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Register a new userThe universal instability in general geometry
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The universal instability has recently been revived by Landreman, Antonsen and Dorland [1], who showed that it indeed exists in plasma geometries with straight (but sheared) magnetic field lines. Here it is demonstrated analytically that this instability can be present in more general sheared and toroidal geometries. In a torus, the universal instability is shown to be closely related to the trapped-electron mode, although the trapped-electron drive is usually dominant. However, this drive can be weakened or eliminated, as in the case in stellarators with the maximum-$J$ property, leaving the parallel Landau resonance to drive a residual mode, which is identified as the universal instability.
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We present a theory of the nonlinear growth of zonal flows in magnetized plasma turbulence, by the mechanism of secondary instability. The theory is derived for general magnetic geometry, and is thus applicable to both tokamaks and stellarators. The predicted growth rate is shown to compare favorably with nonlinear gyrokinetic simulations, with the error scaling as expected with the small parameter of the theory.
A general theory of the onset and development of the plasmoid instability is formulated by means of a principle of least time. The scaling relations for the final aspect ratio, transition time to rapid onset, growth rate, and number of plasmoids are derived, and shown to depend on the initial perturbation amplitude $left({hat w}_0right)$, the characteristic rate of current sheet evolution $left(1/tauright)$, and the Lundquist number $left(Sright)$. They are not simple power laws, and are proportional to $S^{alpha} tau^{beta} left[ln f(S,tau,{hat w}_0)right]^sigma$. The detailed dynamics of the instability is also elucidated, and shown to comprise of a period of quiescence followed by sudden growth over a short time scale.
The quasilinear particle flux arising from gyrokinetic instabilities is calculated in the electrostatic and collisionless approximation, keeping the geometry of the magnetic field arbitrary. In particular, the flux of electrons and heavy impurity ions is studied in the limit where the former move quickly, and the latter slowly, along the field compared with the mode frequency. Conclusions are drawn about how the particle fluxes of these species depend on the magnetic-field geometry, mode structure and frequency of the instability. Under some conditions, such as everywhere favourable or unfavourable magnetic curvature and modest temperature gradients, it is possible to make general statements about the fluxes independently of the details of the instability. In quasi-isodynamic stellarators with favourable bounce-averaged curvature for most particles, the particle flux is always outward if the temperature gradient is not too large, suggesting that it might be difficult to fuel such devices with gas puffing from the wall. In devices with predominantly unfavourable magnetic curvature, the particle flux can be inward, resulting in spontaneous density peaking in the centre of the plasma. In the limit of highly charged impurities, ordinary diffusion (proportional to the density gradient) dominates over other transport channels and the diffusion coefficient becomes independent of mass and charge. An estimate for the level of transport caused by magnetic-field fluctuations arising from ion-temperature-gradient instabilities is also given and is shown to be small compared with the electrostatic component.
The effects of line-tying on resistive tearing instability in slab geometry is studied within the framework of reduced magnetohydrodynamics (RMHD).citep{KadomtsevP1974,Strauss1976} It is found that line-tying has a stabilizing effect. The tearing mode is stabilized when the system length $L$ is shorter than a critical length $L_{c}$, which is independent of the resistivity $eta$. When $L$ is not too much longer than $L_{c}$, the growthrate $gamma$ is proportional to $eta$ . When $L$ is sufficiently long, the tearing mode scaling $gammasimeta^{3/5}$ is recovered. The transition from $gammasimeta$ to $gammasimeta^{3/5}$ occurs at a transition length $L_{t}simeta^{-2/5}$.
We report for the first time the intrinsically three-dimensional (3D) geometry of the magnetic reconnection process induced by ballooning instability in a generalized Harris sheet. The spatial distribution and structure of the quasi-separatrix layers, as well as their temporal emergence and evolution, indicate that the associated magnetic reconnection can only occur in a 3D geometry, which is irreducible to that of any two-dimensional reconnection process. Such a finding provides a new perspective to the long-standing controversy over the substorm onset problem, and elucidates the combined roles of reconnection and ballooning instabilities. It also connects to the universal presence of 3D reconnection processes previously discovered in various natural and laboratory plasmas.
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