Momentum Confinement Time Research Articles

Toroidal plasma acceleration due to NBI fast ion losses in LTX-β

The recent Lithium Tokamak Experiment-Beta (LTX-β) upgrade includes the addition of neutral beam injection (NBI) in the same direction as the plasma current (co-I P ) and a new toroidal Mirnov array for MHD characterization. In initial NBI experiments, a spontaneously rotating n = 1 MHD mode is seen to accelerate during NBI in the counter-beam direction, accompanied by a rise in electron density consistent with the beam-injected inventory but without a clear increase in plasma pressure. Together with analytic and numerical modeling of beam optics and fast ion confinement, these observations indicate the prompt loss of all or nearly all beam ions. However, the same modeling also suggests that planned upgrades to the Ohmic heating system should provide the fast ion confinement necessary for beam heating and core fueling. A simple analytic model relates the momentum confinement time to the observed evolution of mode rotation due to the combination of NBI momentum coupling, fast ion loss , and anomalous viscous torques, yielding values consistent with past measurements of electron energy confinement time τ E,e .

Validation of a tearing mode locking model using a database of disruptive plasmas at ASDEX Upgrade

An exploratory study is presented that aims at validating a model for mode locking on the basis of a large set of ASDEX Upgrade (AUG) discharges. Not discriminating between plasma configurations, the model allows to estimate the duration of the deceleration phase, as well as the critical mode width for locking. Both quantities are important for the design of disruption avoidance algorithms that aim to affect the MHD mode rotation. It was found that the model successfully described locking of large modes in those cases where the deceleration started in a quasi-stationary phase of the discharge (i.e. with low variability of the global plasma angular momentum prior to mode seeding) and where deceleration took place over temporal intervals comparable to the momentum confinement time. Theoretical braking curves and locking durations predicted with the model were in good quantitative agreement with the experiment. On the other hand, the model failed to reproduce the braking curves of modes appearing towards the end of a transient phase, e.g. during an impurity influx or when approaching the disruptive density limit. It can be concluded that the modes were not the primary cause of the plasma momentum losses within the scope of the model. A modified mode equation of motion is proposed, which accounts for transient variation of the plasma density, e.g. during the development of a MARFE, and its impact on braking predictions is discussed. Furthermore, it was observed that a substantial fraction of modes was rotating at the onset of a major disruptive event. Consequences of this observation on disruption prediction schemes in AUG are examined.

Predicting rotation for ITER via studies of intrinsic torque and momentum transport in DIII-D

Experiments at the DIII-D tokamak have used dimensionless parameter scans to investigate the dependencies of intrinsic torque and momentum transport in order to inform a prediction of the rotation profile in ITER. Measurements of intrinsic torque profiles and momentum confinement time in dimensionless parameter scans of normalized gyroradius and collisionality are used to predict the amount of intrinsic rotation in the pedestal of ITER. Additional scans of Te/Ti and safety factor are used to determine the accuracy of momentum flux predictions of the quasi-linear gyrokinetic code TGLF. In these scans, applications of modulated torque are used to measure the incremental momentum diffusivity, and results are consistent with the E×B shear suppression of turbulent transport. These incremental transport measurements are also compared with the TGLF results. In order to form a prediction of the rotation profile for ITER, the pedestal prediction is used as a boundary condition to a simulation that uses TGLF to determine the transport in the core of the plasma. The predicted rotation is ≈20 krad/s in the core, lower than in many current tokamak operating scenarios. TGLF predictions show that this rotation is still significant enough to have a strong effect on confinement via E×B shear.

Dependence of intrinsic torque and momentum confinement on normalized gyroradius and collisionality in the DIII-D tokamak

The dependence of intrinsic torque and momentum confinement time on normalized gyroradius (ρ*) and collisionality (ν*) has been measured in the DIII-D tokamak. The intrinsic torque normalized to temperature is found to have ρ* and ν* dependencies of ρ*−1.5±0.8 and ν*0.26±0.04. This dependence on ρ* is unexpectedly favorable (increasing as ρ* decreases). The choice of normalization is important, and the implications are discussed. The unexpected dependence on ρ* is found to be robust, despite some uncertainty in the choice of normalization. The dependence of momentum confinement on ρ* does not clearly demonstrate Bohm or gyro-Bohm like scaling, and a weaker dependence on ν* is found. The calculations required to use these dependencies to determine the intrinsic torque in future tokamaks such as ITER are presented, and the importance of the normalization is explained. Based on the currently available information, the intrinsic torque predicted for ITER is 33 N m, comparable to the expected torque available from neutral beam injection. The expected average intrinsic rotation associated with this intrinsic torque is small compared to current tokamaks, but it may still aid stability and performance in ITER.

