Ion Heat Conductivity Research Articles

EFFECT OF INDUCED TOROIDAL ROTATION ON POLOIDAL ROTATION AND ION HEAT CONDUCTIVITY OF TOKAMAK EDGE PLASMAS

The transport processes in edge (collisional) plasmas of tokamaks with smooth profiles of macroscopic plasma parameters and induced poloidal and toroidal plasma flows, are considered. The toroidal and poloidal velocities of particles, the radial electric field and the ion heat flux are derived. It is shown that forces, induced by radio frequency waves, plasma turbulence or neutral beam injection, can be used to control the poloidal and toroidal plasma velocities, as well as ion heat conductivity, in a wide range of these values.

Review of D-T Results from TFTR

Experiments with plasmas having nearly equal concentrations of deuterium and tritium have been carried out on TFTR. To date, the maximum fusion power has been 10.7 MW, using 39.5 MW of neutral-beam heating, in a supershot discharge and 6.7 MW in a high-{beta}{sub p} discharge following a current ramp-down. The fusion power density in the core of the plasma has reached 2.8 MWm{sup {minus}3}, exceeding that expected in the International Thermonuclear Experimental Reactor (ITTER). The energy confinement time, {tau}{sub E}, is observed to increase in D-T, relative to D plasmas, by 20% and the n{sub i}(O){center_dot}{tau}{sub E} product by 55%. The improvement in thermal confinement is caused primarily by a decrease in ion heat conductivity in both supershot and limiter-H-mode discharges. Extensive lithium pellet injection increased the confinement time to 0.27 s and enabled higher current operation in both supershot and high-{beta}{sub p} discharges. First measurements of the confined alpha particles have been performed and found to be in good agreement with TRANSP simulations assuming classical confinement. Measurements of the alpha ash profile have been compared with simulations using particle transport coefficients from helium gas puffing experiments. The loss of energetic alpha particles to a detector at the bottom ofmore » the vessel is well described by the first-orbit loss mechanism. No loss due to alpha-particle-driven instabilities has yet been observed. ICRF heating of a D-T plasma, using the second harmonic of tritium, has been demonstrated. D-T experiments on TFTR will continue both to explore the physics underlying the ITER design and to examine some of the physics issues associated with an advanced tokamak reactor.« less

Effect of plasma toroidal flows on ion poloidal rotation and heat conductivity in edge plasmas of elongated tokamaks

The transport processes in edge (collisional) plasmas of axially symmetric tokamaks with elongated cross sections and with toroidal plasma flows are considered. The poloidal velocity of particles and the ion heat flux are derived. It is shown that toroidal plasma flows, induced by neutral beam injection or radio frequency waves, can be used to control the poloidal plasma velocity and ion heat conductivity in a wide range of these values. The ellipticity allows one to achieve these effects at smaller values of the toroidal Mach number.

H-factors derived from electron dynamics in tokamaks

The tokamak database indicates a trend that the electron heat conductivity in H-mode plasmas is less variable than the ion heat conductivity. This can be explained theoretically if we assume that the ion channel is laminarized on magnetic surfaces due to poloidal rotation but that the parallel electron dynamics remains turbulent due to asymmetries along the flux tube. Core H-mode density asymmetry data indicate that a poloidal shock is present with . This type of magnetic configuration leads to persistent anomalous electron heat transport as indicated earlier [1]. The magnetically trapped particle turbulence may be masked due to the existence of the above poloidal asymmetry along the flux tubes. In L-mode these flux tubes further deteriorate confinement due to associated electric braiding which increases the radial correlation scale. An H-mode regime electron heat conductivity formula is given for a flux tube turbulence limited plasma channel. Thus an H-mode factor may be computed for tokamaks relative to popular L-mode scaling laws.

Overview of DT results from TFTR

Experiments with plasmas having nearly equal concentrations of deuterium and tritium have been carried out on TFTR. To date (September 1995), the maximum fusion power has been 10.7 MW, using 39.5 MW of neutral beam heating, in a supershot discharge and 6.7 MW in a high beta P discharge following a current ramp-down. The fusion power density in the core of the plasma has reached 2.8 MW/m3, exceeding that expected in the International Thermonuclear Experimental Reactor (ITER). The energy confinement time tau E is observed to increase in DT, relative to D plasmas, by 20% and the n1(0).T1(0). tau E product by 55%. The improvement in thermal confinement is caused primarily by a decrease in ion heat conductivity in both supershot and limiter H mode discharges. Extensive lithium pellet injection increased the confinement time to 0.27 s and enabled higher current operation in both supershot and high beta P discharges. First measurements of the confined alpha particles have been performed and found to be in good agreement with TRANSP simulations assuming classical confinement. Measurements of the alpha ash profile have been compared with simulations using particle transport coefficients from helium gas puffing experiments. The loss of energetic alpha particles to a detector at the bottom of the vessel is well described by the first-orbit loss mechanism. No loss due to alpha particle driven instabilities has yet been observed. ICRF heating of a DT plasma, using the second harmonic of tritium, has been demonstrated. DT experiments on TFTR will continue both to explore the physics underlying the ITER design and to examine some of the physics issues associated with an advanced tokamak reactor

