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The paper deals with time domain-deterministic stochastic assessment of a transient electric field generated by a ground penetrating radar (GPR) dipole antenna and transmitted into a lower half-space. The deterministic time domain formulation is based on the space-time Hallen integral equation for half-space problems. The Hallen equation is solved via the Galerkin–Bubnov variant of the Indirect Boundary Element Method (GB-IBEM) and the space-time current distribution along the dipole antenna is obtained, thus providing the field calculation. The field transmitted into the lower medium is obtained by solving the corresponding field integrals. As GPR systems are subjected to a rather complex environment, some input parameters, for example the antenna height over ground or earth properties, are partly or entirely unknown and, therefore, a simple stochastic collocation (SC) method is used to properly access relevant statistics about GPR time responses. The SC approach also aids in the assessment of corresponding confidence intervals from the set of obtained numerical results. The expansion of statistical output in terms of mean and variance over a polynomial basis, via the SC method, is shown to be a robust and efficient approach providing a satisfactory convergence rate.

Fast particle driven m=1/n=1 modes in the form of fishbones frequently initiate neoclassical tearing modes (NTMs) on Axisymmetric Divertor Experiment Upgrade [W. Koppendorfer et al., 14th International Conference on Plasma Physics and Controlled Fusion (International Atomic Energy Agency, Vienna, 1993), Vol. I, p. 127] and other neutral-beam-injection heated tokamaks, but disappear after the NTMs have reached a quasistationary state. A burst of other magnetohydrodynamic phenomena, described in this paper, appear instead, similar in repetition rate and time signature of frequency and amplitude. They are associated with the growth of the m=2/n=2 satellite of the m=3/n=2 neoclassical tearing mode, and a transient increase (termed FJ=frequency jump event) in the rotation frequency of the coupled mode system. They lead to a thermal crash, originating at q=3/2, propagating inwards up to the q=1 surface. With a lower repetition rate (more characteristic of sawteeth) similar events occur, where a large 1/1 component also appears and the fast crash propagates to the plasma center frequency jump with sawtooth character (FJST). The analogies to the fishbone case suggest that this phenomenon is caused by the interaction with fast particles, which transiently impress their precession frequency on the pre-existing magnetic perturbation of the NTM.

MHD phenomena in ASDEX Upgrade in standard shear discharge regimes as well as in weak and reversed shear discharges are investigated. The onset of neoclassical tearing modes leads to the most serious β limit at ASDEX Upgrade. The βp value for the onset of neoclassical tearing modes is found to be proportional to the poloidal ion gyroradius for collisionless plasmas, as proposed by the ion polarization current model. Larger collisionalities have a stabilizing effect. Sawtooth crashes or fishbones can trigger the mode, and in a few cases it appears spontaneously. The fractional energy loss due to a (3,2) mode saturates for large pressures at around 25%, in agreement with the result of theoretical calculations. Owing to its large and flexible heating power, ASDEX Upgrade is well equipped for investigations of fast particle driven or influenced MHD modes. The observed TAEs have been shown to agree well with theoretical predictions regarding the frequency as well as the drive by fast particles. Fishbones have been shown to not only affect the fast particle distribution but also directly to affect the background plasma. For low and reversed shear discharges, theoretical predictions for the growth of neoclassical tearing modes in regimes with a large fraction of bootstrap current at the rational surface, as well as for neoclassical double tearing modes, are given. In discharges with large impurity accumulation in the plasma centre, unusual MHD phenomena such as cascades of high n tearing modes and modes driven by positive pressure gradients have been found at ASDEX Upgrade. For similar discharges, double tearing modes have been investigated at TEXTOR.

