Peaked Pressure Profiles Research Articles

Prospects of negative triangularity tokamak for advanced steady-state confinement of fusion plasmas in MHD stability consideration

The steady-state confinement, beta limit, and divertor heat load are among the most concerned issues for toroidal confinement of fusion plasmas. In this work, we show that the negative triangularity tokamak has promising prospects to address these issues. We first demonstrate that the negative triangularity tokamak generates the filed line rotation transform more effectively. This brings bright prospects for the advanced steady-state tokamak scenario. Given this, the MHD stability and equilibrium confinement of negative triangularity tokamak are investigated. We point out that the negative triangularity configuration with a broad pressure profile is indeed more unstable for low-n magnetohydrodynamic modes than the positive triangularity case so that the H-mode confinement can hardly be achieved in this configuration, where n is the toroidal mode number. Nevertheless, we found that the negative triangularity configuration with high bootstrap current fraction, high poloidal beta, and peaked pressure profiles can achieve higher normalized beta for low-n modes than the positive triangularity case. In a certain parameter domain, the normalized beta can reach about twice the extended Troyon limit, while the same computation indicates that the positive triangularity configuration is indeed constrained by the Troyon limit. This shows that the negative triangularity tokamaks are not only favorable for divertor design to avoid the edge localized modes but also can have promising prospects for advanced steady-state confinement of fusion plasmas in high beta.

The Formation and Stationary Maintenance of Peaked Pressure Profiles in Turbulent Tokamak Plasmas

The theoretical model for increasing peaking of radial distribution of plasma thermal energy and plasma energy confinement time improvement due to the formation of current profiles those provide the increased value of the safety factor qb at the outer plasma boundary is considered. The model for the formation and stationary maintenance of the peaked current density profiles those ensure the maintenance of plasma column equilibrium state with increased qb value and conservation of q0=1 at the magnetic axis is developed. The model is based on the significant ramp down of the Iind current maintained by the inductor with simultaneous central ECR heating and electron cyclotron current drive (ECCD) switching on. It is shown by the computer simulations of the self-consistent time evolution of turbulent plasma for the conditions of T-10 and T-15MD tokamaks that in the shot scenarios with three- or four-fold decrease in the Iind current at the ECRH stage of shots it was achieved an approximately two-fold enhancement of the electron and ion temperatures at the axis of the plasma column as compared to the standard shots with the same heating powers.

The Formation and Stationary Maintenance of Peaked Pressure Profiles in Turbulent Tokamak Plasmas

The theoretical model for increasing peaking of radial distribution of plasma thermal energy and plasma energy confinement time improvement due to the formation of current profiles those provide the increased value of the safety factor {{q}_{b}} at the outer plasma boundary is considered. The model for the formation and stationary maintenance of the peaked current density profiles those ensure the maintenance of plasma column equilibrium state with increased {{q}_{b}} value and conservation of {{q}_{0}} approx 1 at the magnetic axis is developed. The model is based on the significant ramp down of the {{I}_{{{text{ind}}}}} current maintained by the inductor with simultaneous central ECR heating and electron cyclotron current drive (ECCD) switching on. It is shown by the computer simulations of the self-consistent time evolution of turbulent plasma for the conditions of T-10 and T-15MD tokamaks that in the shot scenarios with three- or four-fold decrease in the {{I}_{{{text{ind}}}}} current at the ECRH stage of shots it was achieved an approximately two-fold enhancement of the electron and ion temperatures at the axis of the plasma column as compared to the standard shots with the same heating powers.

Observation of helical m/n = 1/1 saturated steady mode in EAST pure electron heating scenario with q0 ≼ 1

We observed for the first time a helical m/n = 1/1 (m is the poloidal mode number and n is the toroidal mode number) saturated steady mode (SSM) in the center of the EAST electron heating dominant plasma where the core safety factor was close to but slightly below unity and the profile had an extreme peak at the plasma center ( is the electron temperature). An internal crash can be caused by the dynamics of the SSM, and its influence on the electron temperature profile is as large as that of a typical sawtooth crash (SC) in magnitude. Due to the weak magnetic shear in the core, the SSM regularly exhibits an m/n = 2/2 harmonic component. For low shear auxiliary heated plasma, the SSM cannot cause the degradation of plasma confinement ( or ), but an SC is indeed a harmful factor. Three-dimensional resistive magnetohydrodynamic simulations with a realistic EAST strong elongated magnetic configuration, a high Lundquist number () and a strong central peaked pressure profile, have been made to demonstrate the formation of the SSM in the case of and the destabilization of the SC in another case with . These nonlinear simulation results agree well with the observations of both the SSM and SC in EAST electron heating dominant discharges with an extreme central peaked . An M3D simulation found that the SC is caused by additional newly developed harmonics of the m/n = 1/1 helical instability. Nonlinear simulation also predicted a modulation of the SSM on current in the plasma core, which is favorable for maintaining in the plasma core. Furthermore, nonlinear simulation also showed that a small toroidal plasma flow can be generated by the SC.

