Collisionless ion collection by a sphere in a weakly magnetized plasma

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2007.Includes bibliographical references (p. 133-135).The interaction between a probe and a plasma has been studied since the 1920s and the pioneering work of Mott-Smith and Langmuir [1], and is still today an active topic of experimental and theoretical research. Indeed an understanding of the current collection process by an electrode is relevant to diverse matters such as Langmuir and Mach-probes calibrations, dusty plasma physics, or spacecraft charging. Recent simulations relying on the ad hoc designed code SCEPTIC have fully addressed the collisionless and unmagnetized problem for a drifting collector idealized as a sphere. SCEPTIC is a 2d/3v hybrid Particle In Cell (PIC) code, in which the ion motion is fully resolved, while the electrons are treated as a Boltzmann distributed fluid [2, 3]. In the present work we tackle the transition between the unmagnetized and the weakly magnetized regime of ion collection by a spherical probe (The mean ion Larmor radius rL > rp) in a collisionless plasma (The ion mean free path Am,fp > rp). When the sphere is at space potential, we demonstrate that the ion current dependence on the background magnetic field B is linear for low B, and provide analytical expressions for this dependence. When the probe potential can not be neglected, the problem shows two distinct scale lengths: A collisionless layer of a few rp close to the probe, followed by a collisional presheath of a few AX,fp. The chosen approach is to resolve the collisionless scale-length with SCEPTIC, while using appropriate outer boundary conditions on the potential and ion distribution function to connect with the unresolved collisional presheath. We present results of our numerical simulations for a wide range of plasma parameters of direct relevance to Langmuir and Mach-probes.by Leonardo Patacchini.S.M

Forces on a spherical conducting particle in E x B fields

The forces acting on a spherical conducting particle in a transversely flowing magnetized plasma are calculated in the entire range of magnetization and Debye length, using the particle code SCEPTIC3D (Patacchini and Hutchinson 2010 Plasma Phys. Control. Fusion 52 035005, 2011 Plasma Phys. Control. Fusion 53 025005). In short Debye length (i.e. high density) plasmas, both the ion-drag and Lorentz force arising from currents circulating inside the dust show strong components antiparallel to the convective electric field, suggesting that a free dust particle should gyrate faster than what predicted by its Larmor frequency. In intermediate to large Debye length conditions, by a downstream depletion effect already reported in unmagnetized strongly collisional regimes, the ion-drag in the direction of transverse flow can become negative. The internal Lorentz force, however, remains in the flow direction, and large enough in magnitude so that no spontaneous dust motion should occur.National Science Foundation (U.S.)United States. Dept. of Energy (grant DE-FG02-06ER54891

Collisionless ion collection by non-emitting spherical bodies in E x B fields

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 211-216).The three-dimensional interaction of a magnetized, collisionless flowing plasma with a non-emitting conducting sphere is solved in the entire range of physically allowed parameters, in the ion-collecting regime. This can be considered as the "spherical Mach probe" problem, establishing how the ion flux to the surface varies with orientation and external velocity; the study is however of broader interest, as the sphere can also be seen as a dust particle or any ionospheric body. The core tool developed for this study is the fully parallelized (particle + field solver) Particle-In-Cell code SCEPTIC3D, three-dimensional evolution of SCEPTIC, accounting for the full ion distribution function and Boltzmann electrons. Investigations are first carried out in the quasineutral limit. Results include a report of ion current dependence on the external plasma parameters, as well as a theoretical calibration for transverse Mach probes with four electrodes oriented at 450 to the magnetic field in a plane of flow and magnetic field, valid for arbitrary temperature and ion magnetization. The analysis is preceded by an independent semi-analytic treatment of strongly magnetized ion collection by oblique surfaces, successfully validating SCEPTIC3D's behaviour.(cont.) The finite shielding length regime is more complex, and an important transition in plasma structure occurs when the Debye length goes over the average ion Larmor radius. Studies of ion collection show that the ion current can exceed the (unmagnetized) OML limit at weak magnetization, and the Mach probe calibration method proposed in the context of quasineutral plasmas holds up to Debye lengths equal to about 10% of the probe radius. A further analysis consists in calculating the force exerted by the flow on spherical dust. In short Debye length plasmas a strong drag component antiparallel to the convective electric field forms, causing the dust to spin faster than what predicted by its Larmor frequency. At intermediate and large Debye length the ion-drag in the direction of transverse flow is found to reverse in subsonic conditions, but the internal Laplace force appears to be positive, and larger in magnitude than the negative ion-drag.by Leonardo Patacchini.Ph.D

