Ideal Stability Limit Research Articles

High internal inductance for steady-state operation in ITER and a reactor

Increased confinement and ideal stability limits at relatively high values of the internal inductance () have enabled an attractive scenario for steady-state tokamak operation to be demonstrated in DIII-D. Normalized plasma pressure in the range appropriate for a reactor has been achieved in high elongation and triangularity double-null divertor discharges with at , near the ideal kink stability limit calculated without the effect of a stabilizing vacuum vessel wall, with the ideal-wall limit still higher at . Confinement is above the H-mode level with . At , the current is overdriven, with bootstrap current fraction , noninductive current fraction and negative surface voltage. For ITER (which has a single-null divertor shape), operation at is a promising option with and the remaining current driven externally near the axis where the electron cyclotron current drive efficiency is high. This scenario has been tested in the ITER shape in DIII-D at , so far reaching and at with performance appropriate for the ITER Q=5 mission, . Modeling studies explored how increased current drive power for DIII-D could be applied to maintain a stationary, fully noninductive high discharge. Stable solutions in the double-null shape are found without the vacuum vessel wall at , and , and at with the vacuum vessel wall.

Ideal ballooning modes in the tokamak scrape-off layer

A drift-reduced Braginskii fluid model is used to carry out a linear and non-linear study of ideal ballooning modes in the tokamak scrape-off layer. First, it is shown that the scrape-off layer finite connection length and boundary conditions modify the ideal stability limit with respect to the closed flux-surface result. Then, in a two-fluid description, it is found that magnetic induction effects can destabilize long wavelength resistive ballooning modes below marginal ideal stability. Non-linear simulations confirm a gradual transition from small scale quasi-electrostatic interchange turbulence to longer wavelength modes as the plasma beta is increased. The transition to global ideal ballooning modes occurs, roughly, at the linearly obtained stability threshold. The transport levels and the pressure gradient as a function of plasma beta obtained in non-linear simulations can be predicted using the non-linear flattening of the pressure profile from the linear modes as a turbulent saturation mechanism.

Status and prospect of the JT-60SA project

The mission of the JT-60SA project is to contribute to the early realization of fusion energy by supporting the exploitation of ITER and research towards DEMO by addressing key physics issues associated with these machines. The JT-60SA will be capable of confining break-even equivalent class high-temperature deuterium plasmas at a plasma current I p of 5.5 MA and a major radius of ∼3 m lasting for a duration longer than the timescales characteristic of plasma processes, pursue full non-inductive steady-state operation with high plasma beta close to and exceeding no-wall ideal stability limits, and establish ITER-relevant high density plasma regimes well above the H-mode power threshold. Re-baselining of the project was completed in late 2008 which has been worked on since late 2007, where all the scientific missions are preserved with the newly designed machine to meet the cost objectives. The JT-60SA project made a large step forward towards its construction, which now foresees the first plasma in 2016. Construction of JT-60SA begins at Naka in Japan with launching the procurement of PF magnet, vacuum vessel and in-vessel components by Japan. In this year, the procurement of TF magnet, cryostat and power supply will be launched by Europe.

Validation of the linear ideal magnetohydrodynamic model of three-dimensional tokamak equilibria

The first quantitative comparison of linear ideal magnetohydrodynamic (MHD) theory with external magnetic measurements of the nonaxisymmetric plasma perturbation driven by external long-wavelength magnetic fields in high-temperature tokamak plasmas is presented. The comparison yields good (within 20%) agreement for plasma pressures up to ∼75% of the ideal stability limit calculated without a conducting wall. For higher plasma pressures, the ideal MHD model tends to overestimate the perturbed field indicating the increasing importance of stabilizing nonideal effects.

