G J M Hagelaar

Model of an inductively coupled negative ion source: II. Application to an ITER type source

The injection of energetic neutral deuterium atoms will be one of the major heating methods of the ITER plasma. The 1 MeV, 16.5 MW neutral atom beam will be obtained by acceleration and collisional neutralization of negative ions extracted from an inductively coupled low-temperature plasma source. This negative ion source is composed of driver volumes where the RF (radio-frequency) power is inductively coupled to the plasma electrons, an expansion chamber including a magnetic filter, and the extraction grids. In this paper we present the first results of a 2D fluid model of a single-driver prototype of the source, for an H2 plasma under realistic ITER-relevant conditions. We discuss the general plasma properties: plasma density, electron and neutral particle temperatures, ion composition (H+, , ), the dissociation degree of H2 and the effect of the magnetic filter, in a large range of input powers (10–80 kW) and source pressures (0.2–0.8 Pa). Negative ions are not described self-consistently in this first approach. The results show a decrease in the gas density when the plasma is turned on, due to gas heating and to the neutral gas depletion induced by ionization. The low gas density leads to a high electron temperature in the driver, and to the saturation of the plasma density growth with power for pressures below 0.3–0.4 Pa. The H2 temperature is in the 0.1 eV range while the H temperature is much higher (up to 1 eV) because hydrogen atoms are generated at high energies by the dissociation of H2 or ion recombination at the wall surface. The simulation results are globally consistent with recent experiments on the negative ion source developed at IPP Garching. Because of the large Hall parameter in the magnetic filter, electron transport across the filter is complex and the ability of a 2D fluid model to grasp this complexity is discussed.

Model of an inductively coupled negative ion source: I. General model description

The experimental fusion reactor ITER will be heated by injection of a fast neutral beam generated by acceleration and neutralization of negative ions. The negative ion source used for this purpose, developed by the IPP Garching, consists of driver volumes where radio-frequency (RF) power is inductively coupled to the plasma electrons and an expansion chamber containing a magnetic filter. This paper documents the physical and numerical principles of a comprehensive fluid model of a single-driver prototype of this source. The model gives a qualitative but self-consistent two-dimensional description of the source, including the neutral gas flow, plasma chemistry, inductive RF coupling in the source driver and plasma transport through the magnetic filter. The different particle species are described by separate continuity, momentum and energy equations, including magnetic fields, inertia and viscosity, with boundary conditions accounting for surface processes. The electrostatic coupling between electrons and ions is described by the Poisson equation using a semi-implicit numerical method which modifies the sheath thickness but yields the correct sheath voltage. Steady-state results are shown for simple configurations to illustrate the influence of the neutral gas kinetics, RF coupling, and magnetic field on the plasma properties. Results for more realistic conditions are presented in a companion paper.

Physics of a magnetic barrier in low-temperature bounded plasmas: insight from particle-in-cell simulations

The use of magnetic fields is quite common in low-pressure, low-temperature, gas-discharge devices for industrial applications. However, transport in such devices is still not very well clarified, mainly due to the presence of walls playing a crucial role and to the variety of configurations studied. The latter often obstruct the underlying basic physical phenomena and make the different studies valid only for very specific configurations. This work presents a numerical study of particle transport in low-pressure (0.3Pa) plasmas across a localized transverse magnetic field (magnetic barrier) by means of the 2D3V particle-in-cell with Monte Carlo collisions method. The problem is treated as generally as possible while trying to reveal the basic physics, using very simplified chemistry and considering a simple rectangular configuration. The conditions chosen for the magnetic field are common to many applications—magnetized electrons and almost unmagnetized ions. Two basic configurations with different magnetic field directions are analyzed in detail: magnetic field perpendicular to the simulation plane and along the simulation plane. An extensive parametric study is carried out in order to obtain the main trends and scaling laws for particle transport with respect to different parameters: plasma density, magnetic barrier size and magnetic field magnitude. The total current of electrons crossing the barrier is found to scale linearly with the plasma density, which extends the validity of the obtained results to a wide range of plasma density values. (Some figures may appear in colour only in the online journal)

Empirical electron cross-field mobility in a Hall effect thruster

Electron transport across the magnetic field in Hall effect thrusters is still an open question. Models have so far assumed 1∕B2 or 1∕B scaling laws for the “anomalous” electron mobility, adjusted to reproduce the integrated performance parameters of the thruster. We show that models based on such mobility laws predict very different ion velocity distribution functions (IVDF) than measured by laser induced fluorescence (LIF). A fixed spatial mobility profile, obtained by analysis of improved LIF measurements, leads to much better model predictions of thruster performance and IVDF than 1∕B2 or 1∕B mobility laws for discharge voltages in the 500–700V range.

