Finite Magnetic Shear Research Articles

Real-time control of electron cyclotron wave polarization in the LHD

Peripheral plasma with finite electron density gradients and finite magnetic shear is known to affect polarization of electron cyclotron (EC) waves. Calculation of the ratio between the ordinary (O) mode and the extraordinary (X) mode, integrated in the ray-tracing code developed for EC heated plasmas in the Large Helical Device (LHD), enables the search for the optimum EC wave polarization in order to excite the pure O/X mode at the EC resonance layer. The real-time control system of the incident polarization was developed for maximum single-pass absorption of EC waves, based on the dependence of optimum EC wave polarization on peripheral density profiles. The polarization control system is equipped with a fast field programmable gate array, which processes in real time the calculation of the peripheral electron density profile and the optimum EC wave polarization for motion control of the polarization rotator and the elliptical polarizer on the transmission line. The real-time control in LHD experiments functioned properly in maintaining the absorbed power of the EC wave higher than that without the control, demonstrating that the purer heating mode was successfully excited.

Magnetic Shear Damped Polar Convective Fluid Instabilities

AbstractThe influence of the magnetic field shear is studied on the E × B (and/or gravitational) and the Current Convective Instabilities (CCI) occurring in the high‐latitude F layer ionosphere. It is shown that magnetic shear reduces the growth rate of these instabilities. The magnetic shear‐induced stabilization is more effective at the larger‐scale sizes (≥ tens of kilometers) while at the scintillation causing intermediate scale sizes (∼ a few kilometers), the growth rate remains largely unaffected. The eigenmode structure gets localized about a rational surface due to finite magnetic shear and has broken reflectional symmetry due to centroid shift of the mode by equilibrium parallel flow or current.

Transport bifurcation induced by sheared toroidal flow in tokamak plasmas

First-principles numerical simulations are used to describe a transport bifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear than one of finite magnetic shear, because in the former case the component of the sheared toroidal flow that is perpendicular to the magnetic field has the strongest suppressing effect on the turbulence. In the zero-magnetic-shear regime, there are no growing linear eigenmodes at any finite value of flow shear. However, subcritical turbulence can be sustained, owing to the existence of modes, driven by the ion temperature gradient and the parallel velocity gradient, which grow transiently. Nonetheless, in a parameter space containing a wide range of temperature gradients and velocity shears, there is a sizeable window where all turbulence is suppressed. Combined with the relatively low transport of momentum by collisional (neoclassical) mechanisms, this produces the conditions for a bifurcation from low to high temperature and velocity gradients. A parametric model is constructed which accurately describes the combined effect of the temperature gradient and the flow gradient over a wide range of their values. Using this parametric model, it is shown that in the reduced-transport state, heat is transported almost neoclassically, while momentum transport is dominated by subcritical parallel-velocity-gradient-driven turbulence. It is further shown that for any given input of torque, there is an optimum input of heat which maximises the temperature gradient. The parametric model describes both the behaviour of the subcritical turbulence (which cannot be modelled by the quasi-linear methods used in current transport codes) and the complicated effect of the flow shear on the transport stiffness. It may prove useful for transport modelling of tokamaks with sheared flows.

3D edge transport analysis of ITER start-up configuration for limiter power load assessment

The edge transport properties of the toroidally discrete limiter configuration in the ITER start-up phase has been analysed, using the 3D edge transport code, EMC3-EIRENE. Because of the finite magnetic shear in the edge, the interaction of the limiters with flux surfaces of different q-values introduces a complex 3D pattern in the connection length (LC) profiles, where long and short flux tubes co-exist in the scrape-off layer. The severity of problems associated with very long flux tubes in the edge, which could bring a large amount of energy (proportional to the square root of LC) and cause a hot spot on the limiter, was mitigated and no significant localized power load was found. This can be justified as follows. (i) For long flux tubes, the perpendicular energy transport time becomes shorter than the parallel energy transport time, resulting in no net energy input to the flux tube. (ii) Perpendicular transport was found to be very effective to smear out the difference in the parallel energy flux conducted by the various flux tubes, if they interact within a perpendicular transport scale, about a few cm, which is usually the case in high plasma current ITER start-up configuration. These two effects significantly reduce the dependence of energy deposition on LC. At the high plasma current (e.g. 6.5 MA), the peak power load is found to be close to the engineering limit, especially for lowest perpendicular transport coefficients and the highest input power. Comparing the results of the 3D modelling with a radial exponential decay model, it was found that by neglecting the 3D geometrical effects, the simple model overestimates the peak power load by ∼30% for corresponding input power and radial decay of energy flux.

