Electron Skin Depth Research Articles

Mitigation of multispecies Weibel instability in a finite non-neutral magnetized beam-plasma system.

Compressing and charge neutralization of the heavy-ion beam in an inertial fusion reactor are considered as pivotal processes for increasing the energy gain. For this purpose, the ion beam is usually transported through the plasma channel so that multispecies Weibel instability can grow in this system. Recently, a small solenoidal magnetic field has been added to this method to have additional control of these processes. On the other hand, charge and current may not be completely neutralized in this transport; as a result, the fractional charge and current neutralization can affect the growth rate of this instability. In this work, the dispersion equation has been obtained in cylindrical, cold, magnetized, non-neutral plasma in the macroscopic fluid frame. Numerical results show that if the electron cyclotron frequency of the background plasma normalized by plasma frequency is larger than the ion beam velocity normalized by the speed of light, as well as the current fraction being smaller than 1/2, the eigenmodes of multispecies Weibel instability can be completely stabilized. Moreover, these results are valid when the percent deviation from the charge-neutral state is positive. In the negative regime of percent deviation, the instability increases drastically so that the system can be completely unstable only for more than 2%. Therefore, selecting the radius of the ion beam smaller than the electron skin depth of the plasma and the beam pulse duration much longer than the plasma oscillation time are proposed for quenching of this instability.

Simulation Study of Solar Wind Interaction with Lunar Magnetic Fields

Particle-in-cell simulations were performed to understand the interaction of the solar wind with localized magnetic fields on the sunlit surface of the Moon. The results indicated a mini-magnetosphere was formed which had a thin magnetopause with the thickness of the electron skin depth. It was also found that the solar wind penetrated into the cavity of the magnetosphere intermittently rather than in a steady manner. The solar wind that moved around the magnetosphere was observed to hit the surface of the Moon, implying that it may be the cause of the lunar swirl formation on the surface.

Electron skin depth in low density plasmas

We rescale the generalized Ohm’s law and consider the limits that imply the electric field which moves with an ideal (inviscid and perfectly conducting) plasma be proportional to the time rate of change of the current density. Therefore, we show that those limits are satisfied by a sufficiently low electron number density, $n_{\text{e}}$ . We also show that the electron–ion collision frequency, $\unicode[STIX]{x1D708}_{\text{ei}}$ , is much smaller than the ion cyclotron frequency, $\unicode[STIX]{x1D714}_{\text{ci}}$ . The combination of that condition with the Lawson criterion for a typical deuterium–tritium fusion in ITER reveals a lower bound for the geometric mean of the confinement time, $\unicode[STIX]{x1D70F}_{\text{C}}$ , and collision interval, $\sqrt{\unicode[STIX]{x1D70F}_{\text{C}}/\unicode[STIX]{x1D708}_{\text{ei}}}\gg 10^{-5}~\text{s}$ . For that reaction, we estimate that $n_{\text{e}}\sim 10^{19}~\text{m}^{-3}$ , and contrast typical parameters of our fully ionized gas with those of warm, hot and thermonuclear plasmas. When, in addition, $n_{\text{e}}$ varies slowly in time and weakly in space, we generalize Alfvén’s theorem, by showing that the frozen-in condition holds true for an effective magnetic field, which depends on a finite electron skin depth. We perform a (divergenceless) helical perturbation on an axisymmetric equilibrium, to derive a dispersion relation in the cylindrical tokamak limit, and, subsequently, apply our analytical formulation to the peaked model, which assumes a logarithmic derivative profile for the poloidal component of the equilibrium magnetic field. In that formulation, the definition of the safety factor in terms of the effective field yields a shift in the magnetic surfaces. We find that the instability peak may triple that predicted on neglect of a finite electron mass. We also find that inertial effects may centuple the radius of the stable cylindrical column.

Drift-Alfvén fluctuations and transport in multiple interacting magnetized electron temperature filaments

The results of a basic electron heat transport experiment using multiple localized heat sources in close proximity and embedded in a large magnetized plasma are presented. The set-up consists of three biased probe-mounted crystal cathodes, arranged in a triangular spatial pattern, that inject low energy electrons along a strong magnetic field into a pre-existing, cold afterglow plasma, forming electron temperature filaments. When the three sources are activated and placed within a few collisionless electron skin depths of each other, a non-azimuthally symmetric wave pattern emerges due to interference of the drift-Alfvén modes that form on each filament’s temperature gradient. Enhanced cross-field transport from chaotic ( $\boldsymbol{E}\times \boldsymbol{B}$ , where $\boldsymbol{E}$ is the electric field and $\boldsymbol{B}$ the magnetic field) mixing rapidly relaxes the gradients in the inner triangular region of the filaments and leads to growth of a global nonlinear drift-Alfvén mode that is driven by the thermal gradient in the outer region of the triangle. Azimuthal flow shear arising from the emissive cathode sources modifies the linear eigenmode stability and convective pattern. A steady-current model with emissive sheath boundary predicts the plasma potential and shear flow contribution from the sources.