Stability Limits of High-Beta Plasmas in DIII-D

Stability at high beta is an important requirement for a compact, economically attractive fusion reactor. DIII-D experiments have shown that ideal magnetohydrodynamic (MHD) theory is an accurate predictor of the ultimate stability limits for tokamaks, and the Troyon scaling law has provided a useful approximation of ideal stability limits for discharges with “conventional” profiles. However, variation of the discharge shape, pressure profile, and current density profile can lead to ideal MHD beta limits that differ significantly from simple Troyon scaling. The need for profiles consistent with steady-state operation places an important additional constraint on plasma stability. Nonideal effects can also be important and must be taken into account. For example, neoclassical tearing modes (NTMs), resulting from plasma resistivity and the nonlinear effects of the bootstrap current, can become unstable at beta values well below the ideal MHD limit. DIII-D experiments are now entering a new era of unprecedented control over plasma stability, including suppression of NTMs by localized current drive at the island location, and direct feedback stabilization of kink modes with a resistive wall. The continuing development of physics understanding and control tools holds the potential for stable, steady-state fusion plasmas at high beta.

Integrated, advanced tokamak operation on DIII-D

Recent experiments on DIII-D have demonstrated the ability to sustain plasma conditions that integrate and sustain the key ingredients of advanced tokamak (AT) operation: high β with 1.5<q min <2.5, good energy confinement, and high current drive efficiency. Utilizing off-axis (ρ = 0.4) electron cyclotron current drive (ECCD) to modify the current density profile in a plasma operating near the no-wall ideal stability limit with q min >2.0, plasmas with β≈2.9% and 90% of the plasma current driven non-inductively have been sustained for nearly 2 s (limited only by the duration of the ECCD pulse). Negative central magnetic shear is produced by the ECCD, leading to the formation of a weak internal transport barrier even in the presence of Type I ELMs. Separate experiments have demonstrated the ability to sustain a steady current density profile using ECCD for periods as long as 1 s with β = 3.3% and >90% of the current driven non-inductively. In addition, stable operation well above the ideal no-wall β limit has been sustained for several energy confinement times with the duration only limited by resistive relaxation of the current profile to an unstable state. Stability analysis indicates that the experimental β limit depends on the degree to which the no-wall limit can be exceeded and weakly on the actual no-wall limit. Achieving the necessary density levels required for adequate ECCD efficiency requires active divertor exhaust and reducing the wall inventory buildup prior to the high performance phase. Simulation studies indicate that the successful integration of high β operation with current profile control consistent with these experimental results should result in high β, fully non-inductive plasma operation.

Physics basis for a spherical torus power plant

The spherical torus, or low-aspect-ratio tokamak, is considered as the basis for a fusion power plant. A special class of wall-stabilized high- β high-bootstrap fraction low-aspect-ratio tokamak equilibrium are analyzed with respect to MHD stability, bootstrap current and external current drive, poloidal field system requirements, power and particle exhaust and plasma operating regime. Overall systems optimization leads to a choice of aspect ratio A=1.6, plasma elongation κ=3.4, and triangularity δ=0.64. The design value for the plasma toroidal β is 50%, corresponding to β N=7.4, (based on the toroidal β, not the total β) which is 10% below the ideal stability limit. The bootstrap fraction of 99% greatly alleviates the current drive requirements, with tangential neutral beam injection mainly for profile control and rotation drive. The design is such that 45% of the thermal power is radiated in the plasma by Bremstrahlung and trace Krypton, with Neon in the scrapeoff layer radiating the remainder. The scarcity of spherical torus experimental data caused the design to be based largely on theoretical predictions, some of which may turn out to be overly optimistic. This highlights the need for a strong experimental research program in this area.

Resistive instabilities in reversed shear discharges and wall stabilization on JT-60U

Resistive instabilities and wall stabilization of ideal kink modes with low toroidal mode number n are investigated in JT-60U reversed shear discharges. Localized burst-like MHD activity with n⩽3 is observed in the negative shear region with large pressure gradient near the internal transport barrier; this activity is identified as the resistive interchange mode.The burst-like MHD activity is benign with respect to the internal transport barrier and no clear degradation of plasma stored energy by the burst-like MHD activity is observed. The resistive interchange mode, however, results in a major collapse through non-linear coupling with a tearing mode in the positive shear region. A resistive wall mode (RWM) followed by a major collapse is observed in wall stabilized high β discharges exceeding the ideal stability limit with the wall at infinity (βN>βNno-wall).No clear continuous slowing down of the plasma toroidal rotation is observed before the growth of an RWM.