Review of deuterium–tritium results from the Tokamak Fusion Test Reactor

After many years of fusion research, the conditions needed for a D–T fusion reactor have been approached on the Tokamak Fusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)]. For the first time the unique phenomena present in a D–T plasma are now being studied in a laboratory plasma. The first magnetic fusion experiments to study plasmas using nearly equal concentrations of deuterium and tritium have been carried out on TFTR. At present the maximum fusion power of 10.7 MW, using 39.5 MW of neutral-beam heating, in a supershot discharge and 6.7 MW in a high-βp discharge following a current rampdown. The fusion power density in a core of the plasma is ≊2.8 MW m−3, exceeding that expected in the International Thermonuclear Experimental Reactor (ITER) [Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 239] at 1500 MW total fusion power. The energy confinement time, τE, is observed to increase in D–T, relative to D plasmas, by 20% and the ni(0) Ti(0) τE product by 55%. The improvement in thermal confinement is caused primarily by a decrease in ion heat conductivity in both supershot and limiter-H-mode discharges. Extensive lithium pellet injection increased the confinement time to 0.27 s and enabled higher current operation in both supershot and high-βp discharges. Ion cyclotron range of frequencies (ICRF) heating of a D–T plasma, using the second harmonic of tritium, has been demonstrated. First measurements of the confined alpha particles have been performed and found to be in good agreement with TRANSP [Nucl. Fusion 34, 1247 (1994)] simulations. Initial measurements of the alpha ash profile have been compared with simulations using particle transport coefficients from He gas puffing experiments. The loss of alpha particles to a detector at the bottom of the vessel is well described by the first-orbit loss mechanism. No loss due to alpha-particle-driven instabilities has yet been observed. D–T experiments on TFTR will continue to explore the assumptions of the ITER design and to examine some of the physics issues associated with an advanced tokamak reactor.

Effects of neutral beam injection on poloidal rotation and energy transport in tokamaks

The poloidal mass flow and ion energy transport driven by friction between thermal ions and fast ions resulting from neutral beam injection are investigated. Transport coefficients are derived which relate the poloidal mass flow and the radial ion heat flux to the fast ion friction and the radial temperature gradient. An Onsager symmetry condition shows that the coefficient of the fast ion friction in the radial heat flux is the negative of the coefficient of the temperature gradient in the poloidal mass flow. Numerical results are given for the banana regime. The driven poloidal mass flow can be significantly larger than the standard neoclassical poloidal rotation driven by the ion temperature gradient. The resulting viscous heating of the ions can be larger than the standard neoclassical ion heat conduction term in the ion energy equation. The driven ion energy flux contains a convective contribution, due to the diffusional mixing of the fast ions and thermal ions. This energy flux is inward (a heat pinch) in the case of coinjection, and can be significantly larger than the standard neoclassical energy flux.

Interplanetary shocks generated by expanding magnetic loops

We present a self-consistent numerical model of shock wave formation in the heliosphere by an expanding magnetic loop. In the model a coronal mass ejection is initiated by a loss of magnetohydrostatic equilibrium of the loop as a result of an increase of underlying magnetic field strength. The expanding magnetic loops produce propagating shock waves.The plasma motions are described by a system of two-fluid Navier-Stokes equations taking account of modified coefficients for electron and ion heat conduction, ion viscosity and energy exchange between ions and electrons.We obtain shock wave parameters in the outer heliosphere vs initial perturbations of the magnetic loops, and show that the shocks can be divided into two types, depending on their intensity. In the case of relatively weak shocks a typical feature is formation of a dense and cold layer (“piling-up” of material) near the upper boundary of the loop. In the case of strong shocks large-scale turbulence and viscous heating in the relaxation zone behind the front play an important role, and no appreciable piling-up of plasma occurs.We demonstrate that expanding magnetic loops, which are observed as magnetic clouds in the outer heliosphere, can effectively drive transient shocks ahead.

