Victor Kowalenko

Response theory of particle-anti-particle plasmas

Abstract The physical motivation for our work on particle-anti-particle systems comes primarily from astrophysical objects such as pulsars and white dwarf stars. We deal first with the longitudinal dielectric response of an electron-positron or pair plasma in zero and non-zero magnetic fields. The response function must be renormalized using the standard techniques of quantum electrodynamics. For zero magnetic field, the dispersion relation and damping for plasma oscillations are given together with the screening potential about a test charge. For the case of non-zero magnetic field, the longitudinal dielectric response function is again calculated after renormalization. The response function takes on a different form depending upon whether the longitudinal oscillations are parallel or perpendicular to the direction of the magnetic field. The real and imaginary parts of the response function are then exhibited for both cases. The next topic is concerned with the plasma thought to exist in the deep interior of neutron stars or in the ephemeral plasmas of heavy ion collisions. Use of the Feshbach-Villars formalism for the Klein-Gordon equation allows for a similar approach to that previously used for the fermion-anti-fermion case. An adaption of the formalism developed here to two-dimensional systems is also given.

Statistical mechanics of the magnetized pair quantum gases

Abstract In this report, we present a full study of the statistical mechanics of the zero-field and magnetized pair-boson and pair-fermion gases in d spatial dimensions. An extensive literature has developed over the past decade on the zero-field pair gases. These studies are extensively reviewed and further developed, and we give explicitly results for various thermodynamic functions, such as the specific heat. For the Bose gas, this allows us to give a thorough exposition of d -dimensional pair Bose-Einstein condensation. The generalization to an original study of the statistical mechanics of the magnetized pair quantum gases forms the remaining body of this report. The results presented give a complete investigation, again in d -dimensions, of these systems which are considerably more intricate than their zero-field counterparts. For the Bose gas, we show that although Bose-Einstein condensation does occur for all d ≥ 5, the magnetization for all d ≥ 3 is remarkably different in form to that of the nonrelativistic Bose gas. There is still a Meissner effect, but of a new nature; in fact magnetized pair Bose systems are relativistic superconductors. In the case of the zero-field pair Fermi gas, we review the existing literature, and develop expansions for various thermodynamic functions. For the pair-fermion gas in an external magnetic field, we find new results for relativistic para/diamagnetism. In this case, the effect of intrinsic spin upon the magnetization is an important one. For both systems, external fields ranging in strength from weak to extremely strong are considered. The physical scenarios for the manifestation of these systems are thus many, and include exotic stellar objects in the present epoch, and cosmology and the early universe. Using these contexts as a background, the emphasis of this report is on the statistical mechanics of pair systems. The Mellin-transform technique is used to develop expansions for the thermodynamic functions, and we give a full presentation of this and other analytical machinery that is necessary to deal with the inherent mathematical intricacy of calculating the relevant thermodynamic functions. This complete study of the zero-field and magnetized Bose and Fermi gases allows comparison between the effects of critical phenomena, thermal pair creation, statistics, spin, and external fields upon the macroscopic behaviour of these fundamental pair systems at temperatures above pair threshold.

Exactification of the asymptotics for Bessel and Hankel functions

Exactification is the process of showing how a complete asymptotic expansion can be evaluated to yield exact values of the original function it represents. Because the process does not involve neglecting the remainders of truncated component asymptotic series within a complete asymptotic expansion, techniques for evaluating divergent series are required. One such technique is Borel summation, but in many instances, it can be computationally slow and consequently, lacking in precision. Another is the numerical technique of Mellin-Barnes regularization, which is capable of evaluating divergent series with great precision far more rapidly than Borel summation. Here, both techniques are presented in the evaluation of exact values for Bessel and Hankel functions from their complete asymptotic expansions.

Basic trigonometric power sums with applications

We present the transformation of several sums of positive integer powers of the sine and cosine into non-trigonometric combinatorial forms. The results are applied to the derivation of generating functions and to the number of the closed walks on a path and in a cycle.