Trapped electron stabilization of ballooning modes in low aspect ratio toroidal plasmas

The kinetic effects of trapped electron dynamics and finite gyroradii and magnetic drift motion of ions are shown to give rise to a large parallel electric field and hence a parallel current that greatly enhances the stabilizing effect of field line tension for ballooning modes in low aspect ratio toroidal plasmas. For large aspect ratio the stabilizing effect increases (reduces) the β(=2P/B2) threshold for the first (second) stability of the kinetic ballooning mode (KBM) from the magnetohydrodynamics (MHD) β threshold value by a factor proportional to the trapped electron density fraction. For small aspect ratio the stabilizing effect can greatly increase the β threshold of the first stability of KBMs from the MHD β threshold by Sc≃1+(ne/neu)δ, where ne/neu is the ratio of the total electron density to the untrapped electron density, and δ depends on the trapped electron dynamics and finite gyroradii and magnetic drift motion of ions. If ne/neu≫1 as in the National Spherical Torus Experiment (NSTX) [M. Ono, Nucl. Fusion 40, 557 (2000)] with an aspect ratio of ≃1.4, the KBM should be stable for β⩽1 for finite magnetic shear. Therefore, unstable KBMs are expected only in the weak shear region near the radial location of the minimum of the safety factor in NSTX reverse shear discharges.

Stability of E×B zonal flow in electron temperature gradient driven turbulence

The electron temperature gradient driven turbulence in a slab configuration modeling the negative shear tokamak is studied using a gyrokinetic finite element particle-in-cell code. It is found that quasisteady Er×B zonal flows are generated in finite magnetic shear regions in both sides of the qmin-surface, where the electron thermal transport is reduced substantially compared with the qmin-surface region. Stability analyses of the electrostatic Kelvin–Helmholtz (KH) mode show that the quasisteady Er×B zonal flow pattern is closely related to the q profile or the magnetic shear, which has a stabilizing effect on the KH mode. By changing the q profile to reduce the magnetic shear, the KH mode becomes unstable for the quasisteady Er×B zonal flow, and the Er×B zonal flows disappear in the weak magnetic shear region. Numerical results show a possibility of controlling Er×B zonal flows with the magnetic shear, which depends on the stability of the KH mode.

Global Electrostatic Drift Waves in Self-Consistently Stationary Cylindrical Plasmas

The radial eigenvalue equations governing the stability properties of global electrostatic drift waves in self-consistently stationary cylindrical plasmas confined by sheared magnetic fields are derived and examined from a new point of view. The dissipative electon drift waves that are not localized near the mode rational surface are shown to be more unstable when the plasma current (which produces magnetic shear) flows in the opposite direction to the mode propagation. The effect of finite magnetic shear on its mode structure is also investigated. The density response of the ion drift waves exhibits the non-Boltzmann like behavior and its ratio to the electrostatic potential increases toward the plasma edge.

On Spontaneous Reconnection in the Earth's Magnetotail

The release of energy stored in the Earth's magnetotail is a major feature of the coupling between solar wind and magnetosphere. Spontaneous reconnection due to tearing mode instability in the magnetotail provides an appropriate mechanism, explaining energy release, delays the response to changes in the interplanetary medium, non stationary features of the magnetospheric behaviour, problems, however, exist in the theory of spontaneous reconnection. Here in this paper new theoretical results are discussed, which help to advance the understanding of collisionless nonstationary reconnection processes in the tail. It is discussed, how the stabilizing influence of adiabatic electrons can be canceled. Further it is shown that in addition to the instability of a shearless tail, usually discussed, another route to instability appears in the presence of a finite magnetic shear. Finally the transition to a nonlinear, explosive mode of instability is examined.

ON THE STABILITY OF DRIFT WAVES WITH STRONG COLLISION

An integral eigenequation is derived for the strongly collisional plasma by applying the gyrokinetic technique. An analytical proof of the absolute stability for the drift wave in a slab geometry with finite magnetic shear is presented. The macroscopic motion of electrons parallel to the ambient magnetic field is taken into consideration and Lee-Chen-Nevins method is adopted in the proof.