Electron and ion heat transport with lower hybrid current drive and neutral beam injection heating in ASDEX

Transport code calculations were made for experiments with the combined operation of lower hybrid current drive and heating and of neutral beam injection heating on ASDEX. Peaking or flattening of the electron temperature profile are mainly explained by modifications of the MHD induced electron heat transport. They originate from current profile changes due to lower hybrid and neutral beam current drive and to contributions from the bootstrap current. Ion heat transport cannot be described by one single model for all heating scenarios. The ion heat conductivity is reduced during lower hybrid heated phases with respect to Ohmic and neutral beam heating

Anomalous ion thermal diffusion from ηi modes

Models of ion temperature gradient-driven turbulence are reexamined in terms of the structure of the turbulent spectrum for radially localized modes to explain the significant difference between the radial profiles of ion heat conductivity inferred from local turbulence models and those observed in experiments. The strong radial inhomogeneity of the effective density of the turbulence spectrum in k is shown to produce a significant increase of the fluctuation level and ion thermal diffusion toward the plasma edge as compared with the local models under certain conditions. The conditions required are stated and should be tested with numerical simulations.

Longitudinal Ion Transport Coefficients in Magnetized D‐He and H‐C Plasmas

AbstractBased on analytical formulae derived in ref./1/, longitudinal ion viscosities, heat conductivities and thermal diffusion ratios in magnetized D‐He and H‐C plasmas are calculated within Grad's 21‐moment approximation. Calculations taking full account of the finite mass ratio m+/mZ between hydrogen (deuterium) and impurity ion mass are compared with those for m+/mz≫ 1. As is to be expected, the largest discrepancies between exact and approximate results (with respect to the mass ratio) arise for D‐He plasmas. It turns out that the approximate formula for the impurity ion heat conductivity has to be extended to remove some hitherto existing deficiencies already mentioned in ref. /1/.

Optimum-confinement in the wendelstein 7-AS stellarator

Optimum confinement is realized in Wendelstein 7-AS by wall conditioning and by properly adjusting the parameters determining the magnetic field configuration. The effective heating of net current free plasmas by ECRF and neutral beam injection (NBI) involves different plasma parameters and transport regimes. Stationary plasmas are generally produced by ECRF, whereas density and impurity control is a severe problem during NBI. This has initiated different kinds of impurity and particle control scenarios. An extended parameter range with electron temperatures of 200 eV<or=Te<or=3 keV, ion temperatures of 100 eV<or=Ti <or= 0.7 keV and electron densities of 1019 <or= ne<or=3.1020 m-3 was accessible. The characteristics of the energy confinement and the particle and impurity transport are described and related to the specific heat and particle sources. The investigations comprise the analysis of electron and ion heat conductivity, particle transport modelling and impurity transport studies by laser blow-off-experiments. The influence of the ambipolar electric field is discussed.

Toroidal equilibrium and radial profiles from magnetic measurements in Extrap T1

The toroidal equilibrium position in the Extrap T1 toroidal Z-pinch is studied by measuring the currents induced in the external octupole field rings. Radial profiles are obtained by an internal magnetic coil array. From the magnetic field, profiles of current density, plasma pressure, safety factor, resistivity and input power density are deduced. A polynomial model is developed to simulate the measured profiles. The classical ion heat conduction losses in Extrap discharges are calculated using this model and compared to the power input. For polynomials matched to magnetic field profiles measured in experiments, these losses are small. By varying the coefficients of the polynomials, a region is found where the power input can balance the classical heat conduction losses at higher values of Theta and beta 0.

Ion temperature gradient driven turbulence in the weak density gradient limit

The anomalous heat transport arising from the ion temperature gradient driven mode or ηi-mode turbulence is extended to the range of the weak density gradient limit (ηi=Ln/LT→∞), which is appropriate for H-mode dishcarges. It is shown that the anomalous ion heat conductivity χi with Ln→∞ scales as χi=g(ρs/LT) (cTi/eB) exp(−βσ) with σ=(Te/Ti) (LT/Ls), β≂4, and g≂1. This χi scaling is the natural extension for high ηi of the scaling of χi for K=(Ti/Te) (1+ηi)≲4 obtained [Phys. Fluids B 2, 1833 (1990)] from analytical and numerical studies.

Fluctuation spectrum and transport from ion temperature gradient driven modes in sheared magnetic fields

The ion temperature gradient driven mode or ηi-mode turbulence is reinvestigated based on two-component compressible fluid equations with the polarization drift velocity and adiabatic electrons. The scaling of the anomalous ion heat conductivity with magnetic shear s=Ln/Ls and the excess of ηi over the critical value ηi,c for marginal stability is found to vary as χi=g(ρs/Ln)(cTi/eB) (ηi−ηi,c)exp(−αs), where g≂1 and α≂5.

