Parallel Velocity Shear Instability Research Articles

Parallel electron velocity shear instability in a magnetized plasma

It is shown that the parallel electron velocity shear can destabilize low-frequency (in comparison with the electron gyrofrequency) electrostatic waves in a magnetized plasma. A new dispersion relation is derived and solved for the parameters relevant for laboratory experiments of velocity shear instabilities in a magnetized plasma.

Linear gyrokinetic calculations of toroidal momentum transport in a tokamak due to the ion temperature gradient mode

It is shown from a symmetry in the gyrokinetic equation that for up–down symmetric tokamak equilibria and for uϕ⪢ρυthi∕r (where uϕ is the toroidal velocity, υthi is the thermal ion velocity, ρ is the Larmor radius, and r is the radius of the flux surface), the transport of parallel momentum can be written as the sum of a diffusive and a pinch contribution with no off-diagonal terms due to temperature and pressure gradients. The measured parallel velocity gradient in ASDEX Upgrade [O. Gruber, H.-S. Bosch, S. Günter et al., Nucl. Fusion 39, 1321 (1999)] is insufficient to drive the parallel velocity shear instability. The parallel velocity is then transported by the ion temperature gradient mode. The diffusive contribution to the transport flux is investigated using a linear gyrokinetic approach, and it is found that the diffusion coefficient for parallel velocity transport divided by the ion heat conductivity coefficient is close to 1, and only weakly dependent on plasma parameters.

Stability of the ion-temperature-gradient-driven mode with negative magnetic shear

A model for transition to the enhanced reverse shear or negative central shear mode triggered in tokamaks is proposed. This model takes into account the linear behavior of the ion temperature gradient (ITG) driven perturbation, considered nowadays as the dominant source of anomalous energy losses in the low confinement mode, in the presence of a radially varying parallel velocity. Analytic and numerical studies show that when the magnetic shear has the same sign as the second derivative of the parallel velocity with respect to the radial coordinate, the ITG mode may become more unstable. On the other hand, when the magnetic shear has the opposite sign to the second derivative of the parallel velocity, the linear ITG mode may be completely stabilized. This result is similar to our earlier works on parallel velocity shear instability [S. Sen et al., Phys. Plasmas 7, 1192 (2000); D. R. McCarthy et al., Phys. Plasmas 8, 3645 (2001)].

Theoretical interpretation of the toroidal rotation velocityobserved in Alcator C-Mod Ohmic H-mode discharges

It is shown that neoclassical theory explains quite well the origin of the co-current toroidal rotation velocity measured in the core of stationary Alcator C-Mod edge localized mode (ELM)-free Ohmic high confinement (H)-mode discharges. Both edge and core toroidal rotation velocity profiles are determined to a good approximation by the edge ion temperature and density pedestals, where the gradients are large and the plasma is in the high collisionality regime. Under these conditions, the predicted radial electric field profile is similar to those measured in the DIII-D tokamak whereas the usual expression for the poloidal velocity is modified by finite Larmor radius (FLR) effects. Over the entire plasma cross section, the expression of the toroidal velocity can approximately be cast as the product of a dimensionless non-local functional of the pedestal normalized profiles Ti(r)/Ti(rinf) and Ni(r)/Ni(rinf) with powers of the plasma density, temperature, safety factor and magnetic field at the pedestal inflexion point rinf provided the FLR related corrections are independent of the latter parameters. The collapse of the core toroidal rotation velocity when either an internal transport barrier forms (that leads to impurity accumulation), or the plasma experiences a transition from the H- to the low confinement (L)-mode, or ELMs appear, and the spin up at the L-H transition are also explained. In the edge region, power balance is consistent with the prediction from sub-neoclassical ion energy transport theory at high collisionality. The role of charge exchange neutrals is discussed and the critical density above which they are expected to noticeably slow down the rotation is estimated. The toroidal velocity gradient predicted by theory at the edge of the ELM-free Ohmic H-mode discharge mainly under study (qs = 3.4) is near the onset value for the Kelvin-Helmholtz (K-H) parallel velocity shear (PVS) instability; this result is very interesting since a transition from ELM-free to enhanced Dα (EDA) H-modes occurs at q≅3.5-4; the PVS K-H instability appears to have the characteristics of the `quasi-coherent' mode that is present in all EDA plasmas, but not in ELM-free H-modes.