Application of ECH to the Study of Transport in ITER Baseline Scenario-like Discharges in DIII-D

Recent DIII-D experiments in the ITER Baseline Scenario (IBS) have shown strong increases in fluctuations and correlated reduction of confinement associated with entering the electron-heating-dominated regime with strong electron cyclotron heating (ECH). The addition of 3.2 MW of 110 GHz EC power deposited at � ~0.42 to IBS discharges with ~3 MW of neutral beam injection causes large increases in low-k and medium-k turbulent density fluctuations observed with Doppler backscatter (DBS), beam emission spectroscopy (BES) and phase-contrast imaging (PCI) diagnostics, correlated with decreases in the energy, particle, and momentum confinement times. Power balance calculations show the electron heat diffusivitye increases significantly in the mid-radius region 0.4<� <0.8, which is roughly the same region where the DBS and BES diagnostics show the increases in turbulent density fluctuations. Confinement of angular momentum is also reduced during ECH. Studies with the TGYRO transport solver show that the model of turbulent transport embodied in the TGLF code quantitatively reproduces the measured transport in both the neutral beam (NB)-only and in the NB plus EC cases. A simple model of the decrease in toroidal rotation with EC power is set forth, which exhibits a bifurcation in the rotational state of the discharge.

Momentum losses by charge exchange with neutral particles in H-mode discharges at JET

The effect of a neutral density background on the toroidal angular momentum and kinetic energy profiles has been investigated in JET. Under equivalent conditions but with increasing gas fuelling during the flat top phase, it has been observed that both the edge rotation and temperature decrease. The increase in electron density was not sufficient to compensate the rotation and temperature loss such that both energy and momentum confinement times are significantly reduced. The edge localized mode behaviour is observed to be significantly affected by the increased neutral influx. A simple 1.5D fluid model has been used to qualitative capture the neutral transport response within the plasma, followed by a forward model of the passive charge-exchange (CX) emission of carbon to obtain a corrected radial neutral density profile. It has been found that the neutral density is sharply attenuated over the edge region, with similar edge magnitudes in both the non-fuelled (Γ0/ne ∼ 1.2 m s−1) and maximum fuelled case (Γ0/ne ∼ 2.5 m s−1). Discharges with reversed-B operation exhibited even higher normalized neutral fluxes related to first orbit effects and increased wall interactions. Over the full neutral influx range, a decrease in pedestal thermal Mach number from 0.25 to 0.14 was observed. Increased neutral penetration up to the pedestal top (r/a ∼ 0.9) due to multiple CX interactions is obtained from the interpretive model. Under these multiple neutral–ion interactions, the impact on the CX loss of angular momentum is larger compared with the CX energy loss. The drag torque was seen to increase up to 10% of the total applied torque, while energy losses appeared to be smaller. The accuracy of this global approach method is unfortunately limited; however, the estimated momentum sink was found comparable to the torque required to explain the discrepancy between observed global energy and momentum confinement.

Sub-Alfvénic velocity limits in magnetohydrodynamic rotating plasmas

Magnetized plasmas in shaped fields rely on large, supersonic rotation to effect centrifugal confinement of plasma along magnetic field lines. The results of experiments on the Maryland Centrifugal Experiment (MCX) [R. F. Ellis et al., Phys. Plasmas 12, 055704 (2005)] to document velocity limits are reported. Previous results have shown a limit at the Alfvén speed, consistent with equilibrium limits from ideal magnetohydrodynamic theory. Another speed limit, previously reported as possibly related to a critical ionization phenomenon and depending only on the ion species and the shape of the confining magnetic field, is investigated here for a broad range of the applied parameters. We show that this speed limit manifests at sub-Alfvénic levels and that, as externally applied torques on the plasma are increased, the extra momentum input shows up as enhanced plasma density or lower momentum confinement time, accompanied by an increase in the neutral radiation level. Several key parameters are scanned, including the mirror ratio, the length between insulators, and the species mass. We show that this velocity limit is consistent with the species-dependent critical ionization velocity postulated by Alfvén.