Ignition and anomalous transport processes

Using a modified version of the 1½-D BALDUR transport code, important aspects of the time evolution of D-T plasmas in a compact, high field tokamak of the Ignitor type with strong Ohmic heating are investigated. For the canonical electron heat transport, a generalization of the Coppi-Mazzucato-Gruber diffusion for axisymmetric toroidal geometry is assumed as well as alpha particle heating contributions; this reproduces the power dependent degradation of confinement observed in present-day auxiliary heated experiments. Anomalous ion heat conductivity is based on the existence of the ηi mode halfway out in the discharge, with an assumed spatial dependence of the transport magnitude superimposed on a parameter scaling related to wave breaking in the direction perpendicular to the magnetic field. The particle density profiles are held fixed, and convective energy fluxes are ignored. Results from three model examples associated with the set of transport coefficients are considered, and the impact of variations in density, conductivity magnitudes, resistivity, plasma impurity level and flux surface equilibrium configuration on the approach to ignition is discussed.

A review of models for collisionless one-dimensional plasma flow to a boundary

Four models of collisionless one-dimensional plasma flow to a boundary are compared with regard to their predictions of particle and heat fluxes to the boundary for a given plasma density and temperature far from the boundary. The models include two kinetic treatments, that of Emmert et al. [Phys. Fluids 23, 803 (1980)], and that of Bissell and Johnson [Phys. Fluids 30, 779 (1987)], an isothermal fluid model, Self and Ewald [Phys. Fluids 9, 2486 (1966) and Stangeby, [Phys. Fluids 27, 2699 (1984)], and an adiabatic fluid model, Zawaideh, Najmabadi, and Conn [Phys. Fluids 29, 463 (1986)]. The fluid models do not explicitly include collisions; however, the adiabatic closure condition employed, namely, neglect of ion heat conduction, implies a degree of ion self-collisionality. It is found that the particle and heat fluxes to the boundary differ very little among the four models—spanning a range of about ±10%. It is therefore concluded that, with regard to modeling of such important practical quantities as outfluxes, a simple and convenient formulation, such as the isothermal fluid model, is adequate. Substantial differences among the models are found for certain other predicted quantities, namely, the spatial variation of ion temperature along the flow and the magnitude of the electric field near the boundary.

Scaling of the thermonuclear fusion neutron yield in the Doublet III tokamak

The fusion neutron yield during hydrogen neutral beam injection into deuterium plasmas is examined and compared with the neoclassical model, using the Doublet III data obtained in 1983. This provides scalings of thermonuclear fusion neutron yields for the discussion of ion energy transport in tokamak devices. – Experimental data show that fusion neutron yield appears to have a scaling of in low recycling divertor discharges (so called H mode). The neoclassical theory for ion heat conduction satisfactorily described the scaling of fusion neutron yield. With a neutral injection power of Pinj = 4.6 MW, the Doublet III deuterium plasma yields thermonuclear neutrons at a rate of 1.2 × 1013 n·s−1 in low recycling divertor discharge, which is equivalent to a D+ T+ plasma with a thermonuclear fusion power multiplication factor of Q = 7.8 × 10−5 or a beam driven T+ plasma with Q = 8.6 × 10−2. A limiter discharge yields fewer neutrons.

Enhancement of tokamak ion transport due to electron collisions

In tokamaks where auxiliary ion heating leads to Ti> Te, the neglect of electron collisions is no longer a good approximation in determining ion transport coefficients. The enhancement of the ion heat conduction due to electron collisions is determined for (a) the Pfirsch-Schliiter regime and (b) the banana regime for the case where is large. The enhancement of ion transverse viscosity (P|) is particularly important; the contribution due to ion-electron collisions is approximately equal to the ion-ion collision term even for Ti = Te.

Ion thermal conductivity for a pure tokamak plasma

The neoclassical and Pfirsch–Schlüter components of the ion heat conduction for a pure hydrogen tokamak plasma are recalculated without assuming large aspect ratio and without neglecting energy scattering collisions. Using a model collision operator, the conductivity is determined numerically for various collision frequencies and aspect ratios. An approximate algebraic expression is fitted to the results. Even for comparatively large aspect ratios (∼10) energy scattering increases the conductivity in the banana regime by about 50% and for small aspect ratios (approximately 3.3) the Pfirsch–Schlüter contribution causes a further increase of approximately 60%.