Equilibrium Electron Temperature Research Articles

Detecting neoclassical tearing modes in high-temperature ITER plasma scenarios with the ITER prototype electron cyclotron emission diagnostic

Abstract Electron cyclotron emission (ECE) diagnostics for ITER serve two key purposes. The diagnostics will measure plasma electron temperature with high spatial and temporal resolution. Additionally, they will be used to detect neoclassical tearing modes (NTMs), a deleterious and nonlinearly unstable mode causing the growth of magnetic ‘seed’ islands. Interpreting ECE requires anticipation of physical limits including frequency cut-offs and harmonic overlap. In high temperature plasmas, the relativistic shift and broadening of the emission must also be considered to accurately reconstruct the electron temperature spatial profile. Accounting for these effects allows ECE diagnostics to be used for accurate measurement of the equilibrium electron temperature profile, as well as fluctuations about this equilibrium. One such fluctuation is caused by the fast radial transport of heat across rotating magnetic islands. ECE diagnostics can detect this change as an oscillation at the plasma rotation frequency to determine the existence and location of NTMs. This paper presents work on a synthetic diagnostic for ECE. The synthetic diagnostic tests simulated ECE signals, which are inferred from ITER scenarios perturbed by magnetic islands after accounting for all ECE physics. The synthetic diagnostic tests conventional ECE detection algorithms for NTMs in real-time on ITER-recommended hardware. Combined, these two areas of focus help determine design of the ECE system.

Gyrofluid analysis of electron β e effects on collisionless reconnection

The linear and nonlinear evolutions of the tearing instability in a collisionless plasma with a strong guide field are analysed on the basis of a two-field Hamiltonian gyrofluid model. The model is valid for a low ion temperature and a finite $\beta _e$ . The finite $\beta _e$ effect implies a magnetic perturbation along the guide field direction, and electron finite Larmor radius effects. A Hamiltonian derivation of the model is presented. A new dispersion relation of the tearing instability is derived for the case $\beta _e=0$ and tested against numerical simulations. For $\beta _e \ll 1$ the equilibrium electron temperature is seen to enhance the linear growth rate, whereas we observe a stabilizing role when electron finite Larmor radius effects become more relevant. In the nonlinear phase, stall phases and faster than exponential phases are observed, similarly to what occurs in the presence of ion finite Larmor radius effects. Energy transfers are analysed and the conservation laws associated with the Casimir invariants of the model are also discussed. Numerical simulations seem to indicate that finite $\beta _e$ effects do not produce qualitative modifications in the structures of the Lagrangian invariants associated with Casimirs of the model.

On the switching current and the re-trapping current of tungsten nanowires fabricated by Focussed Ion Beam (FIB) technique

We report the superconducting properties of the tungsten (W) nanowires fabricated using focussed ion beam (FIB) technique having different wire widths of ∼120 nm and ∼290 nm. The transport properties of these wires were measured down to a temperature of 20 mK in a dilution refrigerator. We observed hysteretic current- voltage characteristics (IVCs) as a function of temperature, wherein the extend of hysteresis (difference between switching current and re-trapping current) is larger at lower temperature and diminishes near to the transition temperature. The temperature dependence of the switching current and re-trapping current were analysed using conventional models and found out to be of reasonable agreement with the models invoked. The re-trapping current agrees well with the thermal model incorporating phonon contribution in the heat dissipation process along with the electronic contribution. The equilibrium electron temperature calculated using the heat dissipation models at the critical current of the wires agrees well with respect to the transition temperature of the wire having a larger width, while for the wire of lower width, it is slightly elevated. Based on the analysis, it is believed that heat dissipation primarily because of Joule heating is the cause of the hysteretic current voltage characteristics of the nanowires.