Relativistic Plasmoid Instability in Pair Plasmas

The problem of plasmoid instability in relativistic pair plasmas is investigated with a fluid model incorporating kinetic effects through thermal inertia, where both parallel modes and oblique modes are discussed. The dimensionless parameters, Lundquist number and electron skin depth, are found to determine the growth rate of the linear plasmoid instability as well as set the division among different parameter regimes. The onset and cascade of plasmoids are described, with two limits specified: plasmoid instability stemming from a Sweet–Parker-like steady-state current sheet, and the near-ideal limit where the current sheet breaks up on the way to a steady state. The tearing growth rate in evolving current sheets in the near-ideal regime well accounts for the sudden onset of the plasmoid instability. The regimes in between are characterized by modifications to the ideal limit, through which a continuous scaling law is established connecting the two limits. Scaling laws are obtained for the onset as well as the cascading process, and the cascade model in this paper predicts the critical parameters for the onset of plasmoid instability.

Relativistic Tearing Mode in Pair Plasmas and Application to Magnetic Giant Flares

Relativistic magnetic reconnection is an important process in plasmas where relativity enters through large magnetization and relativistic temperature, and the tearing mode plays a significant role in the initial phase of spontaneous reconnection. Starting from general steady equilibrium, parallel as well as oblique tearing modes for relativistic pair plasmas are analyzed in this paper, including resistivity and thermal inertia (the generalization of the nonrelativistic electron inertia). A dispersion relation for arbitrary values of the tearing instability index Δ' is derived, containing both the large-Δ' regime and the small-Δ' regime, where the different limits are discussed with their implications for the tearing mode growth rate. It is found that in relativistic tearing mode, the parallel Lundquist number, electron skin-depth, and α that encodes the structure of the resonant surface all play roles in determining the tearing growth rate, where the parallel Lundquist number is defined with respect to the parallel magnetization σ∥ as well as the perpendicular magnetization σ⊥, and the electron skin-depth assumes the relativistic form for pair plasmas. These results hold for both pressure balance and force-free equilibrium. As an application, tearing instability is hypothesized as a possible mechanism for triggering fast gamma-ray burst. This work is important for understanding tearing modes in relativistic pair plasmas, and it serves as a basis for an analysis of relativistic plasmoid instability and relevant problems.

Whistler wave propagation and interplay between electron inertia and Larmor radius effects

The influence of Larmor radius effects on the propagation of whistler waves is investigated experimentally in laboratory plasma. The waves are excited using a loop antenna of diameter less than the electron skin depth, the natural scale length in this regime. In an earlier experiment [G. Joshi et al., Phys. Plasmas 24, 122110 (2017)], it was shown that such waves assume an elongated shape with perpendicular dimensions of the order of skin depth. In the present work, we show that wave propagation is significantly modified when the external guiding magnetic field is decreased. The wave spreads in the perpendicular direction in spite of starting of as an elongated whistler due to electron inertia effects. In the near region, the antenna field becomes dominant even forming null points, with the physical processes taking shape and wave still being guided by the net background magnetic field. However, the feeble external magnetic field in the region away from the antenna is unable to guide the wave any further and the wave spreads. In spite of a large current pulse, the wave remains linear (ΔB/B0 ≤ 1). The observed results are attributed to the interplay between electron inertia and finite Larmor radius effects and are explained in terms of a modified physical model.

