One-dimensional particle simulation of the filamentation instability: Electrostatic field driven by the magnetic pressure gradient force

Two counterpropagating cool and equally dense electron beams are modeled with particle-in-cell simulations. The electron beam filamentation instability is examined in one spatial dimension, which is an approximation for a quasiplanar filament boundary. It is confirmed that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. The electrostatic field reduces the confining force close to the stable equilibrium of each filament and increases it farther away, limiting the peak density. The confining time-averaged total potential permits an overlap of current filaments with an opposite flow direction.

A variational approach to the relaxation of single domain magnetic particles based on Brown's model

Brown's model for the relaxation of the magnetization of a single domain ferromagnetic particle is considered. This model results in the Fokker-Planck equation of the process. The solution of this equation in the cases of most interest is non- trivial. The probability density of orientations of the magnetization in the Fokker-Planck equation can be expanded in terms of an infinite set of eigenfunctions and their corresponding eigenvalues where these obey a Sturm-Liouville type equation. A variational principle is applied to the solution of this equation in the case of an axially symmetric potential. The first (non-zero) eigenvalue, corresponding to the largest time constant, is considered. From this we obtain two new results. Firstly, an approximate minimising trial function is obtained which allows calculation of a rigorous upper bound. Secondly, a new upper bound formula is derived based on the Euler-Lagrange condition. This leads to very accurate calculation of the eigenvalue but also, interestingly, from this, use of the simplest trial function yields an equivalent result to the correlation time of Coffey et at. and the integral relaxation time of Garanin. (C) 2004 Elsevier B.V. All rights reserved.

Rotation of a nanoparticle cloud in an inductively coupled plasma induced by weak static magnetic fields

Hydrocarbon nanoparticles with diameters between 10 and 30 nanometres are created in a low pressure plasma combining capacitive and inductive power coupling. The particles are generated in the capacitive phase of the experiment and stay confined in the plasma in the inductive phase. The presence of these embedded particles induces a rotation of a particle-free region (void) around the symmetry axis of the reactor. The phenomenon is analysed using optical emission spectroscopy both line integrated and spatially resolved via an intensified charge coupled device camera. From these data, electron temperatures and densities are deduced. We find that the rotation of the void is driven by a tangential component of the ion drag force induced by an external static magnetic field. Two modes are observed: a fast rotation of the void in the direction opposite to that of the tangential component and a slow rotation in the same direction. The rotation speed decreases linearly with the size of the particles. In the fast mode the dependence on the applied magnetic field is weak and consequently the rotation speed can serve as a monitor to detect particle sizes in low temperature plasmas.

Proton Probing Measurement of Electric and Magnetic Fields Generated by ns and ps Laser-Matter Interactions

The use of laser-accelerated protons as a particle probe for the detection of electric fields in plasmas has led in recent years to a wealth of novel information regarding the ultrafast plasma dynamics following high intensity laser-matter interactions. The high spatial quality and short duration of these beams have been essential to this purpose. We will discuss some of the most recent results obtained with this diagnostic at the Rutherford Appleton Laboratory (UK) and at LULI - Ecole Polytechnique (France), also applied to conditions of interest to conventional Inertial Confinement Fusion. In particular, the technique has been used to measure electric fields responsible for proton acceleration from solid targets irradiated with ps pulses, magnetic fields formed by ns pulse irradiation of solid targets, and electric fields associated with the ponderomotive channelling of ps laser pulses in under-dense plasmas.

Preparation of magnetic cellulose composites using ionic liquids

Cellulose-magnetite composites have been prepared by suspension and dispersion of magnetite particles in a homogenous ionic liquid solution of cellulose, followed by regeneration into water, enabling the preparation of magnetically responsive films, flocs, fibers, or beads. The materials prepared were ferromagnetic, with a small superparamagnetic response, characteristic of the initial magnetite added. X-ray diffraction data indicated that the magnetite particles were chemically unaltered after encapsulation with an average particle size of approximately 25 nm.

Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties

The properties and characteristics of a recently proposed anisotropic metamaterial based upon layered arrays of tightly coupled pairs of "dogbone" shaped stripe conductors have been explored in detail. It has been found that a metamaterial composed of such stacked layers exhibits artificial magnetism and may support backward wave propagation. The equivalent network models of the constitutive conductor pairs arranged in the periodic array have been devised and applied to the identification of the specific types of resonances, and to the analysis of their contribution into the effective dielectric and magnetic properties of the artificial medium. The proposed "dogbone" configuration of conductor pairs has the advantage of being entirely realizable and assemblable in planar technology. It also appears more prospective than simple cut-wire or metal-plate pairs because the additional geometrical parameters provide an efficient control of separation between the electric and magnetic resonances that, in turn, makes it possible to obtain a fairly broadband left-handed behaviour of the structure at low frequencies.

Fokker-Planck equation for a test-particle weakly coupled to a magnetized plasma

We consider the derivation of a kinetic equation for a charged test particle weakly interacting with an electrostatic plasma in thermal equilibrium, subject to a uniform external magnetic field. The Liouville equation leads to a generalized master equation to second order in the `weak' interaction; a Fokker-Planck-type equation then follows as a `Markovian' approximation. It is shown that such an equation does not preserve the positivity of the distribution function f(x,v;t). By applying techniques developed in the theory of open systems, a correct Fokker-Planck equation is derived. Explicit expressions for the diffusion and drift coefficients, depending on the magnetic field, are obtained.

