The 3D effects on sheath connected plasma blobs that result from parallel electron dynamics are studied by allowing for the variation of blob density and potential along the magnetic field line and using collisional Ohm's law to model the parallel current density. The parallel current density from linear sheath theory, typically used in the 2D model, is implemented as parallel boundary conditions. This model includes electrostatic 3D effects, such as resistive drift waves and blob spinning, while retaining all of the fundamental 2D physics of sheath connected plasma blobs. If the growth time of unstable drift waves is comparable to the 2D advection time scale of the blob, then the blob's density gradient will be depleted resulting in a much more diffusive blob with little radial motion. Furthermore, blob profiles that are initially varying along the field line drive the potential to a Boltzmann relation that spins the blob and thereby acts as an addition sink of the 2D potential. Basic dimensionless parameters are presented to estimate the relative importance of these two 3D effects. The deviation of blob dynamics from that predicted by 2D theory in the appropriate limits of these parameters is demonstrated by a direct comparison of 2D and 3D seeded blob simulations. V C 2012 American Institute of Physics. [http://dx.
Most of the work to date on plasma blobs found in the edge region of magnetic confinement devices is limited to 2D theory and simulations which ignore the variation of blob parameters along the magnetic field line. However, if the 2D convective rate of blobs is on the order of the growth rate of unstable drift waves, then drift wave turbulence can drastically alter the dynamics of blobs from that predicted by 2D theory. The density gradients in the drift plane that characterize the blob are mostly depleted during the nonlinear stage of drift waves resulting in a much more diffuse blob with a greatly reduced radial velocity. Sheath connected plasma blobs driven by effective gravity forces are considered in this Letter and it is found that the effects of resistive drift waves occur at earlier stages in the 2D motion for smaller blobs and in systems with a smaller effective gravity force. These conclusions are supported numerically by a direct comparison of 2D and 3D seeded blob simulations.
Fluctuations in fusion boundary and similar plasmas often have the form of filamentary structures, or blobs, that convectively propagate radially. This may lead to the degradation of plasma facing components as well as plasma confinement. Theoretical analysis of plasma blobs usually takes advantage of the so-called Boussinesq approximation of the potential vorticity equation, which greatly simplifies the treatment analytically and numerically. This approximation is only strictly justified when the blob density amplitude is small with respect to that of the background plasma. However, this is not the case for typical plasma blobs in the far scrape-off layer region, where the background density is small compared to that of the blob, and results obtained based on the Boussinesq approximation are questionable. In this report, the solution of the full vorticity equation, without the usual Boussinesq approximation, is proposed via a novel numerical approach. The method is used to solve for the evolution of 2D and 3D plasma blobs in a regime where the Boussinesq approximation is not valid. The Boussinesq solution under predicts the cross field transport in 2D. However, in 3D, for parameters typical of current tokamaks, the disparity between the radial cross field transport from the Boussinesq approximation and full solution is virtually non-existent due to the effects of the drift wave instability. V C 2014 AIP Publishing LLC.
The standard local linear analysis of drift waves in a plasma slab is generalized to be valid for arbitrarily collisional electrons by considering the electrons to be governed by the drift-kinetic equation with a BGK-like (Bhatnagar-Gross-Krook) collision operator. The obtained dispersion relation reduces to that found from collisionless kinetic theory when the collision frequency is zero. Electron temperature fluctuations must be retained in the standard fluid analysis in order to obtain good quantitative agreement with our general solution in the highly collisional limit. Any discrepancies between the fluid solution and our general solution in this limit are attributed to the limitations of the BGK collision operator. The maximum growth rates in both the collisional and collisionless limits are comparable and are both on the order of the fundamental drift wave frequency. The main role of the destabilizing mechanism is found to be in determining the parallel wave number at which the maximum growth rate will occur. The parallel wave number corresponding to the maximum growth rate is set by the wave-particle resonance condition in the collisionless limit and transitions to being set by the real frequency being on the order of the rate for electrons to diffuse a parallel wavelength in the collisional limit.
The inviscid evolution of localized density stratifications under the influence of a uniform gravity field in a homogeneous, ambient background is studied. The fluid is assumed to be incompressible, and the stratification, or filament, is assumed to be initially isotropic and at rest. It is shown that the center of mass energy can be related to the center of mass position in a form analogous to that of a solid object in a gravity field g by introducing an effective gravity field geff, which is less than g due to energy that goes into the background and into non-center of mass motion of the filament. During the early stages of the evolution, geff is constant in time and can be determined from the solution of a 1D differential equation that depends on the initial, radially varying density profile of the filament. For small amplitude filaments such that ρ0 ≪ 1, where ρ0 is the relative amplitude of the filament to the background, the early stage geff scales linearly with ρ0, but as ρ0→∞, geff→g and is thus independent of ρ0. Fully nonlinear simulations are performed for the evolution of Gaussian filaments, and it is found that the time tmax, which is defined as the time for the center of mass velocity to reach its maximum value Umax, occurs very soon after the constant acceleration phase and so Umax≈geff(t=0)tmax. The simulation results show that Umax∼1/tmax∼ρ0 for ρ0 ≪ 1, in agreement with theory and results from previous authors, but that Umax and tmax both scale approximately with ρ0 for ρ0 ≫ 1. The fact that Umax and tmax have the same scaling with ρ0 for large amplitude filaments is in agreement with the theory presented in this paper.
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