Electron Dissipation Research Articles

Whistler‐mediated magnetic reconnection in large systems: Magnetic flux pileup and the formation of thin current sheets

We compute numerical solutions of the resistive Hall MHD equations corresponding to pairwise magnetic island coalescence. The simulation results can be organized according to the relative sizes of three length scales: the electron dissipation length, ℓe; the ion inertial length, di; and the island wavelength, λ. We identify three qualitatively distinct regimes of magnetic island coalescence: (1) the resistive MHD limit, di ≲ ℓe ≪ λ; (2) the “whistler‐mediated” limit, ℓe ≪ di ≪ λ; and (3) the “whistler‐driven” limit, ℓe ≪ λ ≲ di. In the resistive MHD limit, magnetic flux piles up outside thin current sheets between the islands. The upstream Alfvén speed increases with increasing Lundquist number, and the reconnection rate is insensitive to the Lundquist number. In the whistler‐driven limit, the electron and ion bulk flows decouple on the island wavelength scale. Magnetic flux pileup does not occur, and the coalescence proceeds on a whistler timescale that is much shorter than the Alfvén time. In the whistler‐mediated limit, electron and ion bulk flows decouple in spatially localized “ion inertial sheets” around the island separatrices. Flux pileup is reduced, and the upstream Alfvén speed approaches a nearly constant value as the Lundquist number is increased. The maximum reconnection rate in the whistler‐mediated limit is comparable to that observed in the resitive MHD limit over the Lundquist number range 500 < Sλ < 10000.

The basic reality of mind and spongiform diseases

A change in handedness (chirality) in some amino acids appears to be the basic physical change in degradation-resistant proteins (prions) found in conditions such as Creutzfeldt–Jacob disease (CJD), Alzheimer's disease (AD), bovine spongiform encephalopathy (BSE) and ovine scrapie. The affected structures are primarily innervated by cholinergic nerves. Much evidence suggests that these so-called prions (here named chirons) are harmless, non-infectious products. The importance of the cholinergic system allows a new simplified interpretation of these conditions. The main steps are the acetylcholine-cholinesterase splitting of body water with release of free protons in solution, followed by electron dissipation, dioxygen activation and Ca-fluxes. Abiotic physics conserves parity and symmetry by equal amounts of L- and D-forms of molecules. In contrast, the asymmetric pattern of life must be homochiral. Such biomolecules dissolve in water and are thus able to interact in cholinergic hydrodynamics. It is supposed that the instability of the composite weak force by β-decay causes changes in chirality. These extremely rare events are not frequent enough to explain disease pathology. Experimental, accidental, surgical and abusive inoculations will propagate chirons according to the physical law of self-replication, which also occurs in test tubes without added biological products. Chirons will not be degraded into amino acids in the alimentary canal and will, because they are indigestible, leave the body with the faeces. Chirons are inert also to the immune system and will be engulfed without reaction by phagocytosing cells. They are then stored away in tissues, where they do no harm (if not detected and suspected to be deleterious, thereby causing pathogenic anxiety). The cholinergic system reacts to all kinds of integrity threats and it is this reaction which I propose causes the so-called prion diseases. This pathology seems generally valid, and is here exemplified in AD, CJD, and Kuru disease. It is the cholinergic reaction and not the agent per se that is pathogenic. This is also true of viral infections where the interaction between viral infection and response may explain the enigmatic epidemiology of many neurodegenerative diseases. Intensity and duration of challenges will determine pathophysiology. The new variant of CJD, vCJD, is assumed to result from mutation of a slow virus agent into a more intense variant, which will give disease in younger patients. The pathology is primary protonic, with overactivity in most sub-systems of either enhancing or inhibiting character, but also functional failure or cell death by membrane damage and acidification, for instance in the CNS. The practical results of this proposal will be alleviation of the current BSE crisis. The important main aspects are: chirons are not infectious proteins but inert physical by-products; they are indigestible and not immunogenic, so beef is safe; properly processed and handled meat and bone-meal are not likely to transmit neurodegenerative diseases; chirons cannot even serve as markers in neurologic diseases.