Oblique instability and electron acceleration in relativistic unmagnetized cloud-plasma interaction

Relativistic unmagnetized cloud-plasma interaction is analyzed by performing linear analysis and particle-in-cell simulation. This course consists of an electron-ion cloud injected into a stationary ambient plasma and has long been a favorite topic in laboratory and space plasmas. An oblique electromagnetic instability dominates the unstable spectrum. In the interaction with the generated electromagnetic fields, the cloud electrons are entirely mixed with the ambient ones and form a hot electron population. The velocity of the cloud ions, however, has not changed significantly from the initial bulk velocity. As this ion cloud propagates into the plasma, it derives an electrostatic field which can accelerate the electrons up to energy equipartition between electrons and ions. The electrostatic field is amplified at the expense of the kinetic energy of ions, and its spatial scale is on the order of the electron skin depth. The electron acceleration in such an electrostatic field is, therefore, a likely process for pre-acceleration of electrons in unmagnetized plasmas.

On annihilation of the relativistic electron vortex pair in collisionless plasmas

In contrast to hydrodynamic vortices, vortices in a plasma contain an electric current circulating around the centre of the vortex, which generates a magnetic field localized inside. Using computer simulations, we demonstrate that the magnetic field associated with the vortex gives rise to a mechanism of dissipation of the vortex pair in a collisionless plasma, leading to fast annihilation of the magnetic field with its energy transforming into the energy of fast electrons, secondary vortices and plasma waves. Two major contributors to the energy damping of a double vortex system, namely, magnetic field annihilation and secondary vortex formation, are regulated by the size of the vortex with respect to the electron skin depth, which scales with the electron$\unicode[STIX]{x1D6FE}$factor,$\unicode[STIX]{x1D6FE}_{e}$, as$R/d_{e}\propto \unicode[STIX]{x1D6FE}_{e}^{1/2}$. Magnetic field annihilation appears to be dominant in mildly relativistic vortices, while for the ultrarelativistic case, secondary vortex formation is the main channel for damping of the initial double vortex system.

Turbulence in Magnetized Pair Plasmas

Abstract Alfvénic-type turbulence in strongly magnetized, low-beta pair plasmas is investigated. A coupled set of equations for the evolution of the magnetic and flow potentials are derived, covering both fluid and kinetic scales. In the fluid (magnetohydrodynamic) range those equations are the same as for electron–ion plasmas, so turbulence at those scales is expected to be of the Alfvénic nature, exhibiting critical balance, dynamic alignment, and transition to a tearing-mediated regime at small scales. The critical scale at which a transition to a tearing-mediated range occurs is derived, and the spectral slope in that range is predicted to be (or , depending on details of the reconnecting configuration assumed). At scales below the electron (and positron) skin depth, it is argued that turbulence is dictated by a cascade of the inertial Alfvén wave, which we show to result in the magnetic energy spectrum .

Normal modes in magnetized two-fluid spin quantum plasmas

We extend the classical two-fluid magnetohydrodynamic (MHD) formalism to include quantum effects such as electron Fermi pressure, Bohm pressure and spin couplings. At scales smaller than the electron skin-depth, the Hall effect and electron inertia must be taken into account, and can overlap with the quantum effects. We write down the full set of two-fluid quantum MHD (QMHD) and analyze the relative importance ofthese effects in the high density environments of neutron star atmospheres and white dwarf interiors, finding that for a broad range of parameters all these effects are operative. Of all spin interactions we analyze only the spin-magnetic coupling, as it is linear in $\hbar$ and consequently it is the strongest spin effect. We re-obtain the classical two-fluid MHD dispersion relations corresponding to the magnetosonic and Alfv\'en modes, modified by quantum effects. In the zero-spin case, for propagation parallel to the magnetic field, we find that the frequency of the fast mode is due to quantum effects modified by electron inertia, while the frequency of the Alfv\'en-slow sector has no quantum corrections. For perpendicular propagation, the fast-mode frequency is the same as for the parallel propagation plus a correction due only to classical two-fluid effects. When spin is considered, a whistler mode appears, which is due to two-fluid spin-magnetic interaction. There are no modifications due to spin for parallel propagation of magnetosonic and Alfv\'en waves, while for perpendicular prop agation a dispersive term due to spin arises in the two-fluid expression for the fast magnetosonic mode.

The Role of the Parallel Electric Field in Electron‐Scale Dissipation at Reconnecting Currents in the Magnetosheath

AbstractWe report observations from the Magnetospheric Multiscale satellites of reconnecting current sheets in the magnetosheath over a range of out‐of‐plane “guide” magnetic field strengths. The currents exhibit nonideal energy conversion in the electron frame of reference, and the events are within the ion diffusion region within close proximity (a few electron skin depths) to the electron diffusion region. The study focuses on energy conversion on the electron scale only. At low guide field (antiparallel reconnection), electric fields and currents perpendicular to the magnetic field dominate the energy conversion. Additionally, electron distributions exhibit significant nongyrotropy. As the guide field increases, the electric field parallel to the background magnetic field becomes increasingly strong, and the electron nongyrotropy becomes less apparent. We find that even with a guide field less than half the reconnecting field, the parallel electric field and currents dominate the dissipation. This suggests that parallel electric fields are more important to energy conversion in reconnection than previously thought and that at high guide field, the physics governing magnetic reconnection are significantly different from antiparallel reconnection.