Impact of electron temperature anisotropy on the collisionless tearing mode instability in the presence of a strong guide field

We derive and analyze a dispersion relation for the growth rate of collisionless tearing modes, driven by electron inertia and accounting for equilibrium electron temperature anisotropy in a strong guide field regime. For this purpose, a new gyrofluid model is derived and subsequently simplified to make the derivation of the dispersion relation treatable analytically. The main simplifying assumptions consist in assuming cold ions, neglecting electron finite Larmor radius effects, decoupling ion gyrocenter fluctuations, and considering β⊥e≪1, with β⊥e indicating the ratio between the perpendicular electron thermal pressure and the magnetic pressure exerted by the guide field. This simplified version of the gyrofluid model is shown to possess a noncanonical Hamiltonian structure. The dispersion relation is obtained by applying the theory of asymptotic matching and does not predict an enhancement of the growth rate as the ratio Θe between perpendicular and parallel equilibrium electron temperatures increases. This indicates a significant difference with respect to the case of absent or moderate guide field. For an equilibrium magnetic shear length of the order of the perpendicular sonic Larmor radius and at a fixed β⊥e, we obtain that the tearing mode in the strong guide field regime gets actually weakly damped, as Θe increases. In the isotropic limit Θe=1, the dispersion relation reduces to a previously known formula. The analytical predictions are tested against numerical simulations, showing a very good quantitative agreement. We also provide a detailed discussion of the range of validity of the derived dispersion relation and of the compatibility among the different adopted assumptions.

Toroidal and slab ETG instability dominance in the linear spectrum of JET-ILW pedestals

Local linear gyrokinetic simulations show that electron temperature gradient (ETG) instabilities are the fastest growing modes for in the steep gradient region for a JET pedestal discharge (92174) where the electron temperature gradient is steeper than the ion temperature gradient. Here, ky is the wavenumber in the direction perpendicular to both the magnetic field and the radial direction, and ρi is the ion gyroradius. At , the fastest growing mode is often a novel type of toroidal ETG instability. This toroidal ETG mode is driven at scales as large as and at a sufficiently large radial wavenumber that electron finite Larmor radius effects become important; that is, , where Kx is the effective radial wavenumber. Here, ρe is the electron gyroradius, R0 is the major radius of the last closed flux surface, and 1/LTe is an inverse length proportional to the logarithmic gradient of the equilibrium electron temperature. The fastest growing toroidal ETG modes are often driven far away from the outboard midplane. In this equilibrium, ion temperature gradient instability is subdominant at all scales and kinetic ballooning modes are shown to be suppressed by shear. ETG modes are very resilient to shear. Heuristic quasilinear arguments suggest that the novel toroidal ETG instability is important for transport.

Linear stability of magnetic vortex chains in a plasma in the presence of equilibrium electron temperature anisotropy

The linear stability of chains of magnetic vortices in a plasma is investigated analytically in two dimensions by means of a reduced fluid model assuming a strong guide field and accounting for equilibrium electron temperature anisotropy. The chain of magnetic vortices is modeled by means of the classical ‘cat’s eyes’ solutions and the linear stability is studied by analysing the second variation of a conserved functional, according to the energy-Casimir method. The stability analysis is carried out on the domain bounded by the separatrices of the vortices. Two cases are considered, corresponding to a ratio between perpendicular equilibrium ion and electron temperature much greater or much less than unity, respectively. In the former case, equilibrium flows depend on an arbitrary function. Stability is attained if the equilibrium electron temperature anisotropy is bounded from above and from below, with the lower bound corresponding to the condition preventing the firehose instability. A further condition sets an upper limit to the amplitude of the vortices, for a given choice of the equilibrium flow. For cold ions, two sub-cases have to be considered. In the first one, equilibria correspond to those for which the velocity field is proportional to the local Alfvén velocity. Stability conditions imply: an upper limit on the amplitude of the flow, which automatically implies firehose stability, an upper bound on the electron temperature anisotropy and again an upper bound on the size of the vortices. The second sub-case refers to equilibrium electrostatic potentials which are not constant on magnetic flux surfaces and the resulting stability conditions correspond to those of the first sub-case in the absence of flow.

