Effect of nonlinear wave collapse on line shapes in a plasma

Abstract

The nonlinear interaction of waves can change the structural and radiative properties of plasmas. We describe the main features of a fully ionized unmagnetized plasma affected by strong Langmuir turbulence characterized by nonlinear wave collapse, and propose a simple model for evaluating the changes expected on a hydrogen line shape affected by such conditions. Our model is based on a stochastic renewal model using an exponential waiting time distribution and a half-normal probability density function for the electric field magnitude of the turbulent wave packet. The first results obtained with a simulation calculation of the hydrogen L  line show that strong Langmuir turbulence can provide an additional broadening to a Stark profile.

Stark Broadening from Impact Theory to Simulations

“…A larger broadening effect would be observed by considering wave collapse, a phenomenon occurring as W takes larger values of the order of 1 or more for such plasma conditions. The emitters then experience the effect of a sequence of solitons which can significantly increase the broadening [37]. Looking at the line shape obtained with a Fourier transform, we can see in Figure 4 that the peak of the line including the wave effect is about 10% lower than the impact line peak, but this with almost no effect on the line width.…”

“…A larger broadening effect would be observed by considering wave collapse, a phenomenon occurring as W takes larger values of the order of 1 or more for such plasma conditions. The emitters then experience the effect of a sequence of solitons which can significantly increase the broadening [37]. …”

Possible spectroscopic signature of wave collapse in edge plasmas

“…The time width of S i ( t ) is taken equal to be 20% of the cycle duration τ i as discussed in ref. . We sample the wave packet duration using an exponential law ν exp(− νt ), with the jumping frequency ν from one soliton to another chosen as the inverse of the average duration T of a wave collapse cycle.…”

“…We have recently studied the non‐linear effect of wave collapse in an unmagnetized plasma on the Lyman α line shape, using a sequence of envelope solitons oscillating at the plasma frequency. Our model retains several known properties of non‐linear wave collapse in a plasma, obtained in the last decades by numerical simulations and studies of the Zakharov equations .…”

“…In the presence of linear Langmuir waves, early studies predicted [3] and observed [4] the formation of satellites with a frequency separation from the line centre close to p , as well as some additional changes on the line shape of atomic and ion emitters. [2] We have recently studied the non-linear effect of wave collapse in an unmagnetized plasma on the Lyman line shape, [5] using a sequence of envelope solitons oscillating at the plasma frequency. Our model retains several known properties of non-linear wave collapse in a plasma, [1] obtained in the last decades by numerical simulations and studies of the Zakharov equations.…”