The negative triangularity tokamak: stability limits and prospects as a fusion energy system

The paper discusses edge stability, beta limits and power handling issues for negative triangularity tokamaks. The edge magnetohydrodynamic stability is the most crucial item for power handling. For the case of negative triangularity the edge stability picture is quite different from that for conventional positive triangularity tokamaks: the second stability access is closed for localized Mercier/ballooning modes due to the absence of a magnetic well, and nearly internal kink modes set the pedestal height limit to be weakly sensitive to diamagnetic stabilization just above the margin of the localized mode Mercier criterion violation. While a negative triangularity tokamak is thought to have a low beta limit with its magnetic hill property, it is found that plasmas with reactor-relevant values of normalized beta βN > 3 can be stable to global kink modes without wall stabilization with appropriate core pressure profile optimization against localized mode stability, and also with increased magnetic shear in the outer half-radius. The beta limit is set by the n = 1 mode for the resulting flat pressure profile. The wall stabilization is very inefficient due to strong coupling between external and internal modes. The n > 1 modes are increasingly internal when approaching the localized mode limit, and set a lower beta in the case of the peaked pressure profile leading to a Mercier unstable core. With the theoretical predictions supported by experiments, a negative triangularity tokamak would become a prospective fusion energy system with other advantages including a larger separatrix wetted area, more flexible divertor configuration design, wider trapped particle-free scrape-off layer, lower background magnetic field for internal poloidal field coils, and larger pumping conductance from the divertor room.

Steady state scenario development with elevated minimum safety factor on DIII-D

On DIII-D (Luxon 2005 Fusion Sci. Technol. 48 828), a high β scenario with minimum safety factor (qmin) near 1.4 has been optimized with new tools and shown to be a favourable candidate for long pulse or steady state operation in future devices. The new capability to redirect up to 5 MW of neutral beam injection (NBI) from on- to off-axis improves the ability to sustain elevated qmin with a less peaked pressure profile. These changes increase the ideal magnetohydrodynamics (MHD) n = 1 mode βN limit thus providing a path forward for increasing the noninductive current drive fraction by operating at high βN. Quasi-stationary discharges free of tearing modes have been sustained at βN = 3.5 and βT = 3.6% for two current profile diffusion timescales (about 3 s) limited by neutral beam duration. The discharge performance has normalized fusion performance expected to give fusion gain Q ≈ 5 in a device the size of ITER. Analysis of the poloidal flux evolution and current drive balance show that the loop voltage profile is almost relaxed even with 25% of the current driven inductively, and qmin remains elevated near 1.4. These observations increase confidence that the current profile will not evolve to one unstable to a tearing mode. In preliminary tests a divertor heat flux reduction technique based on producing a radiating mantle with neon injection appears compatible with this operating scenario. 0D model extrapolations suggest it may be possible to push this scenario up to 100% noninductive current drive by raising βN. Similar discharges with qmin = 1.5–2 were susceptible to tearing modes and off-axis fishbones, and with qmin > 2 lower normalized global energy confinement time is observed.

Stable anisotropic plasma confinement in magnetic configurations with convex–concave field lines

It is shown that a combination of the convex and the concave part of a field line provides a strong stabilizing action against convective (flute-interchange) plasma instability (Tsventoukh 2011 Nucl. Fusion 51 112002). This results in internal peaking of the stable plasma pressure profile that is calculated from the collisionless kinetic stability criterion for any magnetic confinement system with combination of mirrors and cusps. Connection of the convex and concave field line parts results in a reduction of the space charge that drives the unstable E × B motion, as there is an opposite direction of the particle drift in a non-uniform field at convex and concave field lines. The pressure peaking arises at the minimum of the second adiabatic invariant J that takes place at the ‘middle’ of a tandem mirror–cusp transverse cross-section. The position of the minimum in J varies with the particle pitch angle that results in a shift of the peaking position depending on plasma anisotropy. This allows one to improve a stable peaked pressure profile at a convex–concave field by changing the plasma anisotropy over the trap cross-section. Examples of such anisotropic distribution functions are found that give an additional substantial enhancement in the maximal central pressure. Furthermore, the shape of new calculated stable profiles has a wide central plasma layer instead of a narrow peak.

