal plasma, to the scrape-off layer and later to the divertor mostly along field lines.
The impacts of dust density inhomogeneity and dust size distribution (DSD) on linear dust acoustic (DA) wave propagation have been investigated theoretically in an inhomogeneous unmagnetized dusty plasma having powerlaw DSD. Two different types of wave modes, viz. slow and fast mode, are found to propagate in this inhomogeneous medium. It is shown that the linear dispersion characteristics of the DA waves are substantially affected by the DSD and density inhomogeneity. Also, it is found that the phase velocity increases with increasing dust density.
New unstable temperature gradient driven modes in an inhomogeneous plasma are identified. These modes represent transient $ω\simeq k_{\Vert }v_{th}^{(e,i)}$ sound oscillations in magnetized plasma that are kinetically destabilized via Landau interactions. Electron and ion sound branches are unstable for large values of the Larmor radius parameter $% k_{\bot}ρ_{e,i}\gg 1,$ respectively. The instability occurs due to a specific plasma response that significantly deviates from Boltzmann distribution in the region $k_{\bot}ρ_{i,e}\gg 1$ . Pacs: 52.35 Kt, 52.35 Qz
Exact solutions of the self-consistent relativistic magnetohydrodynamics equations for an anisotropic magnetized plasma on the background of Bondi-Pirani-Robinson's vacuum plane gravitational wave (PGW) metric with an arbitrary polarization are obtained, which generalize the results obtained earlier by one of the authors for the transverse polarization of a gravitational wave. Based on the reformulated energobalance equation it is shown that in the linear approximation by gravitational wave amplitude only the transverse polarization of PGW interacts with magnetized plasma.
In a previous work [16], a new model was introduced, taking into account the role of the Fermi weak force due to neutrinos coupled to magnetohydrodynamic plasmas. The resulting neutrino-magnetohydrodynamics was investigated in a particular geometry associated with the magnetosonic wave, where the ambient magnetic field and the wavevector are perpendicular. The corresponding fast, short wavelength neutrino beam instability was then obtained in the context of supernova parameters. The present communication generalizes these results, allowing for arbitrary direction of wave propagation, including…
A recent experimental observation has shown efficient transport of Mega Ampere of electron currents through aligned carbon nanotube arrays [Phys. Rev Letts. 108, 235005 (2012)]. The result was subsequently interpreted on the basis of suppression of the filamentation instability in an inhomogeneous plasma [Phys. Plasmas 21, 012108 (2014)]. This inhomogeneity forms as a result of the ionization of the carbon nanotubes. In the present work a full 1D3V Particle-in-Cell (PIC) simulations have been carried out for the propagation of relativistic electron beams (REB) through an inhomogeneous backgrou…
A method for the controlled generation of intense high frequency electromagnetic fields by a breaking Langmuir wave (relativistic flying mirrors) in a gradually inhomogeneous plasma is proposed. The wave breaking threshold depends on the local plasma density gradient. Compression, chirping and frequency multiplication of an electromagnetic wave reflected from relativistic mirrors is demonstrated using Particle-In-Cell simulations. Adjusting the shape of the density profile enables control of the reflected light properties.
A unified energy principle approach is presented for analysing the magnetohydrodynamic (MHD) stability of plasmas consisting of multiple ideal and relaxed regions. By choosing an appropriate gauge, we show that the plasma displacement satisfies the same Euler-Lagrange equation in ideal and relaxed regions, except in the neighbourhood of magnetic surfaces. The difference at singular surfaces is analysed in cylindrical geometry: in ideal MHD only Newcomb's [W. A. Newcomb (2006) Ann. Phys., 10, 232] small solutions are allowed, whereas in relaxed MHD only the odd-parity large solution and even-pa…
Cross-helicity dominated distributed chaos (CHDC) for magnetohydrodynamic (large-scale) and kinetic (small-scale) ranges of space plasmas has been studied using results of direct numerical simulations and of measurements made in the Earth's magnetosheath and in free solar wind by the instruments onboard of the Magnetospheric Multiscale Mission and CLUSTER spacecrafts. Existence of two generic types of transition from the magnetohydrodynamic (MHD) to kinetic range has been shown: 1) from the Kolmogorov-like (scaling) MHD turbulence to the kinetic CHDC and 2) from the magnetohydrodynamic CHDC to…
Propagation of Langmuir solitons in inhomogeneous plasmas is investigated numerically. Through numerical simulation solving Zakharov equations, the solitons are accelerated toward the low density side. As a consequence, isolated cavities moving at ion sound velocities are emitted. When the acceleration is further increased, solitons collapse and the cavities separate into two lumps released at ion sound velocities. The threshold is estimated by an analogy between the soliton and a particle overcoming the self-generated potential well.
