Negative Magnetic Shear Research Articles

Triggering of internal transport barrier in JET

Internal transport barriers (ITBs) can be produced in JET by the application of strong additional heating during the current rise phase of the plasma discharge. Using up to 3 MW of lower hybrid power to tailor the q-profile prior to the main heating phase, a large variety of q-profiles ranging from low positive to strong negative central shear have been obtained during the current rise (0.4 MA s−1). With negative central magnetic shear s = (r/q)(dr/dq), the analysis of ITB triggering reveals a correlation between the formation of the ITB and q min reaching an integer value (q = 2 or q = 3). This observation is confirmed by the analysis of the Alfvèn cascades. The minimum power required to access regimes with ITBs is probably related to the transport and magnetohydrodynamic properties of integer magnetic surfaces. Laser ablation and shallow pellet injection have also been attempted in recent JET ITB triggering experiments.This article was scheduled to appear in issue 7 of Plasma Phys. Control. Fusion. To access this special issue on advanced Tokamak research in EFDA-JET please follow this link: http://stacks.iop.org/0741-3335/44/7

Stability analysis of improved confinement discharges: internal transport barriers in Tore Supra and radiative improved mode in TEXTOR

Results of stability analysis are presented for two types ofplasma with good confinement: internal transport barriers (ITBs) onTore Supra and the radiative improved (RI) mode on TEXTOR. The stabilityanalysis has been performed with an electrostatic linear gyrokineticcode, evaluating the growth rates of microinstabilities. The codedeveloped, KINEZERO, is aimed at systematic microstability analysis.Therefore the trade-off between having perfect quantitative agreementand minimizing computation time is made in favour of the latter. In theplasmas analysed, it is found that the onset of the confinementimprovement involves a trigger. For the ITB discharges, negativemagnetic shear is involved, whereas for the RI discharges, thetriggering role is played by the increase of the impurity concentration.Once the improved confinement is triggered, the simultaneous increasesof temperature and density gradients imply an increase in both thegrowth rate and the rotation shearing rate. The rotation shear is foundto be high enough to maintain an improved confinement through thestabilization of the large scale modes.

Impact of different heating and current drive methods on the earlyshape q-profile evolution in JET

Transport calculations illustrate that the lower hybrid current drive(LHCD) and off-axis electron cyclotron current drive (ECCD) are theonly preheating methods that can create a wide, deeply reversedq-profile, i.e. large negative magnetic shear, on the JETtokamak. Off-axis neutral beam injection (NBI) and off-axision cyclotron resonance heating (ICRH) preheating yields a weaklyreversed q-profile (small negative magnetic shear), whereas NBI andICRH on-axis heating as well as ohmic preheating produce a monotonicq-profile in the preheating phase. Here, on-axis power depositionand current drive refers to heating and current drive at or close tomagnetic axis and correspondingly, off-axis refers to heating andcurrent drive deposited typically around the half minor radius(r/a = 0.3-0.6). The results on LHCD, ICRH and ohmic preheating havebeen verified in the recent JET experiments. The current driveefficiency scan shows that in the case of LHCD, ECCD and off-axis NBI,the driven current is absolutely crucial to obtain a reversedq-profile and to modify the current profile evolution drasticallyin the preheating phase. Taking into account only the direct electronheating effect, LHCD does not create a reversed q-profile. Thetiming scans indicate that the radial location of qmin at theend of the preheating phase is generally quite insensitive to thestart time of the preheating, once started 0-2 s after the plasmainitiation if the method relies upon the driven current. On the otherhand, methods relying only upon electron heating are very sensitive tothat. In both cases, the magnitude of the negative magnetic shear,however, seems to be very sensitive to the start time of the preheating.

Influence of the q-profile shape on plasma performance in JET

The fusion performance of JET plasmas can be enhanced by the generation of internal transport barriers. The influence of the q-profile shape in the local and global plasma performance has been investigated in cases where the core magnetic shear ranges from small and positive to large and negative. Internal barriers extending to large plasma radii can be effective in raising the global performance of the plasma. It is found that such barriers tend to be generated more easily if the q-profile contains a region of negative magnetic shear. The formation is favoured by neutral beam injection compared with ion cyclotron resonance heating in scenarios where the two systems are used together. The minimum power level required to observe a local transport reduction is significantly lower than the value at which very steep pressure gradients can be achieved. This results in a practical threshold in the power to access a regime of high plasma performance that is sensitive to the q-profile shape.

