Session NW4: Basic Plasma Physics I

Measurement of a comprehensive plasma parameter set in low pressure H$_{\mathrm{2}}$ discharges for extended benchmarking of CR models

In low pressure hydrogen discharges a variety of particles is present: besides electrons, the neutral species H$_{\mathrm{2}}$ and H, the molecular ions H$_{\mathrm{2}}^{\mathrm{+}}$ and H$_{\mathrm{3}}^{\mathrm{+}}$ as well as protons and H$^{\mathrm{-}}$. For a detailed assessment of the individual reactions occurring in those discharges, knowledge about the particular particle densities and temperatures is inevitable. An extensive determination of these plasma parameters has been carried out in a planar ICP in order to conduct an extended benchmark of collisional radiative models for atomic and molecular hydrogen as well as a benchmark of a dissociation model. As diagnostic methods energy resolved ion mass spectrometry has been applied for determining the ion densities and absolutely calibrated optical and VUV emission spectroscopy for measuring atomic and molecular emissivities as well as the density ratio of atomic to molecular hydrogen. A spatially movable Langmuir probe has been used for measuring the profiles of the electron temperature, density and the EEDF. Results are going to be presented for a variation of RF power and pressure.   

Non-invasive determination of kinetic ion quantities and plasma parameters throughout the plasma sheath and bulk

Ion velocity distribution functions (IVDF) are routinely measured to obtain information about the ions interacting with the surface. Here, we show that in charge-exchange (CX) collision dominated plasmas the distribution of the ions at the walls contains also information about the spatial distribution of the plasma parameters. This information can be extracted with the help of an exact solution of the Boltzmann equation including CX and ionization. Using the translation property of the solution the IVDF at any point in the plasma is reconstructed from the one measured at the wall. These spatially resolved distributions give the ionic parameters (density, mean velocity, energy and temperature) as exact kinetic averages. Further, the electric field, the plasma potential, and the electron density and temperature are also obtained from the IVDF. Good agreement with probe measurements is found. The method is most sensitive in the sheath and the near sheath region where the charge separation can be readily obtained. Results from an inductively-coupled plasma in neon are shown.   

The correct kinetic Bohm criterion

Space charge sheaths are characteristic for bounded plasmas and are a key element in plasma-surface interactions. Hence, one of the most fundamental concepts in plasma physics -- the Bohm criterion -- is related to the definition of a sheath edge. However, its kinetic formulation is stirring controversies for a long time -- from questioning its validity at high collisionality to claiming a divergence in its formulation. Here, based on a solution of the Boltzmann equation for ions with charge-exchange collisions and ionization both of these disputes are resolved: 1) The obtained form of the kinetic Bohm criterion removes the divergence in the ionic part. 2) It also introduces a new equally important term that describes collisional and geometric effects. This new term reestablishes the validity of the criterion at high collisionality. 3) It also restores agreement with the fluid counterpart of the criterion. The developed theory is supported by non-invasive spatially resolved measurements and a numerical model.   

Reconsideration of basic concepts for the low-pressure discharge maintenance

The Schottky condition and the concept for the ambipolar field known as bases of the low-pressure discharge maintenance are reconsidered. Whereas the Schottky condition results in a value of the electron temperature independent of the plasma density, the discussed generalized form of the Schottky condition relates -- due to the nonlinear processes in the charged particle balance -- the electron temperature to the plasma density, thus, ensuring self-consistency of the plasma description. The concept for equality of the electron and ion fluxes resulting into the ambipolar field is the second issue discussed. Localization of the power input outside the high plasma-density region, a common case in many rf plasma sources, breaks it down by transforming the ambipolar field into a vortex, non-conservative, field. Since the dc field in the discharge should be a potential (conservative) field, it appears to be composed by two vortex field: the ambipolar field and a field related to a vortex dc current, the latter driven by a deviation from the Boltzmann distribution of the electron density. In addition, due to the steady-state magnetic field self-induced by the vortex current in the discharge, the plasma appears magnetized without having an external magnetic field applied.   

Non-locality, adiabaticity, thermodynamics and electron energy probability functions.

Thermodynamic properties are revisited for electrons that are governed by nonlocal electron energy probability functions in a plasma of low collisionality. Measurements in a laboratory helicon double layer experiment have shown that the effective electron temperature and density show a polytropic correlation with an index of gamma$_{\mathrm{e}} \quad =$ 1.17 \textpm 0.02 along the divergent magnetic field, implying a nearly isothermal plasma (gamma$_{\mathrm{e}} \quad =$ 1) with heat being brought into the system. However, the evolution of electrons along the divergent magnetic field is essentially an adiabatic process, which should have a gamma$_{\mathrm{e}} \quad =$ 5/3. The reason for this apparent contradiction is that the nearly collisionless plasma is very far from local thermodynamic equilibrium and the electrons behave nonlocally. The corresponding effective electron enthalpy has a conservation relation with the potential energy, which verifies that there is no heat transferred into the system during the electron evolution. The electrons are shown in nonlocal momentum equilibrium under the electric field and the gradient of the effective electron pressure. The convective momentum of ions, which can be assumed as a cold species, is determined by the effective electron pressure and the effective electron enthalpy is shown to be the source for ion acceleration. For these nearly collisionless plasmas, the use of traditional thermodynamic concepts can lead to very erroneous conclusions regarding the thermal conductivity.   

Effect of collisions on the two-stream instability in a finite length plasma

The instability of a monoenergetic electron beam in a collisional one-dimensional plasma bounded between grounded walls is considered both analytically and numerically. Collisions between electrons and neutrals are accounted for the plasma electrons only. Solution of a dispersion equation shows that the temporal growth rate of the instability is a decreasing linear function of the collision frequency which becomes zero when the collision frequency is two times the collisionless growth rate. This result is confirmed by fluid simulations. Practical formulas are given for the estimate of the threshold beam current which is required for the two-stream instability to develop for a given system length, neutral gas pressure, plasma density, and beam energy. Particle-in-cell simulations carried out with different neutral densities and beam currents demonstrate good agreement with the fluid theory predictions for both the growth rate and the threshold beam current.   

Modeling of High-voltage Breakdown in Helium

We investigate the breakdown in extremely high reduced electric fields (E/N) between parallel-plate electrodes in helium. The left branch of the Paschen curve in the voltage range of 20-350kV and inter-electrode gap range of 0.5-3.5cm is studied analytically and with Monte-Carlo/PIC simulations. The model incorporates electron, ion, and fast neutral species whose energy-dependent anisotropic scattering, as well as backscattering at the electrodes, is carefully taken into account. Our model demonstrates that (1) anisotropic scattering is indispensable for producing reliable results at such high voltage and (2) due to the heavy species backscattered at cathode, breakdown can occur even without electron- and ion-induced ionization of the background gas. Fast atoms dominate in the breakdown process more and more as the applied voltage is increased, due to their increasing ionization cross-section and to the copious flux of energetic fast atoms generated in charge-exchange collisions.