Transient growth in stable linearized Vlasov–Maxwell plasmas

Abstract

Large amplitude transient growth of kinetic scale perturbations in stable collisionless magnetized plasmas has recently been demonstrated using a linearized Landau fluid model. Initial perturbations with lengthscales of the order of the ion gyroradius were shown to have transient timescales that in some cases were long compared to the ion gyroperiod, ⍀ i t ӷ 1. Moreover, it was suggested that such perturbations are not rare but instead form a large class within the set of all possible initial conditions. For collisionless plasmas, the Vlasov-Maxwell equations provide a more complete description of kinetic physics and the existence of transient growth of solutions for the linearized Vlasov-Maxwell system is an interesting question. The existence of transient growth of solutions is demonstrated here for a special case of the Vlasov-Maxwell equations, namely, the one dimensional Vlasov-Poisson system. The analysis is different from the standard approach of nonmodal analysis since the initial value problem is described by a Volterra integral equation of the second kind, reflecting the fact that the time evolution of the system depends on the memory of the state from time zero through time t. For the case of a thermal equilibrium plasma, it is shown how initial conditions may be constructed to obtain solutions that grow linearly in time; the duration of this growth is the time required for a thermal electron to traverse the wavelength of the initial perturbation, a timescale that can last for many plasma periods 2 / pe , thus demonstrating the existence of transient growth of solutions for the linearized Vlasov-Poisson system. The results suggest that the phenomenon of transient growth may be a common feature of the linearized Vlasov-Maxwell system as well as for Landau fluid models.

The need to consider ion Bernstein waves as a dissipation channel of solar wind turbulence

“…It is well known that for any given value of k, there exists an infinite series of solutions of the longitudinal dispersion relation D L (w, k) = 0 in a Maxwellian plasma. For an illustration of the infinite hierarchy of roots in the Landau problem see, for example, Figure 2 in Podesta [2010]. [23] Figure 2 shows the dispersion relation for all available modes including the KAW, the magnetosonic-whistler (MSW), and the IBWs.…”

Integral equation for electrostatic waves generated by a point source in a spatially homogeneous magnetized plasma

“…Integral equation formulations of the Vlasov-Poisson system in unmagnetized plasmas are well known [44][45][46][47][48][49][50][51][52]. However, to the authors' knowledge, the integral equation formulation for a magnetized plasma given by (8) and (9) is new.…”

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

“…In case of the Vlasov plasma, the distribution function evolves according to Eq. (8), and the electric field follows the linearized MaxwellianAmpère law, Eq. (5)…”

“…(35) was considered by Podesta for one-dimensional field-free Vlasov plasma. 8 We further introduce the following dimensionless quantities:…”

“…1, i.e., within the framework of a modal stability theory. 7 A non-modal approach was employed by Podesta 8 to study the transient growth in a 1D collisionless field-free Vlasov plasma. In a previous study, we demonstrated the emergence of the transient growth of the disturbances in a homogeneously magnetized Vlasov plasma.…”