Berry phase for a spin 1/2 particle in a classical fluctuating field

The effect of fluctuations in the classical control parameters on the Berry phase of a spin 1/2 interacting with an adiabatically cyclically varying magnetic field is analyzed. It is explicitly shown that in the adiabatic limit dephasing is due to fluctuations of the dynamical phase.

Temporally and spatially resolved measurements of multi-megagauss magnetic fields in high intensity laser-produced plasmas

We report spatially and temporally resolved measurements of self-generated multi-megagauss magnetic fields produced during ultrahigh intensity laser plasma interactions. Spatially resolved measurements of the magnetic fields show an asymmetry in the distribution of field with respect to the angle of laser incidence. Temporally resolved measurements of the self-generated third harmonic suggest that the strength of the magnetic field is proportional to the square root of laser intensity (i.e., the laser B-field) during the rise of the laser pulse. The experimental results are compared with numerical simulations using a particle-in-cell code which also shows clear asymmetry of the field profile and similar magnetic field growth rates and scalings.

Large quasistatic magnetic fields generated by a relativistically intense laser pulse propagating in a preionized plasma

Two spatially separated toroidal magnetic fields in the megagauss range have been detected with Faraday rotation during and after propagation of a relativistically intense laser pulse through preionized plasmas. Besides a field in the outer region of the plasma oriented as a conventional thermoelectric field, a field with the opposite orientation closely surrounding the propagation axis is observed, in conditions under which relativistic channeling occurs. A 3D particle-in-cell code was used to simulate the interaction under the conditions of the experiment.

TIME-RESOLVED ELECTRON-ENERGY DISTRIBUTION FUNCTION MEASUREMENTS IN A PULSED MAGNETIC MULTIPOLE HYDROGEN DISCHARGE

The time evolution of measured plasma parameters, including the electron energy distribution function (EEDF), in the discharge and post-discharge regime of a pulsed hydrogen magnetic multipole plasma is presented. The time necessary for the plasma to reach equilibrium has been established as 160-mu-s. The present results clarify the mechanisms which initiate the discharge. The decay rates of the charged-particle density and energy in the post-discharge have been measured. These measurements indicate that particle transport to the wall is the dominant loss mechanism for both charged-particle density and energy. The time-resolved EEDF is found to be non-Maxwellian in the discharge and Maxwellian in the late post-discharge.

Particle simulation study of electron heating by counter-streaming ion beams ahead of supernova remnant shocks

The growth and saturation of Buneman-type instabilities is examined with a particle-in-cell (PIC) simulation for parameters that are representative for the foreshock region of fast supernova remnant shocks. A dense ion beam and the electrons correspond to the upstream plasma and a fast ion beam to the shock-reflected ions. The purpose of the 2D simulation is to identify the nonlinear saturation mechanisms, the electron heating and potential secondary instabilities that arise from anisotropic electron heating and result in the growth of magnetic fields. We confirm that the instabilities between both ion beams and the electrons saturate by the formation of phase space holes by the beam-aligned modes. The slower oblique modes accelerate some electrons, but they cannot heat up the electrons significantly before they are trapped by the faster beam-aligned modes. Two circular electron velocity distributions develop, which are centred around the velocity of each ion beam. They develop due to the scattering of the electrons by the electrostatic wave potentials. The growth of magnetic fields is observed, but their amplitude remains low.

Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function f(x, v; t). Adopting an alternative approach, previously introduced for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

Random particle motion in magnetized plasma

A multivariate Fokker-Planck-type kinetic equation modeling a test - panicle weakly interacting with an electrostatic plasma. in the presence of a magnetic field B . is analytically solved in an Ornstein - Uhlenbeck - type approximation. A new set of analytic expressions are obtained for variable moments and panicle density as a function of time. The process is diffusive.

Magnetic instability in a dilute circular rarefaction wave

The growth of magnetic fields in the density gradient of a rarefaction wave has been observed in simulations and in laboratory experiments. The thermal anisotropy of the electrons, which gives rise to the magnetic instability, is maintained by the ambipolar electric field. This simple mechanism could be important for the magnetic field amplification in astrophysical jets or in the interstellar medium ahead of supernova remnant shocks. The acceleration of protons and the generation of a magnetic field by the rarefaction wave, which is fed by an expanding circular plasma cloud, is examined here in form of a 2D particle-in-cell simulation. The core of the plasma cloud is modeled by immobile charges, and the mobile protons form a small ring close to the cloud's surface. The number density of mobile protons is thus less than that of the electrons. The protons of the rarefaction wave are accelerated to 1/10 of the electron thermal speed, and the acceleration results in a thermal anisotropy of the electron distribution in the entire plasma cloud. The instability in the rarefaction wave is outrun by a TM wave, which grows in the dense core distribution, and its magnetic field expands into the rarefaction wave. This expansion drives a secondary TE wave. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4769128]