Ion Sound Radius Research Articles

Bounds on edge shear layer persistence while approaching the density limit

This paper details the theory of edge shear layer collapse as the density approaches the Greenwald density limit. It significantly extends earlier work, which was restricted in applicability. The zonal shear flow screening length is calculated for banana, plateau and Pfirsch–Schluter regimes. Poloidal field scaling persists in the plateau regime. Neoclassical screening and drift wave–zonal flow dynamics are combined in a theory, which is then reduced to a predator–prey model. Zonal noise, due to incoherent mode coupling, is retained. The threshold condition for edge shear layer collapse is computed, and linked to a critical value of the dimensionless parameter . Here is the ion sound radius, is the zonal flow screening length and is the equilibrium density scale length. The limiting initial edge density for shear layer collapse is derived and shown to scale favorably with the plasma current. The results are discussed in light of the density limit and Ohmic phenomenology.

On the Rayleigh–Kuo criterion for the tertiary instability of zonal flows

This paper reports the stability conditions for intense zonal flows (ZFs) and the growth rate γTI of the corresponding “tertiary” instability (TI) within the generalized Hasegawa–Mima plasma model. The analytical calculation extends and revises Kuo's analysis of the mathematically similar barotropic vorticity equation for incompressible neutral fluids on a rotating sphere [H.-L. Kuo, J. Meteor. 6, 105 (1949)]; then, the results are applied to the plasma case. An error in Kuo's original result is pointed out. An explicit analytical formula for γTI is derived and compared with numerical calculations. It is shown that, within the generalized Hasegawa–Mima model, a sinusoidal ZF is TI-unstable if and only if it satisfies the Rayleigh–Kuo criterion (known from geophysics) and that the ZF wave number exceeds the inverse ion sound radius. For non-sinusoidal ZFs, the results are qualitatively similar. As a corollary, there is no TI in the geometrical-optics limit, i.e., when the perturbation wavelength is small compared to the ZF scale. This also means that the traditional wave kinetic equation, which is derived under the geometrical-optics assumption, cannot adequately describe the ZF stability.

Magnetic Reconnection May Control the Ion-scale Spectral Break of Solar Wind Turbulence

Abstract The power spectral density of magnetic fluctuations in the solar wind exhibits several power-law-like frequency ranges with a well-defined break between approximately 0.1 and 1 Hz in the spacecraft frame. The exact dependence of this break scale on solar wind parameters has been extensively studied but is not yet fully understood. Recent studies have suggested that reconnection may induce a break in the spectrum at a “disruption scale” , which may be larger than the fundamental ion kinetic scales, producing an unusually steep spectrum just below the break. We present a statistical investigation of the dependence of the break scale on the proton gyroradius ρ i , ion inertial length d i , ion sound radius ρ s , proton–cyclotron resonance scale ρ c , and disruption scale as a function of . We find that the steepest spectral indices of the dissipation range occur when β e is in the range of 0.1–1 and the break scale is only slightly larger than the ion sound scale (a situation occurring 41% of the time at 1 au), in qualitative agreement with the reconnection model. In this range, the break scale shows a remarkably good correlation with . Our findings suggest that, at least at low β e , reconnection may play an important role in the development of the dissipation range turbulent cascade and cause unusually steep (steeper than −3) spectral indices.

Two-fluid simulations of driven reconnection in the mega-ampere spherical tokamak

In the merging-compression method of plasma start-up, two flux-ropes with parallel toroidal current are formed around in-vessel poloidal field coils, before merging to form a spherical tokamak plasma. This start-up method, used in the Mega-Ampere Spherical Tokamak (MAST), is studied as a high Lundquist number and low plasma-beta magnetic reconnection experiment. In this paper, 2D fluid simulations are presented of this merging process in order to understand the underlying physics, and better interpret the experimental data. These simulations examine the individual and combined effects of tight-aspect ratio geometry and two-fluid physics on the merging. The ideal self-driven flux-rope dynamics are coupled to the diffusion layer physics, resulting in a large range of phenomena. For resistive MHD simulations, the flux-ropes enter the sloshing regime for normalised resistivity η≲10−5. In Hall-MHD, three regimes are found for the qualitative behaviour of the current sheet, depending on the ratio of the current sheet width to the ion-sound radius. These are a stable collisional regime, an open X-point regime, and an intermediate regime that is highly unstable to tearing-type instabilities. In toroidal axisymmetric geometry, the final state after merging is a MAST-like spherical tokamak with nested flux-surfaces. It is also shown that the evolution of simulated 1D radial density profiles closely resembles the Thomson scattering electron density measurements in MAST. An intuitive explanation for the origin of the measured density structures is proposed, based upon the results of the toroidal Hall-MHD simulations.

Symmetry breaking effects of density gradient on parallel momentum transport: A new ρs* effect

Symmetry breaking effects of density gradient on parallel momentum transport is studied via quasilinear theory. It is shown that finite ρs*(≡ρs/Ln), where ρs is ion sound radius and Ln is density scale length, leads to symmetry breaking of the ion temperature gradient (ITG) eigenfunction. This broken symmetry persists even in the absence of mean poloidal (from radial electric field shear) and toroidal flows. This effect, as explained in the text, originates from the divergence of polarization particle current in the ion continuity equation. The form of the eigenfunction allows the microturbulence to generate parallel residual stress via 〈k‖〉 symmetry breaking. Comparison with the E→×B→ shear driven parallel residual stress, parallel polarization stress and turbulence intensity gradient driven parallel residual stress are discussed. It is shown that this ρs* driven parallel residual stress may become comparable to E→×B→ shear driven parallel residual stress in small Ln region. In the regular drift wave ordering, where ρs*≪1, this effect is found to be of the same order as the parallel polarization stress. This ρs* driven parallel residual stress can also overtake the turbulence intensity gradient driven parallel residual stress in strong density gradient region whereas the later one is dominant in the strong profile curvature region. The parallel momentum diffusivity is found to remain undisturbed by this ρs* effect as long as the turbulence intensity inhomogenity is not important.

Electron drift effects on magnetic islands

Electron drift effects on magnetic islands in a hot-electron plasma are studied. The slab approximation is used. The electron temperature gradient is neglected. The authors analyze the properties of the electrostatic potential profile function and the density profile function in the presence of the electron drift effects and the problem of regularization of these profile functions near the island separatrix. It is emphasized that the electron drift frequency depends on the island magnetic flux and, as a result of this dependence, the resonant interaction of magnetic islands with the electron drift waves is possible. It is shown that, allowing for the finiteness of the “effective” ion Larmor radius ρs (the ion sound radius), the polarization current effect proves to be dependent on the electron drift effects.

Collisionless m=1 reconnection in tokamaks

In high temperature tokamak regimes, the m=1 reconnecting mode is governed by two fluid effects associated with the electron skin-depth de=c/ωpe and the ion sound radius ρs=cs/Ωci. To clarify the early nonlinear dynamics of this mode, numerical simulations of a two fluid model are presented. To simulate physically reasonable parameters in a tokamak geometry, an efficient approach is used in which only a narrow layer surrounding the q=1 surface and m=1 magnetic island must be simulated. In the usual tokamak case ρs≳de, as well as the limit ρs=0, the early nonlinear growth of the mode is faster than exponential due a broadening of the flow layer. This broadening appears to result from tension in the magnetic field lines, which acts to pull the layer open as the island grows.