Neoclassical Bootstrap Current Research Articles

Resistive instabilities in general toroidal plasmas with neoclassical bootstrap currents

In this work, linear neoclassical resistive instabilities are investigated in general toroidal plasmas using standard perturbation theory. Using a neoclassical fluid model, we derive the singular layer equations modified by bootstrap currents and also obtain the dispersion relation of the resistive interchange mode and the neoclassical tearing mode (NTM), respectively. Additionally, we determine the stability criteria DRbs and Δcbs for bootstrap current-modified resistive modes. The resistive interchange mode is stable when DRbs<0 and the NTM is stable when Δ′<Δcbs, where Δ′ is the stability index of the tearing mode. It is found that, in tokamak plasmas with a positive magnetic shear, bootstrap currents have a destabilizing effect on resistive interchange modes, which not only increases the value of the stability criterion (DRbs) but also enhances the growth rate. In addition, bootstrap currents have a stabilizing effect on the growth rate of the NTM in a low growth rate region. However, bootstrap currents can also decrease the critical value Δcbs. In plasmas with negative magnetic shear, the opposite holds. Furthermore, the coupling effect between bootstrap currents and Pfirsch–Schlüter currents via magnetic field curvature is determined for the first time in this work. This coupling always has a stabilizing influence on the resistive interchange mode and can increase the value of Δcbs. The coupling is also independent of the sign of the magnetic shear and can be enhanced in low-aspect-ratio tokamaks (such as spherical tokamaks) or in plasma regions with low magnetic shear (as used in ITER hybrid scenarios). Our results are valid for low-n resistive instabilities in toroidal plasmas with arbitrary aspect ratios and β, where n is the toroidal mode number and β represents the ratio of the plasma pressure to the toroidal magnetic pressure. Overall, this investigation has broad parametric applications and deepens our understanding of the physical mechanisms underlying the influence of neoclassical effects on resistive instabilities.

Improved high-performance fully non-inductive discharge by optimizing the fast-ion confinement on EAST

The attainment of long-pulse, high-performance, fully non-inductive plasma is one of the major scientific objectives of EAST, using the ITER-like tungsten upper divertor. Understanding and optimizing the fast-ion behaviors is the critical issue to extending the performance of EAST. Recently, using both neutral beam injection (NBI) and radio frequency (RF; low hybrid, electron cyclotron, and ion cyclotron) heating, fully non-inductive high-βP scenarios with extension of fusion performance at high density and low rotation have been achieved, with βP up to 2.5, βN up to 2.0, H98y 2 > 1.1, and bootstrap current fraction (f BS) up to 50%. For previous long-pulse H-mode plasma at medium density, when NBI is added into RF plasma, βp is increased from 1.2 to 2.0 compared with RF-only discharges. In fact, f BS for both discharges is nearly the same, at ~22%. Analysis shows that the increase in βp is mostly due to fast ions which do not contribute significantly to the neoclassical bootstrap current. Thus, to obtain high-performance plasmas with improved bootstrap current fraction, key parameters (e.g. density, beam energy, etc.) must be further optimized. Experimental results show that high density improves bootstrap fraction also by reducing fast-ion slowing-down time and loss. The lower beam energy also mitigates fast-ion loss, which is better for heating and CD performance. The extension of high-performance, fully non-inductive experiments on EAST at high density and zero/low NBI torque can potentially offer unique contributions towards ITER and CFETR.

A quasilinear formulation of turbulence driven current

Non-inductive current drive mechanisms, such as the familiar neoclassical bootstrap current correspond to an essential component to the realization of steady state tokamak operation. In this work, we discuss a novel collisionless mechanism through which a mean plasma current may be driven in the presence of microturbulence. In analogy with the traditional neoclassical bootstrap current drive mechanism, in which the collisional equilibrium established between trapped and passing electrons results in the formation of a steady state plasma current, here we show that resonant scattering of electrons by drift wave microturbulence provides an additional means of determining the equilibrium between trapped and passing electrons. The resulting collisionless equilibrium is shown to result in the formation of an equilibrium current whose magnitude is a function of the thermodynamic forces. A mean field formulation is utilized to incorporate the above components into a unified framework through which both collisional as well as collisionless current drive mechanisms may be self-consistently treated. Utilizing a linearized Fokker-Planck collision operator, the plasma current in the presence of both collisions as well as turbulent stresses is computed, allowing for the relative strength of these two mechanisms to be quantified as a function of collisionality and fluctuation amplitude.

Turbulence-Driven Bootstrap Current in Low-Collisionality Tokamaks

Neoclassical bootstrap current is expected to provide a significant fraction of the equilibrium plasma current in tokamak reactors. Here we report a novel mechanism through which a bootstrap current may be driven even in a collisionless plasma. In analogy with the neoclassical mechanism, in which the collisional equilibrium established between trapped and passing electrons produces a steady state current, we show that resonant scattering of electrons by drift wave microturbulence provides an additional means of determining the equilibrium between trapped and passing electrons and thus driving a bootstrap current. Employing a linearized Fokker-Planck collision operator, the plasma current in the presence of both collisions and resonant electron scattering is computed, allowing for the relative strength of these two mechanisms to be quantified as a function of collisionality and fluctuation amplitude.

