E. Faudot

Self consistent radio-frequency wave propagation and peripheral direct current plasma biasing: Simplified three dimensional non-linear treatment in the “wide sheath” asymptotic regime

A minimal two-field fluid approach is followed to describe the radio-frequency (RF) wave propagation in the bounded scrape-off layer plasma of magnetic fusion devices self-consistently with direct current (DC) biasing of this plasma. The RF and DC parts are coupled by non-linear RF and DC sheath boundary conditions at both ends of open magnetic field lines. The physical model is studied within a simplified framework featuring slow wave (SW) only and lateral walls normal to the straight confinement magnetic field. The possibility is however kept to excite the system by any realistic 2D RF field map imposed at the outer boundary of the simulation domain. The self-consistent RFu2009+u2009DC system is solved explicitly in the asymptotic limit when the width of the sheaths gets very large, for several configurations of the RF excitation and of the target plasma. In the case of 3D parallelepipedic geometry, semi-analytical results are proposed in terms of asymptotic waveguide eigenmodes that can easily be implemented n...

A linear radio frequency plasma reactor for potential and current mapping in a magnetized plasma

Langmuir probe measurements in front of high power ion cyclotron resonant frequency antennas are not possible or simply too noisy to be analyzed properly. A linear experiment is a radio frequency (RF) magnetized plasma discharge reactor designed to probe the rectified potential in front of such antennas but at low power level (1 kW) to next improve antenna design and mitigate sheath effects. The maximum magnetic field is 0.1 T, and the RF amplifier can work between 10 kHz and 250 MHz allowing ion cyclotron resonances for argon or helium. The first measurements with no magnetic field are presented here, especially 2D potential maps extracted from the RF compensated probe measurements yield ni ≈ 10(15) m(-3) and Te ≈ 2 eV for RF power lower than 100 W. Series resonances in the chamber are highlighted and allow to deduce the plasma parameters from a simple equivalent impedance model of the plasma in helium gas. Next studies will be focused on magnetized plasmas and especially magnetized RF sheaths.

Plasma sheath properties in a magnetic field parallel to the wall

Particle in cell simulations were carried out with a plasma bounded by two absorbing walls and a magnetic field applied parallel to them. Both the sheath extent and the potential drop in it were derived from simulations for different plasma parameters, such as the electron and ion temperature Ti, particle density, and ion mass. Both of them exhibit a power law dependent on the Larmor to plasma ion pulsation ratio Ωi. For increasing values of the magnetic field, the potential drop within the sheath decreases from a few Ti/e down to zero, where e stands for the electron charge. The space charge extent increases with Ωi and saturates to 2.15 ion Larmor radius. A simple model of sheath formation in such a magnetic field configuration is presented. Assuming strongly magnetized electrons, and neglecting collisions and ionizations, a new typical length is evidenced, which depends on the ratio Ωi. The charge separation sheath width is theoretically found to increase from a combination of the electron gyroradius a...

Fluid modeling of radio frequency and direct currents in a biased magnetized plasma

This model aims at simulating a magnetized plasma column connected on one side to a probe and on the other side to an ICRH (Ion Cyclotron Resonant Heating) antenna. This is a double probe modeling of a plasma flux tube exchanging perpendicular currents: rf polarization current and dc currents (inertia, viscous, and friction) perpendicular to the magnetic field. A self consistent solution for the rectified potential and the density is obtained under the assumptions of flute hypothesis, inertialess electrons, and no collision in parallel direction. The main effect of rf biasing on the antenna side is to shift the IV characteristic so that the floating potential can be increased up to ln(I0(eVrf/(kBTe))), with I0 the modified Bessel function of the first kind. On the contrary, the effect of dc currents is to decrease the plasma potential and the sheath potential which can be lower than 3kBTe/e or even be negative. Experimental characteristics are well matched by the 1D fluid code and exhibit very high negati...

Studies of RF sheaths and diagnostics on IShTAR

IShTAR (Ion cyclotron Sheath Test ARrangement) is a linear magnetised plasma test facility for RF sheaths studies at the Max-Planck-Institut fur Plasmaphysik in Garching. In contrast to a tokamak, a test stand provides more liberty to impose the parameters and gives better access for the instrumentation and antennas. The project will support the development of diagnostic methods for characterising RF sheaths and validate and improve theoretical predictions. The cylindrical vacuum vessel has a diameter of 1u2005m and is 1.1u2005m long. The plasma is created by an external cylindrical plasma source equipped with a helical antenna that has been designed to excite the m=1 helicon mode. In inductive mode, plasma densities and electron temperatures have been characterised with a planar Langmuir probe as a function of gas pressure and input RF power. A 2D array of RF compensated Langmuir probes and a spectrometer are planned. A single strap RF antenna has been designed; the plasma-facing surface is aligned to the cylind...

Designing the IShTAR antenna: Physics and engineering aspects

IShTAR (Ion cyclotron Sheath Test ARrangement) is a magnetised plasma test facility installed at the Max-Planck-Institut fur Plasmaphysik in Garching, Germany. The main purpose of this device is the study of RF sheaths generated in front of ICRF (Ion Cyclotron Range of Frequency) antennas in magnetically confined plasmas. The plasma is generated by a helical RF antenna potentially able to reach a helicon mode. We present in this work recent modelling activities dedicated to IShTAR. On the one hand a parameterized magnetostatic model of the magnetic configuration was created with the finite element solver COMSOL Multiphysics [3]. The model considers two non-axial sets of coils and notably reproduces the magnetic field lines deviation at the center of the main vessel and the ripples observed during experiments. From this model we can infer that kA are required in the 2 main large coils of IShTAR for 1 kA in the 4 small coils to generate a “smooth” magnetic field along field lines. On the other hand an ICRF ...