Role of collisionless trapped electron mode in tokamak plasmas with electron internal transport barrier

A self-sustained turbulence model for collisionless trapped electron mode is presented to examine the role of dynamics of trapped electrons in forming electron internal transport barrier (ITB) in tokamak plasmas with negative magnetic shear. Results show that strong negative magnetic shear as well as large Shafranov shift can lead to the precession drift reversal of trapped electrons and large reduction of anomalous electron heat conductivity; it may further trigger the formation of electron ITB. The complete precession drift reversal seems to be in good agreement with the onset condition of electron ITB observed in JT-60U discharges.

Dynamics of the formation, sustainment and destruction of transport barriers in magnetically contained fusion plasmas*

The formation of transport barriers in fusion plasmas is studied through examination of mechanisms which can stabilize plasma turbulence and, thereby, reduce turbulence-driven transport. These include the effects of E×B velocity shear, negative central magnetic shear and the Shafranov shift. Transport barriers formed at the plasma edge and in the plasma core are considered, as well as the formation of multiple barriers. The access conditions for barrier formation are examined, particularly by considering local conditions compared to global parameters. Processes that can destroy transport barriers, such as magnetohydrodynamic instabilities, are described. Plasmas with high confinement and good plasma stability then require effective control of plasma profiles and transport. Efforts towards real-time control of transport barriers are described.

Progress in internal transport barrier plasmas with lower hybrid current drive and heating in JET (Joint European Torus)

In optimized shear plasmas in the Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)], safety factor (q) profiles with negative magnetic shear are produced by applying lower hybrid (LH) waves during the plasma current ramp-up phase. These plasmas produce a barrier to the electron energy transport. The radius at which the barrier is located increases with the LH wave power. When heated with high power from ion cyclotron resonance heating and neutral beam injection, they can additionally produce transient internal transport barriers (ITBs) seen on the ion temperature, electron density, and toroidal rotation velocity profiles. Due to recent improvements in coupling, q profile control with LH current drive in ITB plasmas with strong combined heating can be explored. These new experiments have led to ITBs sustained for several seconds by the LH wave. Simulations show that the current driven by the LH waves peaks at the ITB location, indicating that it can act in the region of low magnetic shear.

Dynamics of Plasma during the Formation of a Weak Negative Central Magnetic Shear Configuration Using Counter Neutral Beam Injection in the JFT-2M Tokamak.

In the JFT-2M tokamak, discharges exhibiting good performance have been produced by counterNBI after boronization. An improved core confinement mode under an H-mode edge condition is sustained for -5~~E With H89p - 1.5 and pN - 2.0 at a line-averaged electron density of around 70%-80% of the Greenwald density limit. It is found that the q-profile changes from a monotonic one having qo ~ 1 to a zero or weak negative central magnetic shear configuration having I < qmin ~ qo < 3 during improved core confinement mode using counter-NBI under an H-mode edge condition. The central electron temperature very clearly increases when the sawtooth activity disappears, while the previous result without boronization exhibited a significant degradation of the energy confinement due to the accumulation of impurities. The mechanism governing the improved core confinement mode including the density peaking and/or ITB formation due to negative shear is presently unclear.

Local magnetic shear and drift waves in stellarators

A study of the effect of local magnetic shear on the drift wave stability is presented. The eigenvalue problem for the drift wave equation is solved numerically in fully three-dimensional stellarator plasma using the ballooning mode formalism. It is found that negative local magnetic shear has a stabilizing effect on the drift wave instability and positive local shear is destabilizing. This is in agreement with the effect of negative global magnetic shear in tokamaks and also agrees with the simple estimates. As a consequence the highly unstable modes found on a specific magnetic surface are localized in the region of positive local magnetic shear.

Performance, heating and current drive scenarios of ASDEX Upgrade advanced tokamak discharges

Various approaches to high performance and steady state operation are presented. Strong neutral beam heating in the current ramp leads to internal transport barriers (ITBs) in conjunction with negative central magnetic shear. To avoid the destabilizationof external kink modes this regime is limited to L mode edge operation with βN < 1.7. In high poloidal β, βp, discharges, full non-inductive current drive has been achieved transiently. At Greenwald density, values of βp = 3.1, βN = 2.8 and HITER89-P = 1.8 have been reached simultaneously. In plasmas with ITBs and L mode edge, additional ECRH and ECCD facilitates high core confinement with Te ≈ Ti. CentralECCD has been applied in low density low current discharges. For ECCD in the co-current direction a current drive fraction of 82% is calculated. In the case of counter-ECCD, negative central shear withqmin > 1 leads to the formation of an electron ITB.

