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In a variety of discharge conditions on DIII-D it is observed that rf electron heating reduces the toroidal rotation speed and core ion temperature. The rf heating can be with either fast wave or electron cyclotron heating and this effect is insensitive to the details of the launched toroidal wavenumber spectrum. To date all target discharges have rotation first established with co-directed neutral beam injection. A possible cause is enhanced ion momentum and thermal diffusivity due to electron heating effectively creating greater anomalous viscosity. Another is that a counter directed toroidal force is applied to the bulk plasma via rf driven radial current.

The power deposition profiles for different poloidal and toroidal launch angles have been determined by modulating the ECH power and measuring the electron temperature response. The peak of the measured power density follows the poloidal steering of the ECH launcher, and perpendicular launch gives a narrower deposition profile than does oblique (current drive) launch. The difference in wave refraction between X-mode and O-mode allows positive identification of an unwanted O-mode component of the launched beam.

Plasma rotation has many beneficial effects on tokamak operation including stabilization of MHD and microturbulence to improve the beta limit and confinement. Contrary to present-day tokamaks, neutral beams may not be effective in driving rotation in fusion reactors; hence the investigation of radiofrequency (RF) induced plasma rotation is of great interest and potential importance. This paper reviews the experimental results of RF induced rotation and possible physical mechanisms, suggested by theories, to explain the observations. This subject is only in the infancy of its research and many challenging issues remained to be understood and resolved.

In plasmas with toroidal rotation, the ions are pushed towards the low-field side of the torus by the centrifugal force. An electrostatic potential is set up to maintain charge neutrality which tends to attract electrons towards the low-field side of the torus. Due to this electrostatic potential, the trapped/passing boundary in the electron velocity space changes from a cone for stationary plasmas to an hyperboloid in a rotating plasma. This reduces the phase space for passing electrons. This paper attempts to address rotation effects on the electron cyclotron current drive efficiency.

A velocity-space connection formula is proposed to estimate the collisionality effect on electron cyclotron current drive efficiency. The collisionality correction gives modest improvement in agreement between theoretical and recent DIII-D experimental results

Neoclassical tearing modes are found to limit the achievable beta in many high performance discharges in DIII-D. Electron cyclotron current drive within the magnetic islands formed as the tearing mode grows has been proposed as a means of stabilizing these modes or reducing their amplitude, thereby increasing the beta limit by a factor around 1.5. Some experimental success has been obtained previously on Asdex-U. Here we examine the parameter range in DIII-D in which this effect can best be studied.

The physics of non-inductive current drive and current profile control using the fast magnetosonic wave has been demonstrated on the DIII-D tokamak. In non-sawtoothing discharges formed by neutral beam injection (NBI), the radial profile of the fast wave current drive (FWCD) was determined by the response of the loop voltage profile to co, counter, and symmetric antenna phasings, and was found to be in good agreement with theoretical models. The application of counter FWCD increased the magnetic shear reversal of the plasma and delayed the onset of sawteeth, compared to co FWCD. The partial absorption of fast waves by energetic beam ions at high harmonics of the ion cyclotron frequency was also evident from a build up of fast particle pressure near the magnetic axis and a correlated increase in the neutron rate. The anomalous fast particle pressure and neutron rate increased with increasing NBI power and peaked when a harmonic of the deuterium cyclotron frequency passed through the center of the plasma. The experimental FWCD efficiency was highest at 2 T where the interaction between the fast waves and the beam ions was weakest; as the magnetic field strength was lowered, the FWCD efficiency decreased to approximately half of the maximum theoretical value.

In modeling electron cyclotron (EC) waves for heating (ECH) and current drive (ECCD) applications, the standard approach describes wave propagation using geometric optic ray tracing with cold plasma dispersion and wave absorption using a relativistic warm plasma expression. However, recent vertical O-mode transmission measurements on Tore Supra indicate that wave trajectories near the fundamental resonance frequency can significantly deviate from predictions of cold plasma analysis. The experimental results were attributed to warm plasma refraction effects caused by the anomalous dispersion associated with wave-particle resonance. Here, warm plasma refraction effects on wave propagation and absorption are examined in the context of a slab model in the parameter regime of interest to the upcoming 110 GHz electron cyclotron heating and current drive experiments on DIII-D.

