Approximate Analytic Solution for the Spatiotemporal Evolution of Wave Packets undergoing Arbitrary Dispersion

The incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semi-infinite, rather than infinite, domain. It is useful for describing the linear dielectric response and wave dispersion in non-Maxwellian plasmas when the distribution functions can be approximated as Maxwellian over finite, or semi-infinite, intervals in velocity phase-space. A ubiquitous example is the depleted Maxwellian electron distri...

Plasma, which constitutes 99\% of the visible matter in the universe, is characterized by a wide range of waves and instabilities that play a pivotal role in space physics, astrophysics, laser-plasma interactions, fusion research, and laboratory experiments. The linear physics of these phenomena is described by kinetic dispersion relations (KDR). However, solving KDRs for arbitrary velocity distributions remains a significant challenge, particularly for non-Maxwellian distrib...

The spatio-temporal evolution and breaking of relativistically intense wave packets in a cold homogeneous unmagnetized plasma has been studied analytically and numerically. A general expression for phase mixing time scale as a function of amplitude of the wave packet and width of the spectrum has been derived. Results have been compared with the existing formulae in literature. It is shown that phase mixing time scale crucially depends on the relative magnitude of the amplitu...

This paper describes the partial wave expansion and integral representation of Bessel beams in free space and in the presence of dispersion. The expansion of the Bessel beam wavepacket with constant spectrum is obtained as well. Furthermore, the sum of a triple Legendre polynomial product of same order but different argument follows naturally from the partial wave expansion. The integration of all Bessel beams over all conical angles is shown to have a simple series represent...

We discuss four general features of force-free evolution: (1) The spatial spread of any packet changes with time in a very simple way. (2) Over sufficiently short periods of time (whose duration is related to the spread in momentum of the packet) the probability distribution moves but there is little change in shape. (3) After a sufficiently long period (related to the initial spatial spread) the packet settles into a simple form simply related to the momentum distribution in...

Numerical modeling of electromagnetic waves is an important tool for understanding the interaction of light and matter, and lies at the core of computational electromagnetics. Traditional approaches to injecting and evolving electromagnetic waves, however, can be prohibitively expensive and complex for emerging problems of interest and can restrict the comparisons that can be made between simulation and theory. As an alternative, we demonstrate that electromagnetic waves can ...

We present a systematic study on linear propagation of ultrashort laser pulses in media with dispersion, dispersionless media and vacuum. The applied method of amplitude envelopes gives the opportunity to estimate the limits of slowly warring amplitude approximation and to describe an amplitude integro-differential equation, governing the propagation of optical pulses in single cycle regime. The well known slowly varying amplitude equation and the amplitude equation for vacuu...

We develop an effective theory of pulse propagation in a nonlinear {\it and} disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena which we refer to as "locked explosion" and "diffusive" collapse. The equation can be applied to such distinct physical systems as laser beams propagating in disordered photonic crystals or Bose-Einstein condensates expanding in a disordered e...

A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the $\delta$, flat top, triangular, $\kappa$ or Lorentzian, slowing down, and incomplete Maxwellian distributions. The singularity and analytic continuation problems are also solved generally. Given that the usual conclusion $\gamma\propto\partial f_0/\partia...

We consider viscosity and thermal conductivity as dissipation mechanisms to derive a general dispersion relation for MHD waves propagating in a homogeneous plasma. We show that the actual dispersion relation for MHD waves in a homogeneous medium must be six-order. The finding is in agreement (except some coefficients) with the results of Porter et al. (1994) but it is in disagreement with the previous results obtained by Kumar et al. (2006). We also discuss in detail differen...