Energy equilibria and the plasma-wall boundary condition in a diffuse pinch

A tensor conductivity model for a fully ionized, two-temperature, cylindrical and diffuse pinch is constructed and its properties analyzed under energy and momentum equilibria conditions. The set of Braginskii's classical two-temperature tensor transport equations are solved for the strict steady state and the radial equilibria profiles of the relevant parameters produced. Unlike the scalar conductivity model (part 1 of this series) tensor coefficients yield profiles with the appropriate ideal boundary conditions, namely zero pressure and temperatures at the plasma radius. Furthermore, spatial oscillations of the electron temperature only occur for extreme values of the free parameters.

A general investigation of linear drift-wave phenomena in cylindrically bounded plasmas, immersed in a magnetic field without shear and curvature, is performed within the two-fluid hydrodynamical approximation, taking into account electron-temperature oscillations and inhomogeneous radial distributions of the undisturbed electron density and temperature. For plasmas in which the electron temperature strongly exceeds the ion temperature the problem is reduced to an ordinary complex second-order differential equation describing the radial distribution of the oscillating electric potential. It is shown that the presence of electron-temperature oscillations (which must always exist in order to satisfy electron-energy conservation) and of radial gradients in the undisturbed electron temperature (which must always exist owing to cooling of the plasma at the boundary) leads to an important modification of the theory of drift waves in cylindrical plasmas (with regard to their stability and the radial distribution of the oscillating quantities) compared with previous papers in which these phenomena were disregarded. A numerical program for solving the corresponding complex-eigenvalue problem has been derived that allows a realistic calculation of all the quantities pertaining to drift-wave phenomena. It has been applied, in particular, to the calculation of the radial distribution of the oscillating coherent magnetic fields accompanying the coherent drift waves. The numerical results prove to be in good agreement with experiments performed with a helium plasma.

To meet the demand for information on electron temperature fluctuations in low magnetic field experiments in the Large Helical Device (LHD), a new ECE radiometer covering the Q and V bands has been installed. Combination mirrors are installed in the vacuum vessel to focus the beam and efficiently propagate the radiated electron cyclotron waves. Notch filters are used to eliminate stray light from the gyrotron, and a 32-channel heterodyne radiometer is constructed using a filter bank system. As a result, oscillations of electron temperature and both electromagnetic and electrostatic fluctuations were successfully observed.

Global plasma oscillations, involving electron temperature, plasma density and current, have been observed during electron cyclotron current driven ECCD discharges on TCV (Tokamak à Configuration Variable; R/a = 0.88 m/0.25 m, k ≤ 2.8, BT < 1.54 T). This is confirmed by multiple diagnostics operating on different physical principles: electron cyclotron emission radiometer, soft x-ray, far-infrared reflectometer, bolometer and magnetic probes. The oscillations develop in the presence of electron internal transport barriers and reversed magnetic shear. They are reminiscent of the central electron temperature oscillations (the so-called O-regime) seen in low-loop voltage or fully non-inductive lower-hybrid current driven plasmas with reversed central magnetic shear on Tore Supra (Giruzzi et al 2003 Phys. Rev. Lett. 91 935001). The oscillations have m/n = 0/0 periodicity and are not the manifestation of a magnetohydrodynamic (MHD) instability in itself, but they are invariably linked to the presence of MHD modes on TCV. In fact, no plasma discharge has been obtained so far displaying oscillations in the absence of MHD activity. The interaction of the oscillations with MHD can play a strong role in the coupled dynamics of heat and current transport, as the modes can significantly perturb the q profile. More generally the presence of MHD modes can aid in the correct identification of rational q-surfaces [4]. The interplay between MHD and the plasma oscillations, with the first being the cause for the development of the second, is the main focus of this paper. It is also shown that the global oscillations can be removed by adding an Ohmic current perturbation and therefore by modifying the current density profile.

The parametric dependence of electron thermal conductivity was studied in the trapped electron regime by utilizing a localized heating method in a shear stabilizing configuration in the FM-1 spherator. The electron thermal conductivity K⊥ and the particle diffusion coefficient D⊥ show similar dependence on the shear length, Ls, and the electron temperature Te[K⊥ ∼ (1/400 ∼ 1/800)(Ls/a) (kTe/16eB)]. The conductivity was larger when the electron temperature gradient was parallel to the density gradient compared with the antiparallel case. The fluctuations associated with the heat flow are compared with the prediction of the trapped electron particle instability. Relevance to tokamak experiments is discussed.