Observations on ASDEX Upgrade show that fishbones can have a much stronger effect on the background plasma parameters than expected from an ideal, fast particle driven instability. They lead to a redistribution of electron temperature and impurity densities, similar in form and magnitude to sawteeth, albeit with the plasma parameter variation occurring on a significantly longer time-scale. Simulations of the current diffusion in discharges with favourable core confinement require fishbones to be furthermore associated also with magnetic reconnection to yield consistency between the conductivity and current profile information derived from ECE, bremsstrahlung, MSE and the localization of m = 1,n = 1 activity.

Stationary discharges with $H$-mode edge and internal transport barrier for energy, momentum, and particle transport have been obtained on ASDEX Upgrade. At a line averaged density of $4\ifmmode\times\else\texttimes\fi{}{10}^{19}{\mathrm{m}}^{\ensuremath{-}3}$ an $H$ factor of ${H}_{\mathrm{ITER}89\ensuremath{-}P}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2.4$ and ${\ensuremath{\beta}}_{N}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ could be maintained for 6 s corresponding to 40 confinement times, limited only by the possible discharge duration. The $q$ profile is flat in the center and close to 1. Current diffusion calculations suggest that reconnection is required to clamp the safety factor at 1, which in the absence of sawteeth is explained by the strong fishbone activity.

The early phase of the neoclassical (3,2) + (2,2) tearing mode at ASDEX Upgrade has been investigated in order to study the seed island. Sawtooth crashes or fishbones can trigger this mode, and in few cases it appeared spontaneously.

The βp value for the onset of the neoclassical (3, 2) tearing mode at ASDEX Upgrade is found to be proportional to the ion gyro-radius as proposed in the ion polarization model. This scaling law has been proven by varying the ion temperature, the magnetic field and the mass of the plasma ions.

If the ion Bernstein wave (IBW) heating power in an H mode discharge of the PBX-M experiment exceeds a threshold power of about 200 kW, a core transport barrier is created in the central region of the plasma. At lower neutral beam injection (NBI) powers, the core barrier is accompanied by an edge L mode. The high edge localized mode (ELM) repetition frequency (1 kHz) prevents the creation of a strong barrier, so the edge first has to make an H-to-L transition before a strong core transport barrier can be created. At higher NBI powers, the ELM repetition frequency is lowered to less than 200 Hz, which allows the immediate creation of a strong core barrier. Edge localized mode loss, which propagates radially first on a fast (non-diffusive) and then on a slow (diffusive) time-scale all the way to the plasma core, is strongly reduced in the core barrier region. Correlated with the reduced ELM loss, the fluctuations in the core barrier region are also strongly reduced, both during the ELM and during the quiet periods between the ELMs. There is strong evidence that the IBW induced poloidal flow shear is responsible for the stabilization of core turbulence and the creation of the core transport barrier. The large perpendicular E ? B flow shear component of the measured toroidal velocity in co-injection neutral beam heated discharges seems to be largely cancelled by the ion diamagnetic drift shear produced by large ion pressure gradients in the core barrier region. The value of IBW induced poloidal flow has not been experimentally determined, but its numerical value is found to be a factor of 4 larger than either the toroidal velocity or the ion diamagnetic drift shear components, leaving only IBW induced flow shear as the most probable cause for the turbulence stabilization. The core turbulence suppression and the creation of the core transport barrier is also consistent with expectations from a comparison between the E ? B flow shear rate and a rough estimate of the linear ion temperature gradient (ITG) growth rate. The presence of the core barrier region also strongly modifies the other MHD events: crashes on the q = 1.5, 2 surfaces and the disruption.