Helical core tokamak MHD equilibrium states

Bifurcated magnetohydrodynamic (MHD) tokamak equilibrium states with axisymmetric or helical core structure are computed. When a peaked pressure profile is chosen, the helical core structures appear like the snakes that are observed in the JET tokamak. They also have the allure of saturated ideal internal kinks. The existence of a magnetic island is not a requisite condition. Novel equilibrium states that can model the snake are obtained for a JET configuration when the q-profile has weak reversed magnetic shear with minimum q values in the range 0.94 to 1.03. At the lower end of this qmin range, the equilibrium snake structure lies radially well inside the domain for which qmin ⩽ 1. Free boundary equilibria computed for the TCV tokamak develop helical cores when βN exceeds 0.3 and have a significant axis excursion for βN ⩾ 0.4. At fixed ⟨β⟩ = 1.6%, the distortion of the magnetic axis is large in the range 0.95 ⩽ qmin ⩽ 1.01. The plasma–vacuum interface is not significantly altered by the internal helical deformations.

Shafranov shift measurements by a soft x-ray CCD camera for internal diffusion barrier discharges in the Large Helical Device

Magnetic axis shift (Shafranov shift) in a high density operational regime with an internal diffusion barrier (IDB) formation in Large Helical Device experiments has been studied using a two-dimensional imaging system composed of a soft x-ray CCD camera and beryllium filters. Magnetic axis positions are derived from the fitting of pre-calculated equilibria to measured (line-integrated) soft x-ray profiles assuming that the emissivity profile could be expressed by Fourier–Bessel series expansion. It has been clearly observed that the Shafranov shift in a plasma with IDB is much larger than that without IDB at a similar average beta value measured by a diamagnetic loop because of the strongly peaked pressure profile in this regime. According to systematic analyses of the Shafranov shift for various high density plasmas in this regime, the dependence of the Shafranov shift on the central beta value is summarized and compared with that in discharges without IDB.

Long-pulse hybrid scenario development in JT-60U

The performance and sustained duration of long-pulse discharges for the ‘ITER hybrid scenario’ have been improved in JT-60U. The modification of power supply systems for three perpendicular neutral beam (NB) injections provides a long period of central NB heating up to 30 s, which is important for keeping the internal transport barrier (ITB). The peaked density profile in the core plasma can be maintained even when the density at the pedestal increased in the latter phase of the discharge due to the increase in the divertor recycling. Then, the peaked pressure profile attributed to the ITB can be kept constant through the discharge with the peaked power deposition profile. In these long-pulse discharges, MHD activity with toroidal mode number n = 1 is observed even when neoclassical tearing modes (NTMs) are suppressed. When the amplitude of the mode in the peripheral region becomes large, the pedestal pressure is degraded. The mode amplitude is sensitive to the toroidal magnetic field (or edge safety factor) and heating power. After the adjustment of the toroidal magnetic field so as to reduce the mode amplitude, a high normalized beta (βN) of 2.6 and a high thermal confinement enhancement factor (HH98(y,2) > 1) are sustained for 25 s (∼14τR, where τR is the current diffusion time) under the ITER relevant small toroidal rotation condition. The peaked pressure profile in low safety factor plasma (safety factor at 95% flux surface q95 ∼ 3.2) is stable against NTMs up to βN ∼ 3. A high βNHH98(y,2) of 2.6 gives a high G-factor () of 0.25 and a peaked pressure profile gives a large bootstrap current fraction (fBS > 0.43).

JET and the Physics Basis of ITER

JET has made unique contributions to the physics basis of ITER by virtue of its ITER-like geometry, large plasma size and D-T capability. The paper discusses recent JET results and their implications for ITER in the areas of standard ELMy H-mode, D-T operation and advanced tokamak modes. In ELMy H-mode the separation of plasma energy into core and pedestal contributions shows that core confinement scales like gyroBohm transport. High triangularity has a beneficial effect on confinement and leads to an integrated plasma performance exceeding the ITER Q = 10 reference case. A revised type I ELM scaling predicts acceptable ELM energy losses for ITER, while progress in physics understanding of NTMs shows how to control them in ITER. The D-T experiments of 1997 have validated ICRF scenarios for heating ITER/a reactor and identified ion minority schemes (e.g. (3He)DT) with strong ion heating. They also show that the slowing down of alpha particles is classical so that the self-heating by fusion alphas should cause no unexpected problems. With the Pellet Enhanced Performance mode of 1988, JET has produced the first advanced tokamak mode, with peaked pressure profiles sustained by reversed magnetic shear and strongly reduced transport. More recently, LHCD has provided easy tuning of reversed shear and reliable access to ITBs. Improved physics understanding shows that rational q-surfaces play a key role in the formation and development of ITBs. The demonstration of real time feedback control of plasma current and pressure profiles opens the path towards fully controlled steady-state tokamak plasmas.

