R. C. Tautz

A new simulation code for particle diffusion in anisotropic, large-scale and turbulent magnetic fields

A new Monte Carlo code is presented that simulates the scattering processes of energetic particles in turbulent magnetic fields. The growing number of analytical models for anisotropic turbulence geometries gives rise to the need of fast and adaptable simulation codes that, in order to be able to judge the accuracy of the results, calculate the estimated mean errors of the transport parameters. Furthermore, the need to understand the interplay of scattering in anisotropic large-scale (such as the solar magnetic field) and turbulent (such as the Maltese cross-like structured solar wind turbulence) magnetic fields is accounted for with the calculation of the off-diagonal elements of the diffusion tensor.

The relativistic kinetic Weibel instability: Comparison of different distribution functions

Investigations of the relativistic Weibel instability have burgeoned in the last few years because of their potential use in various astrophysical scenarios. In this article, the parameters for the growth rates of well-known distribution functions are provided, based on a recently developed general description. The four distributions to be dealt with are the monochromatic, waterbag, bi-Maxwellian and the κ distribution. The advantages of this treatment are: (i) One has to solve only one integral to obtain the growth rates, thus (ii) one may compare the different distributions easily. Numerical illustrations of the growth rates for each distribution are given. The growth rates can be classified due to the ansatz of the distributions functions. In addition, some formulas of a previous paper are corrected.

Spontaneous emission of Weibel fluctuations by anisotropic distributions

Recently [Yoon, Phys. Plasmas 14, 064504 (2007)], the spontaneous emission of magnetic field fluctuations in isotropic particle distribution functions was investigated. Here, the question is addressed as to how these fluctuations develop for an anisotropic distribution function that supports the Weibel instability. It is shown that, depending on the parameters, either electromagnetic or aperiodic magnetic fluctuations are dominant.

Nonresonant kinetic instabilities of a relativistic plasma in a uniform magnetic field: Longitudinal and transverse mode coupling effects

The stability properties of relativistic plasmas embedded in a uniform magnetic field are investigated for longitudinal and transverse modes and with coupling effects between these modes. The direction of wave propagation in the plasma is not necessarily either parallel or transverse to the ambient magnetic field. The basic dispersion relation equations are given for arbitrary propagation directions. Detailed examination is focused on perpendicular wave propagation in this paper. The concept of neutral points in wave number space, introduced by Harris [Phys. Rev. Lett. 2, 34 (1959)], is generalized to allow for the inclusion of ion effects and the effects of fluctuating magnetic fields. Starting from the relativistic conductivity tensor, an expansion procedure for low wave frequencies is used to determine the stability properties in the neighborhood of neutral points and in the frequency regime below the ion cyclotron frequency. The bulk plasma properties determine stability or instability but the mode st...

Magnetic field amplification in anisotropic counterstreaming pair plasmas

The growth rates of the counterstream instability in magnetized electron-positron plasma is investigated by using a two-dimensional, electromagnetic, and relativistic particle-in-cell code. It is shown that strong electromagnetic ordinary-mode waves are excited, that propagate perpendicularly to the background magnetic field and with electric field parallel to that direction. For these waves, the linear growth rates are determined and compared to previous analytical results by Tautz and Schlickeiser [Phys. Plasmas 13, 062901 (2006)]. The simulations confirm the analytically derived growth rates very well. Furthermore, it is shown that for a strong background magnetic field, the linear instability is suppressed which, again, agrees with previous theoretical considerations.

Weakly propagating unstable modes in unmagnetized plasmas

The basic theory of isolated kinetic Weibel modes [Tautz et al., J. Phys. A: Math. Gen. 39, 13831 (2006)] is extended to include small real frequencies, describing unstable wave modes that propagate while growing. The new method is applicable for all kinds of arbitrary (therefore including symmetric as well as asymmetric) relativistic particle distribution functions, where the axis of wave propagation describes an oblique angle with respect to a symmetry axis. For the two examples of a warm, counterstreaming Cauchy distribution and a cold two-stream distribution it is shown that, although there are now broad regions in wavenumber space of unstable wave modes, the isolated Weibel modes (which, per definition, do not propagate) are recovered. Thus, this phenomenon deserves future investigation, because, in astrophysical plasmas, virtually all distribution functions are likely to be asymmetric, therefore giving rise to isolated Weibel modes.

Coupling, degeneracy breaking and isolation of Weibel modes in relativistic plasmas. I. General theory

A general proof is given that for an asymmetric particle phase-space distribution function, and in the absence of a homogeneous background magnetic field, any unstable linear Weibel modes are isolated, i.e., restricted to discrete wavenumbers. Starting from the linearized relativistic Vlasov equation it is shown that, unless the asymmetry in the distribution function is precisely zero, the broad ranges of unstable wavenumbers occurring for symmetric distribution functions are reduced to discrete, isolated wavenumbers for which unstable modes can exist. For asymmetric plasmas, electrostatic and electromagnetic wave modes are coupled to each other and the degeneracy of the two electromagnetic wave modes (that holds for symmetric distributions) is therefore broken.

Cosmic ray diffusion: Detailed investigation of a recent model

A recently proposed model [A. Shalchi, Astrophys. J. 720, L127 (2010)] of perpendicular cosmic ray scattering is investigated in detail, with special emphasis to the relevant diffusion coefficients. Solution of a pair of critical equations, as well as a fundamental integral needed to describe the particle transport, are represented via a mathematically correct expansion procedure, thus modifying the previously available approximations. It is hoped that these significant improvements will aid in allowing a clearer understanding of precisely what the model is capable of evaluating.

Kapteyn series arising in radiation problems

In discussing radiation from multiple point charges or magnetic dipoles, moving in circles or ellipses, a variety of Kapteyn series of the second kind arises. Some of the series have been known in closed form for a hundred years or more, others appear not to be available to analytic persuasion. This paper shows how 12 such generic series can be developed to produce either closed analytic expressions or integrals that are not analytically tractable. In addition, the method presented here may be of benefit when one has other Kapteyn series of the second kind to consider, thereby providing an additional reason to consider such series anew.

Unstable longitudinal plasma oscillations in a magnetic field: Nonrelativistic and relativistic considerations

The nonrelativistic and relativistic stability properties are investigated of longitudinal waves propagating in a plasma embedded in an ambient magnetic field, when the wave propagation direction is not necessarily either parallel or perpendicular to the ambient magnetic field. The analysis is based on the concept introduced by Harris [Phys. Rev. Lett. 2, 34 (1959)] of neutral points in wavenumber space to determine plasma instability to one side or the other of such neutral points. The critical need is to determine whether a particular plasma distribution function permits the existence of a neutral point. Relativistic considerations, although necessary to include for many astrophysical plasmas, complicate significantly the determination of instability conditions. In this paper it is shown how one can provide a general argument for such neutral point determination and for determining instability rates in the neighborhood of such neutral points. Only waves independent of resonant wave-particle effects are ...