ALBERT

Notes: One of the scientific success stories of fusion research over the past decade is the development of the E×B shear stabilization model to explain the formation of transport barriers in magnetic confinement devices. This model was originally developed to explain the transport barrier formed at the plasma edge in tokamaks after the L (low) to H (high) transition. This concept has the universality needed to explain the edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines. More recently, this model has been applied to explain the further confinement improvement from H (high) mode to VH (very high) mode seen in some tokamaks, where the edge transport barrier becomes wider. Most recently, this paradigm has been applied to the core transport barriers formed in plasmas with negative or low magnetic shear in the plasma core. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to a higher energy state with reduced turbulence and transport when an additional source of free energy is applied to it. The transport decrease that is associated with E×B velocity shear effects also has significant practical consequences for fusion research. The fundamental physics involved in transport reduction is the effect of E×B shear on the growth, radial extent, and phase correlation of turbulent eddies in the plasma. The same fundamental transport reduction process can be operational in various portions of the plasma because there are a number of ways to change the radial electric field Er. An important theme in this area is the synergistic effect of E×B velocity shear and magnetic shear. Although the E×B velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of E×B velocity shear and facilitate turbulence stabilization. Considerable experimental work has been done to test this picture of E×B velocity shear effects on turbulence; the experimental results are generally consistent with the basic theoretical models. © 1997 American Institute of Physics.

Notes: Detailed analysis of recent high beta discharges in the DIII-D [Plasma Physics Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] tokamak demonstrates that the resistive vacuum vessel can provide stabilization of low n magnetohydrodynamic (MHD) modes. The experimental beta values reaching up to βT=12.6% are more than 30% larger than the maximum stable beta calculated with no wall stabilization. Plasma rotation is essential for stabilization. When the plasma rotation slows sufficiently, unstable modes with the characteristics of the predicted "resistive wall'' mode are observed. Through slowing of the plasma rotation between the q=2 and q=3 surfaces with the application of a nonaxisymmetric field, it has been determined that the rotation at the outer rational surfaces is most important, and that the critical rotation frequency is of the order of Ω/2π=1 kHz. © 1995 American Institute of Physics.

Notes: A better understanding of helium transport in the plasma core and edge in enhanced confinement regimes is now emerging from recent experimental studies on DIII-D [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159]. Overall, the results are encouraging. Significant helium exhaust (τHe*/τE∼11) has been obtained in a diverted, H-mode plasma with edge-localized modes (ELM's) simultaneous with a central source of helium. There is no evidence of central peaking of the helium density profile even in the presence of this central source. Detailed analysis of the helium profile evolution indicates that the exhaust rate is limited by the exhaust efficiency of the pump (∼5%) and not by the intrinsic helium transport properties of the plasma. Perturbative helium transport studies using gas puffing have shown that DHe/χeff ∼1 in all confinement regimes studied to date (including H mode and VH mode). Furthermore, there is no evidence of preferential accumulation of helium in any of these regimes. © 1995 American Institute of Physics.

Notes: Reliable operation of discharges with negative central magnetic shear has led to significant increases in plasma performance and reactivity in both low confinement, L-mode, and high confinement, H-mode, regimes in the DIII-D tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159]. Using neutral beam injection early in the initial current ramp, a large range of negative shear discharges have been produced with durations lasting up to 3.2 s. The total noninductive current (beam plus bootstrap) ranges from 50% to 80% in these discharges. In the region of shear reversal, significant peaking of the toroidal rotation [fφ(0)∼30–60 kHz] and ion temperature [Ti(0)∼15–22 keV] profiles are observed. In high-power discharges with an L-mode edge, peaked density profiles are also observed. Confinement enhancement factors up to H≡τE/τITER-89P∼2.5 with an L-mode edge, and H∼3.3 in an edge localized mode (ELM)-free H mode, are obtained. Transport analysis shows both ion thermal diffusivity and particle diffusivity to be near or below standard neoclassical values in the core. Large pressure peaking in the L mode leads to high disruptivity with βN≡βT/(I/aB)≤2.3, while broader pressure profiles in the H mode gives low disruptivity with βN≤4.2. © 1996 American Institute of Physics.

Notes: The radial correlation length of the turbulence responsible for transport can have a different gyroradius scaling in low (L)-mode and high (H)-mode plasmas due to E×B flow shear effects, as predicted by the two-point nonlinear analysis in general tokamak geometry [Phys. Plasmas 2, 1648 (1995)]. This difference offers a possible understanding of the recent ρ*-scan experiment results on DIII-D [Fusion Technol. 8, 441 (1985)] L-mode and H-mode plasmas [Phys. Plasmas 2, 2342 (1995)]. Within our model, thermal diffusivity in H-mode plasmas scales like gyro-Bohm, independent of the scaling in L-mode plasmas. © 1996 American Institute of Physics.