In spherical tokamaks (ST), the magnetic field strength varies over a wide range across the plasma, and at high betas it deviates significantly from the 1/R dependence of conventional tokamaks. This, together with the high density expected in ST, poses challenging problems for RF heating and current drive. In this paper, the authors investigate the various possible applications of fast waves (FW) in ST. The adjoint technique of calculating current drive is implemented in the raytracing code CURRAY. The applicability of high harmonic and subharmonic FW to steady state ST is considered. They find that high harmonic FW tends to be totally absorbed before reaching the core and may be considered a candidate for off axis current drive while the subharmonic FW tends to be absorbed mainly in the core region and may be considered for central current drive. A difficult problem is the maintenance of current at the startup stage. In the bootstrap ramp-up scenario, the current ramp-up is mainly provided by the bootstrap current. Under this condition, the role of rf becomes mainly the sustainment of plasma through electron heating. Using a slab full-wave code SEMAL, the authors find that the ion-ion-hybrid mode conversion scheme is a promising candidate. The effect of possible existence of edge Alfven resonance and high harmonic cyclotron resonance is investigated and regimes of minimization of edge heating identified.

The application of fast wave power in DIII-D has proven effective for both electron heating and current drive. Since the last RIF Conference FW power has been applied to advanced confinement regimes in DIII-D; negative central shear (NCS), VH- and H-modes, high {beta}{sub p}, and high-{ell}i. Typically these regimes show enhanced confinement of toroidal momentum exhibited by increased toroidal rotation velocity. Indeed, layers of large shear in toroidal velocity are associated with transport barriers. A rather common occurrence in these experiments is that the toroidal rotation velocity is decreased when the FW power is turned on, to lowest order independent of whether the antennas are phased for co or counter current drive. At present all the data is for co-injected beams. The central toroidal rotation can be reduced to 1/2 of the non-FW level. Here the authors describe the effect in NCS discharges with co-beam injection.

To fully utilize the available power sources in DIII–D (FW, NBI, ECH), understanding of the synergism between the heating mechanisms is important. In this paper the ion distribution, under simultaneous application of NBI and FW, is calculated from Fokker‐Planck code CQL3D coupled to ray‐tracing code CURRAY. It is found that interaction between energetic ions and FW can be minimized or maximized by adjusting various parameters such as magnetic field, density, beam energy, and FW frequency. Specifically, in DIII–D, we find negligible interactions above 1.8 T and above 80 MHz, while the interaction increases at lower fields and frequencies. The results are compared with experiments in DIII–D including the calculated neutron rate. Energetic ion orbit losses may play an important role in the ion distribution, and this effect is being investigated.

The physics of electron heating and current drive with the fast magnetosonic wave has been demonstrated on DIII-D, in reasonable agreement with theoretical modeling. A recently completed upgrade to the fast wave capability should allow full noninductive current drive in steady state advanced confinement discharges and provide some current density profile control for the Advanced Tokamak Program. DIII-D now has three four-strap fast wave antennas and three transmitters, each with nominally 2 MW of generator power. Extensive experiments have been conducted with the first system, at 60 MHz, while the two newer systems have come into operation within the past year. The newer systems are configured for 60 to 120 MHz. The measured FWCD efficiency is found to increase linearly with electron temperature as {gamma} = 0.4 {times} 10{sup 18} T{sub eo} (keV) [A/m{sup 2}W], measured up to central electron temperature over 5 keV. A newly developed technique for determining the internal noninductive current density profile gives efficiencies in agreement with this scaling and profiles consistent with theoretical predictions. Full noninductive current drive at 170 kA was achieved in a discharge prepared by rampdown of the Ohmic current. Modulation of microwave reflectometry signals at the fast wave frequency is beingmore » used to investigate fast wave propagation and damping. Additionally, rf pick-up probes on the internal boundary of the vessel provide a comparison with ray tracing codes, with dear evidence for a toroidally directed wave with antenna phasing set for current drive. There is some experimental evidence for fast wave absorption by energetic beam ions at high cyclotron harmonic resonances.« less

