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Lower hybrid (LH) current drive experiments on the Princeton Beta Experiment-Modified (PBX-M) [Phys. Fluids B 2, 1271 (1990)] have shown that the current profile can be changed by varying the phase velocity of the waves. The radial profile of the current carrying electrons was deduced from two-dimensional hard x-ray tomography. For a certain range of phase velocities, there is a correlation between the peak of the fast electron profile and the launched wave spectrum, despite the presence of a wide spectral gap between the phase velocity and the thermal electron energy distribution. A new model is proposed to explain how first-pass wave damping is possible in such plasmas. The rf power can form a tail of energetic electrons, and subsequently waves with moderate phase velocity can damp on them. For waves with very fast phase velocity, there must be an upshift of the n∥ spectrum for any damping to occur. These hypotheses are supported by ray tracing results which are coupled to relativistic Fokker–Planck cal...

The physics of current profile modification with lower hybrid waves has been investigated in the Princeton Beta Experiment-Modification tokamak by comparing experimental internal magnetic field profiles with ray tracing code predictions. When the n| spectrum of the launched waves was varied, local changes in the current profile were observed according to equilibria, reconstructed from motional Stark effect polarimetry measurements. Changes in the central safety factor (q) were also determined to be a function of the applied radiofrequency (RF) power. Calculations of the non-inductive current with the Tokamak Simulation Code/Lower Hybrid Simulation Code were unable to duplicate the measured current profiles. Instead, a current broadening mechanism like a finite fast electron diffusion coefficient had to be hypothesized to fit the data. This study was possible only with recent improvements in diagnostics and numerical analysis tools, and it constitutes an important contribution to our understanding of non-inductive current drive for future fusion reactors

Lower hybrid current drive (LHCD) in the tokamak Princeton Beta Experiment-Modification (PBX-M) is computed with a dynamic model in order to understand an actual discharge aimed at raising the central q above unity. Such configurations offer advantages for steady state operation and plasma stability. For the particular parameters of this PBX-M experiment, the calculation found singular profiles of plasma current density J and safety factor q developing soon after LHCD begins. Smoothing the lower hybrid wave driven current and power using a diffusion-like equation and a velocity-independent diffusivity for fast-electron current brought the model into reasonable agreement with the measurements if Dfast approximately=1.0 m2/s. Such a value for Dfast is in the range suggested by other work

Recent experiments in the ion cyclotron range of frequencies (ICRF) in the Tokamak Fusion Test Reactor [Fusion Technol. 21, 13 (1992)] are discussed. These experiments include mode conversion heating and current drive, fast wave current drive, and heating of low (L)‐ mode deuterium–tritium (D–T) plasmas in both the hydrogen minority and second harmonic tritium regimes. In mode conversion heating, a central electron temperature of 10 keV was attained with 3.3 MW of radio‐frequency power. In mode conversion current drive experiments, up to 130 kA of current was noninductively driven, on and off axis, and the current profiles were modified. Fast wave current drive experiments have produced 70–80 kA of noninductively driven current. Heating of L‐mode deuterium and D–T plasmas by hydrogen minority ICRF has been compared. Finally, heating of L‐mode D–T plasmas at the second harmonic of the tritium cyclotron frequency has been demonstrated.

The first experiments utilizing high‐power radio waves in the ion cyclotron range of frequencies to heat deuterium–tritium (D–T) plasmas have been completed on the Tokamak Fusion Test Reactor [Fusion Technol. 21, 13 (1992)]. Results from the initial series of experiments have demonstrated efficient core second harmonic tritium (2ΩT) heating in parameter regimes approaching those anticipated for the International Thermonuclear Experimental Reactor [D. E. Post, Plasma Physics and Controlled Nuclear Fusion Research, Proceedings of the 13th International Conference, Washington, DC, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 239]. Observations are consistent with modeling predictions for these plasmas. Efficient electron heating via mode conversion of fast waves to ion Bernstein waves has been observed in D–T, deuterium‐deuterium (D–D), and deuterium–helium‐4 (D–4He) plasmas with high concentrations of minority helium‐3 (3He) (n3He/ne≳10%). Mode conversion current drive in D–T plasmas ...

