Collisionless Drift Waves Research Articles

STABILITY OF COLLISIONLESS DRIFT WAVES IN A HOT ELECTRON PLASMA

The low frequency interchange mode and d ift wave in a hot electron plasma are analyzed by using the Vlasov equation, and the effect of hot electrons is discussed. The stabilization of the drift wave occurs when α～30%, and the stabilization of the interchange mode occurs when α～10%, where a is the fraction of hot electrons. The influences of ion Larmor radius, density gradient and temperature of plasma, wavelength of perturbation, and magnetic curvature, on the stability are discussed. Comparing with the results of the strongly collisional drift wave derived from the MHD approximation, the collisionless drift wave can be stabilized by the ho electrons more easily.

Three-dimensional particle simulation of drift-wave fluctuations in a sheared magnetic field.

Three-dimensional particle simulations of collisionless drift waves in sheared magnetic fields were performed in order to determine the nonlinear behavior of inverse--electron-resonance dynamics in the presence of thermal fluctuations. It is found that stochastic electron diffuision in the electron-resonance overlap region can destabilize the drift-wave eigenmodes. Numerical evaluations based on a nonlinear electron-resonance broadening theory give predictions in accord with the frequency and growth rates found in the simulation of short-wavelength modes (${\mathrm{k}}_{\mathrm{y}}$${\mathrm{\ensuremath{\rho}}}_{\mathrm{s}}$\ensuremath{\gtrsim}1).

Theory of the renormalized dielectric for electrostatic drift wave turbulence in tokamaks

A theory of collisionless electrostatic drift wave turbulence in a circular cylinder with shear is presented. A renormalized electron drift kinetic equation which is consistent with conservation of energy is derived. For low levels of turbulence, a perturbative solution indicates that the turbulence has a stabilizing effect and that total mode spectrum energy decreases. For strongly turbulent regimes, results quantitatively but not qualitatively different from those of Hirshman and Molvig are found. In particular, additional stabilizing terms lead to a lower saturation amplitude, but the basic picture of turbulent destabilization competing against linear and nonlinear shear damping persists.

Recent work at Hiroshima on drift wave turbulence and associated transport

Recent developments in the theory of drift wave turbulence and associated transport phenomena are reviewed within the framework of the weak turbulence theory. Basic physical effects leading to anomalous cross-field transport of particles and energies are discussed in detail for the case of collisionless electrostatic drift waves in a uniform magnetic field. Effects of electro-magnetic perturbations (finite-β effect), magnetic shear and toroidal geometry are also discussed.

Fluctuations and transport in an inhomogeneous plasma

A formalism is developed to calculate the equilibrium fluctuation level in an inhomogeneous plasma. This formalism is applied to the collisionless drift wave in a sheared magnetic field. The fluctuation level is found to be anomalously large due to both the presence of weakly damped normal modes and convective amplification. As the magnetic shear is reduced, the steady-state fluctuation spectrum is found to increase both in coherence and in amplitude. The transport associated with this mode is evaluated. The diffusion coefficient is found to scale as D∝B2/nT1/2.

Collisionless drift instability and ion heating in a current-carrying inhomogeneous plasma

Low-frequency collisionless drift waves grow intensively when electron currents parallel to a magnetic field are drawn in a single-ended Q machine. For a smaller electron drift velocity, the measured dispersion relations of the wave are consistent with the linear theory of the current-driven collisionless drift instability. The temperature of the ions is observed to increase anisotropically concomitant with the growth of the drift wave. The heating rate is found to be proportional to the wave energy estimated from the saturated frequency spectrum and its dependence on the electron drift is measured to be of the form (u/ve)4. A further increase in the electron drift results in the excitation of an ion acoustic wave and a flute-like instability.

Ion Heating Due to Collisionless Drift-Wave Turbulence

Ion temperatures parallel and perpendicular to the magnetic field are observed to increase as the current-driven collisionless drift instability takes place; the anisotropic turbulence resulting from the onset of the instability qualitatively explains the measured heating.

Variational method for drift waves in a sheared magnetic field

A variational method is developed, which permits systematic improvement of the test function by increasing the number of variational parameters. The method is applied to the case of collisionless drift waves in a plasma slab with cold fluid ions. Using first the simplest test function, the authors obtain analytical expressions for the conditions under which this approximation yields marginal stability, and they compare these expressions with numerical results obtained by other authors. They then show numerically that the mode frequency converges as the number of variational parameters is increased. In the parameter range where the simplest test function yields marginal stability, they find weak damping when a sufficiently large number of variational parameters is included.

Anomalous Plasma Transport Due to Electron Temperature Gradient Instability

The collisionless drift wave instability driven by an electron temperature inhomogeneity (electron temperature gradient instability) and the enhanced transport processes associated with it are studied using a two-and-a-half dimensional particle simulation code. The simulation results show that quasilinear diffusion in phase space is an important mechanism for the saturation of this instability. The instability yields particle fluxes toward the hot plasma regions. The magnetic shear stabilizes the instability. However the heat conductivity of the electron temperature perpendicular to the magnetic field, T e⊥ , is not reduced by the magnetic shear but remains high, whereas the heat conductivity of the parallel temperature, T e// , is effectively reduced.