The effect of co and counter fast wave current drive (FWCD) on the plasma current profile has been measured for neutral beam heated plasmas with reversed magnetic shear on the DIII‐D tokamak. Although the response of the loop voltage profile was consistent with the application of co and counter FWCD, little difference was observed between the current profiles for the opposite directions of FWCD. The evolution of the current profile was successfully modeled using the ONETWO transport code. The simulation showed that the small difference between the current profiles for co and counter FWCD was mainly due to an offsetting change in the ohmic current profile. In addition, the time scale for the loop voltage to reach equilibrium (i.e., flatten) was found to be much longer than the FWCD pulse, which limited the ability of the current profile to fully respond to co or counter FWCD.

A combined moment and kinetic approach is developed to consider rf effects on plasma rotation. Appropriate relaxation times for driven toroidal and poloidal rotation are discussed.

A formula based on the solutions to the drift kinetic equation is proposed for modeling the trapped electron correction to the electron shielding current in neutral beam current drive in general tokamak equilibria and arbitrary collisionality regime.

In the present work the authors present simulations which show that the hollow current profile can be maintained in quasi-steady state through a self-consistently determined combination of bootstrap current and neutral beam and rf current drive. Controllability of the q profile is demonstrated by eliminating low m/n mode number instabilities from these discharges by maintaining q > 1.5 at all times, starting from appropriate initial conditions. At moderately high {beta}{sub p}, the bootstrap current can be a substantial fraction of the total current and the ability to maintain the proper total current density profile depends on the bootstrap current profile and the availability of suitable localized heating and current drive. In these simulations, they use electron cyclotron heating, ion cyclotron heating, and electron cyclotron and fast wave current drive. The ability to maintain the profiles is demonstrated using several energy transport models. Self-consistent transport simulations are used to model the SSC discharges using the ONETWO transport code coupled to rf heating and current drive packages FASTWAVE and TORAY. To accurately model inductive and driven current profile evolution, the additional source terms that arise in Faraday`s law due to internal flux surface motion are included by coupling the transport calculations tomore » a fixed boundary equilibrium code. To test the sensitivity of the results to the transport model used, they model DIII-D discharges using thermal conductivities consistent with improved confinement DIII-D discharges, and with the Rebut-Lallia-Watkins model of energy transport.« less

Current drive by fast waves (FWCD) is an important candidate for steady‐state operation of tokamaks. Major experiments using this scheme are being carried out on DIII‐D. There has been considerable study of the theoretical efficiency of FWCD. In Refs. 4 and 5, the nonrelativistic efficiency of FWCD at arbitrary frequencies was studied. For DIII‐D parameters, the results can be considerably different from the Landau and Alfven limits. At the high temperatures of reactors and DIII‐D upgrade, relativistic effects become important. In this paper, the relativistic FWCD efficiency for arbitrary frequencies is studied. Assuming that the plasma is weakly relativistic, i.e., Te/mc2 is small, an analytic expression for FWCD is obtained for high resonant energies (uph/uTe≫1). Comparisons with the results from a numerical code ADJ and the nonrelativistic results shall be made and analytical fits in the whole range of velocities shall be presented.

Current drive during second harmonic, electron cyclotron heating experiments performed on the T‐10 tokamak have been simulated with the onetwo transport code to determine the effects of induction on the time evolution of the loop voltage and current density profile. Ray tracing shows the well focused rf power can generate centrally peaked current densities which exceed the Ohmic current densities by a factor of five, causing very peaked current profiles which will be unstable to sawteeth. A Kadomtsev model of the sawtooth shows that a limit cycle is quickly reached which maintains a broad current profile and requires generation of a negative dc component of the loop voltage localized near the magnetic axis. This negative electric field effectively reduces the measured current drive efficiency. A broader profile of driven current, as in the fundamental current drive experiment on T‐10, would not suffer this effect.