Application of Ion Bernstein Wave Heating (IBWH) into the Princeton Beta Experiment‐Modification (PBX‐M) [Phys. Fluids B 2, 1271 (1990)] tokamak stabilizes sawtooth oscillations and generates peaked density profiles. A transport barrier, spatially correlated with the IBWH power deposition profile, is observed in the core of IBWH‐assisted neutral beam injection (NBI) discharges. A precursor to the fully developed barrier is seen in the soft x‐ray data during edge localized mode (ELM) activity. Sustained IBWH operation is conducive to a regime where the barrier supports large ∇ne, ∇Te, ∇νφ, and ∇Ti, delimiting the confinement zone. This regime is reminiscent of the H(high) mode, but with a confinement zone moved inward. The core region has better than H‐mode confinement while the peripheral region is L(low)‐mode‐like. The peaked profile enhances NBI core deposition and increases nuclear reactivity. An increase in central Ti results from χi reduction (compared to the H mode) and better beam penetration. Boot...

Ray tracing simulations based on experimental PBX-M equilibria show a limited range of the parallel wavenumber (n||=k||c/ω) along a ray trajectory. The range of n|| accessible to the excited wave is shown to have both a lower and an upper bound. The ray's phase volume is projected into (n||, R, Z) space to define a domain of wave accessibility for each toroidal mode number excited by the launcher. A comparison of circular and bean shaped plasmas with a high aspect ratio (A ~ 5.5) shows that the rays fill a substantially larger portion of the accessible domain in bean shaped plasmas. Furthermore, in the bean shaped case the accessible domain tends to extend to higher n

During lower hybrid current drive on tokamaks, suprathermal electrons are generated that emit hard x‐ray bremsstrahlung. A pinhole camera has been installed on the PBX‐M tokamak that records 128×128 pixel images of the hard x‐ray plasma bremsstrahlung emitted in the 30–200 keV photon energy range. The camera has a temporal resolution of 3 ms and a spatial resolution of 3–4 cm in the plasma. The detector is a 230‐mm‐diam hard x‐ray image intensifier. This instrument has identified hollow radiation profiles on PBX‐M, indicating off‐axis current drive. A detailed account of the construction of the hard x‐ray camera, its operation, and its performance is given.

Fast electron localization and transport are important for tokamak current profile control schemes. The hard X-ray camera on PBX-M produces two-dimensional, time resolved tangential images of fast electron bremsstrahlung, from which a fast electron diffusion constant is calculated. Assuming a radially narrow lower hybrid power absorption profile, a momentum space absorption profile and a transport model, a model fast electron current density profile is calculated and compared to an experimentally derived profile, and the diffusion coefficient is adjusted until a good fit is found. Using this model, the authors compute an upper limit for an effective diffusion constant of D*

The experimental program of the Princeton Beta Experiment‐Modified (PBX‐M) tokamak [Phys. Fluids B2, 1271 (1990)] is directed toward tailoring plasma profiles to achieve greater stability and confinement and to gain access to the second stability region. Modification of the current density profile has been achieved with lower‐hybrid current drive (LHCD), leading to a regime free of global magnetohydrodynamic modes, while raising the value of q(0) above unity. The diffusion of the fast electrons produced by LHCD has been examined using two‐dimensional hard x‐ray imaging. Ion Bernstein waves (IBW) have been used for ion heating: a preliminary analysis shows that ion heating was spatially localized and in agreement with theoretical calculations. Divertor biasing has modified the electric field inside the last closed surface, resulting in the formation of a transport barrier, which in turn has reduced the threshold power of neutral beam injection (NBI) for H‐mode transition by 25%.

The advanced tokamak (AT) capability of the Fusion Ignition Research Experiment (FIRE) burning plasma experiment is examined with 0-D systems analysis, equilibrium and ideal-MHD stability, radio-frequency current-drive analysis, and full discharge dynamic simulations. These analyses have identified the required parameters for attractive burning advanced tokamak plasmas, and indicate that these are feasible with the present progress on existing experimental tokamaks.