Modelling of a dipolar microwave plasma sustained by electron cyclotron resonance

Multi-dipolar plasmas are sustained in large-volume chambers by a network of antennas located at the wall. Each antenna consists of a permanent magnet, trapping electrons in an axisymmetric dipole field, and a microwave applicator, heating the trapped electrons by cyclotron resonance (ECR). This paper presents a two-dimensional self-consistent model of a plasma sustained by one such antenna. The microwave fields and power absorption are calculated from the Maxwell equations coupled with a local electron momentum equation by an adaptation of the finite difference time domain method. The plasma is described by fluid equations for magnetized electrons and inertial ions, where quasi-neutrality is imposed through a semi-implicit numerical method based on Poissons equation, which also yields the sheath potentials. Steady-state model results for argon show that below the critical plasma density (7.4×1016 m−3) the microwave power is absorbed in a narrow region all along the ECR surface around the end of the antenna; beyond this density the main absorption occurs near the plasma edge. Although the electron temperature varies considerably across the magnetic field lines, the plasma potential is nearly uniform all around the antenna and is controlled by the maximum electron temperature.

Chemical composition of SF6 low-pressure plasma in magnetic field

The chemical composition of a low-pressure SF6 plasma in a homogeneous magnetic field is studied using a one-dimensional fluid model. This model takes into account the magnetization of electrons and light negative ions F−. The influence of different parameters such as gas pressure, heating power and magnetic field strength is studied within a parameter range of interest for negative ion sources. The scheme of plasma chemical reactions is analysed in order to identify the main reactions responsible for the generation and decay of plasma species. This sensitivity analysis shows that the scheme of reactions can be significantly simplified.

Physics and modeling of an end-Hall (gridless) ion source

In an end-Hall source, an ion beam is extracted from a magnetized plasma and accelerated by the plasma electric field without grids. The principle of end-Hall sources is similar to that of Hall effect thrusters (or closed-drift thrusters), but their design is optimized for processing applications (ion beam assisted deposition or substrate cleaning) rather than propulsion. The beam divergence is larger in end-Hall ion sources, and these sources can operate at low ion energies. Although end-Hall sources are commonly used in the surface processing industry, no detailed modeling of these sources is available, and their operation is quite empirical. In this paper, a self-consistent, two-dimensional, quasineutral model of an end-Hall ion source is developed and used in order to improve the understanding of the basic physics of these plasma sources and to quantify the parameters controlling the properties of the extracted ion beam.

Method to obtain the electric field and the ionization frequency from laser induced fluorescence measurements

Laser induced fluorescence (LIF) diagnostic provides a means to measure an ion velocity distribution function (VDF) by Doppler effect with excellent resolution in velocity. This diagnostic has a wide range of applications in low pressure plasma physics and has been used for the past twenty years to study many plasma sources. Most commonly, authors only deduce from the LIF measurements mean ion velocities or accelerating potentials from these mean velocities. However, LIF provides at each measurement position a full VDF which contains much more information than the average velocity. We propose in this paper a new method capable of evaluating the spatial profiles of electric field and ionization frequency. This method consists of establishing a relationship between these quantities and the moments of the measured VDF. We first validate the method by means of numerical simulations and then apply it to two different plasmas: an ICP argon reactor and a Hall effect thruster.

Modeling of breakdown during the post-arc phase of a vacuum circuit breaker

After a high-current interruption in a vacuum circuit breaker (VCB), the electrode gap is filled with a high density copper vapor plasma in a large copper vapor density (~1022 m−3). The copper vapor density is sustained by electrode evaporation. During the post-arc phase, a rapidly increasing voltage is applied to the gap, and a sheath forms and expands, expelling the plasma from the gap when circuit breaking is successful. There is, however, a risk of breakdown during that phase, leading to the failure of the VCB. Preventing breakdown during the post-arc phase is an important issue for the improvement of VCB reliability. In this paper, we analyze the risk of Townsend breakdown in the high copper vapor density during the post-arc phase using a numerical model that takes into account secondary electron emission, volume ionization, and plasma and neutral transport, for given electrode temperatures. The simulations show that fast neutrals created in the cathode sheath by charge exchange collisions with ions generate a very large secondary electron emission current that can lead to Townsend breakdown. The results also show that the risk of failure of the VCB due to Townsend breakdown strongly depends on the electrode temperatures (which govern the copper vapor density) and becomes important for temperatures greater than 2100 K, which can be reached in vacuum arcs. The simulations also predict that a hotter anode tends to increase the risk of Townsend breakdown.

Fluid description of non-local electron kinetics in inductively coupled plasmas

Due to thermal motion, the electrons in inductively coupled plasmas (ICPs) show a non-local response to the electromagnetic field, which gives rise to the anomalous skin effect and stochastic heating. In a recent letter (Hagelaar G J M 2008 Phys. Rev. Lett. 100 025001) we have shown that this can be approximately described through a fluid equation for electron momentum including a viscosity term with an effective viscosity coefficient. The present paper provides a more extensive presentation and discussion of our effective viscosity fluid approach. We present analytical solutions of the improved fluid equations coupled to the Maxwell equations for a semi-infinite plasma, showing scaling laws for the non-monotonic spatial structure of the anomalous skin and a condition for the appearance of local negative power absorption. We also present a numerical comparison with a particle-in-cell model, including non-linear effects due to the ponderomotive force. Consistent results are obtained for a wide range of conditions. The proposed equations have a simple form and could be of practical use for ICP modeling.