Nonlinear three-dimensional self-consistent simulations of negative central shear discharges in the DIII-D tokamak

Nonlinear simulations of experimentally observed magnetohydrodynamic (MHD) bursts in DIII-D [J. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] L-mode negative central magnetic shear (NCS) discharges were performed with a full three-dimensional nonlinear MHD code. The effects of plasma rotation in the presence of resistivity and viscosity are included and an effectively implicit numerical scheme allows the transport profile to evolve self-consistently with the nonlinear MHD instabilities and externally applied sources and sinks. The simulations follow the MHD bursts and disruptions through the linear and nonlinear phases and identify the connections between the early MHD bursts and the ultimate disruption phase. Specific predictions of the growth and saturation of the modes are directly compared with experimental diagnostic measurements in DIII-D. The simulations show that the bursts observed in experiments are triggered by MHD instability of a resistive interchange mode and a resistive kink mode that are excited for critical plasma profiles. The critical profiles are determined by the balance between inductive and noninductive sources of current density.

Linear and nonlinear resistive magnetohydrodynamic stability of tokamak discharges with negative central shear

Linear and nonlinear magnetohydrodynamic (MHD) calculations have been performed to study the stability of tokamak discharges with reversed or negative central magnetic shear using the finite aspect ratio (FAR) suite of MHD codes [Charlton et al., J. Comput. Phys. 86, 270 (1990)]. The linear calculations confirm anew that radially localized resistive interchange modes can be unstable in the reversed or negative central magnetic shear region. The calculations further show that these resistive interchange modes are more unstable for toroidal mode numbers n higher than n=1. The nonlinear calculations do however demonstrate that toroidal mode number n=1, enhanced by the nonlinear couplings of the linearly more unstable higher n toroidal harmonics, dominates the nonlinearly saturated steady state. While the resistive interchange modes may account for the precursors detected experimentally, the saturated levels of magnetic fluctuations obtained in the nonlinear calculations do not appear large enough to cause the experimentally observed global collapse of such discharges.

Modelling of `advanced tokamak' scenarioswith radiofrequency heating and current drive for Tore Supra

A possibility of `advanced tokamak' operation based on RF heating and current drive is studied using 1-D transport modelling for long pulse tokamaks such as Tore Supra. A current drive with lower hybrid and fast magnetosonic waves and strong electron heating with ion cyclotron waves are applied in this scenario. The self-consistent evolution of the energy, particles and current densities is simulated, starting from an ohmic plasma and arriving at a non-inductive steady state equilibrium. An estimation of the RF power required for the setting up of this equilibrium characterized by an improved confinement due to the building up of particle and energy internal transport barriers in the reversed magnetic shear configuration is presented. The maximum bootstrap current fraction attained in this scenario is about 50%. A limit on the bootstrap current fraction in plasmas with an L mode edge and improved core confinement produced due to the stabilizing effect of a low or negative magnetic shear is found. The conventional operational techniques with fixed plasma current or controlled plasma flux and non-inductive current are compared with the operation with the current profile control algorithm, and the advantages of current profile control are shown. The results presented are relevant to present tokamaks operating with RF heating and current drive and possibly to future tokamak projects aimed at advanced operation.

Particle transport in DIII-D discharges with internal regions of enhanced confinement and counter injected neutral beams

An analysis of experimentally measured particle transport in tokamak plasmas with negative central magnetic shear is presented. The analysis is presented in terms of a simple model for turbulent transport which allows the separation of diagonal and off diagonal terms and allows the direct comparison of particle and energy transport. Comparing the measured fluxes to the fluxes predicted by a simple quasi analytical model which specifies a relation between the diagonal and off diagonal terms allows an understanding of the reason for the difference between energy and particle fluxes. In the center of discharges with a region of enhanced confinement (or internal transport barrier), the ion thermal diffusivity becomes small and comparable to neoclassical values and the particle diffusivity also becomes small and approaches the neoclassical values.

