Kinetic theory of instability in the interaction of an electron beam and plasma with an arbitrary anisotropic electron velocity distribution function

Based on the kinetic approach, this work investigates the stability of the system consisting of a fast electron beam and a dense plasma at an arbitrary (anisotropic) electron velocity distribution function. It is shown that during the interaction of a fast electron beam with a cold plasma, both the conditions for losing stability and the increment do not depend on the form of the electron distribution function (EDF) of a plasma and are determined only by the ratio of the electron beam energy to the mean energy in a plasma. With an increase in the mean electron energy in the plasma, it becomes necessary to take into account the moments of the EDF following for energy moment. It was found that the plasma anisotropy has a significant effect on both the stability loss conditions and the increment. The physical reason for this effect is the shift in the plasma frequency due to the Doppler effect caused by the plasma anisotropy in the coordinate system moving along with the beam. Other findings include a region of anomalous dispersion of the electron beam - plasma system and regions of negative group velocity of perturbations in such system. Physical interpretations are proposed for all the observed effects.

Beam-Plasma Stabilizer for the New Type of Nuclear Power Energy Systems

In this paper the electrokinetic characteristics of helium low-voltage beam discharge plasma in operating conditions of a three-electrode device with a hot cathode are studied. A method and a device are proposed to ensure effective voltage stabilization in a range up to 110 V by controlling the electron velocity distribution function using the plasma channel external boundaries.

Assessment of shutdown dose rates in the ITER Collective Thomson Scattering system and in equatorial port plug 12

The ITER Collective Thomson Scattering (CTS) system will be the main diagnostic responsible for measuring the velocity distribution function of fusion-born alpha particles in the plasma. As the CTS diagnostic is integrated in the equatorial port plug 12 (drawer 3), with direct apertures to the port interspace where maintenance hands-on operation will be carried out, it is essential to assess the shutdown dose rates (SDDR) in these maintenance areas. In this work, the D1S-UNED3.1.4 Monte-Carlo transport code, based on the implementation of the direct-one-step methodology in MCNP5 v1.60, was used to estimate the dose rate level 12 days (106 s) after shutdown in the port interspace. The results show that the CTS system does not contribute significantly to the SDDR in the area where hands-on maintenance is foreseen with contribution to dose rates less than 1 µSv/h. This is consistent with previous estimates, although with the most recent model of the CTS design there is a slight increase of the SDDR values. This deviation can be attributed to design changes and improved shielding modelling and/or most importantly, to statistical fluctuations of the D1S simulations. From a neutronics point of view, the increase in the SDDR falls within the range of the statistical fluctuations, and the design is still compliant with the radiation safety ALARA principle aiming at minimizing radiation doses, and there is no requirement for further design optimizations.

Kinetic simulations of collision-less plasmas in open magnetic geometries†

Laboratory plasmas in open magnetic geometries can be found in many different applications such as (1) Scrape-Of-Layer (SOL) and divertor regions in toroidal confinement fusion devices , (2) linear divertor simulators, (3) plasma-based thrusters and (4) magnetic mirrors. A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along flux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic Particle-In-Cell (PIC) simulations can be applied but at the expense of large computational effort. A common way to resolve this is to use a hybrid approach: kinetic ions and fluid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (1) the effect of non-uniform magnetic fields, (2) finite fully-absorbing boundaries for the particles and (3) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. Results show that the effect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric field is calculated and is shown to modify the ion velocity distribution function in manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, inclusion of a Monte-Carlo based Fokker-Planck collision operator is discussed in the context of future work.

A fast convergence fourth-order Vlasov model for Hall thruster ionization oscillation analyses

A 1D1V hybrid Vlasov-fluid model was developed for this study to elucidate ionization oscillations of Hall thrusters (HTs). The Vlasov equation for ions velocity distribution function (IVDF) with ionization source term is solved using a constrained interpolation profile conservative semi-Lagrangian (CIP-CSL) method. The fourth-order weighted essentially non-oscillatory (4th WENO) limiter is applied to the first derivative term to minimize numerical oscillation in the discharge oscillation analyses. The fourth-order spatial accuracy is verified through a 1D scalar test case. Nonoscillatory and high-resolution features of the Vlasov model are confirmed by simulating the test cases of the Vlasov–Poisson (VP) system and by comparing the results with a particle-in-cell (PIC) method. A 1D1V Hall thruster simulation is performed through the hybrid Vlasov-fluid model. The ionization oscillation is analysed. The macroscopic plasma properties are compared with those obtained from a hybrid PIC method. The comparison indicates that the hybrid Vlasov-fluid model yields noiseless results and that the steady-state waveform is calculable in a short time period.

Bayesian inference of ion velocity distribution function from laser-induced fluorescence spectra

The velocity distribution function is a statistical description that connects particle kinetics and macroscopic parameters in many-body systems. Laser-induced fluorescence (LIF) spectroscopy is utilized to measure the local velocity distribution function in spatially inhomogeneous plasmas. However, the analytic form of such a function for the system of interest is not always clear under the intricate factors in non-equilibrium states. Here, we propose a novel approach to select the valid form of the velocity distribution function based on Bayesian statistics. We formulate the Bayesian inference of ion velocity distribution function and apply it to LIF spectra locally observed at several positions in a linear magnetized plasma. We demonstrate evaluating the spatial inhomogeneity by verifying each analytic form of the local velocity distribution function. Our approach is widely applicable to experimentally establish the velocity distribution function in plasmas and fluids, including gases and liquids.

Development of a Plasma Chemistry Model for Helicon Plasma Thruster analysis

The present work is part of a wider project aimed at improving the description of the plasma dynamics during the production phase of a Helicon Plasma Thruster. In particular, the work was focused on the development of a chemical model for Argon- and Xenon-based plasma. The developed model consists of a collisional radiative model suitable to describe the dynamics of the 1s and 2p excited levels. The model is meant to be complementary to 3D-VIRTUS, a numerical tool which enforces a fluid description of plasma, developed by the University of Padova to analyse helicon discharges. Once identified, the significant reactions for both propellants, the reaction rate coefficients, have been integrated exploiting cross sections from literature and assuming a Maxwellian velocity distribution function for all the species. These coefficients have been validated against experimental measurements of an Argon Inductively Coupled Plasma and compared with a well-established code. For Argon, the selected reactions have been reduced through a proposed lumping methodology. In this way, it was possible to reduce the number of equations of the system to solve, and implement them into 3D-VIRTUS. A validation against an experimental case taken from literature was performed, showing good agreement of the results. Regarding the Xenon model, only a verification has been performed against the results of another collisional-radiative model in literature. Finally, a predictive analysis of the propulsive performances of a Helicon Plasma Thruster for both Argon and Xenon is presented.

COMPUTER CALCULATION OF PROBABILITY FOR BINARY COLLISIONS OF ELECTRONS WITH IONS AND MOLECULES

Computer calculation of rate coefficient for binary collision i <σix> as a function of temperature is presented, and the Maxwell electron velocity distribution function is chosen. The finite elements of the fifth order made it possible to significantly speed up the process of calculation i <σix>. The result of the approximation is a smooth function and the values of this function, its first and second derivatives, have no jumps at the mesh nodes and the accuracy of calculation is within the limits of statistical errors for the source data. These advantages and the results will be used in future tasks.