Observation of Self-Generated Flows in Tokamak Plasmas with Lower-Hybrid-Driven Current

In Alcator C-Mod discharges lower hybrid waves have been shown to induce a countercurrent change in toroidal rotation of up to 60 km/s in the central region of the plasma (r/a approximately <0.4). This modification of the toroidal rotation profile develops on a time scale comparable to the current redistribution time (approximately 100 ms) but longer than the energy and momentum confinement times (approximately 20 ms). A comparison of the co- and countercurrent injected waves indicates that current drive (as opposed to heating) is responsible for the rotation profile modifications. Furthermore, the changes in central rotation velocity induced by lower hybrid current drive (LHCD) are well correlated with changes in normalized internal inductance. The application of LHCD has been shown to generate sheared rotation profiles and a negative increment in the radial electric field profile consistent with a fast electron pinch.

Observations of counter-current toroidal rotation in Alcator C-Mod LHCD plasmas

Following the application of lower hybrid current drive (LHCD) power, the core toroidal rotation in Alcator C-Mod L- and H-mode plasmas is found to increment in the counter-current direction, in conjunction with a decrease in the plasma internal inductance, li. Along with the drops in li and the core rotation velocity, there is peaking of the electron and impurity density profiles, as well as of the ion and electron temperature profiles. The mechanism generating the counter-current rotation is unknown, but it is consistent in sign with an inward shift of energetic electron orbits, giving rise to a negative core radial electric field. The peaking in the density, toroidal rotation (in the counter-current direction) and temperature profiles occurs over a time scale similar to the current relaxation time but slow compared with the energy and momentum confinement times. Most of these discharges exhibit sawtooth oscillations throughout, with the inversion radius shifting inward during the LHCD and profile evolution. The magnitudes of the changes in the internal inductance and the central rotation velocity are strongly correlated and found to increase with increasing LHCD power and decreasing electron density. The maximum effect is obtained with a waveguide phasing of 60° (a launched parallel index of refraction n‖ ∼ 1.5), with a significantly smaller magnitude at 120° (n‖ ∼ 3.1), and with no effect for negative or heating (180°) phasing. Regardless of the plasma parameters and launched n‖ of the waves, there is a strong correlation between the rotation velocity and li changes, possibly providing a clue for the underlying mechanism.

Scaling of rotation and momentum confinement in JET plasmas

An extensive database to study the scaling of rotation and momentum transport has been constructed at JET. The database contains information from various operational scenarios, amongst them H-mode discharges, and parameters that characterize the rotation, as well as those that describe the general plasma conditions. JET plasmas are predominantly heated by neutral beam injection which is also the main source for the observed toroidal rotation. Dimensionless Mach numbers are introduced to quantify rotation. The scaling of plasma rotation and the Mach numbers in particular has been studied. The thermal and Alfvén Mach numbers were found to scale inversely with q and with the ratio of torque and additional heating power. Although the momentum and energy confinement times were found to be of the same magnitude, the ratio was found to vary. Regression analyses showed a dependence of both the energy and momentum confinement times on plasma rotation. If rotation was included in the scaling model of energy and momentum confinement the quality of the fits substantially improved. Detailed analysis of the core and edge (pedestal) confinement showed that momentum confinement was improved in the core of the plasma compared with the energy confinement. However, the pedestal proved to be less confining for the momentum than for the energy.