Ion heat pinch in reversed magnetic shear tokamak plasmas

In the well-known reversed shear discharges, it is observed that the ion thermal diffusivity (χi) falls below the standard neoclassical value (χineo), i.e., χi&amp;lt;χineo. In this paper, local turbulent ion thermal pinch (χit&amp;lt;0) is proposed as a candidate for interpreting the experimental results from χi=χineo+χit&amp;lt;χineo. To test the idea, the two-fluid theory, developed by Weiland and the Chalmers group [J. Weiland et al., Nucl. Fusion 29, 1810 (1989); H. Nordman et al., ibid 30, 983 (1990)], is used in the reversed magnetic shear tokamak plasma to study the drift mode and associated ion heat transport. The theory is extended here to include both the radial electrical field shear (dEr/dr) and electron fluid velocity (Ve) in the sheared coordinate system. Remarkably different from B−1dEr/dr, k⋅Ve directly includes the safety factor q as well as the E×B velocity VE itself, where k is the magnetic configuration-dependent wave vector. As a result, the synergetic effects of B−1dEr/dr and k⋅Ve, especially those of k⋅Ve, lead to the local turbulent ion heat pinch in the negative and weak magnetic shear region because of the wave-particle resonance. The impact of B−1dEr/dr and k⋅Ve on the growth rate and ion heat pinch is numerically investigated. Qualitatively, the present results are in good agreement with the experimental trends.

Effect of E×B flows on global linear ion temperature gradient modes

Strong electric fields generate an E×B rotation of the equilibrium plasma. Experiments have shown that this effect could lower the anomalous transport in tokamaks. The study of the effect of these flows on the linear stability of ion temperature gradient (ITG) modes has therefore been undertaken. The question is addressed solving the spectrum of the gyrokinetic equation in the full two-dimensional poloidal plane for a large aspect ratio tokamak with concentric circular magnetic surfaces. Results show a strong stabilizing effect of E×B flows on the ITG modes. Study with respect to different profiles of the flow shows that the so-called curvature of flow (second derivative) has no effect, while the intensity of flow itself produces the strongest effect. Study with respect to different magnetic shears did not allow the discovery of any particular behavior of the negative magnetic shear cases. Eventually, an experimental comparison was conducted.

Modeling of electron cyclotron current drive in a tokamak with internal transport barrier

Current drive by the electromagnetic waves in the electron cyclotron range of frequency was numerically studied by the newly developed code TASK/EC. The dependence on the poloidal injection angle and the effect of negative magnetic shear associated with the internal transport barriers are studied.

Could reversed-field pinches and quasi-helical stellarators benefit from transport suppression in tokamaks?

The trapped particle theory of turbulent transport successfully explains key features of tokamak transport: the canonical L-mode, supershort plasma profiles, and the transport suppression by negative magnetic shear and poloidal rotation. Here, this theory is applied to reversed-field pinch (RFP) profiles, which can be justified if the magnetic fluctuations are suppressed, and to stellarators. A canonical density profile for RFPs is suggested, and it is found that no analogue of the transport suppression by negative shear in tokamaks is possible in RFPs. In quasi-helical stellarators, on the other hand, it appears possible to create an analogue of the tokamak reversed shear mode in the entire plasma volume.

Response to “Comment on ‘Alfvén wave current drive in tokamak rotating plasma with negative magnetic shear’ ” [Phys. Plasmas 7, 3119 (2000)

The current drive due to low-frequency waves—Alfvén waves, ω≪Ωi (Ωi is the ion cyclotron frequency) in tokamak rotating plasma with negative magnetic shear has been considered in the paper [Phys. Plasma 6, 4633 (1999)]. In that paper, both the poloidal rotation frequency Ω and the magnetic shear parameter δ̄ have been assumed to be the first-order corrections, that is, Ω/ω≪1 and δ̄≪1. The single-fluid magnetohydrodynamic (MHD) model with a scalar resistivity and viscosity, and an Ohm’s law, nj=E+(1/c)V×B, is adequate for our first analysis in the linear theory.

Comment on “Alfvén wave current drive in tokamak rotating plasma with negative magnetic shear” [Phys. Plasmas 6, 4633 (1999)

Comment on “Alfvén wave current drive in tokamak rotating plasma with negative magnetic shear” [Phys. Plasmas <b>6</b>, 4633 (1999)