Equilibrium Plasma Density Research Articles

Phase Mixing of Propagating Alfvén Waves in a Single-fluid Partially Ionized Solar Plasma

The phase mixing of Alfvén waves is one of the most promising mechanisms for the heating of the solar atmosphere. The damping of waves in this case requires small transversal scales, relative to the magnetic field direction; this requirement is achieved by considering a transversal inhomogeneity in the equilibrium plasma density profile. Using a single-fluid approximation of a partially ionized chromospheric plasma, we study the effectiveness of the damping of phase-mixed shear Alfvén waves and investigate the effect of varying the ionization degree on the dissipation of waves. Our results show that the dissipation length of shear Alfvén waves strongly depends on the ionization degree of the plasma, but more importantly, in a partially ionized plasma, the damping length of shear Alfvén waves is several orders of magnitude shorter than in the case of a fully ionized plasma, providing evidence that phase mixing could be a large contributor to heating the solar chromosphere. The effectiveness of phase mixing is investigated for various ionization degrees, ranging from very weakly to very strongly ionized plasmas. Our results show that phase-mixed propagating Alfvén waves in a partially ionized plasma with ionization degrees in the range μ = 0.518–0.657, corresponding to heights of 1916–2150 km above the solar surface, can provide sufficient heating to balance chromospheric radiative losses in the quiet Sun.

A theoretic analysis of magnetoactive GES-based turbulent solar plasma instability

ABSTRACT A recently reported gravito-electrostatic sheath (GES) model is procedurally applied to study the turbumagnetoactive helioseismic oscillation features in the entire bi-fluidic solar plasma system. The bounded solar interior plasma (SIP, internally self-gravitating), and the unbounded solar wind plasma (SWP, externally point-gravitating) are coupled through the interfacial diffused solar surface boundary (SSB) due to an exact gravito-electrostatic interplay. A numerical platform on the developed theoretic formalism reveals the evolution of both dispersive and non-dispersive features of the modified GES mode fluctuations in new parametric windows. Different colourspectral profiles exhibit important features of the GES-based SIP–SWP perturbations elaborately. It is illustratively shown that the thermostatistical GES stability depends mainly on the radial distance, magnetic field, equilibrium plasma density, and plasma temperature. We see that their dispersive features are more pertinently pronounced in the self-gravitational domains (SIP) than the electrostatic counterparts (SWP). Besides, different characteristic parameters with accelerating (or decelerating) and stabilizing (or destabilizing) effects influencing the entire solar plasma stability are illustratively portrayed. We speculate that, in the SIP, the long-wave (gravitational-like) helioseismic fluctuations become highly dispersive showing more propagatory nature than the shorter ones (acoustic-like). The short waves show more propagatory propensity than the longer ones in the SSB and SWP regime. The reliability of our proposed investigation is bolstered along with the tentative applicability and future scope in light of the current solar observational scenarios, such as SOHO, STEREO, SDO, PSP, and SolO.

Oscillatory Reconnection as a Plasma Diagnostic in the Solar Corona

Oscillatory reconnection is a relaxation process in magnetized plasma, with an inherent periodicity that is exclusively dependent on the properties of the background plasma. This study focuses on the seismological prospects of oscillatory reconnection in the solar corona. We perform three sets of parameter studies (for characteristic coronal values of the background magnetic field, density, and temperature) using the PLUTO code to solve the fully compressive, resistive MHD equations for a 2D magnetic X-point. From each parameter study, we derive the period of the oscillatory reconnection. We find that this period is inversely proportional to the characteristic strength of the background magnetic field and the square root of the initial plasma temperature, while following a square root dependency upon the equilibrium plasma density. These results reveal an inverse proportionality between the magnitude of the Alfvén speed and the period, as well as the background speed of sound and the period. Furthermore, we note that the addition of anisotropic thermal conduction only leads to a small increase in the mean value for the period. Finally, we establish an empirical formula that gives the value for the period in relation to the background magnetic field, density, and temperature. This gives us a quantified relation for oscillatory reconnection, to be used as a plasma diagnostic in the solar corona, opening up the possibility of using oscillatory reconnection for coronal seismology.