The CQL3D Fokker‐Planck code is used to investigate effects of quasilinear distortion of the electron tail in the T–10 second harmonic electron cyclotron current (ECCD) drive experiment. The experiment operates in a regime of substantial tail formation. Current drive efficiency may be doubled relative to low power cases. That portion of electric field‐driven current which is synergetic with the rf‐induced nonthermal tail may tend to cancel the ECCD current in relevant cases.

A weakly relativistic Fokker–Planck operator for electron-electron collision was first used by Karney and Fisch to calculate the efficiencies of current drive by waves with fast phase velocity [C. F. F. Karney and N. J. Fisch, Phys. Fluids 28, 116 (1985)]. The present work extends Karney and Fisch’s work by expressing the weakly relativistic collision operator in potential form, and working out a general Legendre expansion of the potential functions. This general Legendre expansion reproduces the results in Karney and Fisch’s paper and is useful in implementing the weakly relativistic operator in Fokker–Planck codes. To justify the use of the weakly relativistic collision operator for current drive applications under ITER conditions, a comparison is made of current drive efficiencies predicted by this operator and a fully relativistic collision operator. Good agreement between efficiencies predicted by these two models is found. This suggests that the weakly relativistic collision operator is sufficiently...

DIII-D has a major effort underway to develop the physics and technology of fast wave electron heating and current drive in conjunction with electron cyclotron heating. The present system consists of a four strap antenna driven by one 2 MW transmitter in the 32--60 MHz band. Experiments have been successful in demonstrating the physics of heating and current drive. In order to validate fast wave current drive for future machines a greater power capability is necessary to drive all of the plasma current. Advanced tokamak modeling for DIII-D has indicated that this goal can be met for plasma configurations of interest (i.e. high [beta] VH-mode discharges) with 8 MW of transmitter fast wave capability. It is proposed that four transmitters drive fast wave antennas at three locations in DIII-D to provide the power for current drive and current profile modification. As the next step in acquiring this capability, two modular four strap antennas are in design and the procurement of a high power transmitter in the 30--120 MHz range is in progress. Additionally, innovations in the technology are being investigated, such as the use of a coupled combine antenna to reduce the number of required feedthroughs and to provide formore » parallel phase velocity variation with a relatively small change in frequency, and the use of fast ferrite tuners to provide millisecond timescale impedance matching. A successful test of a low power fast ferrite prototype was conducted on DIII-D.« less

Reference CRPP-ARTICLE-2002-025doi:10.1063/1.1517052View record in Web of Science Record created on 2008-04-16, modified on 2017-05-12

A molecular theory of cholesteric liquid crystals is presented. By means of symmetry considerations we obtain a general form of the intermolecular potential containing chiral contributions, which are then shown to be responsible for forming the cholesteric phase. The temperature dependence of the cholesteric pitch is calculated. It is found that the pitch depends on temperature through a ratio of orientational order parameters in the form ${[\frac{{\ensuremath{\sigma}}_{4}(T)}{{\ensuremath{\sigma}}_{2}(T)}]}^{2}$. A general mean-field theory for binary cholesteric mixtures is also presented, along with a formula showing how the pitch depends on temperature and concentration. Under certain conditions, the formula reduces at fixed $T\ensuremath{-}{T}_{c}$ to a simple quadratic rational fraction in the concentration. This is consistent with experimental observation.