Two new types of high frequency (HF) MHD mode activity are observed when a core transport barrier is formed during ion Bernstein wave (IBW) heating in PBX-M. These modes, localized in the core transport barrier, seem to be mainly responsible for the soft saturation in the strength of the core transport barrier. The two types of HF mode activity are determined by the presence or absence of a strong 1/1 mode. The n = m modes are observed with the 1/1 mode, while the n = m - 1 modes are seen when the 1/1 mode is absent. The m numbers of both of these modes vary between 4 and 13. They all seem to be coupled and rotate as a rigid body. The n = m - 1 modes seemed to be narrowly localized on their corresponding rational surface, i.e. q = m/(m - 1). The modes are ballooning-like, and their amplitudes increase with increasing β. Calculations with the CASTOR code show that the n = m - 1 modes are most probably pressure driven tearing modes, but the possibility of kinetic ballooning modes (KBMs) cannot be fully excluded. The n = m modes appear on or around the q = 1 surface, and are localized at the X point of the 1/1 mode island. The frequency offset of the n = m modes, which is too low for a TAE, is shown to be consistent with β-induced toroidal Alfven eigenmodes (BAEs).

Cascades of high-n tearing modes with mode bursts in order of increasing n number have recently been observed in ASDEX Upgrade in the vicinity of the q = 1 surface. The relationship between the poloidal and toroidal mode numbers is m = n + 1. A cascade commences with a low n number, typically , and can reach values around 22. They are observed in discharges with impurity accumulation and with a transient evolution of the q profile, where the magnetic shear is low and the resistivity high. Calculations with the CASTOR code have shown that high-n tearing modes become unstable if the magnetic shear is low, resistivity is high and the pressure gradient high enough to make mode coupling important. All three conditions are needed to obtain a positive and large growth rate. These CASTOR code calculations are consistent with the experimental observations.

Recent results from ASDEX Upgrade are presented. An improved understanding of energy and particle transport emerges in terms of a 'critical gradient' model for the temperature gradients. Coupling this to particle diffusion explains most of the observed behaviour of the density profiles, in particular the finding that strong central heating reduces the tendency for density profile peaking. Internal transport barriers with Te and Ti in excess of 20 keV (but not simultaneously) have been achieved. By shaping the plasma, a regime with small type II ELMs has been established. Here, the maximum power deposited on the target plates was greatly reduced at constant average power. Also, an increase of the ELM frequency by injection of shallow pellets was demonstrated. ELMfree operation is possible in the QH-mode regime previously found in DIII-D which has also been established on ASDEX Upgrade. Regarding stability, a regime with benign NTMs was found. During ECCD stabilisation of NTMs, bN could be increased well above the usual onset level without a reappearance of the NTM. ECRH and ECCD have also been used to control the sawtooth repetition frequency at a moderate fraction of the total heating power. The inner wall of the ASDEX Upgrade vessel has increasingly been covered with tungsten without detrimental effects on plasma performance. Regarding scenario integration, a scenario with a large fraction of noninductively driven current ( 50%), but without internal tranport barrier has been established. It combines improved confinement (tE=tITER98 1:2) and stability (bN 3:5) at high Greenwald fraction (ne=nGW 0:85) in steady state and with type II ELMy edge

A straight wire antenna model of the vertical grounding electrode has been presented in the paper. The formulation is based on the homogeneous integral equation of Pocklington type for half-space problems. The influence of a finitely conducting half-space is taken into account via the corresponding reflection coefficients. The Pocklington equation is solved both numerically and analytically. The numerical solution is carried out via the Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM). Some illustrative computational examples are presented at the end.

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

The characteristics of high- beta , low-q disruptions have been studied in PBX-M, a device with a nearby conducting shell. The coupling between the wall and the plasma was varied by choosing different plasma shapes, including nearly circular plasmas, D-shaped plasmas and bean-shaped plasmas (indented on the midplane), and by increasing the effective coverage of the plasma by the shell. Disruption precursors were observed to have a strong dependence on the coupling between the plasma and the shell. Measured mode growth times vary from between several times the Alfven time-scale (~100 mu s) to the L/R time-scale of the wall (~20 ms). The behaviour of observed disruption precursors is interpreted in terms of the resistive wall mode theory of ideal plasmas, and a detailed calculation of the stability of a strongly coupled bean configuration using the NOVA-W linear stability code is presented. The experimental observations are in good agreement with the theoretical predictions

