Ion acoustic traveling waves

Abstract

Models for travelling waves in multi-fluid plasmas give essential insight into fully nonlinear wave structures in plasmas, not readily available from either numerical simulations or from weakly nonlinear wave theories. We illustrate these ideas using one of the simplest models of an electron-proton multi-fluid plasma for the case where there is no magnetic field or a constant normal magnetic field present. We show that the travelling waves can be reduced to a single first order differential equation governing the dynamics. We also show that the equations admit a multi-symplectic Hamiltonian formulation in which both the space and time variables can act as the evolution variable. An integral equation useful for calculating adiabatic, electrostatic solitary wave signatures for multi-fluid plasmas with arbitrary mass ratios is presented. The integral equation arises naturally from a fluid dynamics approach for a two fluid plasma, with a given mass ratio of the two species (e.g. the plasma could be an electron proton or an electron positron plasma). Besides its intrinsic interest, the integral equation solution provides a useful analytical test for numerical codes that include a proton-electron mass ratio as a fundamental constant, such as for particle in cell (PIC) codes. The integral equation is used to delineate the physical characteristics of ion acoustic travelling waves consisting of hot electron and cold proton fluids.

Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas

“…The role of generalised vorticities and Bernoulli integrals in the formulation of travelling waves in multi-fluid plasmas is studied by . Webb et al ( , 2014 show that there are two different Hamiltonian formulations for the travelling waves, which use the x-momentum integral and the energy integral of the system. The momentum integral can be thought of as the Hamiltonian of the system, in which the variables are constrained by the energy integral.…”

Ion Acceleration in Multi-Fluid Plasma: Including Charge Separation Induced Electric Field Effects in Supersonic Wave Layers

“…The interesting feature of the (essentially numeric, gas dynamic) treatment considered here, however, is that we show how an additional non-smooth, or shock-like, ESW can also be constructed by the explicit insertion of a jump through the charge neutral point of the wave. This extra jump solution (denoted here as an accelerating upper solution in the text) is associated with negative potential wells, whereas the smooth solution that would naturally arise using more analytic methods (denoted here as a decelerating lower solution in the text) is associated with positive potential hills (e.g., see [33].) As suggested above, the proximate excitation of both upper and lower ESWs, by small perturbations from the same plasma background conditions, may be supported by observations.…”

Multi-symplectic, Lagrangian, one-dimensional gas dynamics

“…This is useful in the formulation of travelling wave problems, where two distinct Hamiltonian formulations of the equations are possible with, distinct Hamiltonians (e.g. Bridges (1992), Webb et al ( , 2007Webb et al ( , 2008Webb et al ( , 2014d). For systems in one Cartesian space variable x and one time variable t, both x and t can be regarded as the evolution variable.…”