We have developed a theory of the first-order phase transition in intermediate-valence (IV) solids at zero temperature. Inputs into the theory are ${m}^{*}$, the effective mass of the $5d$ electrons, $\ensuremath{\kappa}$, the electronic dielectric constant at low frequencies, ${I}_{0}$, a formation energy of an electron-hole pair ${(4f)}^{\ensuremath{\alpha}}\ensuremath{\rightarrow}{(4f)}^{\ensuremath{\alpha}\ensuremath{-}1}$ ($5d$ or $6s$) in the metallic state, and the repulsive energy between positive [both ${(4f)}^{\ensuremath{\alpha}}$ and ${(4f)}^{\ensuremath{\alpha}\ensuremath{-}1}5d$] and negative ions. All these quantities, except ${I}_{0}$, can be obtained from independent measurements. The many-body properties of the $5d$ electrons, including the important screening effects, are obtained by suitable scaling from density-functional calculations of metallic hydrogen. Depending on the values of ${m}^{*}$, $\ensuremath{\kappa}$, ${I}_{0}$, the lattice parameter $a$, and the ionic repulsive energies, the system is in conventional insulating, Mott insulating, integral, or nonintegral valence (IV) metallic states. We have applied the theory to SmS, where ${m}^{*}\ensuremath{\simeq}1$ and $\ensuremath{\kappa}\ensuremath{\sim}4.5$. We have treated ${I}_{0}$ as a free parameter. With the choice of ${I}_{0}=2.5$ eV, the experimental first-order phase transition between insulating and IV metallic states was well reproduced: $P\ensuremath{\sim}6.5$ kbar, $\frac{\ensuremath{\Delta}V}{V}\ensuremath{\simeq}13%$, and a valence change of about 0.6.

The effects of interchain coupling on soliton confinement in crystalline polyacetylene are considered. The analysis of Baeriswyl and Maki on the confinement problem involving two solitons on different ${(\mathrm{CH})}_{x}$ chains is extended to the case of two charged solitons on the same chain. Owing to the mutual repulsion between two charged solitons and the confinement effect due to interchain coupling, there exists a equilibrium confinement distance $2{x}_{0}$ between two solitons. The value of $2{x}_{0}$ is estimated to range between $3\ensuremath{\xi}$ and $4\ensuremath{\xi}$ where $\ensuremath{\xi}$ is the width of a soliton. A detailed study of the problem employing Green's functions in the coordinate representation is presented.

The NMR frequencies of the helical texture in 3He-A in the presence of a magnetic field parallel to the superflow are reexamined in the entire stability region. The effects of the anisotropic contribution to the spin susceptibility are explicitly included and are shown to leave previous results qualitatively unchanged. On the other hand, we find that the anisotropic contribution gives rise to quantitative corrections of maximally 20% at T/T c = 0.95, while its contribution in the immediate vicinity of T c is negligibly small.

Making use of a variational solution $\ensuremath{\Delta}(x)$ the dimerization pattern, we calculate the interaction energy of two solitons within the Su, Shrieffer, and Heeger model for polyacetylene. It is found that two solitons attract each other in general except for the case of two solitons having the same charge and the case of the spin triplet pair of neutral solitons. We have also studied the electronic structure of a regular array of solitons with the same charge.

The anisotropy of orientational order in cholesteric liquid crystals is investigated within a mean-field model of the cholesteric phase. It is shown that this biaxiality emerges as a direct consequence of the helical structure of the phase and the chiral character of the intermolecular interactions. The dependence of the biaxiality on temperature and pitch is compared with recent NMR measurements.

In the presence of tilted magnetic fields, surface n textures are generated in the vicinity of a flat wall in superfluid /sup 3/He-B. The spatial conformations of the surface textures in the semi-infinite space and in parallel-plate geometry are determined. The surface texture gives rise to a series of longitudinal spin-wave bound states, which should be accessible to NMR experiments.

As a first step toward constructing a general molecular model for cholesteric liquid crystals, we propose here a planar model in which the intermolecular potential is required to contain chiral contributions as a result of symmetry considerations. By means of a mean-field analysis, we identify the microscopic basis for the existence of the cholesteric phase. The latter is shown to be a consequence of chirality. The temperature dependence of the cholesteric pitch is discussed, and several numerical examples are given. Our theoretical deductions are consistent with experimental observations. We indicate, however, that under exceptional circumstances two unobserved phenomena may be found to exist. First, particular systems made up of chiral molecules may exist in the nematic phase. Next, as temperature is varied, a particular pure cholesteric substance may undergo untwisting and reverse its helicity after passing through a divergence in pitch.

