Semicollisional Regime Research Articles

Kinetic investigation of the effect of lower hybrid current drive on tearing mode instability

Effect of lower-hybrid current drive on tearing mode instability is investigated in a drift kinetic formalism. In collisional regime the co-driven current plays a stabilizing role to tearing mode but a destabilizing role to drift tearing mode. A competitive effect among the gradients of density, temperature and driven current at the rational surface may exist. In semicollisional regime, lower hybrid current drive increases the growth rate of tearing mode and reduces the growth rate of drift tearing mode.

Atomic physics effects on tokamak edge drift-tearing modes

The effects of ionization and charge exchange on the linear stability of drift-tearing modes are analytically investigated. In particular, the linear instability threshold ΔTh, produced by ion sound wave coupling [Phys. Rev. Lett. 40, 1500 (1978)] is modified. In the strongly collisional regime, the ionization breaks up the near cancellation of the perturbed electric field and the pressure gradient along the magnetic field, and increases the threshold. In the semicollisional regime, both ionization and charge exchange act as drag on the ion parallel velocity [Phys. Fluids B 4, 2567 (1992)], and consequently decrease the threshold by reducing the effectiveness of ion sound wave propagation.

Nonlinear studies of m=1 modes in high-temperature plasmas

Nonlinear evolution of the m=1 mode is examined in high-temperature plasmas where the mode is in the semicollisional or collisionless regime. Unlike the finite −Δ′(m≥2) tearing modes, the nonlinear evolution of which is collisional, both the semicollisional and collisionless m=1 modes exhibit nonlinearly enhanced growth rates that far exceed their linear values, thus making their nonlinear evolution collisionless; this accelerated growth of a collisionless m=1 mode may explain the fast sawtooth crashes observed in large tokamaks.

Linear studies of m=1 modes in high-temperature plasmas with a four-field model

The m=1 mode in high temperature plasmas is examined using a simple four-field model of tokamak dynamics derived by Hazeltine et al. [Phys. Fluids 30, 3204 (1987)]. It is shown that, despite its simplicity, the model reproduces with remarkable accuracy results obtained with more sophisticated kinetic treatments in various collisionality regimes. The effects of parallel compressibility on the m=1 mode in the collisional, semicollisional, and collisionless regimes are also discussed. Coupling to the ion sound waves is found to be weakly destabilizing in the collisional regime, and stabilizing in the semicollisional and collisionless regimes.

Thermal effects in drift-tearing modes

The stability of drift-tearing modes in the collisional and semi-collisional regimes is studied analytically, when thermal effects are included. The author uses a fluid description of a cylindrical plasma and assume a variable plasma resistivity, depending on the local power input. The linear growth rates for the thermally-modified tearing modes ( Delta '>0) and for the thermal instabilities ( Delta '<0) are derived. The saturation mechanisms for these instabilities are also discussed.

Tearing modes in tokamaks with lower hybrid current drive

In this paper, the effect of current drive on the tearing modes in the semicollisional regime is analyzed using the drift-kinetic equation. A collisional operator is developed to model electron parallel conductivity. For the pure tearing modes the linear and quasilinear growth rates in the Rutherford regimes have been found to have roughly the same forms with a modified resistivity as without current drive. One interesting result is the prediction of a new instability. This instability, driven by the current gradient inside the tearing mode layer, is possibly related to magnetohydrodynamic (MHD) behavior observed in these experiments.

Linear stability of low mode number tearing modes in the banana collisionality regime

The semicollisional layer equations governing the linear stability of small mode number tearing modes in a low beta, large aspect ratio, tokamak equilibrium are derived from an expansion of the gyrokinetic equation. In this analysis only the cases where the ion Larmor radius is either much less than, or much greater than, the layer width are considered. Both the electrons and the ions are assumed to lie in the banana collisionality regime. One interesting feature of the derived layer equations, in the limit of small ion Larmor radius, is a substantial reduction in the effective collisionality of the system due to neoclassical ion dynamics. Next, using a shooting code, a dispersion relation is obtained from the layer equations in the limits of small ion Larmor radius and a vanishingly small fraction of trapped particles. As expected, strong semicollisional stabilization of the mode is found, but, in addition, a somewhat weaker destabilizing effect is obtained in the transition region between the collisional and semicollisional regimes.

Dynamics of magnetic relaxation in a high-temperature, current-carrying plasma

The results of a study of the role of multiple-helicity nonlinear interaction of tearing modes and the dynamics of magnetic relaxation and dynamo activity in a high-temperature, current-carrying plasma are described. A set of fluid equations for tearing modes in the semicollisional regime is derived, and a previous resistive magnetohydrodynamic study of tearing mode turbulence is thus extended to high-temperature regimes. Because of the direct connection between fluctuation evolution and configuration evolution, a generalized nonlinear theory of the turbulent dynamo and magnetic relaxation is proposed, and a two-point 〈(∇⊥p̃)ψ̃〉-correlation evolution is determined by calculating the relaxation time τcl. This calculated relaxation time is shown to serve as the phase shift between ṽr and ψ̃ and hence to control magnetic energy relaxation and dynamo processes. Careful study of the two separated regions of kink-tearing modes (i.e., the resonant region and the exterior region) reveals the direct relationship between the equilibrium magnetic energy relaxation and average magnetic flux evolution. Thus a theoretical interpretation of the observed correlation between magnetic fluctuations and maintenance of field reversal is provided. Finally, the correlation lifetime of the flux transport term is evaluated from the renormalized two-point theory, and the saturated magnetic fluctuation level is estimated. The result shows that the saturation level is independent of or very weakly dependent on the Lundquist number S. The implications of this result for anomalous thermal transport and dynamo activity in high-temperature reversed field pinch experiments are discussed.