Renormalized Compton scattering and nonlinear damping of collisionless drift waves

A kinetic theory for the nonlinear damping of collisionless drift waves in a shear-free magnetic field is presented. The general formalism is a renormalized version of induced scattering on the ions and reduces correctly to weak turbulence theory. The approximation studied explicitly reduces to Compton scattering, systematizes and corrects the earlier calculations of Dupree and Tetreault [Phys. Fluids 21, 425 (1978)], and extends that theory to finite ion gyroradius. Certain conclusions differ significantly from those of Dupree and Tetreault. In particular, at long wavelengths the nonlinear ion growth rate is large and positive, proportional to k2⊥D both at zero and at finite gyroradius. (Here, k⊥ is the perpendicular wavenumber and D is the test particle diffusion coefficient.) Nevertheless, the rate of change of total mean kinetic energy due to the nonlinear interaction is small and proportional to q2∥, where q∥ is a typical parallel wavenumber.

ON THE LOW FREQUENCY DRIFT WAVE AND THE PSEUDOCLASSICAL DIFFUSION

In this paper, the relationship between the low frequency drift wave and the empirical law of anomalous transport in Tokamak the pseudo-classical diffusion is discussed. We show that, it is the collisionless drift wave, rather than the dissipative one, which corresponds to the pseudoelassical diffusion. If the linear unstable collision-less drift wave is saturated mainly by the quasi-linear relaxation process, it can lead to a diffusion of the pseudo-classical type. The estimated diffusion coefficient agrees with experiment within an order of magnitude. The range of the parameters in which the above mentioned mechanism may be effective is discussed.

New nonlocal analysis of collisionless drift wave in Vlasov plasma

The WKB-type eigenmode analysis of an inhomogeneous Vlasov plasma is developed based on the exact integral equation. Thermal effects, namely, effects associated with the finite Larmor radius, Landau damping, cyclotron damping and so on are taken into account even if k2ρ2≳≳1 [k is of the order of ‖ψ′ (x)/ψ‖ ]. The ’’quantization condition,’’ which determines the eigenfrequency, is derived from the global localization condition of solutions. In the case of weak dissipation, this quantization condition reduces to a simple and more tractable form. Drift waves in a straight magnetic field with Gaussian density distributions are discussed numerically and analytically in detail. Results show that the growth rate of the fundamental mode (n=0) is the largest one.

Analytic eigenvalue equations for collisionless drift waves in tokamaks

Recently, collisionless drift waves in sheared magnetic fields were shown to be stable. The validity of the analytic model employed in one of these investigations is examined in detail.

On the numerical solution of the drift wave equations by means of invariant imbedding

The method of invariant imbedding is applied to solve the system of differential equations for the collisionless drift wave in a sheared magnetic field in the case of finite β i . Eigenvalues and eigenfunctions are found. Invariant imbedding is found to be fast and accurate, overcoming the precision problems inherent in the ordinary shooting method.

Numerical Analysis of Current-Driven Drift-Wave Instability in a Finite- β Plasma

Stability of the collisionless drift wave localized to the rational surface is studied numerically. Both the current and the finite- β effects are taken into account. The results confirm the previous analytical and/or numerical results concerning the stableness in the currentless case, instability driven by the current and its finite- β stabilitzation in the short wavelength region. In addition, a strong resonant coupling of the drift wave to the Alfvén wave is found to occur due to the combined effect of the current and the finite- β value, resulting a destabilizing effect in the long wavelength region. The critical electron drift velocity for the onset of the instability is calculated. The result shows a substantial reduction of the critical velocity by the finite- β effect.

Unstable Drift Waves in a Sheared Magnetic Field

Electrostatic collisionless drift waves in a sheared magnetic field have been studied extensively with use of particle-code simulations. When the shear is strong, we have found that the plasma is dominated by spatially uncorrelated small-amplitude oscillations with frequencies close to those prescribed by the local dispersion relation. With a weaker shear, spatially correlated large-amplitude waves with a well-defined frequency have been observed. Theoretically predicted eigenmodes are not the dominant feature of the fluctuation spectrum.

Localized trapped electron drift instability

The full electron dynamics in the collisionless drift wave radial equation is used to discover a class of drift modes which are localized by electron temperature gradients and are unaffected by the ion acoustic term. In the presence of a driving term, such as provided by trapped particles, these modes become strongly unstable.

Analytical Theory of Drift Waves and Drift-Alfvén Waves in Tokamaks

The collisionless drift wave and drift-Alfv\'en wave instabilities in a sheared magnetic field are considered using the complex transformation technique of Antonsen. It is shown that no unstable bounded eigensolutions for the finite-$\ensuremath{\beta}$ radial eigenmode equations exist. We also present a more general technique based on the wave-flux conservation and find, furthermore, that the convective amplification of drift waves in the electrostatic limit can be anomalously large, which could lead to enhanced transport in tokamaks.

Numerical Study of Drift Wave Instability due to Non-Uniform Density Gradient in a Sheared Magnetic Field

Instability of collisionless drift waves due to non-uniform density gradient in a sheared magnetic field is studied numerically for the case of a Gaussian profile of the density gradient taking the full plasma dispersion function into account. A critical shear for stability is obtained, which agrees to the Krall-Rosenbluth criterion within a factor of two.

Linear theory for the collisionless drift wave instability with wavelengths near the ion gyroradius

In a companion paper a role is suggested for drift wave modes in the theory of equatorial spread F. Here, some results of the collisionless theory of electrostatic drift waves are examined. The region of validity for a previously derived expression for the growth rate is determined. The region is then extended, and an expression for the growth rate is derived which is valid over a larger region including wavelengths much smaller than the ion gyroradius. The growth rate is maximum for k⊥ρi ≈ 1.5. These results may have applications in a variety of space plasmas wherein steep gradients in plasma density occur.