Direction of cascades in a magnetofluid model with electron skin depth and ion sound Larmor radius scales

The direction of cascades in a two-dimensional model that takes electron inertia and ion sound Larmor radius into account is studied, resulting in analytical expressions for the absolute equilibrium states of the energy and helicities. These states suggest that typically both the energy and magnetic helicity at scales shorter than the electron skin depth have a direct cascade, while at large scales the helicity has an inverse cascade as established earlier for reduced magnetohydrodynamics (MHD). The calculations imply that the introduction of gyro-effects allows for the existence of negative temperature (conjugate to energy) states and the condensation of energy to the large scales. Comparisons between two- and three-dimensional extended MHD models (MHD with two-fluid effects) show qualitative agreement between the two.

Gyrofluid modeling and phenomenology of low-βe Alfvén wave turbulence

A two-field reduced gyrofluid model including electron inertia, ion finite Larmor radius corrections, and parallel magnetic field fluctuations is derived from the model of Brizard [Brizard, Phys. Fluids B 4, 1213 (1992)]. It assumes low βe, where βe indicates the ratio between the equilibrium electron pressure and the magnetic pressure exerted by a strong uniform magnetic guide field, but permits an arbitrary ion-to-electron equilibrium temperature ratio. It is shown to have a noncanonical Hamiltonian structure and provides a convenient framework for studying kinetic Alfvén wave turbulence, from magnetohydrodynamics to sub-de scales (where de holds for the electron skin depth). Magnetic energy spectra are phenomenologically determined within energy and generalized cross-helicity cascades in the perpendicular spectral plane. Arguments based on absolute statistical equilibria are used to predict the direction of the transfers, pointing out that, within the sub-ion range, the generalized cross-helicity could display an inverse cascade if injected at small scales, for example by reconnection processes.

Merger and reconnection of Weibel separated relativistic electron beam

The relativistic electron beam (REB) propagation in a plasma is fraught with beam plasma instabilities. The prominent amongst them is the collisionless Weibel destabilization which spatially separates the forward propagating REB and the return shielding currents. This results in the formation of REB current filaments which are typically of the size of electron skin depth during the linear stage of the instability. It has been observed that in the nonlinear stage, the size of filaments increases as they merge with each other. With the help of 2-D particle-in-cell simulations in the plane perpendicular to the REB propagation, it is shown that these mergers occur in two distinct nonlinear phases. In the first phase, the total magnetic energy increases. Subsequently, however, during the second phase, one observes a reduction in magnetic energy. It is shown that the transition from one nonlinear regime to another occurs when the typical current associated with individual filaments hits the Alfvén threshold. In the second nonlinear regime, therefore, the filaments can no longer permit any increase in current. Magnetic reconnection events then dissipate the excess current (and its associated magnetic energy) that would result from a merger process leading to the generation of energetic electron jets in the perpendicular plane. At later times when there are only few filaments left, the individual reconnection events can be clearly identified. It is observed that in between such events, the magnetic energy remains constant and shows a sudden drop as and when two filaments merge. The electron jets released in these reconnection events are thus responsible for the transverse heating which has been mentioned in some previous studies [Honda et al., Phys. Plasmas 7, 1302 (2000)].

Rayleigh-Taylor Instability with Finite Skin Depth

In this work, the Rayleigh-Taylor instability is addressed in a viscous-resistive current slab, by assuming a finite electron skin depth. The formulation is developed on the basis of an extended form of Ohm’s law, which includes a term proportional to the explicit time derivative of the current density. In the neighborhood of the rational surface, a viscous-resistive boundary-layer is defined in terms of a resistive and a viscous boundary layers. As expected, when viscous effects are negligible, it is shown that the viscous-resistive boundary-layer is given by the resistive boundary-layer. However, when viscous effects become important, it is found that the viscous-resistive boundary-layer is given by the geometric mean of the resistive and viscous boundary-layers. Scaling laws of the time growth rate of the Rayleigh-Taylor instability with the plasma resistivity, fluid viscosity, and electron number density are discussed.