Notes: The confinement and the stability properties of the DIII-D tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high-performance discharges are evaluated in terms of rotational and magnetic shear, with an emphasis on the recent experimental results obtained from the negative central magnetic shear (NCS) experiments. In NCS discharges, a core transport barrier is often observed to form inside the NCS region accompanied by a reduction in core fluctuation amplitudes. Increasing negative magnetic shear contributes to the formation of this core transport barrier, but by itself is not sufficient to fully stabilize the toroidal drift mode (trapped-electron-ηi mode) to explain this formation. Comparison of the Doppler shift shear rate to the growth rate of the ηi mode suggests that the large core E×B flow shear can stabilize this mode and broaden the region of reduced core transport. Ideal and resistive stability analysis indicates the performance of NCS discharges with strongly peaked pressure profiles is limited by the resistive interchange mode to low βN≤2.3. This mode is insensitive to the details of the rotational and the magnetic shear profiles. A new class of discharges, which has a broad region of weak or slightly negative magnetic shear (WNS), is described. The WNS discharges have broader pressure profiles and higher β values than the NCS discharges, together with high confinement and high fusion reactivity. © 1996 American Institute of Physics.

Notes: A prime goal in physics research is the development of theories which have the universality needed to explain a wide range of observations. Developed over the past decade, the model of turbulence decorrelation and stabilization by sheared E×B flow has the universality needed to explain the turbulence reduction and confinement improvement seen in the edge and core of a wide range of magnetic confinement devices. Because the E×B shear, turbulence, and transport are all intimately intertwined in multiple feedback loops, devising experiments to test whether E×B shear causes a change in turbulence and transport has been a major challenge for experimentalists. Over the past five years, there have been at least four clear demonstrations of causality performed in tokamak plasmas, both at the plasma edge on Doublet III-D (DIII-D) [Plasma Physics and Controlled Fusion Research 1985 (International Atomic Energy Agency, Vienna, 1986) Vol. I, p.159] and Tokamak Experiment for Technologically Oriented Research (TEXTOR) [Plasma Physics and Controlled Nuclear Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991) Vol. I, p. 473] and further into the plasma core on DIII-D and Tokamak Fusion Test Reactor [Phys. Plasmas 5, 1577 (1998)]. This paper discusses these tests in detail; the results agree with the expectations from the E×B shear model. This paper also discusses similarities between flow shear effects in plasmas and in neutral fluids and provides examples of flow shear reduction of turbulence in neutral fluids under the proper conditions. © 1999 American Institute of Physics.

Notes: While core transport barriers have been created in most large tokamaks, including DIII-D [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159], the underlying physics that governs their creation, expansion, and limitations has not been fully elucidated. Although negative central magnetic shear during a discharge aids in the creation of a core transport barrier, the model that has evolved to explain these results includes synergistic effects of magnetic shear and E×B velocity shear as the central elements. In DIII-D, the core barrier initially forms over an interval of several hundred milliseconds during the current ramp, with very low power applied. The barrier subsequently expands outward if the injected power is raised above a threshold, between 2.5 and 5 MW in DIII-D. Electrostatic turbulence reduces as the shearing rate increases to exceed the local turbulence growth rate while the transport barrier expands. Both the existence of the threshold and the barrier expansion with additional power are consistent with the theory. © 1998 American Institute of Physics.

Notes: The scaling of cross-field heat transport with relative gyroradius ρ* was measured in low (L) and high (H) mode tokamak plasmas using the technique of dimensionally similar discharges. The relative gyroradius scalings of the electron and ion thermal diffusivities were determined separately using a two-fluid transport analysis. For L-mode plasmas, the electron diffusivity scaled as χe∝χBρ1.1±0.3* (gyro-Bohm-like) while the ion diffusivity scaled as χi∝χBρ−0.5±0.3* (worse than Bohm-like). The results were independent of the method of auxiliary heating (radio frequency or neutral beam). Since the electron and ion fluids had different gyroradius scalings, the effective diffusivity and global confinement time scalings were found to vary from gyro-Bohm-like to Bohm-like depending upon whether the electron or ion channel dominated the heat flux. This last property can explain the previously disparate results with dimensionally similar discharges on different fusion experiments that have been published. Experiments in H mode were also done with the expected values of beta, collisionality, safety factor, and plasma shape for thermonuclear ignition experiments. For these dimensionally similar discharges, both the electron and ion diffusivities scaled gyro-Bohm-like, χe, χi∝χBρ*, as did the global thermal confinement time. This leads to a very favorable prediction for the confinement time of future ignition devices. © 1995 American Institute of Physics.