Toroidal and poloidal momentum transport studies in tokamaks

The present status of understanding of toroidal and poloidal momentum transport in tokamaks is presented in this paper. Similar energy confinement and momentum confinement times, i.e. τE/τϕ ≈ 1 have been reported on several tokamaks. It is more important though, to study the local transport both in the core and edge plasma separately as, for example, in the core plasma, a large scatter in the ratio of the local effective momentum diffusivity to the ion heat diffusivity χϕeff/χi,eff among different tokamaks can be found. For example, the value of effective Prandtl number is typically around χϕeff/χi,eff ≈ 0.2 on JET while still τE/τϕ ≈ 1 holds. Perturbative NBI modulation experiments on JET have shown, however, that a Prandtl number χϕ/χi of around 1 is valid if there is an additional, significant inward momentum pinch which is required to explain the amplitude and phase behaviour of the momentum perturbation. The experimental results, i.e. the high Prandtl number and pinch, are in good qualitative and to some extent also in quantitative agreement with linear gyro-kinetic simulations. In contrast to the toroidal momentum transport which is clearly anomalous, the poloidal velocity is usually believed to be neo-classical. However, experimental measurements on JET show that the carbon poloidal velocity can be an order of magnitude above the predicted value by the neo-classical theory within the ITB. These large measured poloidal velocities, employed for example in transport simulations, significantly affect the calculated radial electric field and therefore the E × B flow shear and hence modify and can significantly improve the simulation predictions. Several fluid turbulence codes have been used to identify the mechanism driving the poloidal velocity to such high values. CUTIE and TRB turbulence codes and also the Weiland model predict the existence of an anomalous poloidal velocity, peaking in the vicinity of the ITB and driven dominantly by the flow due to the Reynold's stress. It is worth noting that these codes and models treat the equilibrium in a simplified way and this affects the geodesic curvature effects and geodesic acoustic modes. The neo-classical equilibrium is calculated more accurately in the GEM code and the simulations suggest that the spin-up of poloidal velocity is a consequence of the plasma profiles steepening when the ITB grows, following in particular the growth of the toroidal velocity within the ITB.

Momentum confinement at low torque

Momentum confinement was investigated on DIII-D as a function of applied neutral beam torque at constant normalized beta βN, by varying the mix of co (parallel to the plasma current) and counter neutral beams. Under balanced neutral beam injection (i.e. zero total torque to the plasma), the plasma maintains a significant rotation in the co-direction. This ‘intrinsic’ rotation can be modeled as being due to an offset in the applied torque (i.e. an ‘anomalous torque’). This anomalous torque appears to have a magnitude comparable to one co neutral beam source. The presence of such an anomalous torque source must be taken into account to obtain meaningful quantities describing momentum transport, such as the global momentum confinement time and local diffusivities.Studies of the mechanical angular momentum in ELMing H-mode plasmas with elevated qmin show that the momentum confinement time improves as the torque is reduced. In hybrid plasmas, the opposite effect is observed, namely that momentum confinement improves at high torque/rotation. GLF23 modeling suggests that the role of E × B shearing is quite different between the two plasmas, which may help to explain the different dependence of the momentum confinement on torque.

Prompt toroidal momentum balance with collisionless neutral beam injected torque in DIII-D

In electron cyclotron heated (ECH) H-mode discharges with neutral beam injection (NBI) pulses that are short compared with the fast ion scattering or slowing times, and it is observed that the plasma stores all the angular momentum delivered by the NBI torque impulse. The pulse length is also much shorter than the momentum confinement time of the plasma. Source computations with the Monte Carlo code TRANSP [R. J. Goldston, D. C. McCune, H. H. Towner et al., J. Comput. Phys. 43, 61 (1981)] show that during a pulse approximately 90% of this torque impulse is delivered via the collisionless fast radial current injection process, so that the plasma acquires the balancing toroidal acceleration through ion drift motion in the increasing ∂E∕∂t where E is the electric field normal to the flux surfaces. The measured radial profile of the toroidal momentum increase matches the source, i.e., the computed torque impulse profile. We measure the bulk ion toroidal acceleration in helium discharges, as well as that of the primary impurity, carbon. These two species show a common acceleration, consistent with an incremental velocity due to an electric drift. This process is mediated by the dielectric response of the ions. The acceleration measurements are consistent with this being the neoclassical value of the dielectric constant, as computed from measured quantities.

New high rotation mode in magnetized rotating plasmas

A new high-rotation (HR) mode of operation is reported for magnetized rotating plasmas. Plasma is produced by an externally applied radial electric field in the Maryland centrifugal experiment, a mirror magnetic field plasma rotating azimuthally. The HR mode is achieved by optimizing over the discharge current. Previously reported stationary or steadily declining plasma voltages are now replaced by time-increasing voltages in the HR mode, with maximum voltages significantly higher than those previously recorded. Sonic Mach numbers are close to the theoretical values required for centrifugal confinement and for suppressing large scale magnetohydrodynamic (MHD) instabilities. Plasma momentum confinement time is much longer than the MHD instability time scale and longer than in ordinary mode operation. The mode is sustained over several confinement times.