In this paper we examine the evolution of the gradients in toroidal velocity, , and ion temperature, , during the CH-mode in PBX-M. This enhanced confinement mode develops from the H-mode following the application of IBW power and is characterized by strong density peaking and the formation of significant gradients in both toroidal velocity and ion temperature. The radial profiles of both the toroidal velocity and the ion temperature are obtained from the PBX-M charge exchange recombination spectroscopy (CHERS) diagnostic. A significant IBW power threshold is observed in the formation of the gradients. A power step of only 25 kW - from 200 to 225 kW - marks the onset. Details of the evolution of the gradients are given and, in particular, the variation with IBW power is described.

An addition of ion Bernstein wave power of only a tenth of the neutral beam power into an H-mode causes the formation of a core transport barrier. At the location of the barrier, reduced ELM losses in the soft x-ray profile are observed. During the IBW-modified ELM, one can observe enhanced fluctuations in the soft x-ray fluctuation profile over the whole of the observed frequency range. In the region of the core transport barrier, the enhancement of fluctuations seems to be strongly reduced. The ELM loss propagates to the core with a velocity greater than that which would be consistent with a normal energy diffusion process.

A database for the 1993 run period of PBX-M has been documented (i), to investigate whether it was possible to forecast the development of MHD instabilities often observed in LH-assisted discharges and (ii), to detail the origin, the nature and the effects of those instabilities. The deposition radius of the RF current, the plasma internal inductance and the LH power are used to separate MHD active and quiescent regimes prior to the MHD onset. 1/1, 2/1, 3/1 global modes driven by the m = 2, n = 1 component are observed in discharges with LHCD. The destabilization is attributed to an increase of the current density gradient within the q = 2 surface. MHD fluctuations reduce the soft X-ray and hard X-ray intensities mainly around the RF current deposition radius. Minor disruptions with large inversion radius and mode locking are analysed. A possible precursor to the MHD is evidenced on the hard X-ray horizontal profiles. A resonance between fast trapped electrons and turbulent waves present in the background plasma is proposed to support the observations.

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

Routine tritium operation in TFTR has permitted investigations of alpha particle physics in parameter ranges resembling those of a reactor core. ICRF wave physics in a DT plasma and the influence of isotopic mass on supershot confinement have also been studied. Continued progress has been made in optimizing fusion power production in TFTR, using extended machine capability and Li wall conditioning. Performance is currently limited by MHD stability. A new reversed magnetic shear regime is being investigated with reduced core transport and a higher predicted stability limit.

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.

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...

In many of the medium and high beta discharges in PBX-M, low n modes (n=1-4) with different n numbers are observed. The prevalence of low n modes decreases with increasing n number. Furthermore, if two modes of different frequency and n number (?1, and ?2; k1 and k2) are simultaneously present in the plasma, these modes interact non-linearly and create sidebands in frequency (?2 ? ?1) and wavenumber (k2 ? k1 or n2 ? n1 and m2 ? m1). It has also been observed that if these fundamental modes, ?1/k1 and ?2/k2, contain strong harmonics, the harmonics also interact non-linearly, creating more non-linear products: k?2 ? l?1 and kk2 ? lk1, where k and l are integers describing the harmonics. These multiple three wave couplings on a given rational surface can create several modes of the same m and n numbers but of different phase velocities. The multiple perturbations of the rational surfaces can increase the plasma losses. In fact, a decrease in neutron rate and an enhanced loss of medium energy ions are observed during this three wave coupling interaction. Although the three wave coupling has been observed primarily in medium or high beta discharges, it is a more general plasma phenomenon because it also occurs occasionally at low ?

In PBX-M, periods of enhanced transport are often observed in high beta polH-mode discharges. They can reduce the energy confinement time by a factor of two. Their duration is typically between 2 to 20 ms. They are followed by periods of normal transport of a similar duration. These periods of enhanced transport consist of a series of turbulent m=even MHD events, starting several cm inside the plasma edge. They propagate into the confinement region in 600 mu s, causing a progressive erosion of the profile. Each m=even event can also cause an energy loss of 1% or less, mainly from the confinement region. These m=even events are reminiscent of grassy ELMs.

