Kinetic properties of particle-in-cell simulations compromised by Monte Carlo collisions

he particle-in-cell method with Monte Carlo collisions is frequently used when a detailed kinetic simulation of a weakly collisional plasma is required. In such cases, one usually desires, inter alia, an accurate calculation of the particle distribution functions in velocity space. However, velocity space diffusion affects most, perhaps all, kinetic simulations to some degree, leading to numerical thermalization (i.e., relaxation of the velocity distribution toward a Maxwellian), and consequently distortion of the true velocity distribution functions, among other undesirable effects. The rate of such thermalization can be considered a figure of merit for kinetic simulations. This article shows that, contrary to previous assumption, the addition of Monte Carlo collisions to a one-dimensional particle-in-cell simulation seriously degrades certain properties of the simulation. In particular, the thermalization time can be reduced by as much as three orders of magnitude. This effect makes obtaining strictly converged simulation results difficult in many cases of practical interest

Limiting stable currents in bounded electron and ion streams

The classical static analysis of the infinite planar diode has been extended to include the effects of finite transverse beam size. Simple expressions have been found for the increase in maximum stable current density over that of an infinite stream for finite cylindrical and strip streams flowing between plates of infinite diodes. The results are also given in terms of stream perveance. The effect of a nonuniform distribution of current across the stream is shown to be relatively small. Experimental values of maximum stable current agree with those obtained from the analysis. A further extension of the static analysis has been made to include the effects of additional conducting plane boundaries parallel to the stream motion. For length-to-width ratios L/D less than 0.25 the tube is adequately described by the results for the infinite planar diode and for L/D greater than 4, the infinitely-long drift tube theory suffices. At intermediate values of L/D, the maximum amount of current that can be stably passed through the tube is greater than that predicted by either asymptotic theory

Kinetic-Ion Simulations Addressing Whether Ion Trapping Inflates Stimulated Brillouin Backscattering Reflectivities

An investigation of the possible inflation of stimulated Brillouin backscattering (SBS) due to ion kinetic effects is presented using electromagnetic particle simulations and integrations of three-wave coupled-mode equations with linear and nonlinear models of the nonlinear ion physics. Electrostatic simulations of linear ion Landau damping in an ion acoustic wave, nonlinear reduction of damping due to ion trapping, and nonlinear frequency shifts due to ion trapping establish a baseline for modeling the electromagnetic SBS simulations. Systematic scans of the laser intensity have been undertaken with both one-dimensional particle simulations and coupled-mode-equations integrations, and two values of the electron-to-ion temperature ratio (to vary the linear ion Landau damping) are considered. Three of the four intensity scans have evidence of SBS inflation as determined by observing more reflectivity in the particle simulations than in the corresponding three-wave mode-coupling integrations with a linear ion-wave model, and the particle simulations show evidence of ion trapping.Comment: 56 pages, 20 figure

Kinetic Vlasov Simulations of collisionless magnetic Reconnection

A fully kinetic Vlasov simulation of the Geospace Environment Modeling (GEM) Magnetic Reconnection Challenge is presented. Good agreement is found with previous kinetic simulations using particle in cell (PIC) codes, confirming both the PIC and the Vlasov code. In the latter the complete distribution functions $f_k$ ($k=i,e$) are discretised on a numerical grid in phase space. In contrast to PIC simulations, the Vlasov code does not suffer from numerical noise and allows a more detailed investigation of the distribution functions. The role of the different contributions of Ohm's law are compared by calculating each of the terms from the moments of the $f_k$. The important role of the off--diagonal elements of the electron pressure tensor could be confirmed. The inductive electric field at the X--Line is found to be dominated by the non--gyrotropic electron pressure, while the bulk electron inertia is of minor importance. Detailed analysis of the electron distribution function within the diffusion region reveals the kinetic origin of the non--gyrotropic terms

The combined use of selective deuteration and double resonance experiments in assigning the 1H resonances of valine and tyrosine residues of dihydrofolate reductase