The role of the radial electric field for the transition to high confinement regimes

The radial electric field Er(x, t), and particularly its gradient, has been invoked by various theories and empirical models as a crucial parameter ‘per se’ for determining the transition to high confinement regimes, such as the onset of an internal transport barrier (ITB) in the plasma core and of the H-mode pedestal at the plasma edge. This idea, however, does not consider the basic fact that in most experiments the transition to a steady-state higher confinement regimes is produced by applying sufficient additional heating onto a given target density and current profile. In order to test this ansatz on a more routine basis, we have developed here an analytical approximation to the neoclassical calculation of the radial electric field, adapted for the 2D toroidal geometry of JET to describe all collisionality regimes (banana, banana-plateau, Pfirsch–Schlüter) and to include averaging over the potato orbits. An analytic calculation of the error bars on Er(x, t) has also been developed, which has allowed us to compare and successfully benchmark our calculations with the results of neoclassical codes such as JETTO and NCLASS. We are then able to demonstrate a striking similarity in the shape of Er(x, t) in steady-state L-mode, H-mode and ITB plasmas when normalizing Er(x, t) with respect to the total heating power flux. This clearly indicates that, experimentally, there is no direct causality relation between changes in Er(x, t) and steady-state improved confinement, as these are brought about together by changes in the power deposition profile. Only two cases do not satisfy this general rule. First, localized and rapid transients (i.e. occurring on time scales much shorter than the momentum and energy confinement time) could be linked to non-neoclassical changes in Er(x, t), possibly due to turbulence suppression mechanisms. Second, when comparing H-mode plasmas with forward and reversed ion ∇B-drift direction, we demonstrate the role of prompt fast ion losses in affecting Er(x, t), most likely due to the different edge flows and their cascading effect onto the core plasma.

Observation of momentum confinement time scalings in a rotating plasma

The Maryland Centrifugal Experiment (MCX) is designed to explore the use of supersonic rotation and strong perpendicular velocity shear for plasma confinement [R. F. Ellis, A. B. Hassam, S. Messer, and B. R. Osborne, Phys. Plasmas 8, 2057 (2001)]. This paper reports MCX data showing scalings with the strength and geometry of the magnetic field and comparisons to some standard models of confinement, none of which fit the data over the whole range. For midplane fields less than 1200 G and mirror ratios between 3 and 17, the momentum confinement time suggests a combination of Bohm-like diffusion and mirror losses. At mirror ratio 9, τM increases with B, saturates for B≈1kG, and then decreases. The measured confinement times peak in the range of 200μs, which is much longer than a magnetohydrodynamic instability growth time. The data do not exclude the possibility that confinement is strongly affected by charge exchange collisions with neutrals.

Steady supersonically rotating plasmas in the Maryland Centrifugal Experiment

The Maryland Centrifugal Experiment MCX [R. F. Ellis, A. B. Hassam, and S. Messer, Phys. Plasmas 8, 2057 (2000)] studies supersonic rotation and enhanced confinement produced by the application of an electric field perpendicular to an axial confining mirror magnetic field; radial shear in the rotation is predicted to stabilize magnetohydrodynamic (MHD) interchange modes. The MCX mirror field is 2.6 m in length, maximum mirror field 1.9 T, maximum midplane field 0.33 T; an inner coaxial core is driven by a 10 KV capacitor bank, producing the radial electric field which drives azimuthal rotation. MCX produces high density (n&amp;gt;1020m−3) fully ionized plasmas and has two operating modes. In the O (ordinary) mode the plasma rotates supersonically with azimuthal velocities in the range of 100 km/s for discharge times exceeding 8 ms. Ion temperatures are ∼30eV and momentum confinement times 100–200 μs. Sonic Mach numbers (uφ∕vti) in the range 1–2 and Alfvén Mach numbers (uφ∕vA)∼0.3 have been achieved for O mode discharges which remain steady for many milliseconds, much longer than MHD instability time scales; plasma lifetime is limited by the capacitance of the capacitor bank. MCX also has an enhanced mode of operation [higher rotation (HR) mode] with higher rotation velocities (&amp;gt;200km∕s), sonic Mach numbers greater than 3, Alfvén Mach numbers &amp;gt;∼0.5, and momentum confinement times of several hundred microseconds. HR mode occurs at higher B fields and lower discharge currents but is transient, transitioning to O mode after a few milliseconds. Both O and HR mode show spectroscopic evidence of radial velocity shear sufficient to satisfy the simplest criterion for MHD stability, but both modes also show significant fluctuations on magnetic probes.