Low aspect ratio tokamaks pose interesting new challenges for heating and current drive. The NSTX (National Spherical Tokamak Experiment) device to be built at Princeton is a low aspect ratio toroidal device that has the achievement of high toroidal beta (∼45%) and non-inductive operation as two of its main research goals. To achieve these goals significant auxiliary heating and current drive systems are required. Present plans include ECH (Electron cyclotron heating) for pre-ionization and start-up assist, HHFW (high harmonic fast wave) for heating and current drive and eventually NBI (neutral beam injection) for heating, current drive and plasma rotation.

Lower hybrid current drive (LHCD) in the tokamak Princeton Beta Experiment-Modification (PBX-M) is computed with a dynamic model in order to understand an actual discharge aimed at raising the central q above unity. Such configurations offer advantages for steady-state operation and plasma stability. For the particular parameters of this PBX-M experiment, the calculation found singular profiles of plasma current density J and safety factor q developing soon after LHCD begins. Smoothing the lower hybrid-driven current and power using a diffusion-Eke equation and a velocity-independent diffusivity for fast-electron current brought the model into reasonable agreement with the measurements if D{sub fast} {approx} 1.0 m{sup 2}/s. Such a value for D{sub fast} is in the range suggested by other work.

A ‘‘Lower hybrid Simulation Code’’1 provides the dynamic transport computations TSC2 and TRANSP3 with a common model for lower hybrid current drive based on multiple ray tracing, quasilinear absorption of power, and an estimate of the effect of electric field through a parameterization due to Karney and Fisch.4 Treatment of fast wave current drive (FWCD) in the ion cyclotron range of frequencies has been added, while keeping the interface to TSC and TRANSP the same. Electron absorption from Landau damping, transit time magnetic pumping, and cross‐terms yield a modified electron distribution from which current is computed. Cyclotron damping on harmonics of ion species is tracked in the power balance and reported to the governing transport code. Initial results of the stand‐alone computation show quantitative issues associated with unwanted ion heating in the possible TFTR‐extension; and suggest important toroidal effects for FWCD in the NSTX‐the National Spherical Tokamak Experiment.

The TSC‐LSC computational model of the dynamics of lower hybrid current drive has been exercised extensively in comparison with data from a Princeton Beta Experiment‐Modification (PBX‐M) discharge where the measured q(0) attained values slightly above unity. Several significant, but plausible, assumptions had to be introduced to keep the computation from behaving pathologically over time, producing singular profiles of plasma current density and q. Addition of a heuristic current diffusion estimate, or more exactly, a smoothing of the rf‐driven current with a diffusion‐like equation, greatly improved the behavior of the computation, and brought theory and measurement into reasonable agreement. The model was then extended to longer pulse lengths and higher powers to investigate performance to be expected in future PBX‐M current profile modification experiments.

In the Tokamak Fusion Test Reactor (TFTR) the mode converted ion Bernstein wave (IBW) has been shown to heat electrons, drive current (both on and off axis), and to interact with fusion products. D‐3He and D‐T‐3He plasmas have been used as mode conversion targets. On‐axis mode conversion heating increased Te(0) from 3 keV to 10 keV with 4 MW of ICRF. On‐axis currents of 125 kA with 2 MW of ICRF, and off axis currents of 100 kA with 4 MW of ICRF, have been driven. A strong interaction of the IBW with fusion products has been observed. Mode conversion current drive (MCCD) for TPX is briefly discussed.

Current drive experiments have been performed on TdeV over a wide range of parameters. It is found that the current drive efficiency {eta} does not scale with {ital N}{sub {parallel}} as expected from simple theory. Simulations with the ACCOME code suggest that the reduced efficiency at low {ital N}{sub {parallel}} values is mostly due to a large toroidal upshift in the LH wave spectrum. The loss of suprathermal electrons to the divertor plates was monitored during CD experiments. The power loss increases with decreasing {ital N}{sub {parallel}} values and can be reach up to 15{percent} of the injected rf power in low density plasmas. {copyright} {ital 1996 American Institute of Physics.}

Efficient direct majority ion heating in a deuterium‐tritium (D‐T) reactor‐grade plasma via absorption of fast magnetosonic waves in the ion cyclotron range of frequencies (ICRF) is discussed. Majority ion heating results from resonance overlap between the cyclotron layers and the D‐T ion‐ion hybrid layer in hot, dense plasmas for fast waves launched with high parallel wavenumbers. Analytic and numerical models are used to explore the regime in ITER plasmas.

