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Green’s-function techniques are used to calculate electron cyclotron current drive (ECCD) efficiency in general tokamak geometry in the low-collisionality regime. Fully relativistic electron dynamics is employed in the theoretical formulation. The high-velocity collision model is used to model Coulomb collisions and a simplified quasilinear rf diffusion operator describes wave–particle interactions. The approximate analytic solutions which are benchmarked with a widely used ECCD model, facilitate time-dependent simulations of tokamak operational scenarios using the noninductive current drive of electron cyclotron waves.

Significant progress has been made in obtaining high-performance discharges for many energy confinement times in the DIII-D tokamak [J. L. Luxon et al., Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159]. Normalized performance (measured by the product of βNH89 and indicative of the proximity to both conventional β limits and energy confinement quality, respectively) ∼10 has been sustained for >5 τE with qmin>1.5. These edge localized modes (ELMing) H-mode discharges have β∼5%, which is limited by the onset of resistive wall modes slightly above the ideal no-wall n=1 limit, with approximately 75% of the current driven noninductively. The remaining Ohmic current is localized near the half-radius. The DIII-D electron cyclotron heating system is being upgraded to replace this inductively driven current with localized electron cyclotron current drive (ECCD). Density control, which is required for effective ECCD, has been successfully demonstrated in long-pulse high-performance ELMing H-mode discharges with βNH89∼7 for up to 6.3 s. In plasma shapes compatible with good density control in the present divertor configuration, the achieved βN is somewhat less than that in the high βNH89=10 discharges.

A new method of current drive analysis is demonstrated that compares the measured pitch angles from motional Stark effect (MSE) spectroscopy with simulations of the expected MSE response to localized ECCD. By comparing simulations of the MSE signals with measurements, the best fit of the ECCD profile is determined. The ECCD efficiency ascertained in this manner decreases as the current drive location moves to larger minor radius owing to electron trapping effects. The ECCD efficiency is shown to be highest when the driven current is on the high magnetic field side of the plasma, as expected from theory. The width of the ECCD profile is also in good agreement with theory; previous reports of a broader than expected ECCD profile are shown to have been caused by insufficient radial resolution of the magnetic equilibrium reconstruction.

Localized non-inductive currents due to electron cyclotron wave absorption have been measured on the DIII-D tokamak. Clear evidence of non-inductive currents is seen on the internal magnetic field measurements by motional Stark effect spectroscopy. The magnitude and location of the non-inductive current is evaluated by comparing the total and ohmic current profiles of discharges with and without electron cyclotron wave power. The measured current agrees with Fokker-Planck calculations near the magnetic axis, but exceeds the predicted value as the location of the current drive is moved to the half-radius.

Both the dynamic and equilibrium thermal responses of an L?mode plasma to repetitive ECH heat pulses were measured and compared with predictions from several thermal transport models. While no model consistently agreed with all observations, the GLF23 model was most consistent with the perturbed electron and ion temperature responses for one of the cases studied, which may indicate a key role played by electron modes in the core of these discharges. Generally, the IIF and MM models performed well for the perturbed electron response while the GLF23 and IFS/PPPL models agreed with the perturbed ion response for all three cases studied. No single model agreed well with the equilibrium temperature profiles measured.

A weakly relativistic theory of current drive by parallel acceleration of electrons in toroidal geometry is presented. Analytic expressions of efficiency are obtained for superthermal and subthermal electrons. By using a few adjustable parameters for intermediate energies, an accurate formula for the efficiency is obtained by fitting numerical results. This includes trapping effects and is valid for all frequencies up to the lower hybrid range of frequencies. It is found that for low‐frequency fast‐wave current drive, the relativistic and nonrelativistic efficiencies agree to within 15% up to 500 keV, although the relativistic corrections to power absorption and current density can be much larger separately. Relativistic effects on the efficiency become prominent at lower energies for Landau damping.

A fully relativistic theory of electron cyclotron current drive (ECCD) efficiency based on Green’s function techniques is considered. Numerical calculations of the current drive efficiency in a uniform magnetic field are performed. The numerical results with parameter regimes relevant to ITER operation are compared with those of two simplified models in which the electronelectron Coulomb collision operator is respectively approximatedbyitshigh-velocitylimitandasemirelativistic form. Our results indicate that the semirelativistic approximation of the collision operator should be appropriate for modeling the ECCD efficiency under ITER conditions.

Current drive experiments have been performed on the DIII-D tokamak using fast waves, electron cyclotron waves, and neutral injection. Fast wave experiments were performed using a 4-strap antenna with 1 MW of power at 60 MHz. These experiments showed effective heating of electrons, with a global heating efficiency equivalent to that of neutral injection even when the single pass damping was calculated to be as small as 5%. The damping was probably due to the effect of multiple passes of the wave through the plasma. Fast wave current drive experiments were performed with a toroidally directional phasing of the antenna straps. Currents driven by fast wave current drive (FWCD) in the direction of the main plasma current of up to 100 kA were found, not including a calculated 40 kA of bootstrap current. Experiments with FWCD in the counter current direction showed little current drive. In both cases, changes in the sawtooth behavior and the internal inductance qualitatively support the measurement of FWCD. Experiments on electron cyclotron current drive have shown that 100 kA of current can be driven by 1 MW of power at 60 GHz. Calculation with a Fokker-Planck code show that electron cyclotron current drive (ECCD) can be well predicted when the effects of electron trapping and of the residual electric field are included.