Observation of tearing mode deceleration and locking due to eddy currents induced in a conducting shell

Growth to large amplitude of a single core-resonant tearing mode in the Madison Symmetric Torus [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field pinch is accompanied by braking and eventual cessation of mode rotation. There is also a concurrent deceleration of bulk plasma rotation. The mode deceleration is shown to be well described by a time-dependent version of a magnetohydrodynamical model [R. Fitzpatrick et al., Phys. Plasmas 6, 3878 (1999)] in which a braking torque originates from eddy currents induced by the rotating mode in the conducting shell surrounding the plasma. According to the model, the electromagnetic braking torque is localized to the plasma in the immediate vicinity of the mode’s resonant surface, but viscosity transfers the torque to the rest of the plasma. Parametrizing the plasma viscous momentum diffusivity in terms of the global momentum confinement time, the model is used to predict both the momentum confinement time and the time evolution of the decelerating mode velocity. In both respects, the model is quite consistent with experimental data.

Observations of anomalous momentum transport in Alcator C-Mod plasmas with no momentum input

Anomalous momentum transport has been observed in Alcator C-Mod tokamak plasmas. The time evolution of core impurity toroidal rotation velocity profiles has been measured with a tangentially viewing crystal x-ray spectrometer array. Following the L-mode to EDA (enhanced Dα) H-mode transition in both Ohmic and ion cyclotron range of frequencies heated discharges, the ensuing co-current toroidal rotation velocity, which is generated in the absence of any external momentum source, is observed to propagate in from the edge plasma to the core with a timescale of the order of the observed energy confinement time, but much less than the neo-classical momentum confinement time. The ensuing steady state toroidal rotation velocity profiles in EDA H-mode plasmas are relatively flat, with Vϕ ∼ 50 km s−1, and the momentum transport can be simulated using a simple diffusion model. Assuming that the L–H transition produces an instantaneous edge source of toroidal torque (which disappears at the H- to L-mode transition), the momentum transport may be characterized by a diffusivity, with values of ∼0.07 m2 s−1 during EDA H-mode and ∼0.2 m2 s−1 in L-mode. These values are large compared to the calculated neo-classical momentum diffusivities, which are of the order of 0.003 m2 s−1. Velocity profiles of ELM-free H-mode plasmas are centrally peaked (with Vϕ(0) exceeding 100 km s−1 in some cases), which suggests the presence of an inward momentum pinch; the observed profiles are consistent with simulations including an edge inward convection velocity of ∼10 m s−1. In EDA H-mode discharges which develop internal transport barriers, the velocity profiles become hollow in the centre, indicating the presence of a negative radial electric field well in the vicinity of the barrier foot. Upper single null diverted and inner wall limited L-mode discharges exhibit strong counter-current rotation (with Vϕ(0)∼−60 km s−1 in some cases), which may be related to the observed higher H-mode power threshold in these configurations. For plasmas with locked modes, the toroidal rotation is observed to cease (Vϕ ⩽ 5 km s−1).

Comparision of neoclassical rotation theory with experiment under a variety of conditions in DIII-D

A neoclassical theory of gyroviscous radial momentum transport and poloidal and toroidal rotation has been compared with experiment in DIII-D [Luxon, Anderson, Batty et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 (IAEA, Vienna, 1987), Vol. 1, p. 159] discharges in different confinement regimes, with a range of neutral beam powers and with co- and counter-injection, and with various types of dominant impurity species present. Calculated central toroidal rotation velocities and momentum confinement times agreed with experiment over a wide range of these conditions, with one notable exception in which a drift correction may be needed to reduce the gyroviscous toroidal force. Radial distributions of toroidal and poloidal rotation velocities and radial electric field, calculated using the radial distribution of toroidal angular momentum input density, agreed with measured distributions for the one time in an L-mode discharge that was examined in detail.