Geospace Environment Modeling magnetic reconnection challenge: Simulations with a full particle electromagnetic code

The objective of the Geospace Environment Modeling (GEM) magnetic reconnection challenge is to understand the collisionless physics that controls the rate of magnetic reconnection in a two‐dimensional configuration. The challenge involves investigating a standard model problem based on a simple Harris sheet configuration by means of a variety of physical models in order to isolate the essential physics. In the present work the challenge problem is modeled using an electromagnetic particle‐in‐cell code in which full particle dynamics are retained for both electrons and ions and Maxwell's equations are solved without approximation. The timescale for reconnection is of the order of (where Ωi is the ion cyclotron frequency based on the asymptotic field B0), and the corresponding reconnection electric field is (c/vA)Ey/B0 ∼ 0.24. The diffusion region near the neutral line is observed to develop a multiscale structure based on the electron and ion inertial lengths c/ωpe and c/ωpi. The difference between the ion and electron dynamics in the diffusion region gives rise to in‐plane (Hall) currents which produce an out‐of‐plane By field with a quadrupolar structure. In the diffusion region the magnetic field is no longer frozen‐in to the electrons; the inductive Ey field is supported primarily by the off‐diagonal electron pressure terms in the generalized Ohm's law. The reconnection rate is found to be insensitive to electron inertia effects and to the presence of a moderate out‐of‐plane initial field component B0y ≲ B0. The results are consistent with the theory that the reconnection rate is independent of the mechanism which breaks the frozen‐in condition and is controlled by dynamics at length scales much greater than the electron dissipation region.

Nonlocal transport and dissipation properties of electrons in inhomogeneous plasmas

The spatial evolution of the electron component in a neon plasma is investigated under the action of spatially inhomogeneous electric fields. In the center of the studies are those macroscopic quantities which describe the transport and the dissipation of power and momentum of the electrons. These quantities are determined from the velocity distribution function of the electrons obtained by the solution of the spatially inhomogeneous Boltzmann equation. Both a spatially limited disturbance of the field as well as a strongly modulated periodic field typical of s striations are considered. Moreover, the results of the strict kinetic treatment are compared with the corresponding ones obtained by the so-called local field approximation which corresponds to a hydrodynamic description of the electron component assuming a local compensation of power and momentum gain by the respective loss processes. The large deviation of both results from each other confirms the strongly nonlocal character of the electron transport and dissipation coefficients under the plasma conditions considered.

Electron dissipation in collisionless magnetic reconnection

A study of the electron dynamics in the dissipation region of collisionless magnetic reconnection is presented. The investigation is based on a new 2.5‐dimensional electromagnetic particle‐in‐cell simulation code. This code is applied to the problem of reconnection in two differently sized current sheets: one with a thickness of the ion inertial length and the other with electron inertial length thickness. The complete set of contributions to the reconnection electric field is calculated directly from the particle information. The two cases lead to quite different results. In the ion scale, sheet reconnection is significantly slower, and the dissipation is provided virtually exclusively by electron quasi‐viscous effects. The electron scale sheet reconnects much faster, involving a bifurcation of the reconnection region and the formation of a magnetic island. In this latter case, dissipation appears to be primarily provided by electron inertial effects and here foremost by bulk electron acceleration. Finally, an attempt to represent the effects of electron pressure‐based dissipation in a transport model is presented also.

The role of electron dissipation on the rate of collisionless magnetic reconnection

Particle simulations and analytic arguments are presented to demonstrate that the electron dissipation region, including the physics which breaks the frozen‐in condition, does not affect the rate of reconnection in collisionless plasma. The result is a general consequence of the quadratic nature of the dispersion character of whistler waves, which control the plasma dynamics at small scales. The reconnection rate is instead controlled by the dynamics at length scales much greater than the electron dissipation region.

A full wave theory of high-harmonic fast wave absorption in high-beta plasmas

A theory of fast wave absorption in a high-beta plasma is given. A reduced, second-order, ordinary differential equation has been used which includes all collisionless electron dissipation mechanisms and ion cyclotron damping over many harmonics. This is relevant to the high-harmonic fast wave heating scheme proposed by Ono [Phys. Plasmas 2, 4075 (1995)]. The parameters appropriate to the National Spherical Tokamak Experiment NSTX [J. Spitzer et al., Fusion Technol. 30, 1337 (1996)] have been used to investigate the absorption characteristics of electrons and ions under high-beta, high-harmonic conditions.