Edge Localized Modes, or ELMs, are at the same time both disadvantageous and advantageous features of H-modes. ELMs can cause energy and particle losses from the plasma, with instantaneous energy losses reaching 40% of the total stored energy in the case of large-amplitude ELMs. The energy loss from these ELMs, or closely spaced smaller ELMs, may result in what is known as a beta-collapse, an event in which energy is lost over a substantial duration of the discharge. On the other hand, if controlled, the ELM related energy and, especially, impurity losses can lead to near steady-state discharge conditions with relatively low radiative power losses. The importance of ELMs in the development of the H-phase has led to numerous studies which attempt to uncover their nature. The purpose of the present work is to present additional observations of, most notably, high frequency magnetic fluctuations associated with ELMS. There are some observations here that are consistent with previously reported ones, namely the appearance of high frequency ({ge}250 kHz) activity prior to the D{sub {alpha}} increase, suggesting again that the rise in D{sub {alpha}} is some delayed response to an instability occurring farther inside the plasma edge. While this high frequency activitymore » is global, with high coherence for all coil pairs both on the inside and outside midplane, there is no identifiable mode structure. Reported here for the first time are observations of a very intense outward ballooning feature that appears simultaneously with the D{sub {alpha}} increase and lasts for about 5 msec. The toroidal mode structure of this feature is clearly identifiable, consisting of a series of toroidal harmonics from n=3 to 8, at frequencies given by f{sub n}=f{sub 0}+n{Delta}f, with f{sub 0}=30 to 50 kHz and A{Delta}=20 to 30 kHz.« less

Measurements of edge profiles, turbulence, and turbulent-driven transport were made inside the last-closed flux surface (LCFS) and in the scrape-off layer (SOL) of PBX-M L-mode and H-mode plasmas using a fast reciprocating Langmuir probe diagnostic. Direct measurements of the potential profile confirm the generation of a strong inward radial electric field (Er approximately -100 V/cm) just inside the LCFS in H-mode. Density and potential fluctuation levels are reduced at the L-H transition, resulting in significantly lower turbulent transport. The edge density gradient then steepens in response to the reduced cross-field transport. After a stable H-mode edge equilibrium is formed, the fluctuation amplitudes recover back to nearly L-mode values. The poloidal wavenumber spectrum is narrowed in the transport barrier, and the density and potential fluctuations are decorrelated. The reduction in turbulent transport occurs across the LCFS and SOL regions and is not localized to the region of strong radial electric field.

The PBX-M tokamak has an array of unique features that allow it to study regimes of enhanced confinement and stability. In particular, because of its divertor operation, PBX-M has proved to be a valuable contributor to identifying and understanding various features of H-mode physics. To be reported here are recent results of H-mode studies of m = 1 bias induced H-modes, L- to H-transitions, including suppression of turbulent transport, ELMs and other related energy loss mechanisms, and Ion Bernstein Wave modification of H-mode discharges

High frequency pressure driven modes have been observed in high poloidal beta discharges in the Princeton Beta Experiment Modification (PBX-M). These modes are excited in a non-axisymmetric equilibrium characterized by a large, low frequency mt = 1/nt = 1 island, and they are capable of expelling fast ions. The modes reside on or very close to the q = 1 surface and have mode numbers with either mh = nh or (less probably) mh/nh = mh/(mh-1), with mh varying between 3 and 10. Occasionally these modes are simultaneously localized in the vicinity of the ml = 2/nl = 1 island. The high frequency modes near the q = 1 surface also exhibit a ballooning character, being significantly stronger on the large major radius side of the plasma. When a large mt = 1/nt = 1 island is present, the mode is poloidally localized in the immediate vicinity of the X point of the island. The modes occur exclusively in high beta beam heated discharges and are likely to be driven by the beam ions. They can thus be a manifestation of either a toroidicity induced shear Alfven eigenmode (TAE) at q = (2mh+1)/2nh, a kinetic ballooning mode, or some other type of pressure driven (high β) mode. Most of the data are consistent with the theoretical predictions for the TAE gap mode. Since the high frequency modes in PBX-M, however, are found exclusively on or in the immediate neighbourhood of magnetic surfaces with low rational numbers (q = 1, 2,...), other possibilities are not excluded