Asymmetry effects driving secondary instabilities in two-dimensional collisionless magnetic reconnection

In the framework of the studies on magnetic reconnection, much interest has been recently devoted to asymmetric magnetic configurations, which can naturally be found in solar and astrophysical environments and in laboratory plasmas. Several aspects of this problem have been investigated, mainly in a two-dimensional geometry and by means of particle-in-cell (PIC) simulations. Still, there are open questions concerning the onset and the effects of secondary instabilities in the nonlinear phase of an asymmetric reconnection process. In this work, we focus on the conditions that lead to the appearance of the Kelvin-Helmholtz instability following an asymmetric reconnection event in a collisionless plasma. This investigation is carried out by means of two-dimensional numerical simulations based on a reduced fluid model assuming a strong guide field. We show that, unlike the symmetric case, in the presence of asymmetry, a Kelvin-Helmholtz-like instability can develop also for a finite equilibrium electron temperature. In particular, simulations indicate the formation of steep velocity gradients, which drive the instability, when the resonant surface of the equilibrium magnetic field is located sufficiently far from the peak of the equilibrium current density. Moreover, a qualitative analysis of the vorticity dynamics shows that the turbulent behavior induced by the secondary instability not only is confined inside the island but can also affect the plasma outside the separatrices. The comparison between simulations carried out with an adiabatic closure and a Landau-fluid closure for the electron fluid indicates that the latter inhibits the secondary instability by smoothing velocity gradients.

Hamiltonian gyrofluid reductions of gyrokinetic equations

We provide a general framework for deriving Hamiltonian electromagnetic gyrofluid models from a Hamiltonian system of gyrokinetic equations. The presented procedure permits to derive gyrofluid models for an arbitrary number of moments with respect to the velocity coordinate parallel to an equilibrium magnetic field. The resulting gyrofluid models account, in particular, for finite Larmor radius effects, equilibrium temperature anisotropies and fluctuations of the magnetic field in the direction parallel to the equilibrium magnetic field, thus generalizing Hamiltonian gyrofluid models previously presented in the literature. The Hamiltonian reduction procedure leading from the parent gyrokinetic model to the gyrofluid models is formulated in two stages. In the first step, after having shown that the parent gyrokinetic system indeed posseses a Hamiltonian structure, a Hamiltonian system is derived, by means of a Poisson sub-algebra argument, which describes the evolution of the perturbation of the gyrocenter distribution function, averaged with respect to the magnetic moment coordinate. The second stage brings from the latter model to the gyrofluid models by means of a closure relation, applicable at an arbitrary order in the moment hierarchy, which guarantees the preservation of a Hamiltonian structure. Casimir invariants of the noncanonical Poisson brackets of the gyrofluid models are provided. It is also shown how, in the two-dimensional limit, the gyrofluid model equations can be cast in the form of advection equations for Lagrangian invariants transported by generalized incompressible velocity fields, thus extending results obtained for previous Hamiltonian gyrofluid and drift-fluid models. The Hamiltonian reduction procedure is applied to derive a five-field gyrofluid model evolving the first two moments for the electron species and the first three moments for the ion species. The Casimir invariants and the Lagrangian advection formulation are provided explicitly for the five-field model. Remarks concerning possible variants of the procedure are discussed. As an example, it is shown how, by means of a variant of the procedure, it is possible to derive an isothermal two-field model for kinetic Alfvén waves including equilibrium electron temperature anisotropy effects.

Solitary waves with electron temperature inhomogeniety and shear flow in an electron ion magnetoplasma

Electron temperature gradient (ETG) driven solitons are investigated having gradients in equilibrium electron temperature and equilibrium number density and with electron shear flow. In a linear regime, using model equations, a linear dispersion relation has been analysed analytically as well as numerically. ηe and electron to ion temperature ratio effects, real frequency, and growth rate of ETG instability are determined. In the nonlinear regime, the Korteweg--de Vries equation for the ETG mode has been derived and analysed numerically which shows that it admits solitary wave solutions. It can also be noted that soliton amplitude is sensitive to ηe, the magnetic field, and the temperature ratio. This work may be helpful for low frequency electrostatic modes in nonuniform electron-ion plasma having gradients in density and electron temperature and also in tokamak plasma.