Transport in the plateau regime in a tokamak pedestal

In a tokamak H-mode, a strong E × B flow shear is generated during the L-H transition. Turbulence in a pedestal is suppressed significantly by this E × B flow shear. In this case, neoclassical transport may become important. The neoclassical fluxes are calculated in the plateau regime with the parallel plasma flow using their kinetic definitions. In an axisymmetric tokamak, the neoclassical particles fluxes can be decomposed into the banana-plateau flux and the Pfirsch-Schlüter flux. The banana-plateau particle flux is driven by the parallel viscous force and the Pfirsch-Schlüter flux by the poloidal variation of the friction force. The combined quantity of the radial electric field and the parallel flow is determined by the flux surface averaged parallel momentum balance equation rather than requiring the ambipolarity of the total particle fluxes. In this process, the Pfirsch-Schlüter flux does not appear in the flux surface averaged parallel momentum equation. Only the banana-plateau flux is used to determine the parallel flow in the form of the flux surface averaged parallel viscosity. The heat flux, obtained using the solution of the parallel momentum balance equation, decreases exponentially in the presence of sonic Mp without any enhancement over that in the standard neoclassical theory. Here, Mp is a combination of the poloidal E × B flow and the parallel mass flow. The neoclassical bootstrap current in the plateau regime is presented. It indicates that the neoclassical bootstrap current also is related only to the banana-plateau fluxes. Finally, transport fluxes are calculated when Mp is large enough to make the parallel electron viscosity comparable with the parallel ion viscosity. It is found that the bootstrap current has a finite value regardless of the magnitude of Mp.

The charged-particle distribution function in tokamaks modified by a magnetic field gradient

With the help of the standard neoclassical formalism, the particle guiding-centre distribution function in tokamaks is derived, taking into account the effect of magnetic field gradients. It is shown that the radial gradient of the parallel velocity, which depends on the magnetic field strength gradient, produces a parallel current additive to the conventional neoclassical bootstrap current. The existence of the parallel current on the magnetic axis may reduce or eliminate the need for a seed current in a tokamak reactor. The radial gradient of magnetic field also produces thermal and particle pinches. The thermal pinch significantly decreases the net heat flux in the vicinity of the magnetic axis, and this result is found to be in agreement with experimental trends. The particle pinch can play an important role in impurity transport.

Self-Sustained Tokamak Reactor due to Bootstrap Current with Finite Banana-Width Effect

The concept of a tokamak sustained only by the neoclassical bootstrap current is quite attractive. According to the conventional neoclassical transport theory, this completely bootstrapped tokamak is considered to be impossible since the bootstrap current vanishes at the magnetic axis and thus a seed current near the axis must be generated by an external source. However, several authors have suggested that the seed current can be generated through the anomalous radial diffusion of the bootstrap current and the inclusion of this effect may lead to the completely bootstrapped tokamak. Another suggestion for the possibility of the completely bootstrapped tokamak comes from the break-down of the conventional neoclassical transport theory near the magnetic axis. A particle orbit near the magnetic axis is quite different from the conventional banana orbit, and a thin-banana approximation in the conventional theory is broken down. The modification of the conventional neoclassical transport theory around the magnetic axis by the finite banana-width effect has been studied, and several expressions for the bootstrap current are presented. In these studies, the bootstrap current is found to remain finite on the magnetic axis. Therefore, this finite banana-width effect leads to the possibility of the completely bootstrapped tokamak. In order to calculate the bootstrapped tokamak equilibrium, we need the expression for the bootstrap current which can be used in entire region of plasma. Several formulae interpolating the expression at the magnetic axis and that of the conventional neoclassical transport theory have been presented. In a previous paper, the author obtained the bootstrap current at the magnetic axis by applying the Wang’s method, and proposed a more sophisticated interpolation formula between this bootstrap current at the axis and the conventional one. Our obtained expression for the bootstrap current reduces to the conventional one when the ratio 1=3 a = ffiffi p is much less than unity, where is the inverse aspect ratio, and a 1⁄4 2q0 a=kR0 with the major radius R0, the elongation parameter k, the safety factor q0 at the magnetic axis, and the Larmor radius a for species a. The finite banana-width effect is shown to modify the conventional bootstrap current around the magnetic axis satisfying the condition ffiffi p < 1=3 a . This modification is significant for high energy particles. In ref. 12, the author also obtained the expression for the bootstrap current due to fusion-produced alpha particles by taking into account the finite banana-width effect. In this paper, using the modified bootstrap current by the finite banana-width effect, we study a simple equilibrium model of completely bootstrapped tokamak. The bootstrap current Jbulk due to bulk particles is expressed as Jbulk 1⁄4 ðB=hBiÞðneTe=BpÞĴbulk with Ĵbulk 1⁄4 L1 pe pe þ 1