It is shown that the magnetohydrodynamic equilibrium states of an axisymmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second-order partial differential equation for the poloidal magnetic flux function $ψ$ coupled with a Bernoulli type equation for the plasma density (which are identical in form to the corresponding ideal MHD equilibrium equations) along with the relation $Δ^\star ψ=V_c σ$. (Here, $Δ^\star$ is the Grad-Schlüter-Shafranov operator, $σ$ is the conductivity and $V_c$ is the constant toroidal-loop voltage divided by $2 π$)…
The dynamics of the ultra-intense circularly polarized solitons under inhomogeneous plasmas are examined. The interaction is modeled by the Maxwell and relativistic hydrodynamic equations and is solved with fully implicit energy-conserving numerical scheme. It is shown that a propagating weak soliton can be decreased and reflected by increasing plasma background, which is consistent with the existing studies based on hypothesis of weak density response. However it is found that ultra-intense soliton is well trapped and kept still when encountering increasing background. Probably, this founding…
When an electromagnetic transverse wave propagates through an inhomogeneous plasma so that its electric field has a component in the direction of the background density gradient, there appears a disbalance of charge in every plasma layer, caused by the density gradient. Due to this some additional longitudinal electric field component appears in the direction of the wave vector. This longitudinal field may couple with the usual electrostatic longitudinal perturbations like the ion acoustic, electron Langmuir, and ion plasma waves. As a result, these standard electrostatic waves are modified an…
Generation of wake fields by a short electromagnetic pulse in a plasma with an inhomogeneous background magnetic field and density profile is considered, and a wave equation is derived. Transmission and reflection coefficients are calculated in a medium with sharp discontinuities. Particular attention is focused on examples where the longitudinal part of the electromagnetic field is amplified for the transmitted wave. Furthermore, it is noted that the wake field can propagate out of the plasma and thereby provide information about the electron density profile. A method for reconstructing the b…
The Debye shielding of a charge immersed in a flowing plasma is an old classic problem in plasma physics. It has been given renewed attention in the last two decades in view of experiments with complex plasmas, where charged dust particles are often levitated in a region with strong ion flow. Efforts to describe the shielding of the dust particles in such conditions have been focused on the homogeneous plasma approximation, which ignores the substantial inhomogeneity of the levitation region. We address the role of the plasma inhomogeneity by rigorously calculating the point charge potential i…
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential appl…
The propagation of electromagnetic waves in an unmagnetized weakly inhomogeneous cold plasma is examined. We show that the inhomogeneity induces a gauge connection term in wave equation, which gives rise to Berry effects in the dynamics of polarized rays in the post geometric optics approximation. The polarization plane of a plane polarized ray rotates as a result of the geometric Berry phase, which is the Rytov rotation. Also, the Berry curvature causes the optical Hall effect, according to which, rays of left/right circular polarization deflect oppositely to produce a spin current directed a…
Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing magnetic reconnection. By contrast, in the Taylor relaxation model for formation of macroscopically self-organized plasma equilibrium states, all these constraints are relaxed save for global magnetic fluxes and helicity. A Lagrangian variational principle is presented that leads to a new, fully dynamical, \emph{relaxed magnetohydrodynamics} (RxMHD), such that all static solu…
In this article, we provide a general derivation of the nonlinear frequency shift, $δω$, for a sinusoidal electron plasma wave (EPW) that varies slowly enough for the results derived in the companion paper, on the action distribution function, to apply. We first consider the situation when the EPW monotonously grows and then monotonously decays in a homogeneous plasma. In this situation, we show a hysteresis in the wave frequency, which does not converge back to its linear value as the wave decays to small amplitudes. We then address the derivation of $δω$ for an EPW that keeps growing in a on…
