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

Abstract

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.

Comparison of linear modes in kinetic plasma models

“…Such approach is justified by the non-normality of the Vlasov-Maxwell linear operator. We refer to, e.g., (Camporeale et al 2009(Camporeale et al , 2010Podesta 2010;Ratushnaya & Samtaney 2014;Friedman & Carter 2014) and citations therein, for a discussion on non-normal linear operators in plasma physics. In short, and for the purpose of this paper, we recall that non-normality is due to the non-orthogonality of the eigenvectors of a linear operator, and is connected to the phenomena of transient growth, by-pass transitions and, generally, to mode coupling.…”

Transient growth of a Vlasov plasma in a weakly inhomogeneous magnetic field

“…In order to study the effect of the magnetic field inhomogeneity, we consider the same initial condition as in Ref. 9, where we studied the transient growth in a homogeneously magnetized plasma…”

“…In a previous study, we demonstrated the emergence of the transient growth of the disturbances in a homogeneously magnetized Vlasov plasma. 9 This was the first step towards analyzing the stability behavior and possibilities of transient growth in plasma such as that encountered in tokamaks. We showed that linearized Vlasov operator is nonnormal, leading to an algebraic growth of perturbations on the time scales of several plasma periods.…”

Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach

“…The two dimensional Dirac delta is understood as two deltas for real and imaginary parts δ (2) (z) = δ(Rez)δ(Imz), and the measure dµ(z) = dxdy for z = x + iy. D(z, w) introduced in [9,10] is the density of eigenvalues weighted by the invariant overlap of the corresponding eigenvectors.…”