During lower hybrid current drive on PBX-M suprathermal electrons in the 30 to 150 keV range are generated. These electrons emit hard X-ray bremsstrahlung in collisions with plasma ions; the radiation creates images in a hard X-ray pinhole camera. In order to interpret the hard X-ray images, a computer simulation code has been written, the PBXRAY code. It represents an extension of the STEVENS code that calculates the free-free and free-bound radiation for non-Maxwellian relativistic electron tail distributions. The PBXRAY code provides the chord integration in the bean-shaped plasma geometry on PBX-M and integrates over photon energy. The simulations show that the location of the suprathermal electrons can be determined with an accuracy of approximately two centimeters in the plasma. In particular, the authors analyzed discharges whose characteristic ``hollow`` images indicate off-axis LH current drive. A comparison of images taken with different absorber foils reveals that the suprathermal electrons have less than 150 keV parallel energy for the hollow discharges.

An x‐ray pinhole camera helps the PBX‐M experiment diagnose the location of lower hybrid current drive now being used to demonstrate deliberate modification of the current profile to improve plasma stability and beta. One computational model supporting the experiment is the Lower hybrid Simulation Code (LSC), which can predict the image in the camera after doing multiple ray tracing in general beam‐shaped plasmas, and quasilinear damping of waves on electrons. We present experimental and computational images, and discuss the differences and similarities.

Lower hybrid current drive (LHCD) is being explored as a means to control the current density profile on PBX‐M with the goal of raising the central safety factor q(0) to values of 1.5–2 to facilitate access to a full‐volume second stable regime. Initial experiments have been conducted with up to 400 kW of 4.6 GHz LH power in circular and indented plasmas with modest parameters. A tangential‐viewing two‐dimensional hard x‐ray imaging diagnostic has been used to observe the bremsstrahlung emission from the suprathermal electrons generated during LHCD. Hollow hard x‐ray images have indicated off‐axis localization of the driven current. A serious obstacle to the control of the current density profile with LHCD is the concomitant generation of MHD activity, which can seriously degrade the confinement of suprathermal electrons. By combining neutral beam injection with LHCD, an MHD‐free condition has been obtained where q(0) is raised above 1.

The magnetic field pitch angle measurements from the multichannel Motional Stark Effect (MSE) polarimeter system, together with the external poloidal flux values, toroidal plasma current, coil currents, and plasma pressure profile, as computed by the TRANSP code, are used to constrain the numerical solution of the Grad‐Shafranov equation. The experimental results from the soft x‐ray diagnostic and hard x‐ray bremsstrahlung radiation profiles show clear signatures of a change in the current density profile during Lower hybrid injection. Indications of a variation in the q‐profile are supported by the behavior of the measured sawtooth inversion radius. Modifications in the current density profiles, induced by Lower Hybrid waves, are discussed in terms of their effect on q‐profiles and volume‐averaged quantities like Ii.

The energy of suprathermal electrons during lower‐hybrid current drive on PBX‐M is determined. (AIP)

Understanding the wave damping mechanism in the presence of a `spectral gap` is an important issue for the current profile control using Lower Hybrid Current Drive (LHCD). The authors examine a traditional explanation based upon upshifting of the wave parallel refractive index (n{sub {parallel}}) and find that there can be an upper bound in the n{sub {parallel}} upshift. The amount of upshift is not sufficient to bridge the spectral gap completely under some PBX-M LHCD conditions. There is experimental evidence, however, that current was driven even under such conditions. Another mechanism is also considered, based upon the 2-D velocity space dynamics coupled with a compound wave spectrum, here consisting of forward- and backward-running waves. The runaway critical speed relative to the phase speeds of these waves plays an important role in this model.

