Semi-empirical analysis of leptons in gases in crossed electric and magnetic fields. Part II. Transverse compression of muon beams.

This article employs fluid equations to analyze muon beams in gases subject to crossed electric and magnetic fields, focusing, in particular, on a scheme proposed by Taqqu [Phys. Rev. Lett.

Semi-empirical analysis of leptons in gases in crossed electric and magnetic fields. I. Electrons in helium.

In this series, we outline a strategy for analyzing electrons and muons in gases in crossed electric and magnetic fields using the straightforward transport equations of momentum-transfer theory, plus empirical arguments. The method, which can be carried through from first principles to provide numerical estimates of quantities of experimental interest, offers a straightforward, physically transparent alternative to "off-the-shelf" simulation packages, such as Magboltz and GEANT. In this first article, we show how swarm data for electrons in helium gas subject to an electric field only can be incorporated into the analysis to generate electron swarm properties in helium gas in crossed electric and magnetic fields and to estimate the Lorentz angle in particular.

Boltzmann's equation at 150: Traditional and modern solution techniques for charged particles in neutral gases.

Seminal gas discharge experiments of the late 19th and early 20th centuries laid the foundations of modern physics, and the influence of this "golden era" continues to resonate well into the 21st century through modern technologies, medical applications, and fundamental scientific investigations. Key to this continuing success story has been the kinetic equation formulated by Ludwig Boltzmann in 1872, which provides the theoretical foundations necessary for analyzing such highly non-equilibrium situations. However, as discussed here, the full potential of Boltzmann's equation has been realized only in the past 50 years or so, with modern computing power and analytical techniques facilitating accurate solutions for various types of charged particles (ions, electrons, positrons, and muons) in gases.

Positron kinetics in an idealized PET environment.

The kinetic theory of non-relativistic positrons in an idealized positron emission tomography PET environment is developed by solving the Boltzmann equation, allowing for coherent and incoherent elastic, inelastic, ionizing and annihilating collisions through positronium formation. An analytic expression is obtained for the positronium formation rate, as a function of distance from a spherical source, in terms of the solutions of the general kinetic eigenvalue problem. Numerical estimates of the positron range - a fundamental limitation on the accuracy of PET, are given for positrons in a model of liquid water, a surrogate for human tissue.

Electron drift velocities in He and water mixtures: measurements and an assessment of the water vapour cross-section sets.

The drift velocity of electrons in mixtures of gaseous water and helium is measured over the range of reduced electric fields 0.1-300 Td using a pulsed-Townsend technique. Admixtures of 1% and 2% water to helium are found to produce negative differential conductivity (NDC), despite NDC being absent from the pure gases.

Low-energy electron and positron transport in gases and soft-condensed systems of biological relevance.

We present a study of electron and positron transport in water in both the gaseous and liquid states using a Boltzmann equation analysis and a Monte-Carlo simulation technique. We assess the importance of coherent scattering processes when considering transport of electrons/positrons in dense gases and liquids. We highlight the importance of electron and positron swarm studies and experiments as a test of the accuracy and completeness of cross-sections, as well as a technique for benchmarking Monte-Carlo simulations.

Fundamental issues in fluid modeling: direct substitution and aliasing methods.

It is shown how the accuracy of fluid models of charged particles in gases can be improved significantly by direct substitution of swarm transport coefficient data, rather than cross sections, into the average collision terms. This direct substitution method emerges in a natural way for fluid formulations in which the role of the mean energy is transparent, whatever the mass of the charged particles in equation (ions or electrons), and requires no further approximations. The procedure is illustrated by numerical examples for electrons, including the operational window of E/N for an idealized Franck-Hertz experiment.

Fluid-model analysis of electron swarms in a space-varying field: nonlocality and resonance phenomena.

The physically based, benchmarked fluid model developed by Robson et al. [R. E.

Transport coefficients and cross sections for electrons in water vapour: comparison of cross section sets using an improved Boltzmann equation solution.

This paper revisits the issues surrounding computation of electron transport properties in water vapour as a function of E/n(0) (the ratio of the applied electric field to the water vapour number density) up to 1200 Td. We solve the Boltzmann equation using an improved version of the code of Ness and Robson [Phys. Rev.

Analytic solution of the fractional advection-diffusion equation for the time-of-flight experiment in a finite geometry.

A general analytic solution to the fractional advection diffusion equation is obtained in plane parallel geometry. The result is an infinite series of spatial Fourier modes which decay according to the Mittag-Leffler function, which is cast into a simple closed-form expression in Laplace space using the Poisson summation theorem. An analytic expression for the current measured in a time-of-flight experiment is derived, and the sum of the slopes of the two respective time regimes on logarithmic axes is demonstrated to be -2, in agreement with the well-known result for a continuous time random-walk model.

Multiterm solution of a generalized Boltzmann kinetic equation for electron and positron transport in structured and soft condensed matter.

In this paper, we generalize the semiclassical Boltzmann kinetic equation for dilute gases to consider highly nonequilibrium electrons and positrons in soft condensed matter, accounting rigorously for all types of interactions, including positronium formation, and allowing for both coherent and incoherent scattering processes. The limitations inherent in the seminal paper of Cohen and Lekner [M. H.

Transport coefficients for electrons in water vapor: definition, measurement, and calculation.

Comparison of experimental and theoretical transport data for electron swarms in water vapour over a wide range of fields provides a rigorous test of (e(-), H(2)O) scattering cross sections over a correspondingly broad range of energies. That like should be compared with like is axiomatic, but the definition of transport coefficients at high fields, when non-conservative processes are significant, has long been contentious. This paper revisits and distills the most essential aspects of the definition and calculation of transport coefficients, giving numerical results for the drift velocity and ionisation coefficient of electrons in water vapour.