Chapter 9: Performance-Limiting MHD Activity and Possibilities for Its Stabilization in ASDEX Upgrade

Performance-limiting magnetohydrodynamic (MHD) instabilities on ASDEX Upgrade are discussed. In the conventional H-mode scenario, the main MHD performance limitation is found to be the neoclassical tearing mode (NTM). The onset β of NTMs in ASDEX Upgrade scales with the poloidal ion gyroradius, in agreement with theoretical expectations. At higher β values, NTMs occur in a more benign form, the frequently-interrupted-regime NTMs, which lead to a smaller confinement degradation than normal NTMs. Active control of NTMs by electron cyclotron current drive in the island has been demonstrated on ASDEX Upgrade. In advanced tokamak regimes with reversed shear, a variety of performance-limiting instabilities has been observed. The shear reversal zone can be unstable to double tearing modes or to infernal modes; both have been identified in ASDEX Upgrade. Due to the broad current profile in advanced tokamak discharges, the ideal external kink mode can be unstable at relatively low βN ≤ 2; this is a main limitation to strongly reversed shear discharges with peaked pressure profiles. Finally, it is shown that fast-particle-driven modes such as fishbones can also have beneficial effects, such as providing stationary current profiles or triggering internal transport barriers.

Non-existence of normal tokamak equilibria with negative central current

Recent tokamak experiments employing off-axis, non-inductive current drive have found that a large central current hole can be produced. The current density is measured to be approximately zero in this region, though in principle there was sufficient current drive power for the central current density to have gone significantly negative. Recent papers have used a large aspect-ratio expansion to show that normal magnetohydrodynamic equilibria (with axisymmetric nested flux surfaces, non-singular fields, and monotonic peaked pressure profiles) cannot exist with negative central current. That proof is extended here to arbitrary aspect ratio, using a variant of the virial theorem to derive a relatively simple integral constraint on the equilibrium. However, this constraint does not, by itself, exclude equilibria with non-nested flux surfaces, or equilibria with singular fields and/or hollow pressure profiles that may be spontaneously generated.

Sustained reversed magnetic shear mode of operation in the HL-2A tokamak

Realistic reversed magnetic shear (RS) discharges for the HL-2Atokamak are simulated with the TRANSP code. Early NBIheating achieves reversed shear (RS) configurations characterized by highly peaked pressure profiles and a narrow shear reversal region. To avoid excessive peaks in the pressure, and to sustain RS operation towards steady state, LHCD is used to control the current profile. The combined LH and bootstrap current create a quasi-stationary RS discharge with rmin/a ≈ 0.6and qmin ≈ 2.8. A self-consistent internal transport barrier is produced, and the RS configuration is established with a wider shear reversal region and broader pressure profile that is favourable to achieving the high beta limit.

Robustness and flexibility in compact quasiaxial stellarators: Global ideal magnetohydrodynamic stability and energetic particle transport

Concerns about the flexibility and robustness of a compact quasiaxial stellarator design are addressed by studying the effects of varied pressure and rotational transform profiles on expected performance. For thirty, related, fully three-dimensional configurations the global, ideal magnetohydrodynamic (MHD) stability and energetic particle transport are evaluated. It is found that tokamak intuition is relevant to understanding the magnetohydrodynamic stability, with pressure gradient driving terms and shear stabilization controlling both the periodicity preserving, N=0, and the nonperiodicity preserving, N=1, unstable kink modes. Global kink modes are generated by steeply peaked pressure profiles near the half radius and edge localized kink modes are found for plasmas with steep pressure profiles at the edge as well as with edge rotational transform above 0.5. Energetic particle transport is not strongly dependent on these changes of pressure and current (or rotational transform) profiles, although a weak inverse dependence on pressure peaking through the corresponding Shafranov shift is found. While good transport and MHD stability are not anticorrelated in these equilibria, stability only results from a delicate balance of the pressure and shear stabilization forces. A range of interesting MHD behaviors is found for this large set of equilibria, exhibiting similar particle transport properties.