Observation of the diocotron instability in a diode with split cathode

Diocotron instability has been observed in the pure electron plasma formed in a split cathode coaxial diode. This plasma consists of electrons, trapped in the longitudinal potential well between the two parts of the cathode. The mathematical model of the electron squeezed state, which allows the calculation of the equilibrium plasma density, is presented. The model is applied in a comprehensive analysis of experimental data, and the presence of the diocotron instability is unambiguously confirmed.

Theory of gradient drift instabilities in low-temperature, partially magnetised plasmas

A fluid dispersion theory in partially magnetised plasmas is analysed to examine the conditions under which large-wavelength modes develop in Penning-type configurations, that is, where an electric field is imposed perpendicular to a homogeneous magnetic field. The fluid dispersion relation assuming a slab geometry shows that two types of low-frequency, gradient drift instabilities occur in the direction of the $\boldsymbol {E} \times \boldsymbol {B}$ and diamagnetic drifts. One type of instability, observed when the equilibrium electric field and plasma density gradient are in the same direction, is similar to the classic modified Simon–Hoh instability. A second instability is found for conditions in which (i) the diamagnetic drift is in the direction opposite to the $\boldsymbol {E} \times \boldsymbol {B}$ drift and (ii) the magnitude of the diamagnetic drift is sufficiently larger than the electron thermal speed. The present fluid dispersion theory suggests that the rotating spokes driven by such fluid instabilities propagate in the same direction as the diamagnetic drift, which can be in the same direction as or opposite to the $\boldsymbol {E} \times \boldsymbol {B}$ drift, depending on the plasma conditions. This finding may account for the observation, in some plasma devices, of the rotation of large-scale structures in both the $\boldsymbol {E} \times \boldsymbol {B}$ and $-\boldsymbol {E} \times \boldsymbol {B}$ directions.

Non-planar magnetoactive GES-based solar plasma stability

A laboratory plasma-wall interaction-based astrophysical gravito-electrostatic sheath (GES) model is methodologically applied to study the dynamic stability of the magnetoactive bi-fluidic solar plasma system in the presence of turbulence effect. The spherically symmetric GES-model formalism couples the solar interior plasma (SIP, internally self-gravitating, bounded) and the solar wind plasma (SWP, externally point-gravitating, unbounded) through the diffused solar surface boundary (SSB). A normal spherical mode ansatz results in a generalized linear quadratic dispersion relation depicting the modal fluctuations on both the SIP and SWP scales. A constructive numerical platform reveals the evolution of both dispersive and non-dispersive modal features of the modified-GES mode excitations. The reliability of the derived non-planar dispersion laws is concretized with the help of an exact analytic shape matching the previously reported results founded on the plane-wave approximation. It is found that the thermo-statistical GES stability depends mainly on the magnetic field, equilibrium plasma density, and plasma temperature. It is speculated that the dispersive features are more pronounced in the self-gravitational domains against the electrostatic ones. The magneto-thermal interplay introduces decelerating (accelerating) and destabilizing (stabilizing) influences on the SIP (SWP), and so forth. At last, we briefly indicate the applicability of the proposed analysis to understand diverse helioseismic activities from the collective plasma dynamical viewpoint in accordance with the recent astronomical observational scenarios reported in the literature.

Autoresonant excitation of space-time quasicrystals in plasma

We demonstrate theoretically and numerically that a warm fluid model of a plasma supports space-time quasicrystalline structures. These structures are highly nonlinear, two-phase, ion acoustic waves that are excited autoresonantly when the plasma is driven by two small amplitude chirped-frequency ponderomotive drives. The waves exhibit density excursions that substantially exceed the equilibrium plasma density. Remarkably, these extremely nonlinear waves persist even when the small amplitude drives are turned off. We derive the weakly nonlinear analytical theory by applying Whitham's averaged variational principle to the Lagrangian formulation of the fluid equations. The resulting system of coupled weakly nonlinear equations is shown to be in good agreement with fully nonlinear simulations of the warm fluid model. The analytical conditions and thresholds required for autoresonant excitation to occur are derived and compared to simulations. The weakly nonlinear theory guides and informs numerical study of how the two-phase quasicrystalline structure "melts" into a single phase traveling wave when one drive is below a threshold. These nonlinear structures may have applications to plasma photonics for extremely intense laser pulses, which are limited by the smallness of density perturbations of linear waves.

