Angular dependence of the floating potential in a magnetized plasma

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Abstract

The experiments presented in this work are part of an extended investigation aiming to understand the angular dependence of energy and particle fluxes in magnetized plasmas. Here we concentrate on measurements of the floating potential Uf as a function of angle under various conditions (npl, Te, B) and for a number of ion species (H, D, He and Ar). A pronounced reduction of Uf is experimentally observed at oblique incidence. It is found that the magnitude of this reduction correlates with the Debye length while the normalized angular dependence remains similar under all conditions investigated.

Introduction

In what follows we report on measurements of the floating potential as a function of angle under various conditions and for a number of ions. This potential is of crucial importance in all kind of plasma boundary interactions. In particular it is well known that a considerable fraction of the energy flux to a surface exposed to a plasma is transported by the kinetic energy the impinging ions gain within the sheath potential [1]. A reduction of this potential therefore causes a decrease of the energy influx beyond the mere reduction of the electron and ion particle fluxes. The floating voltage Uf is directly linked to the ratio of ion to electron flux density, but in addition it depends on the electron temperature (Te) as well as other parameters. It adjusts itself to ensure the balance of electron and ion flux at the surface by repelling one species (usually the electrons) and attracting the other.

The physics of the plasma sheath at oblique incidence in strong magnetic fields have been subject for intensive theoretical considerations for a long time [1], [2], [3], [4]. It is, for example, vital for the interpretation of data acquired by flush mounted probes [5], [6]. However, most theoretical results can only be made available by numerical calculations.

At moderate magnetic fields like the ones used at the plasma generator PSI-2 or similar facilities, a further complication arises from the fact that the gyro radii of the ions can be of the same order of magnitude as the size of the probes.

In contrast to such complications occurring in a theoretical treatment the floating potential (Uf) is readily obtained experimentally. In this work we present data obtained under various experimental conditions at moderate magnetic fields B≈0.1 T. The corresponding Hall-parameters (he,i=ωe,igyrτe,icol) are of the order of 1300 for electrons and range from about 0.4 (Ar) to 32 (H) for the ions. This means that the electrons are always well magnetized whereas this is only marginally true for the heavy ions. It should be noted, however, that solely the magnetic confinement of the electrons is essential since the ions are coupled to them by electric fields in any case. A considerable variation of the Debye length λD for different gases (H, D, He and Ar) could be achieved by varying the density by almost three orders of magnitude (1015–1018 m−3) while the electron temperature Te was kept rather constant (Te=1–4 eV). Although the ion temperature could not be measured directly, it is known from previous measurements [7] that it is approximately 2/3Te. Finally, the magnetic field was varied in the case of argon to reveal the expected dependencies on the electron and, in particular, ion gyro radii (B=0.05–0.1 T).

Section snippets

Experimental setup

Our experiments were conducted at the PSI-2 plasma generator, a stationary high current arc discharge confined by an axial magnetic field. The plasma is produced between a heated LaB6 cathode and a hollow anode made from molybdenum. The plasma generated in this region streams along the magnetic field lines through a differential pumping stage into a target chamber where it is used for all kind of experiments including plasma–wall interaction studies and tests of various plasma diagnostics [8].

A basic model

It is beyond the scope of this work to present a fully satisfying theory explaining the measurements. Nevertheless, some basic considerations may be helpful to understand the results.

The floating potential is characterized by an ambipolar flux to the surface:ji(Uf)+je(Uf)=0.Applying the well known relations for U<Upl, ji(U)=jsati=constant and je(U)=jsateexp(eU/kTe) (Boltzmann relation), valid for normal incidence α=0°, Uf is found from the equationeUfkTe=lnjsati(α)jsate(α),yielding explicitly

Experimental results

In the scope of this work a large amount of experimental data has been collected. As an example we show the j(U) characteristics for hydrogen in Fig. 2. It is found that even at α=0° the characteristics do not show the jsate/jsati ratio expected from the mass ratio. Furthermore, although jsate/jsati tends to follow the mass ratio it also depends on other parameters. Apart from observing a general reduction of the particle fluxes we find a further reduction in the jsate/jsati ratio at oblique

Summary

The floating potential Uf has been carefully measured with a high angular resolution as a function of the angle α between the surface normal and the magnetic field. It is found that the floating potential is substantially decreased at oblique incidence and may even become positive with respect to the plasma potential. Probe measurements show good saturations for both jsate and jsati at α=0°. However, at α=±90° we observe pronounced non-saturation with different slopes for jsate and jsati (see

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