Edge harmonic oscillations produced by toroidal velocity shear

It is shown that, for a plasma with similar edge density and parallel velocity profiles to that of the Doublet III-D [Fusion Technol. 8, 441 (1985)] tokamak operating in the quiescent double barrier (QDB) regime, the system is unstable to the parallel velocity shear instability. By means of three-dimensional nonlinear simulations, it is found that this system produces turbulence that is radially localized in the vicinity of the parallel velocity gradient and has a toroidal structure. These results are similar to the edge harmonic oscillations (EHOs) that are observed during the QDB discharge. Previously, it was thought that the EHOs were due to a magnetic magnetohydrodynamic mode, yet such structures have not been observed in any one-fluid theoretical models. These results indicate that EHOs may be due to this instability, which can only be realized in a two fluid model.

Reduction in transport by the parallel velocity shear instability due to reversed magnetic shear

A nonlocal theory of the electrostatic parallel velocity shear instability in a three-dimensional slab with a uniformly sheared magnetic field has been developed. It is shown that in the limit of a weak parallel velocity gradient, the linear growth rate can be increased depending upon the direction of the magnetic shear (ŝ) with respect to the radial curvature of the parallel velocity profile (d2v∥/dx2). When these parameters have the same sign, the growth rate can actually be stronger than in the limit of no magnetic shear. In this limit of increased instability, the eigenmode is broadened, thus producing enhanced transport. This effect should be observable when the scale length of the curvature is of order ∼Lsρs. For strong parallel velocity gradients that are more typical of flows in tokamaks, the effect of the varying Doppler shift becomes more prominent on the stability of the mode, the net result being that the sensitivity of the growth rates on the sign of the magnetic shear becomes insignificant. This effect, however, is effectively offset when a finite density gradient is included. When the density scale length is of order the scale length of v∥, the growth rate is moderately reduced, but becomes dependent again upon the sign of the magnetic shear.

The Kelvin–Helmholtz instability in a plasma with negatively charged dust

The effect of negatively charged dust on the Kelvin–Helmholtz (parallel velocity shear) instability is investigated experimentally in a magnetized cesium plasma. The dust generally has a stabilizing effect on the instability, although, in some cases, the addition of negatively charged dust into the plasma results in a slight increase in the instability fluctuation amplitude. The results are in general agreement with theoretical predictions.

Parallel velocity shear instability, Alfven waves and the formation of the transport barrier

It is suggested that the ponderomotive force induced by radio frequency (rf) waves in the range of the Alfven frequency can create a transport barrier in a tokamak. The linear and nonlinear behavior of the driftlike perturbation with a parallel velocity shear is studied in the presence of rf waves. It is shown if the radial profile of the rf field energy is properly chosen the linear mode is stabilized and turbulent momentum transport reduces. The rf power required for this stabilization is found to be rather modest and hence should be easily obtained in actual experiments.

Increased Destabilization of the Parallel Velocity Shear Instabilitydue to Reversed Magnetic Shear

The nonlinear behavior of the parallel velocity shear instability in a shear magnetic field is studied. It is found that the nonlinear fluctuation levels and turbulent momentum transport depend strongly upon the direction of the magnetic shear. When the shear has the same sign as the second derivative of the parallel velocity with respect to the radial coordinate, the fluctuations grow to larger levels than if there were no magnetic shear. The physical mechanism controlling this effect is vortex merging between modes on either side of the velocity peak. It is likely that this behavior may be a general feature of all modes with structure parallel to the magnetic field.