Effective collecting area of a cylindrical Langmuir probe in magnetized plasma

Langmuir probe diagnostic on magnetic plasma devices often encounters more challenges in data processing than in non-magnetized plasmas, the latest itself being far from simple. In this paper, a theory of particle collection by a probe at the plasma potential in collisionless weakly ionized plasmas is constructed, accounting for velocities distributed according to the Maxwell equation and different mechanisms of particle collection depending on their speed. Experimental validation of the presented theory has been done with 2 cylindrical probes (rpr = 75u2009μm and Lpr = 1u2009cm and rpr =u20090.5u2009mm and Lpr = 1u2009cm) parallel to B → on a linear plasma device Aline, with magnetic fields of 0.0024–0.1 T and plasma densities of 1015–1017 m−3 in helium. Cylindrical probe measurements are compared to data from a planar probe perpendicular to the magnetic field, and the results for electron density, temperature, and plasma potential are presented. The introduced theory is initially constructed for a cylindrical probe but is applicable to various probe sizes, shapes, and orientations. Alongside the main subject, a number of associated issues are addressed with different details: a probe design issue relative to the magnetized environment, the “intersection” method of plasma potential evaluation, and the robustness of the conventional “1st derivative” method, a current bump near the plasma potential, lower limit for electron temperature estimation, and self-consistent calculation of electron temperature and density.Langmuir probe diagnostic on magnetic plasma devices often encounters more challenges in data processing than in non-magnetized plasmas, the latest itself being far from simple. In this paper, a theory of particle collection by a probe at the plasma potential in collisionless weakly ionized plasmas is constructed, accounting for velocities distributed according to the Maxwell equation and different mechanisms of particle collection depending on their speed. Experimental validation of the presented theory has been done with 2 cylindrical probes (rpr = 75u2009μm and Lpr = 1u2009cm and rpr =u20090.5u2009mm and Lpr = 1u2009cm) parallel to B → on a linear plasma device Aline, with magnetic fields of 0.0024–0.1 T and plasma densities of 1015–1017 m−3 in helium. Cylindrical probe measurements are compared to data from a planar probe perpendicular to the magnetic field, and the results for electron density, temperature, and plasma potential are presented. The introduced theory is initially constructed for a cylindrical probe bu...

First experimental results on the IShTAR testbed

IShTAR (Ion cyclotron Sheath Test ARrangement) is a linear magnetized plasma test facility dedicated to the investigation of RF wave/plasma interaction [1] in the Ion Cyclotron Range of Frequencies (ICRF). It provides a better accessibility for the instrumentation than tokamaks while being representative of the neighboring region of the wave emitter. It is equipped with a magnetized plasma source (1 m long, 0.4 m diameter) powered by a helical antenna up to 3 kW at 11 MHz. We present the results of the first analysis of the plasma characteristics (plasma density, electron temperature) in function of the operating parameters (injected power, neutral pressure and magnetic field) as measured with fixed and movable Langmuir probes, spectrometer and cameras. The plasma is presently produced only by the helical antenna (no ICRF). We show that the plasma exists in three regime depending on the power level: the first two ones are stable and separated by a jump in density; a first spatial profile of the plasma density has been established for these modes; The third mode is unstable, characterized by strong oscillations of the plasma tube position.

Capacitive and resistive double sheath model in an asymmetric radio frequency plasma discharge

The double asymmetric probe model presented here solves the rectified rf potential and rf currents in an asymmetric rf discharge as a function of the electrode surface ratio S1/S2, the rf potential compared to the floating potential, and the sheath capacitances on both sides of the discharge. It is demonstrated that this asymmetric unmagnetized model can be applied to a magnetized double probe one in which the asymmetry arises from the anisotropy between parallel and perpendicular currents. Asymptotic solutions for highly asymmetric discharges yield a dc saturation current on the rf electrode equal to −Isat/2 for low sheath capacitance and −Isat for high sheath capacitance. The transition capacitance between “low” and “high” is defined as C0. A solution of the rf averaged current and rectified potential as a function of the surface ratio and the rf potential are also proposed for each regime. These analytical solutions are confirmed by the full numerical model taking into account the generator resistance ...

Theory of a cylindrical Langmuir probe parallel to the magnetic field and its calibration with interferometry

A theory for data interpretation is presented for a cylindrical Langmuir probe in plasma parallel to the magnetic field direction. The theory is tested in a linear low-temperature plasma device Aline, in a capacitive radio-frequency (RF) discharge. The probe is placed on a 3D manipulator, and a position scan is performed. To exclude strong RF perturbations, the probe is RF compensated. Using the theory, electron densities are obtained from the current at the plasma potential, where no sheath is present. Results are calibrated by line-integrated density measurements of a 26.5 GHz microwave interferometer. Reasonable agreement is observed for probe and interferometer measurements. Furthermore, preceding, more general probe theory is compared to the one developed in the current work and the application limits are discussed.