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Register a new userTheory of the Drift-Wave Instability at Arbitrary Collisionality
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A numerically efficient framework that takes into account the effect of the Coulomb collision operator at arbitrary collisionalities is introduced. Such model is based on the expansion of the distribution function on a Hermite-Laguerre polynomial basis, to study the effects of collisions on magnetized plasma instabilities at arbitrary mean-free path. Focusing on the drift-wave instability, we show that our framework allows retrieving established collisional and collisionless limits. At the intermediate collisionalities relevant for present and future magnetic nuclear fusion devices, deviations with respect to collision operators used in state-of-the-art turbulence simulation codes show the need for retaining the full Coulomb operator in order to obtain both the correct instability growth rate and eigenmode spectrum, which, for example, may significantly impact quantitative predictions of transport. The exponential convergence of the spectral representation that we propose makes the representation of the velocity space dependence, including the full collision operator, more efficient than standard finite difference methods.
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The dynamics of electron-plasma waves are described at arbitrary collisionality by considering the full Coulomb collision operator. The description is based on a Hermite-Laguerre decomposition of the velocity dependence of the electron distribution function. The damping rate, frequency, and eigenmode spectrum of electron-plasma waves are found as functions of the collision frequency and wavelength. A comparison is made between the collisionless Landau damping limit, the Lenard-Bernstein and Dougherty collision operators, and the electron-ion collision operator, finding large deviations in the damping rates and eigenmode spectra. A purely damped entropy mode, characteristic of a plasma where pitch-angle scattering effects are dominant with respect to collisionless effects, is shown to emerge numerically, and its dispersion relation is analytically derived. It is shown that such a mode is absent when simplified collision operators are used, and that like-particle collisions strongly influence the damping rate of the entropy mode.
In a cross-field (ExB) setup, the electron ExB flow relative to the unmagnetized ions can cause the Electron Cyclotron Drift Instability (ECDI) due to resonances of the ion-acoustic mode and the electron cyclotron harmonics. This occurs in collisionless shocks in magnetospheres and in ExB discharge devices such as Hall thrusters. ECDI induces an electron flow parallel to the background E field at a speed greatly exceeding predictions by classical collision theory. Such anomalous transport might cause unfavorable plasma flows towards the walls of ExB devices. Prediction of ECDI and anomalous transport is often thought to require a fully kinetic treatment. In this work, however, we demonstrate that a reduced variant of this instability, and more importantly, the anomalous transport, can be treated self-consistently in a collisionless two-fluid framework without any adjustable collision parameter, by treating both electron and ion species on an equal footing. We will first present linear analyses of the instability in the two-fluid 5- and 10-moment models, and compare them against the fully kinetic theory. At low temperatures, the two-fluid models predict the fastest-growing mode comparable to the kinetic results. Also, by including more moments, secondary (and possibly higher) unstable branches can be recovered. The dependence of the instability on ion-to-electron mass ratio, plasma temperature, and the background field strength is also thoroughly explored. We then carry out 5-moment simulations of the cross-field setup. The development of the instability and the anomalous transport are confirmed and in excellent agreement with theoretical predictions. The force balance properties are also studied. This work casts new insights into the nature of ECDI and the induced anomalous transport and demonstrates the potential of the two-fluid moment model in the efficient modeling of ExB plasmas.
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 bootstrap current and flow velocity of a low-collisionality stellarator plasma are calculated. As far as possible, the analysis is carried out in a uniform way across all low-collisionality regimes in general stellarator geometry, assuming only that the confinement is good enough that the plasma is approximately in local thermodynamic equilibrium. It is found that conventional expressions for the ion flow speed and bootstrap current in the low-collisionality limit are accurate only in the $1/ u$-collisionality regime and need to be modified in the $sqrt{ u}$-regime. The correction due to finite collisionality is also discussed and is found to scale as $ u^{2/5}$.
Fluid models that approximate kinetic effects have received attention recently in the modelling of large scale plasmas such as planetary magnetospheres. In three-dimensional reconnection, both reconnection itself and current sheet instabilities need to be represented appropriately. We show that a heat flux closure based on pressure gradients enables a ten moment fluid model to capture key properties of the lower-hybrid drift instability (LHDI) within a reconnection simulation. Characteristics of the instability are examined with kinetic and fluid continuum models, and its role in the three-dimensional reconnection simulation is analysed. The saturation level of the electromagnetic LHDI is higher than expected which leads to strong kinking of the current sheet. Therefore, the magnitude of the initial perturbation has significant impact on the resulting turbulence.
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