Kinetic modelling of the jet extraction mechanism in spherical IEC devices
Background and motivation
Inertial Electrostatic Confinement (IEC) devices were originally developed and used for fusion
research purposes . The simplest IEC type of set-up contains a spherical cathode grid, which is cocentrically
placed within in a spherical anode (represented as the vacuum chamber in Fig. 1.)
Figure 1: Scheme of a so-called Farnsworth – Hirsch Fusion Reactor
1.2 Problem statement and Possible Approaches
The cathode, made of stainless steel wires, is negatively charged (typically several kV) while the anode
is grounded. The vacuum chamber contains a highly rarefied neutral gas with a pressure matched to the
electrode distance in order to provide a glow discharge. The produced ions are accelerated by radial
electric fields towards the centre of the sphere where they collide with other ions building a positively
charged ion cloud. This ion cloud itself accelerates electrons towards the centre of the sphere, which
can lead to the creation of a virtual cathode. Due to an effect called micro-channelling the ions are
pushed away from the grid wires such that the effective grid transparency can exceed 95% . An indepth
description of the working principle and the physics of the IEC confinement can be found in [1-
3] and references therein.
Figure 2: IEC in so-called jet mode .
Figure 3: Scheme of grid openings for jet extraction. Outer grid is now the anode, both embedded in vacuum chamber. Blue: plasma within the IEC cathode.
are added according to the extracted plasma mass flow (see Fig. 1). IEC reactors in jet mode would
thus be, in principle, usable for propulsion purposes. In fact, specific impulses of up to 4000s were
estimated in . While such devices have been proposed as space thrusters, arguing that
2 Study Objective
Given that IEC reactors with a steady jet extraction have been experimentally demonstrated, but their parameters have been set without an understanding of the underlying principles, it is very likely that the used configurations are far from optimal. Especially the mechanisms of the jet extraction are not understood. A parametric model is therefore needed, starting with the existing and well described experimental setup and then applying it to different IEC configurations. The understanding of the physical processes of the jet extraction process is crucial to this step. Representative mathematical/physical/numerical modelling needs to be done in order to identify the driving processes on a fundamental level. The main study objective is therefore the modelling and kinetic simulation of this extraction mechanisms and especially the jet particle interactions.
3 Proposed Methodology
IEC related publications superficially describe the IEC jet generation process in a 2-grid IEC set-up to
be based on electrons overcoming the locally decreased potential barrier, which then leads to an
acceleration of ions out of the plasma core. In trying to assess the relevant microscopic processes at the
jet origin it is instructive to perform kinetic particle simulations as it has been done e.g. in [5, 7, 8].
However, care has to be taken with respect to the modelling depth as model assumptions affect the
outcome and, correspondingly, the interpretation of the simulation results. Exemplarily, the grid
openings typically do not obey a symmetric structure, i.e. a rotational-symmetric 2D Particle-In-Cell
code does not reproduce the correct electrostatic field distribution. Also, Particle-In-Cell codes are noncollisional,
i.e. direct Coulomb collisions are ignored. Those interactions between the charged particles
occur on scales smaller than the local Debye length and might become essential for understanding of
the jet extraction, especially since space charging effects influence the Debye length as a measure of
spatial resolution and, therefore, affect the general validity of the governing equations of the Particle-
In-Cell codes. These examples illustrate the importance of kinetic modelling depth as it affects
4 ACT Contributions
The project will be conducted in close cooperation with ACT researchers that will be cooperating
closely with the university’s research group in the achievement of the respective milestones.
 W. C. Elmore, J. L. Tuck, K. M. Watson, “On the Inertial-Electrostatic Confinement of a Plasma"
Physics of Fluids 2, 239 (1959); doi:10.1063/1.1705917