Electric potential in partially magnetized E × B discharges

Ability to control the electric potential inside the plasma is promising for various applications of E × B plasma because the trajectory of particles, which meets the desired purpose, is mainly determined by the drift motions in the external electric and magnetic fields. In the E × B source, it is well known that the equilibrium states and plasma density and temperature gradient can be sources of plasma instability, which, in turn, affects global plasma parameters. However, the effect of instability on the electric potential has not been verified so far. In this work, correlation of the plasma potential and instability is investigated through simplified-circuit modeling. The consideration of the transverse conductivity of electrons across the magnetic field reflecting the turbulence collision frequency well explains the plasma potential closer to the anode potential despite the presence of negatively biased cathodes. Eventually, this result indicates that the instability can restrict the variation of plasma potential in partially magnetized plasma.

Effects of nitrogen seeding in a tokamak plasma

The effects of nitrogen gas seeding in the edge and scrape-off layer (SOL) regions of a tokamak plasma are studied through 2D fluid simulations using the BOUT++ code. Proper account is taken of the presence of multiple charged states of nitrogen ions due to ionization, recombination, and dissociation processes, and a self-consistent study of the interaction of these ions with the turbulent plasma in the edge and SOL regions is carried out. The self-consistent model includes the effects of polarization drifts of the main plasma and impurity ions for determining the plasma vorticity. Nitrogen seeding is found to modify the turbulence as well as to influence the profiles of the equilibrium plasma density and the electron temperature. The densities of N3+ to N5+ ions are found to be relatively higher than the other charged states. This is understood and further validated by a 0D simulation. The radial profiles of these impurity ions are mapped, and their radiation energy losses are estimated. The radial profile of the radiation losses is maximum near to the edge-to-SOL transition region and becomes broader in the edge region than the SOL region.

Forward recursion approach of electromagnetic wave propagation characteristics in a slab of inhomogeneous magnetoplasma

Propagation characteristics of electromagnetic radiation incident on an inhomogeneous magnetoplasma slab near a good conducting metallic surface is investigated. The inhomogeneous plasma slab is divided into thin layers (sub-cells) in order to allow for treating each plasma sub-cell as a homogeneous medium. A global matrix is formed upon matching the fields at all interfaces, which allows for the analytical determination of the reflection, absorption and transmission coefficients. For matching the tangential fields at the metallic surface, an impedance (Leontovich) boundary condition has been used. Propagation characteristics are calculated numerically for a set of parameters that may be suitable for many applications including stealth plasma. Numerical results show resonant absorption peaks near the electron cyclotron frequency that increase by increasing the equilibrium plasma density. They also show absorption enhancement by increasing the plasma slab width.

Stabilizing effects of enhanced resistivity due to lithium-conditioning on low-n edge localized modes in NSTX

The stabilizing effects of enhanced edge resistivity on edge-localized instabilities in high confinement discharges due to lithium-conditioning in the National Spherical Torus Experiment are identified for the first time. Linear stability analysis of the experimentally constrained equilibrium suggests that the change in the equilibrium plasma density and pressure profiles alone due to lithium-conditioning may be insufficient for a complete suppression of low toroidal mode number peeling-ballooning modes. The enhanced resistivity due to the increased effective electric charge number Zeff after lithium-conditioning provides additional stabilization of the edge localized modes. Notably, this stabilizing effect by enhanced edge resistivity becomes evident only in two-fluid magnetohydrodynamic simulations.