Plasma instability of magnetically enhanced vacuum arc thruster

A two-fluid flowing plasma model is applied to describe the plasma rotation and resulted instability evolution in magnetically enhanced vacuum arc thruster (MEVAT). Typical experimental parameters are employed, including plasma density, equilibrium magnetic field, ion and electron temperatures, cathode materials, axial streaming velocity, and azimuthal rotation frequency. It is found that the growth rate of plasma instability increases with growing rotation frequency and field strength, and with descending electron temperature and atomic weight, for which the underlying physics are explained. The radial structure of density fluctuation is compared with that of equilibrium density gradient, and the radial locations of their peak magnitudes are very close, implying that the mode may be driven by density gradient. Temporal evolution of perturbed mass flow in the cross section of plasma column is also presented, which behaves in the form of clockwise rotation (direction of electron diamagnetic drift) at edge and anti-clockwise rotation (direction of ion diamagnetic drift) in the core, separated by a mode transition layer from n = 0 to n = 1. This work, to our best knowledge, is the first treatment of plasma instability caused by rotation and axial flow in MEVAT, and is also of great practical interest for other electric thrusters where rotating plasma is concerned for long-time stable operation and propulsion efficiency optimization.

Understanding the impact of insulating and conducting endplate boundary conditions on turbulence in CSDX through nonlocal simulations

The Controlled Shear Decorrelation Experiment (CSDX) linear plasma device provides a unique platform for investigating the underlying physics of self-regulating drift-wave turbulence/zonal flow dynamics. A minimal model of 3D drift-reduced nonlocal cold ion fluid equations which evolves density, vorticity, and electron temperature fluctuations, with proper sheath boundary conditions, is used to simulate dynamics of the turbulence in CSDX and its response to changes in parallel boundary conditions. These simulations are carried out using the BOUndary Turbulence (BOUT++) framework and use equilibrium electron density and temperature profiles taken from experimental measurements. The results show that density gradient-driven drift-waves are the dominant instability in CSDX. However, the choice of insulating or conducting endplate boundary conditions affects the linear growth rates and energy balance of the system due to the absence or addition of Kelvin-Helmholtz modes generated by the sheath-driven equilibrium E × B shear and sheath-driven temperature gradient instability. Moreover, nonlinear simulation results show that the boundary conditions impact the turbulence structure and zonal flow formation, resulting in less broadband (more quasi-coherent) turbulence and weaker zonal flow in conducting boundary condition case. These results are qualitatively consistent with earlier experimental observations.

Determination of equilibrium electron temperature and times using an electron swarm model with BOLSIG+ calculated collision frequencies and rate coefficients

AbstractElectromagnetic pulse (EMP) events produce low‐energy conduction electrons from Compton electron or photoelectron ionizations with air. It is important to understand how conduction electrons interact with air in order to accurately predict EMP evolution and propagation. An electron swarm model can be used to monitor the time evolution of conduction electrons in an environment characterized by electric field and pressure. Here a swarm model is developed that is based on the coupled ordinary differential equations (ODEs) described by Higgins et al. (1973), hereinafter HLO. The ODEs characterize the swarm electric field, electron temperature, electron number density, and drift velocity. Important swarm parameters, the momentum transfer collision frequency, energy transfer collision frequency, and ionization rate, are calculated and compared to the previously reported fitted functions given in HLO. These swarm parameters are found using BOLSIG+, a two term Boltzmann solver developed by Hagelaar and Pitchford (2005), which utilizes updated cross sections from the LXcat website created by Pancheshnyi et al. (2012). We validate the swarm model by comparing to experimental effective ionization coefficient data in Dutton (1975) and drift velocity data in Ruiz‐Vargas et al. (2010). In addition, we report on electron equilibrium temperatures and times for a uniform electric field of 1 StatV/cm for atmospheric heights from 0 to 40 km. It is shown that the equilibrium temperature and time are sensitive to the modifications in the collision frequencies and ionization rate based on the updated electron interaction cross sections.