Temperature estimates for a railgun plasma armature

A free-flowing plasma in a railgun refers to a plasma which is not impeded by a projectile during a firing. One advantage in performing experiments with such plasmas is that spectroscopic measurements can be made when they are ejected. In this paper we analyse absorption and emission spectra of a free-flowing plasma for wavelengths between 300 and 625 nm in several firings. Calculations of the degree of ionization for the various species identified on the spectra are used to produce an estimate for the temperature of a free-flowing plasma in a RAPID railgun that lies between 11 × 103 and 25 × 103 K. This temperature range is reduced to 11 × 103 K by using a special computer code that predicts the thermochemical functions and transport coefficients of partially- and fully-ionized plasmas. The code is then used to develop temperature estimates of the plasma armature in railgun firings with projectiles. For these plasmas, which are expected to be denser than free-flowing plasmas, a temperature estimate of 14 × 103 K is obtained for a RAPID railgun firing at shot-out.

Mellin - Barnes regularization, Borel summation and the Bender - Wu asymptotics for the anharmonic oscillator

We introduce the numerical technique of Mellin - Barnes integral regularization, which can be used to evaluate both convergent and divergent series. The technique is shown to be numerically equivalent to the corresponding results obtained by Borel summation. Both techniques are then applied to the Bender - Wu formula, which represents an asymptotic expansion for the energy levels of the anharmonic oscillator. We find that this formula is unable to give accurate values for the ground-state energy, particularly when the coupling is greater than 0.1. As a consequence, the inability of the Bender - Wu formula to yield exact values for the energy level of the anharmonic oscillator cannot be attributed to its asymptotic nature.

Revisiting the performance of a plasma armature railgun

Some experimental results obtained from a series of firings using a small-bore two-stage plasma armature railgun are presented which contradict assumptions employed in more recent attempts to model plasma armatures in railgun firings. By introducing the current - time behaviour into the equation of motion for the plasma - projectile system, an expression for a limiting exit velocity is obtained. This general expression is dependent upon the rail inductance per unit length when no anomalous effects occur in a firing. Since current diffusion is not significant close to the plasma - projectile system during a firing, the current distribution can be assumed to be in the form of thin sheets along the inner rail surfaces, thereby enabling the rail inductance per unit length to be evaluated. Different values for the height of the current sheets are then used to evaluate the rail inductance per unit length. When introduced into the expression for the limiting exit velocity, all yield significantly higher exit velocities than those recorded in railgun firings. These results explain the relatively poor performance of a railgun without the need to incorporate relativistic effects as in recent work.

A study of the equations of motion for a plasma-armature railgun

The two derivations of the equation of motion for the plasma armature - projectile system in a railgun are reviewed. Although they describe the same kinematical system, it is shown that they yield conflicting descriptions for the action - reaction forces over the plasma armature. The two inductances per unit length for the equations of motion are then given for the case in which the rail and current distributions are in the form of infinitesimally thin sheets and are shown to be different, although for a RAPID railgun this difference is not significant. Next, the lumped-parameter version of the railgun equation of motion is shown to be incapable of explaining anomalous effects occurring in the plasma armature, which have been observed in railgun firings, whereas no such problem arises with the MHD version. Finally, sufficient conditions under which the equations yield equivalent results are given, though these may not be realized in most railgun applications. .

Dielectric properties of an ultra-cold weakly magnetized charged Bose gas

With a new asymptotic expansion for the specific Kummer function that appears in the response theory of low-temperature quantum plasmas in an external magnetic field, the dielectric properties of the charged Bose gas, namely its collective and transverse modes and screening properties, are evaluated in the weak-field limit.

Dissipation of Turbulent Magnetic Fields in Accreting Black Holes

Calculations of the spectrum resulting from accretion onto a massive black hole often make use of the “equipartition assumption” in order to estimate the magnetic field intensity. Thus, the mechanism for the dissipation of the magnetic field and the resulting dynamical influence on the gas have not been treated quantitatively, nor self-consistently. Here, we introduce an alternative approach for modelling the magnetic field dissipation from basic principles, using current ideas about turbulent fields and tearing mode instabilities.