Theory of ion Bernstein wave induced shear suppression of turbulence

The theory of radio frequency induced ion Bernstein wave- (IBW) driven shear flow in the edge is examined, with the goal of application of shear suppression of fluctuations. This work is motivated by the observed confinement improvement on IBW heated tokamaks [Phys. Fluids B 5, 241 (1993)], and by previous low-frequency work on RF-driven shear flows [Phys. Rev. Lett. 67, 1535 (1991)]. It is found that the poloidal shear flow is driven electrostatically by both Reynolds stress and a direct ion momentum source, analogous to the concepts of helicity injection and electron momentum input in current drive, respectively. Flow drive by the former does not necessarily require momentum input to the plasma to induce a shear flow. For IBW, the direct ion momentum can be represented by direct electron momentum input, and a charge separation induced stress that imparts little momentum to the plasma. The derived Er profile due to IBW predominantly points inward, with little possibility of direction change, unlike low-frequency Alfvénic RF drive. The profile scale is set by the edge density gradient and electron dissipation. Due to the electrostatic nature of ion Bernstein waves, the poloidal flow contribution dominates in Er. Finally, the necessary edge power absorbed for shear suppression on Princeton Beta Experiment-Modified (PBX-M) [9th Topical Conference on Radio Frequency Power in Plasmas, Charleston, SC, 1991 (American Institute of Physics, New York, 1991), p. 129] is estimated to be 100 kW distributed over 5 cm.

Kinetic model of a decaying SF6 plasma over the temperature range 12000 K to 3000 K

A kinetic model is presented for decay of an SF6 arc plasma concerning the period when the electrons disappear (the so-called post-arc phase in SF6 circuit breaker operation). The model is based on solution of the rate equations of the 14 species chosen for the study (electrons, atomic ions, atoms, and diatomic molecules and ions). It is applied to a homogeneous medium at constant pressure in which the variation of temperature is taken as being known. The most interesting results concern electron decay and show the possibility of electron overpopulation with respect to the equilibrium composition. The departures from equilibrium remain slight and are analysed by comparing the variation rate constant of electrons with the relaxation times of the electron dissipation reactions, namely electron-ion recombination and dissociative attachment. Pressure has a strong influence on departures from equilibrium, which decreases as the pressure rises.

Theory of kinetic Alfvén wave helicity injection and current drive

Kinetic shear Alfvén wave (KSAW) helicity injection motivated by the goal of simultaneous implementation of radio frequency current and flow [Phys. Rev. Lett. 67, 1535 (1991)] drive is analyzed. The quasilinear helicity flux results in a net helicity increase only via transport through the boundaries. This, in turn, requires a compressional component at the plasma edge boundary and electron dissipation at the Alfvén resonance, as well as throughout the region, where helicity transport occurs. A comparison is made to direct KSAW current drive, which can add constructively with helicity injection by tailoring of the sign of poloidal and parallel wave numbers. The KSAW helicity flux is related to the α effect due to MHD (magnetohydrodynamic) resistive kink and shear-Alfvén-driven helicity fluxes. The helicity flux need not have a zero flux surface average. Finally, the efficiency (IpR/Pabs) of helicity injection by the KSAW is found to be significantly smaller than that by viscoresistive shear Alfvén waves, and scales as (IpR/Pabs)∼n0−3/2B03, where n0 is the density and B0 is the toroidal magnetic field. Application to edge current drive for ELM control is discussed.

Theory of shear suppression of edge turbulence by externally driven radio-frequency waves.

Here, we propose and analyze a technique for active suppression of tokamak edge turbulence. Suppression occurs due to the effects of a sheared radial electric field generated by externally driven radio-frequency waves. Plasma flow is induced by radially varying wave-driven Reynolds and magnetic stresses, and opposed by neoclassical damping. For Alfv\'enic flow drive, the predicted shear flow profile is determined by ion inertia and electron dissipation effects. Results indicate that a modest amount of absorbed power is required for edge-turbulence suppression. More generally, several novel results in the theory of momentum transport by electromagnetic fluctuations are presented.