A simple theory for the study of stability and beam energy scaling of laser wake field accelerators (LWFA) was derived on the basis of the balance between the ponderomotive force due to the laser pulse and the restoring force due to the background ions. The theoretical analysis shows that the curvature of the accelerating structure is proportional to the relativistic plasma wavelength, which determines the beam energy scaling of a stably operated LWFA. Two dimensional particle-in-cell simulations were performed that demonstrate the fluctuation of the maximum energy gain of an accelerated electron bunch due to the unstable accelerating structure, which length is dynamically oscillating between the plasma wavelength and the relativistic plasma wavelength within a range of the laser intensity. The unstable accelerating structure can be stabilized by varying the laser intensity or reducing the plasma density. The simulation results reveal the existence of the parameter space for stable operations of a LWFA. The comparisons between the energy scaling law derived by the simple theory, the numerical results, and previous experimental results with self-guided laser pulses show good agreement and prove the simple theory can provide a good estimation of the beam energy for designing a new LWFA experiment.

In the limit that the electron thermal velocity greatly exceeds the fast ion velocity for electrical currents driven by neutral beams, the trapped electron correction to the Ohkawa current and the electron density gradient contribution to bootstrap current are shown to share the same transport coefficient in the banana regime. Therefore, existing analytic expressions for the bootstrap coefficient valid for arbitrary aspect ratio tokamaks can also be used to calculate the trapped electron effect.

A271 ELECTRON CYCLOTRON CURRENT DRIVE IN DIII-D: EXPERIMENT AND THEORY. Experiments on the DIII-D tokamak in which the measured off-axis electron cyclotron current drive has been compared systematically to theory over a broad range of parameters have shown that the Fokker-Planck code CQL3D provides an excellent model of the relevant current drive physics. This physics understanding has been critical in optimizing the application of ECCD to high performance discharges, supporting such applications as suppression of neoclassical tearing modes and control and sustainment of the current profile.

Numerical thermalization in collisional one-dimensional (1D) electrostatic (ES) particle-in-cell (PIC) simulations was investigated. Two collision models, the pitch-angle scattering of electrons by the stationary ion background and large-angle collisions between the electrons and the neutral background, were included in the PIC simulation using Monte-Carlo methods. The numerical results show that the thermalization times in both models were considerably reduced by the additional Monte-Carlo collisions as demonstrated by comparisons with Turner's previous simulation results based on a head-on collision model [M. M. Turner, Phys. Plasmas 13, 033506 (2006)]. However, the breakdown of Dawson's scaling law in the collisional 1D ES PIC simulation is more complicated than that was observed by Turner, and the revised scaling law of the numerical thermalization time with numerical parameters are derived on the basis of the simulation results obtained in this study.

A local representation is used to determine localized features in the current profiles due to ECCD in the DIII-D tokamak discharges from equilibrium reconstruction based on spectroscopic and external magnetic measurements. Initial results indicate that reconstruction using a local basis function can resolve very peaked ECCD profiles. The reconstructed narrow ECCD profiles are consistent with the quasi-linear Fokker-Planck results from the CQL3D code.

Lorentz gas model is used to examine collisionality modification of the trapped electron effects on electron cyclotron current drive efficiency. Appreciable collisionality enhancement of the current drive efficiency appears to be possible in the strong trapping cases in present-day current drive experiments.

Increased efficiency of off-axis electron cyclotron current drive (ECCD) has been obtained in discharges in DIII-D with higher electron beta, and these results have been understood by studying computationally the particle fluxes in velocity space driven by the EC waves. The relativistic cyclotron resonance tends to shift away in velocity space from the trapped-passing boundary for low-field-side launch as the electron temperature and/or density rise, increasing the net efficiency toward that of the trapping-free Fisch-Boozer level. Calculations with the CQL3D Fokker-Planck code illustrate clearly that the flux in velocity space due to rf-induced diffusion moves away from the trapping boundary for values of βe which have been realized in the experiments.

Electron cyclotron current drive (ECCD) experiments on the DIII-D tokamak are solidifying the physics basis for localized, off-axis current drive in both standard and advanced operating modes, the goal being to validate a predictive model for ECCD. The measured ECCD efficiency is found to be in agreement with theoretical calculations using the CQL3D Fokker-Planck code over a range of toroidal injection angles, absorption radii, and electron beta. The latter dependence is especially important since the ECCD efficiency is shown to increase with local electron beta, which is favorable for current profile control using off-axis ECCD in high-beta advanced tokamaks.

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.

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.

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

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.

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.

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.

The paraxial WKB code TORBEAM (Poli, 2001) is widely used for the description of electron-cyclotron waves in fusion plasmas, retaining diffraction effects through the solution of a set of ordinary differential equations. With respect to its original form, the code has undergone significant transformations and extensions, in terms of both the physical model and the spectrum of applications. The code has been rewritten in Fortran 90 and transformed into a library, which can be called from within different (not necessarily Fortran-based) workflows. The models for both absorption and current drive have been extended, including e.g. fully-relativistic calculation of the absorption coefficient, momentum conservation in electron–electron collisions and the contribution of more than one harmonic to current drive. The code can be run also for reflectometry applications, with relativistic corrections for the electron mass. Formulas that provide the coupling between the reflected beam and the receiver have been developed. Accelerated versions of the code are available, with the reduced physics goal of inferring the location of maximum absorption (including or not the total driven current) for a given setting of the launcher mirrors. Optionally, plasma volumes within given flux surfaces and corresponding values of minimum and maximum magnetic field can be provided externally to speed up the calculation of full driven-current profiles. These can be employed in real-time control algorithms or for fast data analysis.