Experimental study of the collisional parallel velocity shear instability

Simultaneous density and electric field fluctuation spectra, associated with velocity shear (both in the transverse to the magnetic field ion flow velocity and in the parallel ion flow velocity), have been observed by the DE 2 spacecraft in the F region [Basu et al., 1984]. Basu and Coppi [1988, 1989] argued that the subkilometer scale irregularities are due to collisional electrostatic modes excited in a partially ionized plasma in the presence of shear in the parallel ion flow. In this paper we describe results of a laboratory investigation of the effects of neutral‐particle collisions on the parallel velocity shear instability, performed using a double‐ended Q machine. The critical value of the shear dv0/dx, the derivative of the field‐aligned ion flow with respect to the transverse (to B) coordinate, is determined and compared with theoretical predictions.

Experimental study of the parallel velocity shear instability

The parallel velocity shear instability (PVSI) is experimentally investigated in a double-ended Q machine in which the shear in the ion flow is produced by suitable shaping of the axial magnetic field. Instability fluctuation levels approaching nearly 100% are often observed.

Three-dimensional simulations of the parallel velocity shear instability

The nonlinear mode structure and anomalous momentum transport of the electrostatic parallel velocity shear instability in a uniformly magnetized slab were studied using three-dimensional (3-D) nonlinear fluid simulations. Within this simplified model, the system depends upon two dimensionless parameters α=2πqRρs/Lv2, which is a ratio of the sound transit time to the linear growth time of the mode and ρ̂=ρs/LV, which is a ratio of the ion Larmor radius and the radial scale length of the parallel velocity profile. In the limit of ρ̂=0, the mode structure evolved nonlinearly to a state with m=2/α and n=1 for α<1, and m=2 and n=α for α>1 where m is the poloidal mode number and n is the toroidal mode number. The transport had a value of D∼ρscs/2 for all α. For ρ̂≠0 the system displayed a different saturated state, evolving to m=1 and n=α/2 for all α. The transport remained D∼ρscs/2 for all α. The effect of the Larmor radius is this 3-D system is similar to the well known inverse cascade in a two-dimensional incompressible fluid.

Nonlinear saturation of the parallel velocity shear instability

The linear stability and eventual nonlinear saturation of electrostatic instabilities due to the shear in a plasma flow in the direction parallel to the magnetic field are described, analytically, via collisional fluid equations. Saturation is provided by coupling the linearly unstable eigenmode to a linearly damped nonlinear harmonic (double wave number). These modes are shown to saturate only when the linear instability driving term is below a critical value. The saturation amplitude is a function of the ratio of the ‘‘ideal’’ growth rate to the diamagnetic frequency and can easily reach levels of 25% or more.

New parallel velocity shear instability

Analytic and numerical results on the linear theory of a new instability driven by shear in the parallel velocity v∥′ will be presented. This instability exists in the presence of parallel velocity shear and field line curvature. It also requires either parallel viscosity—the full Braginskii stress tensor [S. I. Braginskii, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p. 205]—or parallel compression. The mode exists in an electromagnetic version, where it can enhance the growth rate of an unstable resistive magnetohydrodynamic (MHD) mode or cause an otherwise stable resistive mode to grow. In its electromagnetic form it is global (matches to an ideal MHD outer region) and can influence modes responsible for disruptions; it can also lead to anomalous transport by stochastic field lines as well as by E×B advection. The instability also exists in an electrostatic form for short wavelengths. For most reasonable edge plasma parameters the effect of parallel compression dominates that of parallel viscosity. The properties of this mode, specifically its growth rate and localization width, are compared with those of the usual v∥′ mode [N. D’Angelo, Phys. Fluids 8, 1748 (1965)]. The importance of this mode in edge fluctuations and on more global resistive MHD is discussed.

Axisymmetric parallel velocity shear instability in the tokamak edge

The parallel velocity shear instability in an axisymmetric toroidal edge plasma is studied numerically. In the presence of a large asymmetric particle transport and a limiter, sonic parallel flows develop that are peaked at the last closed flux surface. For α=ρsqR/aLv≳1, these flows are unstable to axisymmetric modes. The associated turbulence gives order unity fluctuation levels. It is located inside the last closed flux surface (LCFS) and on the inner half of the torus. There is an up–down asymmetry of the turbulence which is due to the diamagnetic drift and poloidal rotation. These results are compared to the experimental results from the Continuous Current Tokamak (CCT) (G. R. Tynan, Ph.D. thesis, 1991).