Core Transport Barriers Research Articles

Effects of velocity shear and magnetic shear in the formation of core transport barriers in the DIII-D tokamak

Core transport barriers can be reliably formed in DIII-D by tailoring the evolution of the current density profile. This paper reports studies of the relative role of magnetic and shear in creating core transport barriers in the DIII-D tokamak and considers the detailed dynamics of the barrier formation. The core barriers seen in DIII-D negative shear discharges form in a stepwise fashion during the initial current ramp. The reasons for the stepwise formation are not known. Their extremely good shot to shot reproducibility suggests the steps are connected to a very reproducible plasma parameter such as the current density profile; however, the simple hypothesis that they occur each time q(0) or crosses an integer value is not consistent with all the data. The data from DIII-D are consistent with previous results that negative magnetic shear facilitates the formation of core transport barriers in the ion transport channel but is not necessary. However, strongly negative magnetic shear does allow formation of transport barriers in particle, electron thermal, ion thermal and angular momentum transport channels. Shots with strong negative magnetic shear have produced the steepest ion temperature and toroidal rotation profiles seen yet in DIII-D. In addition, the shearing rates seen in these shots exceed the previous DIII-D record value by a factor of four.

Magnetohydrodynamic behaviour during core transport barrier experiments with ion Bernstein wave heating in PBX-M: I ELMs, fluctuations and crash events

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.

Magnetohydrodynamic behaviour during core transport barrier experiments with ion Bernstein wave heating in PBX-M: II n = m - 1 and n = m modes

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 Alfvén eigenmodes (BAEs).

Dynamics of core transport barrier formation and expansion in the DIII-D tokamak

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.

Observation of tritium and helium core transport barriers in reversed shear plasmas on TFTR

Tritium and helium gas-puff experiments have been conducted on TFTR to investigate transport in reverse shear plasmas. Small amounts of tritium and helium gas are puffed into the equilibrium phase of these plasmas. Measurements of the 14 MeV neutron fusion product and the charge-exchange spectrum of helium reveal the transport details of tritium and helium, respectively. The inferred tritium and helium density profiles indicate the formation of a core transport barrier for each species in reverse shear plasmas with enhanced confinement.

Microturbulence reduction during internal transport barrier discharges in DIII-D

Increased plasma confinement, temperature and fusion reactivity in negative central shear (NCS) discharges in DIII-D are accompanied by reduced core electrostatic microturbulence. The microturbulence reduces as the local radial electric field and shear increases, consistent with a theoretical model incorporating turbulence stabilization by shear radial electric field. Reduced turbulence and the associated anomalous transport reduction leads to further increased radial electric field shear via a steeper pressure gradient and reduced momentum transport. During the H-mode phase of a core transport barrier discharge, the microturbulence is virtually quenched in the core. Increasing evidence indicates that the transport barrier initially forms in the plasma interior when shear is large.

Formation of core transport barriers by parallel flow

The well-known instability associated with the drift-ballooning modes is shown to be stabilized in the presence of a radially varying parallel flow profile. This is contrary to the usual belief that the parallel flow shear is destabilizing for the drift-like microinstabilities. The scale length of the flow profile required for this stabilization is rather modest and is usually observed in the toroidal flow profile measured during various improvement modes in the tokamak core. This shows that purely parallel flow can be used to create transport barriers to reduce the loss of particle and energy from the plasma. The improved mode formed by the parallel flow will, unlike the reverse shear mode, be nontransient in nature.

Topics in toroidal confinement

In this paper we shall highlight some topics of specific concern for both concepts for magnetic confinement: 2D (tokamaks) and 3D (helical) systems. Section 2 will address the primary goals of fusion: density, confinement and temperature. We shall summarize the density limit, the global confinement time scaling with engineering parameters and some physical elements of improved confinement regimes with edge (H-mode) and core transport barriers (reversed shear cases); progress in relation to temperature originates from the evidence for α-particle heating from TFTR and the successes in drift optimization in helical systems with some confirmation from W7-AS. In the section 3 on the secondary goals of fusion, β will be discussed in terms of equilibrium (including the necessary improvements in helical systems with examples from W7-AS) and in terms of stability (including fast particle-driven Alfvén waves with toroidally induced eigenmodes in cases with high shear and global eigenmodes in cases with low shear). Finally, we shall summarize the status of exhaust physics, with reference to the poloidal field divertor in tokamaks and the island divertor in helical systems. The intention of this report is to emphasize the complementarity of the two concepts of toroidal confinement.

Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices

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.

Plasma transport control and self-sustaining fusion reactor

The possibility of a high-performance/low-cost fusion reactor concept which can simultaneously satisfy (1) high beta, (2) high bootstrap fractio (self-sustaining) and (3) high confinement is discussed. In CDX-U, a tokamak configuration was created and sustained solely by internally generated bootstrap currents, in which a 'seed' current is created through a nonclassical current diffusion process. Recent theoretical studies of MHD stability limits in spherical tori [e.g. the National Spherical Torus Experiment (NSTX)] produced a promising regime with stable beta of 45% and bootstrap current fraction of . Since the bootstrap current is generated by the pressure gradient, to satisfy the needed current profile for MHD stable high beta regimes, it is essential to develop a means to control the pressure profile. It is suggested that the most efficient approach for pressure profile control is through the creation of transport barriers (localized regions of low plasma transport) in the plasma. As a tool for creating the core transport barrier, poloidal-sheared-flow generation by ion Bernstein waves (IBW) near the wave absorption region appears to be promising. In PBX-M, application of IBW power produced a high-quality internal transport barrier where the ion energy and particle transport became neoclassical in the barrier region. The observation is consistent with the IBW-induced-poloidal-sheared-flow model. An experiment is planned on TFTR to demonstrate this concept with D - T reactor-grade plasmas. For edge transport control, a method based on electron ripple injection (ERI), driven by electron cyclotron heating (ECH), is being developed on CDX-U. It is estimated that both the IBW and ERI methods can create a transport barrier in reactor-grade plasmas (e.g. ITER) with a relatively small amount of power .

Roles of Electric Field Shear and Shafranov Shift in Sustaining High Confinement in Enhanced Reversed Shear Plasmas on the TFTR Tokamak

The relaxation of core transport barriers in TFTR enhanced reversed shear plasmas has been studied by varying the radial electric field using different applied torques from neutral beam injection. Transport rates and fluctuations remain low over a wide range of radial electric field shear, but increase when the local $\mathbf{E}\ifmmode\times\else\texttimes\fi{}\mathbf{B}$ shearing rates are driven below a threshold comparable to the fastest linear growth rates of the dominant instabilities. Shafranov-shift-induced stabilization alone is not able to sustain enhanced confinement.

Nonlinear gyrokinetic equations for turbulence in core transport barriers

An energy-conserving set of the nonlinear electrostatic gyrokinetic Vlasov and Poisson equations is derived for the first time in the presence of equilibrium E×B velocity uE∼vTi, via phase-space Lagrangian Lie-perturbation theory. In this general formulation, only the basic small parameter ε with ω/Ω∼k∥/k⊥∼ε and δn/n0∼1/k⊥L∼ε, is used, while no device-specific expansion has been made. Here, L is the equilibrium scale length. For application to microturbulence in tokamak core transport barriers, an additional small ordering parameter δB≡Bθ/B≪1 is utilized. This leads to a useful form of the nonlinear gyrokinetic system which is applicable to a realistic situation in which the gradient lengths of the equilibrium radial electric field and pressure are of the same order as the ion poloidal gyroradius. The ordering for fluctuations is also modified to δn/n0∼εδB≪1/k⊥L∼δB for a better description of sub-mixing-length level fluctuations. uE/vTi∼δB and ρθi∼Lp put the pressure-gradient contribution to Er and the toroidal-flow contribution to Er at the same order. δB∼ε is shown to be a maximal ordering for studying the E×B flow shear suppression of turbulence.

Interaction of ELMs with the core transport barrier in CH-mode in PBX-M

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.

Externally-driven H-mode studies in CCT

Test particle radial flux surface excursions are reduced during the H-mode. Particle transport is reduced by a factor of 10 in the H-mode, but energy confinement increases are small. In the H-mode the evolution of poloidally resolved turbulent statistics are not explained by published theory. Turbulent momentum transport leads to a concentration of poloidal momentum within the transport barrier, and compressibility leads to poloidal shock-like phenomena. The electron distribution functions may be modified by this shock, leading to kinetic instabilities. A physics-based understanding of the H-mode must therefore include toroidal effects combined with an adequate treatment of particle orbits, plasma compressibility and associated kinetic effects, and at least a two-species model of turbulent transport. The results suggest that rapid poloidal core-plasma rotation could form core transport barriers without reliance on fluid shear or reversed magnetic shear effects.

Rotational and magnetic shear stabilization of magnetohydrodynamic modes and turbulence in DIII-D high performance discharges

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.