The modification and control of the plasma current profile by lower hybrid current drive is considered one of the most promising avenues to control MHD instabilities and improve the high beta performance of tokamaks. The Hard X‐ray Camera on PBX‐M records images of the bremsstrahlung emitted by suprathermal electrons that carry part of the plasma current during lower hybrid current drive. The Hard X‐ray Camera is a pinhole camera that uses a 9 in. diam x‐ray intensifier as detector. It provides a tangential view of the tokamak plasma and delivers 64 images with 128×128 pixels per plasma shot. The spatial resolution in the plasma is approximately 2 cm, and the time resolution 3 ms. The camera is sensitive to x rays between 30 and 200 keV. The photon energy (and the energy of the suprathermal electrons) is measured with an absorber foil method. Modeling of the x‐ray emission has reproduced the experimental images with a better than 10% accuracy. In addition, two inversion techniques have been developed: one...

The Compact Ignition Tokamak (CIT) is a proposed modest-size ignition experiment designed to study the physics of alpha particle heating. The basic concept is to achieve ignition in a modest-size minimum cost experiment by using a high plasma density to achieve nT{sub E} {approx} 2 x 10{sup 20}s/m{sup 3} required for ignition. The high density requires a high toroidal field (10 T). The high toroidal field allows a large plasma current (10 MA) which provides a high level of ohmic heating, improves the energy confinement, and allows a relatively high beta ({approx} 6%). The present CIT design also has a high degree of elongation (k {approx} 1.8) to aid in producing the large plasma current. A double null poloidal divertor and pellet injection are part of the design to provide impurity and particle control, improve the confinement, and provide flexibility for improving the plasma profiles. Auxiliary heating is expected to be necessary to achieve ignition, and 10-20 MW of ICRF is to be provided.

Steady currents up to 165 kA for 3.5 seconds and 420 kA for 0.3 seconds have been maintained by 800 MHz lower hybrid waves. For line-averaged densities up to 7 x 10/sup 12/ cm/sup -3/ the current is maintained with no input power from the ohmic heating transformer. The waves are launched with an array of six waveguides. Measurements of X rays and electron cyclotron radiation show that the rf power produces and maintains a suprathermal tail of electrons apparently independent of the number of fast electrons in the plasma prior to turning on the rf power. Measurements of current-drive efficiency and the electron tail provide direct evidence for a resonant wave-particle interaction. The radial profile of the rf-sustained current inferred from x-ray measurements is peaked in the center of the plasma and appears to obey the same q-value restraints as the inductively driven ohmic heating current. Current drive is observed to be accompanied always by radiation at frequencies greater than or equal to ..omega../sub ce/ and less than or equal to ..omega../sub pe/. The connection between this radiation and the current-drive mechanism is under study.

A half-screen foil technique was used with the hard X-ray camera on the PBX-M tokamak to determine the energy distribution of the suprathermal electrons generated during the lower hybrid current drive. The ratio of perpendicular to parallel temperature of the suprathermal electrons was deduced from anisotropy of the bremsstrahlung emission utilizing Abel inversion techniques. Results from lower hybrid current drive discharges are discussed.

During lower hybrid current drive on the Princeton Beta Experiment Modification PBX‐M [Bell et al., Phys. Fluids B 2, 1271 (1990)], suprathermal electrons in the 30–150 keV range are generated. These electrons emit hard x‐ray bremsstrahlung in collisions with plasma ions; the radiation creates images in a hard x‐ray pinhole camera. In order to interpret the hard x‐ray images, a computer simulation code has been written; the ‘‘pbxray’’ code, which is described in this paper. The code represents an extension of the Stevens code [Stevens et al., Nucl. Fusion 25, 1529 (1985)], which calculates the free–free and free–bound radiation for non‐Maxwellian relativistic electron tail distributions. The pbxray code provides the chord integration in the bean‐shaped plasma geometry on the PBX‐M tokamak and integrates over photon energy. The simulations show that the location of the suprathermal electrons can be determined with an accuracy of approximately 2 cm in the plasma. In particular, discharges are analyzed whose...