Nonlinear saturation of the Weibel instability

The growth and saturation of magnetic fields due to the Weibel instability (WI) have important implications for laboratory and astrophysical plasmas, and this has drawn significant interest recently. Since the WI can generate a large magnetic field from no initial field, the maximum magnitudes achieved can have significant consequences for a number of applications. Hence, an understanding of the detailed dynamics driving the nonlinear saturation of the WI is important. This work considers the nonlinear saturation of the WI when counter-streaming populations of initially unmagnetized electrons are perturbed by a magnetic field oriented perpendicular to the direction of streaming. Previous works have found magnetic trapping to be important [Davidson et al., Phys. Fluids 15, 317 (1972)] and connected electron skin depth spatial scales to the nonlinear saturation of the WI [Califano et al., Phys. Rev. E 57, 7048 (1998)]. The results presented in this work are consistent with these findings for a high-temperature case. However, using a high-order continuum kinetic simulation tool, this work demonstrates that when the electron populations are colder, a significant electrostatic potential develops that works with the magnetic field to create potential wells. The electrostatic field develops due to transverse flows induced by the WI and in some cases is strengthened by a secondary instability. This field plays a key role in saturation of the WI for colder populations. The role of the electrostatic potential in Weibel instability saturation has not been studied in detail previously.

A conservative scheme of drift kinetic electrons for gyrokinetic simulation of kinetic-MHD processes in toroidal plasmas

A conservative scheme of drift kinetic electrons for gyrokinetic simulations of kinetic-magnetohydrodynamic processes in toroidal plasmas has been formulated and verified. Both vector potential and electron perturbed distribution function are decomposed into adiabatic part with analytic solution and non-adiabatic part solved numerically. The adiabatic parallel electric field is solved directly from the electron adiabatic response, resulting in a high degree of accuracy. The consistency between electrostatic potential and parallel vector potential is enforced by using the electron continuity equation. Since particles are only used to calculate the non-adiabatic response, which is used to calculate the non-adiabatic vector potential through Ohm's law, the conservative scheme minimizes the electron particle noise and mitigates the cancellation problem. Linear dispersion relations of the kinetic Alfvén wave and the collisionless tearing mode in cylindrical geometry have been verified in gyrokinetic toroidal code simulations, which show that the perpendicular grid size can be larger than the electron collisionless skin depth when the mode wavelength is longer than the electron skin depth.

Electrostatic and magnetic instabilities in the transition layer of a collisionless weakly relativistic pair shock

Energetic electromagnetic emissions by astrophysical jets like those that are launched during the collapse of a massive star and trigger gamma-ray bursts (GRBs) are partially attributed to relativistic internal shocks. The shocks are mediated in the collisionless plasma of such jets by the filamentation instability of counterstreaming particle beams. The filamentation instability grows fastest only if the beams move at a relativistic relative speed. We model here with a particle-in-cell (PIC) simulation the collision of two cold pair clouds at the speed c/2 (c: speed of light). We demonstrate that the two-stream instability outgrows the filamentation instability for this speed and is thus responsible for the shock formation. The incomplete thermalization of the upstream plasma by its quasi-electrostatic waves allows other instabilities to grow. A shock transition layer forms, in which a filamentation instability modulates the plasma far upstream of the shock. The inflowing upstream plasma is progressively heated by a two-stream instability closer to the shock and compressed to the expected downstream density by the Weibel instability. The strong magnetic field due to the latter is confined to a layer 10 electron skin depths wide.

Electron inertia and quasi-neutrality in the Weibel instability

While electron kinetic effects are well known to be of fundamental importance in several situations, the electron mean-flow inertia is often neglected when length scales below the electron skin depth become irrelevant. This has led to the formulation of different reduced models, where electron inertia terms are discarded while retaining some or all kinetic effects. Upon considering general full-orbit particle trajectories, this paper compares the dispersion relations emerging from such models in the case of the Weibel instability. As a result, the question of how length scales below the electron skin depth can be neglected in a kinetic treatment emerges as an unsolved problem, since all current theories suffer from drawbacks of different nature. Alternatively, we discuss fully kinetic theories that remove all these drawbacks by restricting to frequencies well below the plasma frequency of both ions and electrons. By giving up on the length scale restrictions appearing in previous works, these models are obtained by assuming quasi-neutrality in the full Vlasov–Maxwell system.