High poloidal beta discharges in PBX-M routinely enter the H mode regime: typically, a quiescent phase followed by an MHD-active phase characterize the H mode period. An analysis of the energy transport during these phases is conducted using the experimental data and the code TRANSP; effective thermal diffusivities are computed. The quiescent H phase is characterized by a decrease of the thermal ion energy transport and a flattening of the associated effective diffusivity profile. Enhanced fast ion losses are observed during the MHD-active phase; particles in the lower end of the fast-ion energy spectrum with a large perpendicular velocity component are predominantly affected. Folding these losses into the analysis permits to reproduce the measured stored energy and time evolution of the neutron production rate during the MHD-active phase. During the MHD-active phase, the ion thermal diffusivity maintained a profile (magnitude and shape) similar to that obtained at the end of the quiescent H phase, suggesting, within the uncertainty of this analysis, that the MHD activity does not affect the thermal plasma energy transport. The observed stored energy (beta) saturation results from the enhanced losses in the fast-ion population. An analysis without inclusion of enhanced fast ion losses fails to reproduce the experimental measurements. Throughout the H mode period the electron effective diffusivity remains lower than the ion effective diffusivity. An error analysis is presented

Measurements of the flux surface shapes in a tokamak with a non-circular cross-section have been made using a tangentially viewing soft X ray pinhole camera. These measurements allowed the derivation of the value of the axial safety factor, q(0), and the shape of the plasma current profile, during equilibrium modification experiments. Two different equilibrium modification techniques were used: neutral beam current drive and plasma current ramp. In the neutral beam current drive experiment, tangential counter-injection was found to modify the equilibrium significantly, broadening the current profile and raising the value of q(0) above unity. In tangential co-injection discharges, q(0) values as low as 0.4 were observed. Reproduction of the measured q(0,t) using a radial current diffusion model strongly suggests there was a non-classical component to the cross-field current diffusion. A plasma current ramp of 2.5 MA/s was also shown to broaden the current profile; however, the value of q(0) was not altered

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%.

In PBX, an elongated, indented tokamak, an accumulation of impurities leading to strongly peaked radiation profiles was observed, most frequently during the H-mode. The modified device, PBX-M, features a close-fitting stabilizing metallic shell that covers over 85% of the plasma surface and has the capability to produce highly indented plasmas. Two distinct modes of operation were used to generate high-β equilibria in neutral beam heated discharges: 1) high current, highly indented high-βt plasmas, where the plasma was in close proximity to the stabilizing plates and 2) low current, lesser indented high-βp discharges where the plasma equilibrium shape was more oblate than the shell and the plasma was farther from the plates. In co-injected high-βt plasmas, radiative losses were typically 15–25% of the input power and impurity accumulation was mild even in discharges lasting up to 650 ms with 250 ms H-modes. In high-βp discharges, both co- and counter-injection was investigated. In discharges with tangential co-injection, total radiated power gradually peaked on axis, ultimately reaching 60% of the heating power. H-modes were frequently present and the high-Z impurity density profile was strongly peaked. In tangentially counter-injected discharges, the current profile modification led to the suppression of sawteeth and the near elimination of MHD activity outside the q=1 surface. The improved particle confinement led to high electron density, high impurity radiation levels and a thermal collapse; however, the concentration and accumulation of metallic impurities was not as severe as the co-injected case.