Plasma confinement studies in LHD

The initial experiments on the Large Helical Device (LHD) have extended confinement studies on currentless plasmas to a large scale (R = 3.9 m, a = 0.6 m). Heating by NBI of 3 MW produced plasmas with a fusion triple product of 8 × 1018m-3·keV·s at a magnetic field strength of 1.5 T. An electron temperature of 1.5 keV and an ion temperature of 1.1 keV were achieved simultaneously at a line averaged electron density of 1.5 × 1019 m-3. The maximum stored energy reached 0.22 MJ with neither unexpected confinement deterioration nor visible MHD instabilities, which corresponds to ⟨β⟩ = 0.7%. Energy confinement times reached a maximum of 0.17 s. A favourable dependence of energy confinement time on density remains in the present power density (∼40 kW/m3) and electron density (3 × 1019 m-3) regimes, unlike the L mode in tokamaks. Although power degradation and significant density dependence are similar to the conditions on existing medium sized helical devices, the absolute value is enhanced by up to about 50% from the International Stellarator Scaling 95. Temperatures of both electrons and ions as high as 200 eV were observed at the outermost flux surface, which indicates a qualitative jump in performance compared with that of helical devices to date. Spontaneously generated toroidal currents indicate agreement with the physical picture of neoclassical bootstrap currents. Change of magnetic configuration due to the finite β effect was well described by 3-D MHD equilibrium analysis. A density pump-out phenomenon was observed in hydrogen discharges, which was mitigated in helium discharges with high recycling.

Alpha -particle transport-driven current in tokamaks.

It is shown that the radial transport of fusion-born energetic \ensuremath{\alpha} particles, induced by electrostatic waves traveling in one poloidal direction, is directly connected to a net momentum of \ensuremath{\alpha} particles in the toroidal direction in tokamaks. Because the momentum change is almost independent of toroidal velocity, the energy required for the momentum generation remains small on an \ensuremath{\alpha}-particle population sustained by an isotropic time-independent source. By numerical toroidal Monte Carlo calculations it is shown that the current carried by \ensuremath{\alpha} particles in the presence of intense well penetrated waves can reach several mega-amperes in reactor-sized tokamaks. The current obtained can greatly exceed the neoclassical bootstrap current of the \ensuremath{\alpha} particles.

Current drive and bootstrap current in stellarators

A review of the experimental observation of plasma net currents in several stellarator devices and the comparison with theoretical predictions on the neoclassical bootstrap current is given. Good agreement of the experimental findings with neoclassical predictions is found with respect to the parameter dependence, the local distribution of the currents and the magnitude. The compensation of the bootstrap current by electron cyclotron current drive is experimentally demonstrated. Experiments on the ECCD-efficiency are compared with simple theoretical models.

Bootstrap current drive by localized beat wave seeding

Neoclassical bootstrap currents with well controlled central seed current drive in Tokamak plasmas are investigated analytically and numerically. The analytical current scaling predicts a strong bootstrap effect in hot, high density plasmas. The Troyon limit and safety factor profiles in various small seed current cases are considered to find the optimal conditions for a large bootstrap amplification. The Troyon limited bootstrap current is very insensitive to the detailed form of the pressure profile and the beta-limit is determined by the plasma geometry alone. Regarding the current seeding, high frequency methods, like beat-waves, are proposed, which are ideal for the localized central current drive.

Bootstrap current during perpendicular neutral injection in JT-60

The neoclassical bootstrap current effect is investigated in the JT-60 tokamak. The experimental resistive loop voltages are compared with the calculations, using the neoclassical resistivity, with and without the bootstrap current, and the Spitzer resistivity for a wide range of plasma current (Ip = 0.5-2 MA) and poloidal beta (βp = 0.1-3.2). The neoclassical bootstrap current is calculated directly with the force balance equations for viscous and friction forces according to the Hirshman–Sigmar theory. The bootstrap current driven by the fast ion component is also included. The calculated resistive loop voltage is consistent with the neoclassical prediction including the bootstrap current. It is shown that up to 80% of total plasma current is driven by the bootstrap current in the regime with an extremely high poloidal beta value (βp = 3.2) while the beam driven current is negligibly small.

Optimization of the bootstrap current in a large helical system with L = 2

Neoclassical bootstrap currents in the banana and plateau regimes are evaluated for a large helical system with L = 2 and with a major radius of 5 m. Various vacuum magnetic field configurations are studied with a view to optimizing the bootstrap current. In the banana regime, shifting of the magnetic axis and shaping of magnetic surfaces have a remarkable influence on the bootstrap current. It has been found that a small outward shift of the magnetic axis and vertically elongated magnetic surfaces are favourable for a reduction of the bootstrap current. In contrast, in the plateau regime the bootstrap current depends strongly on the toroidal pitch number of the helical winding coils, but shifting of the axis and shaping of magnetic surfaces are not effective. The magnitude of the bootstrap current is estimated for plasmas in a large helical system with parameters given by a one-dimensional radial transport code.

Bootstrap current in TFTR.

Neutral-beam--heated plasmas in TFTR show evidence of substantial non-Ohmically driven toroidal current, even for balanced beam momentum input. The observations are inconsistent with calculations including only Ohmic and beam-driven currents, and presently can only be matched by models including the neoclassical bootstrap current.