On the stability of drift waves with the integral eigenmode equation

An analytical theory on the stability properties of drift-wave eigenmodes in a slab plasma with finite magnetic shear is presented. The corresponding eigenmode equation is the integral equation first given by Coppi et al. (1967) and rederived here, in a relatively simpler fashion, via the gyrokinetic equation. It is then proved that the universal drift-wave eigenmodes remain absolutely stable and finite electron temperature gradients do not alter the stability.

Stability of general plasma equilibria. III

For pt.II see ibid., vol.23, p.265 (1971). A general method for investigating stability of low-frequency electrostatic oscillations of magnetically confined plasma, which was developed in Part I (1968) for equilibria with closed field lines (e.g. multipoles), is extended to axisymmetric toroidal equilibria with finite magnetic shear (e.g. Tokamaks). The analysis encompasses all perturbations whose parallel wavelengths are comparable to equilibrium scale lengths and whose perpendicular wavelengths are comparable to ion Larmor radii. Once the problem of reconciling these characteristics with toroidal periodicity has been overcome, the investigation of any axisymmetric toroidal equilibrium becomes very similar to that of closed line equilibria and the ion and electron charge densities resulting from an arbitrary potential perturbation are calculated by a small Larmor radius expansion as in Part I. Using these expressions the determination of stability is reduced to a single one dimensional integro-differential equation-which must be solved numerically for each given equilibrium. In the most general case this requires considerable computation, but in many circumstances one can use simpler approximate forms of this equation which are also derived.

Theory of dissipative drift instabilities in sheared magnetic fields

Several different techniques are used to study the stability of electrostatic drift wave eigenmodes in a resistive plasma with finite magnetic shear. It is found that in the slab approximation, where usual shear damping is operative, resistivity contributes to an enhancement of this damping and the enhancement factor increases with the electron-ion collision frequency νei. Thus no unstable eigenmodes result. If the shear damping is nullified, either by introducing a strong spatial variation of the density gradient or by working in toroidal geometry with strong toroidal coupling effects, then unstable eigenmodes with growth rates increasing with νei are recovered. A perturbation calculation shows that retention of electron temperature fluctuations associated with the mode and inclusion of temperature gradients do not alter these conclusions. Extensive numerical calculations are also presented.

Numerical Analysis of Current-Driven Collisional Drift Instability in a Sheared Magnetic Field

Nonlocal collisional drift wave is analyzed in a current-carrying plasma slab with finite magnetic shear. Using the shooting method, eigenvalues are obtained by direct integration of a differential equation. It is shown that plasma current possibly makes the drift waves unstable, which are subject to collision enhanced shear damping.

Finite-Resistivity Instabilities of a Sheet Pinch

The stability of a plane current layer is analyzed in the hydromagnetic approximation, allowing for finite isotropic resistivity. The effect of a small layer curvature is simulated by a gravitational field. In an incompressible fluid, there can be three basic types of ``resistive'' instability: a long-wave ``tearing'' mode, corresponding to breakup of the layer along current-flow lines; a short-wave ``rippling'' mode, due to the flow of current across the resistivity gradients of the layer; and a low-g gravitational interchange mode that grows in spite of finite magnetic shear. The time scale is set by the resistive diffusion time τR and the hydromagnetic transit time τH of the layer. For large S = τR/τH, the growth rate of the ``tearing'' and ``rippling'' modes is of order τR−3/5τH−2/5, and that of the gravitational mode is of order τR−1/3τH−2/3. As S → ∞, the gravitational effect dominates and may be used to stabilize the two nongravitational modes. If the zero-order configuration is in equilibrium, there are no overstable modes in the incompressible case. Allowance for plasma compressibility somewhat modifies the ``rippling'' and gravitational modes, and may permit overstable modes to appear. The existence of overstable modes depends also on increasingly large zero-order resistivity gradients as S → ∞. The three unstable modes merely require increasingly large gradients of the first-order fluid velocity; but even so, the hydromagnetic approximation breaks down as S → ∞. Allowance for isotropic viscosity increases the effective mass density of the fluid, and the growth rates of the ``tearing'' and ``rippling'' modes then scale as τR−2/3τH−1/3. In plasmas, allowance for thermal conductivity suppresses the ``rippling'' mode at moderately high values of S. The ``tearing'' mode can be stabilized by conducting walls. The transition from the low-g ``resistive'' gravitational mode to the familiar high-g infinite conductivity mode is examined. The extension of the stability analysis to cylindrical geometry is discussed. The relevance of the theory to the results of various plasma experiments is pointed out. A nonhydromagnetic treatment will be needed to achieve rigorous correspondence to the experimental conditions.