A unified picture of the structure of steady, one-dimensional shock waves in partially ionized argon, in the absence of external electric or magnetic field, is presented. The investigation is based on a two-temperature, three-fluid continuum approach, using the Navier–Stokes equations as a model and including non-equilibrium ionization. Quasi charge neutrality and zero velocity slip are assumed. The analysis of the governing equations is based on the method of matched asymptotic expansions and results in the following three layers: (1) a broad thermal layer dominated by electron thermal conduction, (2) an atom-ion (A-I) shock structured by the heavy particle (atoms and ions) collisional dissipative mechanisms and (3) an ionization relaxation layer (IRL) wherein electron- atom inelastic collisions dominate. Solutions have been obtained for the first two orders with respect to a small parameter, which is the ratio of energy fluxes due to heavy particle viscous dissipation and electron thermal conduction. Whereas only electron temperature and electric potential show any marked variation in the thermal layer, the changes in all the variables in both the A-I shock and the IRL are significant.Inclusion of electron thermal conduction terms in the governing equations has been observed to introduce numerical instabilities in the analysis of the IRL. They are circumvented by adopting a regular perturbation scheme with respect to a local small parameter, which has been identified to be the ratio of the freestream degree of ionization to the nondimensional characteristic temperature for first ionization. Numerical results show that the effect of electron thermal conduction on the IRL profiles is significant. Results in the form of tables and figures are presented for five sets of equilibrium free-stream conditions.

Wall conditioning using 2.45 GHz ECR-DC on superconducting tokamak TRIAM-1M

Here we present electron temperature variations observed with incoherent scatter radar during a European Incoherent Scatter Scientific Association Heating experiment with high‐frequency (HF) radio wave transmission at frequencies above the peak ionospheric critical frequency. The electron temperature increased from 2000 K up to 2800 K during the HF transmission periods. During the experiment both pump frequency and polarization were altered between pump pulses. The observed temperature variation is compared with numerical solutions to the electron energy equation with ohmic heating modeling the effect of the radio wave heating of the plasma. Agreement between observations and model is found to be good.

A magnetically confined two-fluid plasma is considered in which the Ohmic heating of the electrons by a current driven parallel to an applied magnetic field is balanced by bremsstrahlung and equipartition to the ions. It is found that for a steady state the applied electric field must be below a critical value which in absence of bremsstrahlung is given by where the electrical conductivity is and the total pressure is p. Under this condition it is found that there are two /Futions for Te/Ti which satisfy the steady electron energy balance equation in a homogeneous, fully ionized plasma. One of these /Futions always has values above the critical value of Te/Ti (= 132 in absence of bremsstrahlung) for the onset of the electrothermal instability in a fully ionized gas. Inclusion of electron thermal conduction transverse to the magnetic field (with Hall parameter ) yields a wavelength for maximum growth of the instability of about , where ae is the electron Larmor radius. The steady non linear profiles showing current filamentation have been calculated. Runaway electrons and ion-acoustic instabilities can occur in the spatial maximum of the current density and electron temperature. Inclusion of bremsstrahlung loss reduces the value of Te/Ti for the onset of the instability, and at Te = Ti yields a maximum ion temperature obtainable by Ohmic heating in a stable plasma.

In a post-thermal-quench plasma, mitigated or unmitigated, the plasma power balance is mostly between collisional or Ohmic heating and plasma radiative cooling. In a plasma of atomic mixture with α labeling the atomic species, the power balance sets the plasma temperature, ion charge state distribution with i the charge number, and through the electron temperature and ion charge state distribution the parallel electric field Since the threshold electric field for runaway avalanche growth is also set by the atomic mixture, ion charge state distribution and its derived quantity, the electron density the plasma power balance between Ohmic heating and radiative cooling imposes a stringent constraint on the plasma regime for avoiding and minimizing runaways when a fusion-grade tokamak plasma is rapidly terminated.

The electrical resistivity of high purity solid Nb has been measured at fixed pressures up to 5 GPa in a large volume press and temperatures up to ∼1900 K. The expected resistivity decrease with pressure and increase with temperature were found. A transition was observed in the temperature dependence of resistivity at high temperature. The transition is discussed in terms of the effects of pressure and temperature on the electronic band structure of Nb causing a resistivity behavior characteristic of a change from the “minus group” to the “plus group.” Extrapolation of the pressure dependence of the transition temperature suggests that Nb would show plus group behavior at room T at an estimated pressure of ∼27 ± 7 GPa. The electronic thermal conductivity was calculated using the Wiedemann-Franz law and was in very good agreement with 1 atm data. We show that the temperature dependence of the calculated electronic thermal conductivity increases with a steep slope from room temperature up to the electronic transition temperature for all fixed pressures. Above the transition temperature, the T-dependence of electronic thermal conductivity remained constant at 2 GPa and exhibited an increasingly negative slope at higher pressures. The isothermal pressure-dependence of electronic thermal conductivity is positive.