Resistive electrostatic instabilities

The appropriate toroidal equations governing the stability properties of resistive electrostatic instabilities are derived and analyzed. These equations include the influence of impurity gradients and are valid for both strongly collisional and semicollisional regimes. Analytic and numerical solutions have been obtained in the sheared slab limit with toroidal curvature effects approximated with the familiar constant gravity model. The results indicate that for relevant experimental conditions, the resistivity-gradient-driven class of electrostatic modes is difficult to excite. Hence, with the possible exception of the very edge, these instabilities do not appear to be a likely candidate to account for the large thermal transport observed in the exterior region of most tokamak plasmas.

Numerical study of drift-resistive modes in general toroidal geometry

The linearized resistive boundary layer equations, including electron diamagnetic drift terms in general toroidal geometry, are solved numerically to obtain the dispersion relations of the resistive ballooning modes as well as the resistive interchange and tearing modes in both highly collisional and semicollisional regimes. Numerical solutions with high accuracy are obtained using two different numerical methods. Various physical effects, such as electron diamagnetic drift, parallel and perpendicular compression, and average curvature, are investigated in a wide range of equilibrium parameters. The present work is believed to be the first numerical study of the resistive ballooning modes with finite electron diamagnetic drift effects. These numerical solutions cover a wider range of parameter spaces than thus far available from analytical and other numerical methods. The new solutions contain previously known results as special cases. From the present study it is found that for the resistive ballooning and tearing modes, which have similar forms of dispersion relation, ion sound compression gives a substantial stabilizing effect, while ion-polarization compression gives a destabilizing effect and the stabilizing effect of favorable average curvature is significantly reduced as the diamagnetic drift effect increases. For the resistive interchange modes, these numerical results are shown to be in good agreement with previous results.

Finite ion temperature effects on collisional and semicollisional tearing modes

The finite ion gyroradius effects on the stability of global tearing modes are studied using analytic and numerical techniques. It is found that in the collisional regime the modes are weakly stabilized compared to the zero ion temperature case. In the semicollisional regime, the stabilization is weaker than the polarization drift stabilization in the zero ion temperature case. There is overall a very minor finite ion temperature modification of the stability boundary in the plasma beta, collisionality space.

Analytical theory of nonlinear drift-tearing mode stability

An analytical theory of the nonlinear stability of drift-tearing modes in the semicollisional regime is presented. It is shown that the overall stability depends critically on the initial island width and the plasma beta. Linear and quasilinear treatments demonstrate that islands smaller than the linear tearing layer are stabilized completely by the influence of the electron temperature gradient. A nonlinear theory is developed for larger islands. Standard algebraic growth is obtained unless diamagnetic effects are strong, in which case the time-asymptotic stability is dependent on the density and temperature profiles.

Active nonlinear ultralow-frequency generation in the ionosphere.

Experimental evidence for spontaneous excitation of ultralow-frequency (ULF) waves in the ionosphere through the use of high-frequency (HF) pumping is reported. The ULF waves were excited through beating of two HF pumps. The observed ULF power indicates conversion efficiency exceeding the one predicted by the Manley-Rowe relations consistent with theoretical expectations for stimulated excitation in the semicollisional regime. ULF wave excitation was also observed through the use of one amplitude-modulated HF pump, consistent with generation of ULF magnetic fields caused by the coupling of the heater-induced temperature gradient to ionospheric gradient.

Theory of semicollisional drift-interchange modes in cylindrical plasmas

Resistive interchange instabilities in cylindrical plasmas are studied, including the effects of electron diamagnetic drift, perpendicular resistivity, and plasma compression. The analyses are pertinent to the semicollisional regime where the effective ion gyroradius is larger than the resistive layer width. Both analytical and numerical results show that the modes can be completely stabilized by the perpendicular plasma transport. Ion sound effects, meanwhile, are found to be negligible in the semicollisional regime.

Kinetic theory of tearing instabilities

The transition of the tearing instability from the collisional to the collisionless regime is investigated kinetically using a Fokker–Planck collision operator to represent electron-ion collisions. As a function of the collisionality of the plasma, the tearing instability falls into three regions, which are referred to as collisionless, semi-collisional, and collisional. The width Δ of the singular layer around k⋅B0=0 is limited by electron thermal motion along B0 in the collisional and semi-collisional regimes and is typically smaller than ρi, the ion Larmor radius. Previously accepted theories, which are based on the assumption Δ≫ρi, are found to be valid only in the collisional regime. The effects of density and temperature gradients on the instabilities are also studied. The tearing instability is only driven by the temperature gradient in the collisional and semi-collisional regimes. Numerical calculations indicate that the semi-collisional tearing instability is particularly relevant to present day high temperature tokamak discharges.