M=1 kink mode for layer widths comparable to the ion Larmor radius

A kink-tearing eigenmode equation is derived for a slab layer geometry in the limit me/mi≪βi≪L2n/L2s (me/mi ≡mass ratio, βi≡ ion beta value, Ln ≡gradient scale length, Ls ≡shear length) and when the electron collision frequency is comparable to the eigenfrequency. It is essential for consistency to retain arbitrary ion Larmor radius effects, which are described with the use of the Padé approximation. The asymptotic solution of the inhomogeneous eigenvalue problem is obtained using simple approximations to the eigenfunction. A dispersion relation duplicates previously derived results when a Lorentzian conductivity model is used for electrons, while a new dispersion relation is obtained if electrons are described by kinetic dynamics. The dispersion relation is analytically and numerically investigated. The numerical results are compared to a more complicated and presumably more ‘‘rigorous’’ asymptotic expression. It is shown that this asymptotic expression requires quite a small value for (me/mi)βi for accuracy. A fitting formula is found that is more accurate than the asymptotic formula for moderate values of (me/mi)βi. The dissipationless dispersion relation is discussed and it is shown that local shear at the q=1 surface can have a stronger effect than the value of δŴc [the magnetohydrodynamics (MHD) energy] on the system’s stability properties. When stability is predicted, electron dissipation due to collisions or electron Landau damping destabilizes a low frequency negative energy mode that is present. Electron temperature gradients are shown to reduce Landau damping and thus decrease the destabilizing drive on the negative energy mode.

Micro-tearing stability in Tokamaks

The resonant layer equations governing tearing and micro-tearing modes in toroidal geometry are formulated and solved for a plasma in the banana regime and for wavelengths in the intermediate collisionality range nu e< omega *e< nu e/ epsilon . It is shown that stability of such tearing modes is determined by a competition between destabilizing trapped electron dissipation and stabilizing effects arising from ion magnetization and collisional broadening of the passing-electron Landau resonance. Analytic stability criteria are derived, but for realistic parameters these modes are predicted to be stable.

A model for the power dissipation in rf plasmas

An analysis is made of the relations determining the electron drift velocity in the oscillating boundary between plasma and space-charge region at the electrode surface of an rf-driven parallel-plate discharge. The resulting set of equations is solved directly to yield an expression for the rf power dissipation in the plasma. Similarly, the dissipation in the space-charge region is derived from the equations for mobility-limited and free-fall movement of positive ions to the wall. This model is applied to existing data for the electrical discharge properties in a 13.56-MHz dry etch reactor. The calculated total power dissipation is shown to agree with published transfer efficiencies for the applied rf power. It appears that the electron dissipation term is dominant at high pressure and low rf power, while the ions determine the power input at low pressure and high power. The same set of equations is used to calculate the rf current wave form, the displacement of the plasma boundary with time, and the averaged plasma density. Also here, the model is in agreement with published simulations and experimental work.

Joule heating in the photosphere and chromosphere

Joule dissipation due to the dynamo action in the solar atmosphere is proposed as a possible mechanism for heating the photosphere and chromosphere. In nonactive regions, Joule heating is distributed in both photosphere and chromosphere. The power density (ergs cm−3 s−1) produced by the Joule dissipation in the nonactive photosphere‐chromosphere regions is calculated based on a model under the average quiet Sun condition (Vernazza et al., 1981). The calculated Joule dissipation under quiet conditions exhibits a double‐peak profile within the chromosphere; one is associated with the electron dissipation at lower altitude, while the other is due to the ion dissipation at higher altitude. The energy flux produced by the Joule dissipation can be calculated by integrating the Joule power density over the height of the dissipation region. The resulting energy flux produced by the Joule dissipation in nonactive photosphere‐chromosphere regions is ∼2.4 × 107 ergs cm−2 s−1 which is more than 40 times the energy flux carried away by the high‐speed solar wind streams originating in the coronal holes. In active regions the Joule heating is predicted to be confined to the photosphere and is more than 2 orders of magnitude greater than in nonactive regions.