In the present paper the boundary conditions and the optical absorption are studied for both the discrete and continuum models of solitions in polyacetylene. The topological property of the soliton is incorporated appropriately to derive the correct boundary conditions for the electronic wave functions which are essential for a proper calculation of optical absorption and other properties of the system. A general sum rule for the absorption coefficient is derived for the continuum model which is exactly satisfied by the result of the present calculation. The errors in the previous calculations are indicated. Finally, the theoretical results are compared with the experimental data.

We analyze the stability of a variety of uniform textures in superfluid 3HeA in the presence of superflow p. We find below Tins a class of stable helical l textures, where l is no longer aligned with p but winds around it with a constant pitch .

Pure $\stackrel{^}{l}$ domain walls in superfluid $^{3}\mathrm{He}$ confined between two parallel plates with gap $d$ ($\ensuremath{\sim}{\ensuremath{\xi}}_{\ensuremath{\perp}}$, the dipole coherence length) are considered theoretically. The spatial conformation of the domain wall as well as the domain-wall energy are determined. The domain walls give rise to satellite resonances in NMR experiments. The satellite frequencies are determined.

Detailed measurements of the magnetoresistance of two types of high tensile modulus mesophase-pitch-derived graphite fibers have been performed between 1.4 and 300 K in magnetic fields to 8 T. With increasing magnetic field at low temperatures, the transverse magnetoresistance of these fibers exhibits an unusual oscillatory behavior.

Calculations of the energy for two different nuclear matter models are carried out using Jastrow-Slater wave functions and an integral equation developed previously by Chakravarty and Woo. Even though the same variational parameters are used, our results differ significantly with those of Ceperley, Chester, and Kalos who employed a Monte Carlo technique. The discrepancy, mainly in the potential energy, is traced to short-range behavior of the pair correlation function. No satisfactory explanation can be offered at this time. Our integral equation is then subjected to a formal analysis for a weakly interacting Bose gas. It is shown to perform at least as well for boson systems as the Bogoliubov-Born-Green-Kirkwood-Yvon equation.

The existence of helical textures in $^{3}\mathrm{He}$-$A$ in the presence of both superflow and magnetic field is established theoretically. The magnetic resonance frequencies of the helical textures are determined.

The $\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}$ solitons (i.e., the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}$ domain walls) in the presence of both magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ and superflow ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}_{s}$ with ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}_{s}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ are studied theoretically. In the high-field limit (e.g., kOe) and for ${v}_{s}g~{v}_{0}$(\ensuremath{\sim}0.1cm/sec), there appear three distinct types of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}$ solitons. The spatial conformations as well as the domain-wall energies of these $\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}$ solitons are calculated. These $\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}$ solitons give rise to a series of satellite magnetic resonances. These resonance frequencies are determined theoretically.

The Frank constants and viscosity for a nematic liquid crystal are calculated for a microscopic model: a one-parameter ellipsoid model. A simple relation is established: K 33 / 1 2 (K 11 + K 22 )= 1 2 (η a + η c )/η b , and appears well confirmed by experiment.

If one component of a semiconductor heterojunction has an inverted band gap relative to the other component, e.g. as in HgTe-CdTe, an interface state may exist depending on the valence-band offset. In a quantum well, the mixing of these interface states with the topmost heavy-hole subbands at finite in-plane wave vector changes drastically the in-plane dispersion of the heavy-hole subbands and, hence, the fundamental band gap.

X rays emitted by electrons channeling through a periodically distorted lattice are studied. The lattice distortion works as a wiggler. The intensity of the radiation due to the resonance scattering of the wiggler field can be made comparable with that of the channeling radiation.

Electrostriction effects are considered in a high power dielectric loaded transmission line designed to generate solitons. The Cerenkov emission of elastic waves from the metal‐dielectric interface produces the largest strain among the strain producing mechanisms. The expression for strain as a function of electric field strength is found. The signal loss due to the emission of elastic waves is shown to be insignificant.