Non-modal stability analysis and transient growth in a magnetized Vlasov plasma

Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many plasma instabilities, however, are still open problems. We investigate the stability properties of a collisionless Vlasov plasma in a stationary homogeneous magnetic field. We narrow the scope of our investigation to the case of Maxwellian plasma. For the first time using a fully kinetic approach we show the emergence of the local instability, a transient growth, followed by classical Landau damping in a stable magnetized plasma. We show that the linearized Vlasov operator is non-normal leading to the algebraic growth of the perturbations using non-modal stability theory. The typical time scales of the obtained instabilities are of the order of several plasma periods. The first-order distribution function and the corresponding electric field are calculated and the dependence on the magnetic field and perturbation parameters is studied. Our results offer a new scenario of the emergence and development of plasma instabilities on the kinetic scale.Comment: 6 pages, 5 figure

On initial-value and self-similar solutions of the compressible Euler equations

We examine numerically the issue of convergence for initial-value solutions and similarity solutions of the compressible Euler equations in two dimensions in the presence of vortex sheets (slip lines). We consider the problem of a normal shock wave impacting an inclined density discontinuity in the presence of a solid boundary. Two solution techniques are examined: the first solves the Euler equations by a Godunov method as an initial-value problem and the second as a boundary value problem, after invoking self-similarity. Our results indicate nonconvergence of the initial-value calculation at fixed time, with increasing spatial-temporal resolution. The similarity solution appears to converge to the weak 'zero-temperature' solution of the Euler equations in the presence of the slip line. Some speculations on the geometric character of solutions of the initial-value problem are presented

Shock interactions with heavy gaseous elliptic cylinders: Two leeward-side shock competition modes and a heuristic model for interfacial circulation deposition at early times

We identify two different modes, types I and II, of the interaction for planar shocks accelerating heavy prolate gaseous ellipses. These modes arise from different interactions of the incident shock (IS) and transmitted shock (TS) on the leeward side of the ellipse. A time ratio t_T/t_I(M,η,λ,γ_0,γ_b), which characterizes the mode of interaction, is derived heuristically. Here, the principal parameters governing the interaction are the Mach number of the shock (M), the ratio of the density of the ellipse to the ambient gas density, (η>1), γ_0, γ_b (the ratios of specific heats of the two gases), λ (the aspect ratio). Salient events in shock–ellipse interactions are identified and correlated with their signatures in circulation budgets and on-axis space–time pressure diagrams. The two modes yield different mechanisms of the baroclinic vorticity generation. We present a heuristic model for the net baroclinic circulation generated on the interface at the end of the early-time phase by both the IS and TS and validate the model via numerical simulations of the Euler equations. In the range 1.2⩽M⩽3.5, 1.54⩽η⩽5.04, and λ=1.5 and 3.0, our model predicts the baroclinic circulation on the interface within a band of ±10% in comparison to converged numerical simulations