Benchmark calculations of nonconservative charged-particle swarms in dc electric and magnetic fields crossed at arbitrary angles.

A multiterm solution of the Boltzmann equation has been developed and used to calculate transport coefficients of charged-particle swarms in gases under the influence of electric and magnetic fields crossed at arbitrary angles when nonconservative collisions are present. The hierarchy resulting from a spherical-harmonic decomposition of the Boltzmann equation in the hydrodynamic regime is solved numerically by representing the speed dependence of the phase-space distribution function in terms of an expansion in Sonine polynomials about a Maxwellian velocity distribution at an internally determined temperature. Results are given for electron swarms in certain collisional models for ionization and attachment over a range of angles between the fields and field strengths.

Positron kinetics in soft condensed matter.

We outline a new kinetic theory for positrons in soft matter, which blends together cross sections for positrons scattering from single molecules, with the structure function of the medium as a whole. Numerical results are presented for positrons in liquid argon, where negative differential conductivity arises from both positron formation and the structure of the medium.

Periodic electron structures in gases: a fluid model of the "window" phenomenon.

Periodic electron spatial structures in gases occur within a window of voltages and pressures. Recent accurate solutions of Boltzmann's equation portray this effect, but offer little physical insight into the causes of windowing. Here we show for the first time how such insight can be obtained using the fluid model established by Robson, White, and Petrović [Rev.

DNA double helices recognize mutual sequence homology in a protein free environment.

The structure and biological function of the DNA double helix are based on interactions recognizing sequence complementarity between two single strands of DNA. A single DNA strand can also recognize the double helix sequence by binding in its groove and forming a triplex. We now find that sequence recognition occurs between intact DNA duplexes without any single-stranded elements as well.

Magnetic field effects on spatial relaxation of swarm particles in the idealized steady-state Townsend experiment.

The effect of a magnetic field at right angles to an electric field on spatial relaxation of a swarm of charged particles emitted by a plane source into a gas-the idealized steady-state Townsend experiment-is examined. The Boltzmann equation is solved using an adaptation of the "two-temperature" moment method, involving a Burnett function representation of the velocity distribution function, a technique which is valid for charged particles of arbitrary mass and is intrinsically of a "multiterm" nature. Results are presented for electrons in model and real gases, and are benchmarked against an exact analytical solution of the Boltzmann equation for a particular collision model.

Analytically solvable model in fractional kinetic theory.

In this article we give a general prescription for incorporating memory effects in phase space kinetic equation, and consider in particular the generalized "fractional" relaxation time model equation. We solve this for small-signal charge carriers undergoing scattering, trapping, and detrapping in a time-of-flight experimental arrangement in two ways: (i) approximately via the Chapman-Enskog scheme for the weak gradient, hydrodynamic regime, from which the fractional form of Fick's law and diffusion equation follow; and (ii) exactly, without any limitations on gradients. The latter yields complete and exact expressions in terms of generalized Mittag-Lefler functions for experimentally observable quantities.

Multiterm spherical tensor representation of Boltzmann's equation for a nonhydrodynamic weakly ionized plasma.

The Boltzmann equation corresponding to a general "multiterm" representation of the phase space distribution function f(r,c,t) for charged particles in a gas in an electric field was reformulated entirely in terms of spherical tensors f(l)(m) some time ago, and numerous applications, including extension to time varying and crossed electric and magnetic fields, have followed. However, these applications have, by and large, been limited to the hydrodynamic conditions that prevail in swarm experiments and the full potential of the tensor formalism has thus never been realized. This paper resumes the discussion in the context of the more general nonhydrodynamic situation.

Nonconservative charged-particle swarms in ac electric fields.

A time-dependent multi-term technique has been developed and employed to solve the space- and time-dependent Boltzmann equation for charged-particle swarms in ac electric fields. This technique allows for the accurate calculation of both the full set of transport coefficients and the phase-space distribution function. This technique avoids restrictions on the field amplitude and frequency and/or the charged-particle to neutral molecule mass ratio traditionally associated with many contemporary investigations.

Charged-particle transport in gases in electric and magnetic fields crossed at arbitrary angles: Multiterm solution of Boltzmann's equation.

A multiterm solution of the Boltzmann equation has been developed and used to calculate transport coefficients of charged-particle swarms in gases under the influence of electric and magnetic fields crossed at arbitrary angles psi. The hierarchy resulting from a spherical harmonic decomposition of the Boltzmann equation in the hydrodynamic regime [Ness, Phys. Rev.

Dispersion of meteor trails in the geomagnetic field.

A meteor trail is modeled by a long column of weakly ionized plasma, whose dispersion is controlled by the geomagnetic field and the requirement to maintain effective space charge neutrality. First we consider scattering of a radar signal from an underdense trail and derive an expression for the amplitude of the backscattered signal as a function of time. Then, starting from the basic momentum balance equations for electrons and ions in a partially ionized plasma, we require divergences of ion and electron fluxes to be equal, plus assume equality of the flux components along the magnetic field direction.

Diffusion cooling in a magnetic field.

Diffusion cooling of electrons in a weakly ionized plasma in the presence of a magnetic field is studied using the balance equations of momentum transfer theory, well known in "swarm" or test particle analysis. It is shown that for a cylindrical, axially symmetric system, the electron temperature profile can be "hollow" (i.e.