Spherical probes at ion saturation in E × B fields

The ion saturation current to a spherical probe in the entire range of ion magnetization is computed with SCEPTIC3D, a newthree-dimensional version of the kinetic code SCEPTIC designed to study transverse plasma flows. Results are compared with prior two-dimensional calculations valid in the magneticfree regime (Hutchinson 2002 Plasma Phys. Control. Fusion 44 1953), and with recent semi-analytic solutions to the strongly magnetized transverse Mach probe problem (Patacchini and Hutchinson 2009 Phys. Rev. E 80 036403). At intermediate magnetization (ion Larmor radius close to the probe radius) the plasma density profiles show a complex three-dimensional structure that SCEPTIC3D can fully resolve, and, contrary to intuition, the ion current peaks provided the ion temperature is low enough. Our results are conveniently condensed in a single factor M[subscript c], function of ion temperature and magnetic field only, providing the theoretical calibration for a transverse Mach probe with four electrodes placed at 45◦ to the magnetic field in a plane of flow and magnetic field

Continuum-plasma solution surrounding nonemitting spherical bodies

The classical problem of the interaction of a nonemitting spherical body with a zero mean-free-path continuum plasma is solved numerically in the full range of physically allowed free parameters (electron Debye length to body radius ratio, ion to electron temperature ratio, and body bias), and analytically in rigorously defined asymptotic regimes (weak and strong bias, weak and strong shielding, thin and thick sheath). Results include current-voltage characteristics as well as floating potential and capacitance, for both continuum and collisionless electrons. Our numerical computations show that for most combinations of physical parameters, there exists a closest asymptotic regime whose analytic solutions are accurate to 15% or better

Kinetic solution to the Mach probe problem in transversely flowing strongly magnetized plasmas

The kinetic equation governing a strongly magnetized transverse plasma flow past a convex ion-collecting object is solved numerically for arbitrary ion to electron temperature ratio τ. The approximation of isothermal ions adopted in a recent fluid treatment of the same plasma model [I. H. Hutchinson, Phys. Rev. Lett. 101, 035004 (2008)] is shown to have no more than a small quantitative effect on the solution. In particular, the ion flux density to an elementary portion of the object still only depends on the local surface orientation. We rigorously show that the solution can be condensed in a single “calibration factor” Mc, function of τ only, enabling Mach probe measurements of parallel and perpendicular flows by probing flux ratios at two different angles in the plane of flow and magnetic field.National Science Foundation / Department of Energ

Flowing plasmas and absorbing objects: analytic and numerical solutions culminating 80 years of ion-collection theory

Recent computational and theoretical progress in understanding and calculating ion collection by negatively charged absorbing objects in a flowing plasma is outlined. The results are placed in the context of key theoretical achievements of prior research. Despite the topic's long history, and past profound insights, fully rigorous quantitative solution of the non-linear, multidimensional, self-consistent, kinetic-theory problem has not until recently been feasible. Now we are able to establish the adequacy or inadequacy of approximate treatments, and provide critical quantitative results. In the process, some qualitative surprises have also emerged

Fully self-consistent 3D modeling of spherical Mach-probes in ExB fields

We carry out 3D particle-in-cell simulations accounting for the full ion distribution function, Boltzmann electrons, and the self-consistent potential profiles in the neighborhood of a sphere in a flowing magnetized plasma. This can be considered as the "spherical Mach-probe" problem, establishing how the ion flux to the surface varies with orientation, and with parallel and perpendicular external velocity. This dependence is required to interpret reliably experimental measurements on several tokamaks. We use our code SCEPTIC3D, a recent evolution of the particle-in-cell code SCEPTIC, which includes arbitrary uniform magnetic field, external velocity magnitude and direction, ion temperature and electron Debye length. We compare our results in the strong-field regime with the analytic model which uses an isothermal fluid approximation, within the quasineutral (infinitesimal Debye length) and small Larmor radius limits. Results show that for strongly magnetized plasmas the assumption of isothermal ions gives accurate flux, but can not be justified as the ion Larmor radius becomes finite. We then proceed with an in-depth analysis of how the widely adopted Mach-probe calibration formulas for infinitesimal Debye length are affected by nonzero Larmor radius effects. Accounting for finite Debye length changes the potential profiles around the sphere. In particular for conducting probes, a dipole-like field oriented parallel to the convective electric field appears, drastically changing the ion flow in the immediate vicinity of the probe, hence the collected flux.National Science Foundation (U.S.) (NSF/DOE Grant No DE-FG-06ER54891