MHD beta limits for advanced scenarios on JET

Ideal MHD limits to beta and bootstrap fraction are computed for pressure profiles similar to those of JET discharges with both internal and H mode transport barriers. Several non-monotonic current profiles are tested, and the pressure profile is constrained so that no negative current drive is required in steady state. Calculations are made both with and without an ideally conducting wall. The main result is that, for such peaked pressure profiles, the limits to beta and bootstrap fraction improve at low internal inductance, in particular when wall stabilization is taken into account. The highest limits to beta, and often also to normalized beta, occur for the maximum plasma current. There is also a weak dependence on qmin, for which three favourable regions have been identified. A highly advantageous region is found at qmin ≃ 1.6, where the limits to β* are 7.0% with, and 4.8% without, wall stabilization. The corresponding limits are 68 and 50%, respectively, for the bootstrap fraction and 4.0 and 2.9 for the normalized beta. These equilibria have low internal inductance, li = 0.62. For higher inductance, an optimum occurs when qmin ≃ 1.2, where the limit to β* is 5.3% with a wall and 4.7% without. The corresponding bootstrap fractions are about 46 and 38%, respectively. A third type of equilibrium that is interesting for steady state operation has qmin ≃ 2.1 and low inductance. Here the β* limits are lower, 4.9 and 3.4%, but the bootstrap fractions are higher, 77 and 60%.

Growth of ideal magnetohydrodynamic modes driven slowly through their instability threshold: Application to disruption precursors

The growth of an ideal magnetohydrodynamic (MHD) instability in a high-temperature plasma is calculated in the case where the plasma β is driven slowly through its instability threshold. The MHD perturbation grows faster than exponentially, approximately as exp[(t/τ)3/2]. Its characteristic growth time τ∼(32)2/3γ̂MHD−2/3γh−1/3 is a hybrid of the ideal MHD incremental growth rate γ̂MHD and the heating rate γh. This simple model agrees well with the observed growth of disruption precursors in high β DIII-D [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] discharges having strongly peaked pressure profiles, where the observed growth times of ⩾10−4 s are significantly slower than the typical ideal MHD time scale of ⩽10−5 s.

Beta optimization for peaked pressure profile reversed magnetic shear equilibria with JET type parameters

The ideal MHD β limit of reversed shear equilibria, due to n = 1, n = 2 and ballooning modes, is investigated for peaked pressure profiles, consistent with those occurring when the internal transport barrier is established in JET optimized shear discharges. Higher βN can be reached with the control of the minimum q value, and a conducting wall can further improve the stable domain. The n = 2 mode plays an insignificant role, unless the conducting wall improves the n = 1 stability when the shear reversal is large. Increasing the amount of shear reversal generally improves MHD stability, and the effect is stronger for the n = 2 mode. β* ( = 2μ0 ⟨P2 ⟩1/2/B02) increases with normalized current (Ip/aB0) but βN is only weakly affected.

Synergism between cross-section and profile shaping in beta optimization of tokamak equilibria with negative central shear

Systematic stability studies of the negative central shear (NCS) configuration reveal a synergistic relationship between the gains in the ideal n = 1 magnetohydrodynamic (MHD) β limit from optimizing the profiles and from optimizing the shape. For a circular cross-section with highly peaked pressure profiles, βN = β/(I/aB) is limited to βN∼2% (mT/MA). Small to moderate improvements in βN result either from broadening the pressure or from strong cross-section shaping. At fixed safety factor the latter translates to a much larger increase in β and the root mean square β denoted as β*. With both optimal profiles and strong shaping, however, the gain in all the relevant fusion performance parameters is dramatic, and β and β* can be increased by a factor of 5. The calculations show that stabilization from a nearby conducting wall greatly contributes to this large improvement, since coupling of the plasma to the wall is increased for the optimum profiles and cross-section. Moreover, the alignment of the bootstrap current density profile with the total current density profile is also optimized with broad pressure, strong cross-section shaping and high βN, thus minimizing steady state current drive requirements. Sensitivity studies using other profiles show some variation in the actual β limits, but the general trends remain robustly invariant.

Internal transport barriers in optimized shear plasmas in JET

Experiments using high-power heating during the current ramp-up phase of the discharge have obtained the highest D-D neutron rates in JET; neutrons , with , keV and keV. The best discharges ( MA and tesla) have peaked pressure profiles with a transport barrier located at = 0.55. The pressure peaking is limited by MHD modes and requires active input power control to achieve the best performance. Deuterium neutral beam injection into a tritium-rich target plasma has established internal transport barriers at power levels close to the lowest threshold for pure deuterium plasmas.