H-mode plasmas with high poloidal beta values in the PBX-M tokamak often exhibit periods of edge localized mode (ELM) activity, with each ELM preceded by a short duration (≤ 350 μs) burst of high frequency (200-250 kHz) magnetic activity. The burst grows on a time-scale of 10 μs and disappears just before the rapid increase in the Dα emission that is characteristic of the ELM. The burst of activity is observed at all poloidal locations, with the largest amplitudes at coils on the inner major radius side, indicating that the mode is not outward ballooning in character. Stability calculations indicate that this high frequency ELM precursor is probably the pressure driven ideal kink mode.

The highly indented plasmas of the PBX‐M tokamak experiment [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1989), Vol. 1, p. 97] have reached plasma regimes of both high volume‐averaged beta (βt), and high‐beta poloidal (βp), and show evidence of the suppression of external surface modes by the passive stabilizing system. Values of βt up to 4.0 I/aB (% MA/m T) with Ti(0)≊4 keV have been obtained. A magnetohydrodynamic analysis of plasmas with βp=2.0 indicates that these plasmas are near the threshold of the second stability regime. A value of βt of 6.8% has been reached with Ti(0)>5 keV and an indentation of 28%. Control of plasma shape is accomplished with a feedback system that uses a moment expansion about a single equilibrium and is augmented by time‐dependent waveforms to redefine plasma shape. Diagnostics to measure the safety factor q have been developed and used to make accurate measurements of q(r) and to verify changes made in q(0).

In tokamak plasmas, a key element in the understanding of magnetohydrodynamic (MHD) instabilities is the determination of their toroidal and poloidal mode numbers. This is usually accomplished by correlating measurements of radiation, particles, or magnetic oscillations at separate positions toroidally and poloidally around the torus. It is possible, however, to obtain the same information with arrays of soft x-ray detectors viewing the horizontal midplane and the poloidal cross section of the tokamak from a single location. The perturbation due to an MHD mode on a toroidal shell will modulate the soft x-ray emission along sightlines intersecting it. The number of maxima, and the angular separation between the channels detecting them, have a straightforward geometrical relationship to the mode number. This approach thus avoids the need for complex inversion of line-integrated signals. The method has already been used to determine poloidal mode numbers on the Princeton beta experiment-modification tokamak,...

An important issue for future tokamaks is real‐time plasma control for the avoidance of magnetohydrodynamic instabilities and other applications that require detailed plasma profile and fluctuation data. Although measurements from diagnostics providing this information require significantly more processing than magnetic flux data, recent advancements could make them practical for adjusting operational settings for plasma heating and current drive systems as well as field coil currents. On the Princeton Beta Experiment‐Modification (PBX‐M), the lower hybrid current drive phasing can be varied during a plasma shot using digitally programmable ferrite phase shifters, and neural beam functions can be fully computer controlled. PBX‐M diagnostics that may be used for control purposes include motional Stark‐effect polarimetry for magnetic field pitch angle profiles, soft x‐ray arrays for plasma position control and the separation of βp from li, hard x‐ray detectors for energetic electron distributions, a multich...

The PBX-M passive plate stabilization system provides significant stabilization of long-wavelength external kink modes, the slowing of vertical instability growth rates, and the amelioration of disruption characteristics. The passive plate stabilization system has allowed the use of LHCD and IBW to induce current density and pressure profile modifications, and m=1 divertor biasing for modifying edge plasma transport. Improvements in the passive plate system insulators and support structures have provided reliable operation. Impurity influxes with the close-fitting passive plates are low. Solid target boronization is applied routinely to reduce conditioning time and maintain clean conditions.