Design and initial operation of a two-color soft x-ray camera system on the Compact Toroidal Hybrid experiment.

A multi-camera soft x-ray diagnostic has been developed to measure the equilibrium electron temperature profile and temperature fluctuations due to magnetohydrodynamic activity on the Compact Toroidal Hybrid experiment. The diagnostic consists of three separate cameras each employing two 20-channel diode arrays that view the same plasma region through different beryllium filter thicknesses of 1.8 μm and 3.0 μm allowing electron temperature measurements between 50 eV and 200 eV. The Compact Toroidal Hybrid is a five-field period current-carrying stellarator, in which the presence of plasma current strongly modifies the rotational transform and degree of asymmetry of the equilibrium. Details of the soft x-ray emission, effects of plasma asymmetry, and impurity line radiation on the design and measurement of the two-color diagnostic are discussed. Preliminary estimates of the temperature perturbation due to sawtooth oscillations observed in these hybrid discharges are given.

Modelling Spectral and Timing Properties of Accreting Black Holes: The Hybrid Hot Flow Paradigm

The general picture that emerged by the end of 1990s from a large set of optical and X-ray, spectral and timing data was that the X-rays are produced in the innermost hot part of the accretion flow, while the optical/infrared (OIR) emission is mainly produced by the irradiated outer thin accretion disc. Recent multiwavelength observations of Galactic black hole transients show that the situation is not so simple. Fast variability in the OIR band, OIR excesses above the thermal emission and a complicated interplay between the X-ray and the OIR light curves imply that the OIR emitting region is much more compact. One of the popular hypotheses is that the jet contributes to the OIR emission and even is responsible for the bulk of the X-rays. However, this scenario is largely ad hoc and is in contradiction with many previously established facts. Alternatively, the hot accretion flow, known to be consistent with the X-ray spectral and timing data, is also a viable candidate to produce the OIR radiation. The hot-flow scenario naturally explains the power-law like OIR spectra, fast OIR variability and its complex relation to the X-rays if the hot flow contains non-thermal electrons (even in energetically negligible quantities), which are required by the presence of the MeV tail in Cyg X-1. The presence of non-thermal electrons also lowers the equilibrium electron temperature in the hot flow model to ≲100 keV, making it more consistent with observations. Here we argue that any viable model should simultaneously explain a large set of spectral and timing data and show that the hybrid (thermal/non-thermal) hot flow model satisfies most of the constraints.

MEASURING NEBULAR TEMPERATURES: THE EFFECT OF NEW COLLISION STRENGTHS WITH EQUILIBRIUM AND κ-DISTRIBUTED ELECTRON ENERGIES

In this paper we develop tools for observers to use when analysing nebular spectra for temperatures and metallicities, with two goals: to present a new, simple method to calculate equilibrium electron temperatures for collisionally excited line flux ratios, using the latest atomic data; and to adapt current methods to include the effects of possible non-equilibrium '{\kappa}' electron energy distributions. Adopting recent collision strength data for [O iii], [S iii], [O ii], [S ii], and [N ii], we find that existing methods based on older atomic data seriously overestimate the electron temperatures, even when considering purely Maxwellian statistics. If {\kappa} distributions exist in H ii regions and planetary nebulae as they do in solar system plasmas, it is important to investigate the observational consequences. This paper continues our previous work on the {\kappa} distribution (Nicholls et al. 2012). We present simple formulaic methods that allow observers to (a) measure equilibrium electron temperatures and atomic abundances using the latest atomic data, and (b) to apply simple corrections to existing equilibrium analysis techniques to allow for possible non-equilibrium effects. These tools should lead to better consistency in temperature and abundance measurements, and a clearer understanding of the physics of H ii regions and planetary nebulae.