Electron dynamics and potential jump across slow mode shocks

In the de Hoffmann‐Teller reference frame, defined so that the bulk velocities are aligned with the magnetic field in the uniform media on either side of a shock transition, the cross‐shock electric field is simply the thermoelectric field responsible for preserving charge neutrality. As such, it gives information regarding the heating and dissipation occurring within the shock. The total cross‐shock potential can be determined by integrating a weighted electron pressure gradient through the shock, but this requires knowledge of the density and temperature profiles. Here we exploit a recently proposed alternative approach relying on particle dynamics to provide an independent estimate of this potential. We apply both determinations to slow mode shocks which form the plasma sheet boundary in the deep geomagnetic tail as observed by ISEE 3. The two methods correlate well. There is no indication of the expected transition from resistive to viscous shocks, although the highest Mach number shocks show the highest potentials. We have not found any strong dependence on the various shock parameters, but this may be due in part to the relatively uniform sample of shocks, all of which lie close to the switch‐off limit, and in part to the lack of definitive thermal ion data. We discuss the implications of these results for the electron dissipation mechanisms and turbulence at the shock.

Compressibility effects on ideal and kinetic ballooning modes and elimination of finite Larmor radius stabilization

The dynamics of ideal and kinetic ballooning modes are considered analytically including parallel ion dynamics, but without electron dissipation. For ideal modes and typical tokamak parameters, parallel dynamics predominantly determine the growth rate when β is within ∼20%–40% of the ideal threshold, resulting in a substantial reduction in growth rate. Compressibility also eliminates the stabilization effects of finite Larmor radius (FLR); FLR effects (when temperature gradients are neglected) can even increase the growth rate above the magnetohydrodynamic (MHD) value. Temperature gradients accentuate this by adding a new source of free energy independent of the MHD drive, in the region of ballooning coordinate corresponding in MHD to the continuum. Analytic dispersion relations are derived demonstrating the effects above; the formalism emphasizes the similarities between the ideal MHD and kinetic cases.

Statistical properties and correlation functions for drift waves

The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.

Dissipative trapped particle modes in tandem mirrors

Dissipative trapped particle modes are studied in tandem mirrors by including electron collisions and ion Landau damping. A variational approach is used to obtain a collisional response in terms of the collisionless result plus a collisional term. The collisional term is then self-consistently solved in all collision frequency regimes. When ν/ω≪1 (ν≡electron collision frequency) and the dissipationless mode is stable through a positive (negative) charge uncovering mechanism, there are two stable waves with phase velocities in the ion (electron) diamagnetic direction. The higher frequency wave with ω∼ω*i(ω*e) is destabilized by ion (electron) dissipation while the lower frequency wave is destabilized by electron (ion) dissipation. At high collision frequency (ν&amp;gt;ω*e), the only unstable trapped particle wave has ω∼ω*e, with electron collisions being destabilizing.

Particle simulations of ion-cyclotron turbulence in a mirror plasma

Particle–fluid hybrid simulations of electrostatic ion-cyclotron instabilities in a mirror plasma have been extended to include axial ion bouncing in a nonuniform magnetic field. This model admits unstable ion-bounce modes as well as drift-cyclotron and drift-cyclotron-loss-cone modes. Linear theory showed that ion-bounce modes were as difficult to stabilize as drift-cyclotron-loss-cone modes, but the ion-bounce modes saturated at very low levels in simulations. Simulations have also followed the self-consistent interaction of a mirror plasma with turbulent electric fields in the presence of warm plasma stream, ion drag on electrons, injection of energetic neutral beams, and transit losses. Driven by velocity diffusion due to the drift-cyclotron-loss-cone instability, the plasma evolved to a stable configuration. The wave turbulence was moderated by streaming plasma and axial electron dissipation, was insensitive to the energy width of the neutral beam, and decayed when the neutral beam was removed. The simulation results confirmed many of the predictions of quasilinear theory and theories of orbital stochasticity, and were in qualitative agreement with many (but not all) of the observations in the Lawrence Livermore National Laboratory 2XIIB experiment.