The electronic thermal conductivity of graphene and 2D Dirac materials is of fundamental interest and can play an important role in the performance of nano-scale devices. We report the electronic thermal conductivity, $K_{e}$, in suspended graphene in the nearly intrinsic regime over a temperature range of 20 to 300 K. We present a method to extract $K_{e}$ using two-point DC electron transport at low bias voltages, where the electron and lattice temperatures are decoupled. We find $K_e$ ranging from 0.5 to 11 W/m.K over the studied temperature range. The data are consistent with a model in which heat is carried by quasiparticles with the same mean free-path and velocity as graphene's charge carriers.

Experimental radial ion transport rates and diffusion coefficients are presented for the Constance-B magnetic mirror [Phys. Rev. Lett. 58, 1853 (1987)]. The transport experiments are performed by measuring steady state equilibrium radial profiles of plasma density, ionization source, end loss current, electric field, electron temperature, and ion temperature. A charge coupled device (CCD) camera system [Rev. Sci. Instrum. 60, 2835 (1989)] is used to measure the two-dimensional radial density, source, and electron temperature profiles. End loss diagnostics including movable Faraday cups, electrostatic end loss analyzers, and an ion time-of-flight analyzer [Rev. Sci. Instrum. 59, 601 (1988)] are used to measure radial profiles of potential and ion temperature. The ion confinement time perpendicular to the magnetic field is found to be an order of magnitude shorter than predicted by classical and neoclassical transport theories. The radial profiles of the perpendicular diffusion coefficient (D⊥) are presented for hydrogen, helium, and argon plasmas. The coefficients are a factor of 10 larger than the maximum classical and neoclassical coefficients in all three plasmas. Plasma fluctuations resulting from whistler mode microinstability [Phys. Rev. Lett. 59, 1821 (1987)] as well as nonaxisymmetric potentials are suggested as possible explanations for the experimentally measured radial transport rate.

A theoretical study is made of the steady-state flow of a laser plasma formed by the irradiation of a solid calcium target with q∼1012–1013 W/cm2. In the range p>pcr the self-consistent hydrodynamic problem is solved numerically, with allowance for the electronic thermal conduction, the ionization, and the plasma radiation in the soft x-ray range. In that range, 5–30% of the laser energy may be reemitted from p>pcr; the conversion efficiency depends on the saturated heat flux. It is shown that radiative energy losses together with saturation of the heat flux carried by the electrons cause a subsonic plasma flow in the supercritical part of the corona, leading to a rarefaction jump at the critical surface, a large difference between the electron temperature and the ion and ionization temperatures, elimination of the electronic thermal conduction by ionacoustic waves, and formation of satellites of the resonance helium-like ion line in ions with a lower degree of ionization, including the Ka line.

This paper presents an analysis of the spatial growth of a transverse instability, corresponding to the propagation of an electromagnetic beam, with uniform irradiance along the wavefront in a collisional plasma, along the direction of a static magnetic field; expressions have been derived for the rate of growth, the maximum value of the rate of growth and the corresponding value of the wave number of the instability. The instability arises on account of the ejection of electrons from regions where the irradiance of the perturbation is large. The energy balance of the electrons taking into account ohmic heating and the power loss of electrons on account of (i) collisions with ions and neutral species and (ii) thermal conduction has been taken into account for the evaluation of the perturbation in electron temperature, which determines the subsequent growth of the instability. Further, the relationship between the electron density and temperature, as obtained from the kinetic theory, has been used. The filamentation instability becomes enhanced with the increase of the static magnetic field for the extraordinary mode while the reverse is true for the ordinary mode. Dependence of growth rate on irradiance of the main beam, magnetic field and a parameter proportional to the ratio of power loss of electrons by conduction to that by collisions has been numerically studied and illustrated by figures. The dependence of the maximum growth rate and the corresponding optimum value of the wave number of the instability on the irradiance of the main beam has also been studied. The paper concludes with a discussion of the numerical results, so obtained.