Amplitude modulated drift wave packets in a nonuniform magnetoplasma

We consider the amplitude modulation of low-frequency, long wavelength electrostatic drift wave packets in a nonuniform magnetoplasma with the effects of equilibrium density, electron temperature and magnetic field inhomogeneities. The dynamics of the modulated drift wave packet is governed by a nonlinear Schrödinger equation. The latter is used to study the modulational instability of a Stokeʼs wave train to a small longitudinal perturbation. It is shown that the drift wave packet is stable (unstable) against the modulation when the drift wave number lies in 0<k<1/2 (1/2<k<1). Thus, the modulated drift wave packet can propagate in the form of bright and dark envelope solitons or as a drift wave rogon.

Investigation of the breakdown temperature in capillary discharge plasmas

We developed a simple way to estimate the breakdown temperature T b of plasma electrons in a capillary, which is based on measurement of the electrical breakdown voltage V b . The result shows that the breakdown temperature T b decreases with increasing pressure. The thermal equilibrium electron temperature T e in the capillary plasma after the electrical discharge is also measured by using the optical emission spectroscopy method.

ON THE ORIGIN OF SPECTRAL STATES IN ACCRETING BLACK HOLES

The origin of dramatically different electron distributions responsible for Comptonization in black hole X-ray binaries (BHBs) in their various states is discussed. We solve the coupled kinetic equations for photons and electrons without approximations on the relevant cross-sections accounting for Compton scattering, synchrotron radiation, and Coulomb collisions. In the absence of external soft photons, the electrons are efficiently thermalized by synchrotron self-absorption and Coulomb scattering even for pure nonthermal electron injection. The resulting quasi-thermal synchrotron self-Compton spectra have very stable slopes and electron temperatures similar to the hard states of BHBs. The observed hard X-ray spectral slopes, the cutoff at 100 keV, and the MeV tail together require low magnetic fields, ruling out the magnetic dissipation mechanism. The motion of the accretion disk toward the black hole results in larger Compton cooling and lower equilibrium electron temperature. Our self-consistent simulations show that in this case both electron and photon distributions attain a power-law-dominated shape similar to what is observed in the soft state. The electron distribution in the Cyg X-1 soft state might require a strong magnetic field, being consistent with the magnetically dominated corona.

X-Ray Emission Spectra of Ni-Like Gold Ions under CoronalPlasma Condition

The strong x-ray line emission of n = 4→n = 3 andn = 5→n = 3 transitions of Ni-like Au has been investigatedunder a coronal plasma condition. A complete set of atomic data,including energy level, transition probability and collision strength,has been obtained to simulate the emission spectra. Under a typicalcoronal equilibrium (electron temperature of 2500 eV anddensity of 1.0×1015), the predicted strongest line is due tothe transition of (3d3/2−14f5/2)1 →(3d10)0. Extensive studies show that the relative intensity isinsensitive to temperature and density over a wide plasma condition.

First principles based simulations of instabilities and turbulence

It is now widely believed that low frequency turbulence developing from small-scale instabilities is responsible for the phenomenon of anomalous transport generally observed in magnetic confinement fusion experiments. The micro-instabilities are driven by gradients of equilibrium density, ion and electron temperatures and magnetic field strength. Gyrokinetic theory is based on the Vlasov–Maxwell equations and, consistent with the ordering, averages out the fast particle gyromotion, reducing the phase space from 6 to 5 dimensions. Solving the resulting equations is a non-trivial task. Difficulties are associated with the magnetic confinement geometry, the strong disparities in space and time scales perpendicular and parallel to B, the different time scales of ion and electron dynamics, and the complex nonlinear behaviour of the system. The main numerical methods are briefly presented together with some recent developments and improvements to the basic algorithms. Recent results are shown, with emphasis on the roles of zonal E × B flows, of parallel nonlinearity and of toroidal coupling on the saturation of ion temperature gradient (ITG) driven turbulence in tokamaks.