Fluid simulation of dispersive and nondispersive ion acoustic waves in the presence of superthermal electrons

One-dimensional fluid simulation is performed for the unmagnetized plasma consisting of cold fluid ions and superthermal electrons. Such a plasma system supports the generation of ion acoustic (IA) waves. A standard Gaussian type perturbation is used in both electron and ion equilibrium densities to excite the IA waves. The evolutionary profiles of the IA waves are obtained by varying the superthermal index and the amplitude of the initial perturbation. This simulation demonstrates that the amplitude of the initial perturbation and the superthermal index play an important role in determining the time evolution and the characteristics of the generated IA waves. The initial density perturbation in the system creates charge separation that drives the finite electrostatic potential in the system. This electrostatic potential later evolves into the dispersive and nondispersive IA waves in the simulation system. The density perturbation with the amplitude smaller than 10% of the equilibrium plasma density evolves into the dispersive IA waves, whereas larger density perturbations evolve into both dispersive and nondispersive IA waves for lower and higher superthermal index. The dispersive IA waves are the IA oscillations that propagate with constant ion plasma frequency, whereas the nondispersive IA waves are the IA solitary pulses (termed as IA solitons in the stability region) that propagate with the constant wave speed. The characteristics of the stable nondispersive IA solitons are found to be consistent with the nonlinear fluid theory. To the best of our knowledge, this is the first fluid simulation study that has considered the superthermal distributions for the plasma species to model the electrostatic solitary waves.

Magnetohydrostatics of a vertical flux tube in the solar atmosphere: Coronal loops, a model of a ring flare filament

The magnetohydrostatic theory of a twisted magnetic flux tube (rope) immersed in a realistic solar atmosphere is presented in a closed analytical form for the first time. General formulas that allow the equilibrium plasma density, pressure, and temperature distributions inside an axisymmetric vertical flux tube to be calculated from its magnetic structure, which is assumed to be known (fixed), have been derived. An analytical model of the external hydrostatic medium free of a magnetic field, the solar atmosphere, where the temperature profile of the semi-empirical tabulated Avrett-Loeser model is used, has been constructed. The distribution of plasma parameters in a twisted magnetic flux tube at small deviations of its internal magnetic structure from the force-free one has been calculated as an example of applying the general theoretical formulas. Since the tube cross section does not change with height, the constructed model can be applied to describe the vertical parts of coronal loops. It has been found that the plasma density in the magnetic flux tube rises when the field twisting exceeds the force-free level and falls with decreasing field twisting compared to the force-free level. This property of a twisted magnetic flux tube is of fundamental importance for justifying the mechanism of flare energy release in magnetic flux ropes. A model of a flare in a ring chromospheric configuration is considered.

Convective laser filamentation instability in magnetized plasma

The convective amplification of filamentation instability (FI) of electromagnetic waves traveling along the density ramp of a magnetized plasma is investigated. The generalized amplification factor of the instability in the presence of a DC–magnetic field is derived by obtaining the governing equations of the instability and using the slow-coupling technique to obtain an analytical expression for the amplification factor in weakly magnetized plasma. The result shows enhancement of the convective FI gain by the magnetic field, where the enhancement is stronger for lower equilibrium plasma density values.

On blob generation mechanisms in tokamak edge plasma

The four-wave interaction technique is used to demonstrate the impact of primary electrostatic (drift wave) turbulence on the generation of large-scale electromagnetic structures (blobs). The analysis includes finite ion temperature effects and the associated diamagnetic contributions to the Reynolds stress. The impact of equilibrium plasma density variation on blob propagation is also discussed.