Stability of negative central magnetic shear discharges in the DIII-D tokamak

Discharges with negative central magnetic shear (NCS) hold the promise of enhanced fusion performance in advanced tokamaks. However, stability to long wavelength magnetohydrodynamic modes is needed to take advantage of the improved confinement found in NCS discharges. The stability limits seen in DIII-D [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] experiments depend on the pressure and current density profiles and are in good agreement with stability calculations. Discharges with a strongly peaked pressure profile reach a disruptive limit at low beta, βN=β(I/aB)−1⩽2.5 (% m T/MA), caused by an n=1 ideal internal kink mode or a global resistive instability close to the ideal stability limit. Discharges with a broad pressure profile reach a soft beta limit at significantly higher beta, βN=4 to 5, usually caused by instabilities with n&amp;gt;1 and usually driven near the edge of the plasma. With broad pressure profiles, the experimental stability limit is independent of the magnitude of negative shear but improves with the internal inductance, corresponding to lower current density near the edge of the plasma. Understanding of the stability limits in NCS discharges has led to record DIII-D fusion performance in discharges with a broad pressure profile and low edge current density.

Ideal MHD stability of high βp plasmas and βp collapse in JT-60U

Analyses of ideal MHD stabilities of high βp plasmas show that the occurrence of βp collapse in JT-60U is consistent with the violation of the low n kink mode stability boundary. It is demonstrated theoretically that the pressure profile, internal inductance, li, qs/q0 and ϵβp influence the ideal stability limit, g, imposed by the low n kink mode and the infinite n ballooning mode; here, g = βt/(I/aBt). Peaking of the pressure profile decreases the stability limit g to low values (2-1.5) in both high li (≈ 1.2) and low li (≈ 0.8) plasmas, though the maximum g value does not strongly depend on ϵβp and qs/q0. In a high li plasma with peaked pressure, the stability limit is determined by internal low n kink modes, especially by the infernal mode in the low q0 region, while, in the low li plasma, it is determined by the infinite n ballooning mode. Broadening of the pressure profile combined with the high li (≈ 1.2) significantly increases the stability limit g (≈ 5) and makes the displacement more global, though the g value decreases with ϵβp for fixed values of qs/q0. Experimentally, by the broadening of the pressure profile with high li (>1.2), high g (≈ 4) plasmas are obtained and no βp collapse is observed, which is consistent with non-violation of the ideal MHD stability boundary

Localized resistive instabilities in general toroidal configurations, with applications to INTOR equilibria

A useful method for studying localized resistive instabilities in toroidal equilibria at and near the ideal stability limit is presented. In particular, a valuable relation is given explicitly which allows direct calculation of the resistive growth rate at the ideal ballooning limit in terms of line-averaged equilibrium quantities. The method, which is valid not only for axisymmetric equilibria but also for toroidal, nonsymmetric 3-D configurations, is derived without making any of the usual restricting assumptions such as small inverse aspect ratio, low pressure etc. The actual evaluation of stability criteria and dispersion relations is illustrated by studying the stability of typical INTOR equilibria with respect to localized ideal and resistive modes. Configurations which are stable with respect to ideal ballooning modes (and are therefore also Mercier stable) are shown to be unstable with respect to resistive ballooning instabilities, and the corresponding growth rates are calculated. Considerable growth rates ( gamma -1 approximately 1 ms) are found at values of ( beta ) that are 80-90% of the critical value. Below these values of ( beta ), the growth rates decrease very rapidly. A subject of more general interest is also treated, namely the situation which appears when the Mercier exponent sM exceeds the value 1/2, and a new dispersion relation for a model equation is derived.