High confinement [with $H\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, ITERH- $98(y,2)$] at ${\ensuremath{\beta}}_{N}\ensuremath{\approx}2.3$ has been found in ASDEX Upgrade discharges with existing $(m,n)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(3,2)$ neoclassical tearing modes (NTMs). The reason for the high confinement at high ${\ensuremath{\beta}}_{N}$ values is a transition of the NTMs into the so-called frequently interrupted regime. In this regime, the NTM growth is frequently interrupted by sudden drops in amplitude. Because of the long NTM growth time, the resulting averaged NTM amplitude remains much smaller than the corresponding saturated value. As this behavior with the beneficial effect on energy confinement has been confirmed at JET, such a high confinement regime at ${\ensuremath{\beta}}_{N}g2$ might also be expected for ITER.

High confinement [with H = 1, ITERH- 98( y,2)] at beta(N) approximately 2.3 has been found in ASDEX Upgrade discharges with existing (m,n) = (3,2) neoclassical tearing modes (NTMs). The reason for the high confinement at high beta(N) values is a transition of the NTMs into the so-called frequently interrupted regime. In this regime, the NTM growth is frequently interrupted by sudden drops in amplitude. Because of the long NTM growth time, the resulting averaged NTM amplitude remains much smaller than the corresponding saturated value. As this behavior with the beneficial effect on energy confinement has been confirmed at JET, such a high confinement regime at beta(N)2 might also be expected for ITER.

The efficiency of plasma current drive with lower hybrid waves is reflected in the distribution of suprathermal electrons formed during this process. Past measurements of the bremsstrahlung radiation from these electrons depended on arrays of hard x‐ray detectors at different toroidal and poloidal locations around tokamaks [Nucl. Fusion 25, 1515 (1985)]. To avoid the space requirements and the complex correlation and inversion procedures associated with such systems, a single 23‐cm‐diam hard x‐ray image intensifier tube is being installed for two‐dimensional imaging on PBX‐M. It will be optically coupled to an image processor already in place for a soft x‐ray pinhole camera [Rev. Sci. Instrum. 59, 1831 (1988)], and analysis algorithms similar to those already developed for this diagnostic will be used.

Through semi-independent absolute calibrations of multiply redundant neutron detector systems, the Tokamak Fusion Test Reactor (TFIR) has achieved {+-}7% (one-sigma) accuracy in its fusion power measurements. This has required careful attention to the linearity of detectors up to the present highest fusion power levels achieved on TFTR of over 10 MW. The extended duration of the DT program on TFTR has also tested the stability of the detector systems. These issues of calibration, linearity, and stability are reviewed for the TFTR experience and how it can be applied to plans for ITER.

Since the introduction of tritium into the Tokamak Fusion Test Reactor (TFTR) in December 1993, more than 400 D-T plasmas have been produced, with a total fusion energy of over 900 MJ. Fusion power production in D-T supershots is routinely in the 5–10 MW range, within a factor of ~ 200 of that expected in ITER. Neutron flux at the first wall of TFTR has reached about 10% of values projected for ITER, and central fusion power densities are already at ITER levels. Therefore, experience gained in fusion product measurements during the TFTR D-T experiments is directly relevant to the design of diagnostic systems for ITER.

A peak fusion power production of 9.3±0.7 MW has been achieved on the Tokamak Fusion Test Reactor (TFTR) in deuterium plasmas heated by co and counter injected deuterium and tritium neutral beams with a total power of 33.7 MW. The ratio of fusion power output to heating power input is 0.27. At the time of the highest neutron flux the plasma conditions are: Te(0)=11.5 keV, Ti(0)=44 keV, ne(0)=8.5×1019 m−3, and 〈Zeff〉=2.2 giving τE=0.24 s. These conditions are similar to those found in the highest confinement deuterium plasmas. The measured D‐T neutron yield is within 7% of computer code estimates based on profile measurements and within experimental uncertainties. These plasmas have an inferred central fusion alpha fraction of 0.2% and central fusion power density of 2 MW/m3 similar to that expected in a fusion reactor. Even though the alpha velocity exceeds the Alfven velocity throughout the time of high neutron output in most high power plasmas, MHD activity is not substantially different from that in co...

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.