Excitation of wakefield in a rectangular waveguide: Comparative study with different microwave pulses

AbstractA differential equation governing the wakefield potential (φ) in a plasma filled rectangular waveguide is derived analytically. This equation is solved numerically for the wakefield (Ew) generated with the help of three kinds of microwave pulses, namely sine pulse (SP), rectangular Gaussian pulse (RGP), and rectangular triangular pulse (RTP). The effect of microwave frequency (f), pulse duration (τ), waveguide width (b), equilibrium plasma density (n0), and microwave intensity (I) on the amplitude of the wakefield is studied. This amplitude is increased for the longer pulse duration and higher microwave intensity, but is decreased with growing waveguide width for all types of pulses. With regard to the variation of wakefield amplitude with plasma density, the RTP and SP behave in a similar fashion and the RGP behaves oppositely. The amplitude for the case of RGP gets increased with the plasma density. The amplitude is enhanced at larger microwave frequency for the cases of RGP and SP, but is decreased for the case of RTP. The comparative study of three types of pulses shows that the wakefield with larger amplitude is achieved with the help of rectangular triangular pulse, which is found to be sensitive with waveguide width, pulse duration and microwave intensity.

Numerical studies on wakefield excited by Gaussian-like microwave pulse in a plasma filled waveguide

Based on a differential equation derived analytically in terms of wakefield potential ϕ MW in a plasma filled rectangular waveguide, we investigate the wakefield ( E MW ) generated with the help of Gaussian-like microwave pulse under the effect of microwave frequency ( f), pulse duration ( τ), waveguide width ( b), equilibrium plasma density ( n 0) and microwave intensity ( I). The study conducted for three cases of τ > 1/ f p , τ = 1/ f p and τ < 1/ f p , where f p is the plasma frequency, reveals that the amplitude of the wakefield is increased for the large pulse duration and higher microwave intensity but is decreased with the waveguide width and microwave frequency for all these cases. The wakefield shows stronger dependence on the microwave frequency when the microwave with larger intensity is used. The wakefield decreases at a faster rate with the waveguide width for the case of τ > 1/ f p .

Blob dynamics in an inhomogeneous plasma

Convective blob propagation in the scrape-off-layer and/or limiter shadow region is analyzed analytically and numerically with emphasis on effects of a gradient in the equilibrium plasma density. The gradient of the equilibrium plasma density is taken into account beyond the Boussineque approximation. It is shown that the vorticity modification due to the plasma density gradient leads to the acceleration for the blobs propagating into the region of lower density and de-acceleration for the blobs propagating toward the regions of higher density. Analytical estimates are corroborated by direct numerical simulations.

A1fven Eigenmodes in Spherical Tokamaks

Electromagnetic instabilities are often excited by fast super-Alfvenic ions produced by neutral beam injection (NBI) in plasmas of the spherical tokamaks START and MAST (toroidal magnetic confinement devices in which the minor a and major R0 radii of the torus are comparable, R0/a = 1.2÷1.8). These instabilities are seen as discrete weakly-damped toroidal and elliptical Alfven eigenmodes (TAEs and EAEs) with frequencies tracing in time the Alfven scaling with the equilibrium magnetic field and plasma density, or as energetic particle modes (EPMs) whose frequencies don't start from TAE-frequency and sweep down in time faster than the equilibrium parameters change. In some discharges the beam drives Alfvenic-type modes that start from the TAE frequency and sweep in both up- and down- directions. Such electromagnetic perturbations are interpreted as `hole-clump' long-living nonlinear fluctuations of the fast ion distribution function predicted by Berk-Breizman-Petviashvili [Phys. Lett. A238 (1998) 408]. It is found on both START and MAST that the Alfven instabilities weaken in their mode amplitude and in the number of unstable modes as the pressure of the thermal plasma increases, in agreement with increased thermal ion Landau damping and the pressure effect on core-localised TAEs.

Low frequency electrostatic instability in a helicon plasma

Recent discoveries in a helicon plasma show a decrease in equilibrium plasma density as magnetic field strength is increased. This can be explained in the framework of a low frequency electrostatic instability. However, quiescent plasma behavior in helicon sources has been hitherto accepted. To verify the existence of an instability, extensive measurements of fluctuating quantities and losses as a function of magnetic field were implemented. Furthermore, a theoretical model was developed to compare to the measurements. Theory and measurement show very good agreement; both verifying the existence of a low frequency instability and showing that it is indeed responsible for the observed density characteristic.