It is demonstrated that low frequency shear modes in a strongly coupled, inhomogeneous, dusty plasma can grow on account of an instability involving the dynamical charge fluctuations of the dust grains. The instability is driven by the gradient of the equilibrium dust charge density and is associated with the finite charging time of the dust grains. The present calculations, carried out in the generalized hydrodynamic viscoelastic formalism, also bring out important modifications in the threshold and growth rate of the instability due to collective effects associated with coupling to the compr…
An experimental investigation of the propagation characteristics of shock waves in an inhomogeneous dusty plasma is carried out in the Dusty Plasma Experimental (DPEx) device. A homogeneous dusty plasma, made up of poly-dispersive kaolin particles, is initially formed in a DC glow discharge Argon plasma by maintaining a dynamic equilibrium of the pumping speed and the gas feeding rate. Later, an equilibrium density inhomogeneity in the dust fluid is created by introducing an imbalance in the original dynamic equilibrium. Non-linear wave structures are then excited in this inhomogeneous dusty p…
By taking into account the radiation reaction force, we derive a set of one-fluid relativistic magnetohydrody-namics (RMHD) equations with the Landau-Lifshitz radiation reaction force based on a relativistic two-fluid plasma. These equations could be used to situations where spatiotemporal scales of plasma's motion are suffi-ciently large.
Phase mixing of relativistic large amplitude nonlinear plasma wave in presence of a time independent space periodic ion density profile has been investigated. Inhomogeneous ion along with the relativistic variation of electron mass make the characteristic frequency of the wave to acquire a space dependency and thereby it breaks at arbitrarily small amplitude due to phase mixing. An approximate space time dependent solution is obtained in the weakly relativistic limit by Bogoliuboff and Kryloff method of averaging. We find that the change in the ion density perturbation and also the relativisti…
In this paper, we develop the kinetic and hydrodynamic theories of the convective mesoscale flows driven by the spatially inhomogeneous electrostatic ion cyclotron parametric microturbulence in the pedestal plasma with a sheared poloidal flow. The developed kinetic theory predicts the generation of the sheared poloidal convective flow, and of the radial compressed flow with radial flow velocity gradient. The developed hydrodynamic theory of the convective flows reveals the radial compressed convective flow as the dominant factor in the formation of the steep pedestal density profile with densi…
The magnetohydrodynamic equations describing an inviscid, fully ionized plasma in the vicinity of a rotating black hole are derived from a two-component plasma theory within the framework of the 3+1 split of the Kerr metric. Of central interest is the generalized Ohm's law. In the limit of quasi-neutral plasma it contains no new terms as compared with special relativity. Gravitomagnetic terms appear in Ohm's law only if the plasma is charged in its rest frame or the magnetohydrodynamic approximation is not applied. It is argued that a relativistic single-fluid description of a multiple-compone…
The properties of electrostatic transverse shear waves propagating in a strongly coupled dusty plasma with an equilibrium density gradient are examined using the generalized hydrodynamic equation. In the usual kinetic limit, the resulting equation has similarity to zero energy Schrodinger's equation. This has helped in obtaining some exact eigenmode solutions in both cartesian and cylindrical geometries for certain nontrivial density profiles. The corresponding velocity profiles and the discrete eigenfrequencies are obtained for several interesting situations and their physics discussed.
The present study is a continuation of a previous one on "hyperelliptic" axisymmetric equilibria started in [Tasso and Throumoulopoulos, Phys. Plasmas 5, 2378 (1998)]. Specifically, some equilibria with incompressible flow nonaligned with the magnetic field and restricted by appropriate side conditions like "isothermal" magnetic surfaces, "isodynamicity" or P + B^2/2 constant on magnetic surfaces are found to be reducible to elliptic integrals. The third class recovers recent equilibria found in [Schief, Phys. Plasmas 10, 2677 (2003)]. In contrast to field aligned flows, all solutions found he…