AbstractSelective deuteration is a general solution to the resolution problem which limits the application of double resonance experiments to the assignment of the 1H NMR spectra of proteins. Spin-decoupling and NOE experiments have been carried out on Lactobacillus casei dihydrofolate reductase and on selectively deuterated derivatives of the enzyme containing either [γ-2H6]Val or (α,δ2,ϵ1-2H3]His, [α,δ1,δ2,ϵ1,ϵ2,ζ-2H6]Phe, [α,δ1,ϵ3,ζ2,ζ3,η2-2H6]Trp and [α,ϵ1,ϵ2-2H3]Tyr. When combined with ring-current shift calculations based on the crystal structure of the enzyme, these experiments allow us to assign 1H resonances of Val 61, Val 115, Tyr 46 and Tyr 68

A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system

The stability features of steady states of the spherically symmetric Einstein-Vlasov system are investigated numerically. We find support for the conjecture by Zeldovich and Novikov that the binding energy maximum along a steady state sequence signals the onset of instability, a conjecture which we extend to and confirm for non-isotropic states. The sign of the binding energy of a solution turns out to be relevant for its time evolution in general. We relate the stability properties to the question of universality in critical collapse and find that for Vlasov matter universality does not seem to hold.Comment: 29 pages, 10 figure

On particle acceleration and trapping by Poynting flux dominated flows

Using particle-in-cell (PIC) simulations, we study the evolution of a strongly magnetized plasma slab propagating into a finite density ambient medium. Like previous work, we find that the slab breaks into discrete magnetic pulses. The subsequent evolution is consistent with diamagnetic relativistic pulse acceleration of \cite{liangetal2003}. Unlike previous work, we use the actual electron to proton mass ratio and focus on understanding trapping vs. transmission of the ambient plasma by the pulses and on the particle acceleration spectra. We find that the accelerated electron distribution internal to the slab develops a double-power law. We predict that emission from reflected/trapped external electrons will peak after that of the internal electrons. We also find that the thin discrete pulses trap ambient electrons but allow protons to pass through, resulting in less drag on the pulse than in the case of trapping of both species. Poynting flux dominated scenarios have been proposed as the driver of relativistic outflows and particle acceleration in the most powerful astrophysical jets.Comment: 25 pages, Accepted by Plasma Physics and Controlled Fusio

A comparison of weak-turbulence and PIC simulations of weak electron-beam plasma interaction

Quasilinear theory has long been used to treat the problem of a weak electron beam interacting with plasma and generating Langmuir waves. Its extension to weak-turbulence theory treats resonant interactions of these Langmuir waves with other plasma wave modes, in particular ion-sound waves. These are strongly damped in plasma of equal ion and electron temperatures, as sometimes seen in, for example, the solar corona and wind. Weak turbulence theory is derived in the weak damping limit, with a term describing ion-sound wave damping then added. In this paper we use the EPOCH particle-in-cell code to numerically test weak turbulence theory for a range of electron-ion temperature ratios. We find that in the cold ion limit the results agree well, but increasing ion temperature the three-wave resonance becomes broadened in proportion to the ion-sound wave damping rate. This may be important in, for example, the theory of solar radio bursts, where the spectrum of Langmuir waves is critical. Additionally we establish lower limits on the number of simulation particles needed to accurately reproduce the electron and wave distributions in their saturated states, and to reproduce their intermediate states and time evolution.Comment: Accepted by PO

Optimising selective deuteration of proteins for 2D 1H NMR detection and assignment studies Application to the Phe residues of Lactobacillus casei dihydrofolate reductase

AbstractA selectively deuterated dihydrofolate reductase from L. casei has been prepared containing partially deuterated aromatic amino acids. This provides simplified 2D NMR spectra and allows signals from all 8 Phe residues to be identified. The pattern of deuteration is such that (i) the only cross-peaks detected in the aromatic region of the 2D COSY spectrum are those between the Phe 2′,6′ and 3′,5′ protons and (ii) chemical shift degeneracy in the aromatic region is removed thus allowing unambiguous assignment of cross-peaks in 2D NOESY spectra required for specific assignment purposes