Permittivity Of Free Space Research Articles

Sheath-Convection Effects with Flush-Mounted Electrostatic Probes

Theoretical expressions are derived for the ion current to a planar flush-mounted probe which arises from the convection of ions from a moving plasma into the probe sheath. The two situations considered are those where the sheath is either very large or is small compared with the boundary layer. It is found that sheath effects, with an accompanying lack of true current saturation with increasing probe bias, can be expected to intrude when the parameter REα2χ2 > (X/l)1/4. (RE = electric Reynold's number, α = ratio of Debye length to probe length [X], χ = potential of probe normalized with respect to the electron energy, and l = the distance of the probe from the leading edge of the surface into which it is mounted.) For values of REα2χ2(l/X)2 which exceed unity, the formula[Formula: see text](where ne = plasma electron density, u∞ = free stream flow velocity, V = probe bias, μ∞ = free stream ion mobility, e = electronic charge, and ε0 = permittivity of free space) is derived. At lower values of REα2χ2(l/X)2 theoretical considerations which take compression and cooling effects into account show that the above relation should still be approximately correct down to values of [Formula: see text]. The relation shows good agreement with the recent results presented by Scharfman and Bredfeldt under conditions where they report the conventional diffusion theory to be in error by up to one order of magnitude, and moreover to predict an incorrect variation of current with electron density and probe bias.

Ion Current from a Collision-Dominated Flowing Plasma to a Cylindrical Electrode Surrounded by a Thin Sheath

Experimental results for the ion current to a cylindrical electrode in a flowing continuum plasma are compared with the currents calculated from a convection-dependent thin-sheath theory obtained by extending the theory of Lam to cover convection rather than diffusion-generated currents. The relation derived with this theoryIi≈5.3ε01/4e3/4μi1/4rp1/4vf3/4ne3/4V1/2l, (mks)where ε0 is the permittivity of free space, e is the electronic charge, μi is the ion mobility, rp is the probe radius, vf is the plasma/probe velocity, ne is the ionization density, V is the probe bias, and l is the probe length, is found, on the average, to predict the experimental currents to within ±30% over ranges of 0.1–5 mm in probe radius, 5×102−4×103 cm/sec in probe/plasma velocity, 5×1016−2×1018/m3 ionization density, and 10–100 V in probe bias. Further support for a convection-dependent thin-sheath model is provided by two experimental observations: (1) The current is observed to vary as V1/2 as predicted by the convection-dependent theory rather than to saturate as would be expected of a diffusion-generated current. (2) Separate measurements reveal a marked asymmetry in the current distribution around the probe surface as expected in a thin-sheath situation.

Ion current to a spherical probe in a flowing high-pressure plasma under thin-sheath conditions

The current to a large (radius = 2.4 mm) negatively biased spherical probe in a flowing plasma (a propane/air flame) has been measured over wide ranges of plasma-ionisation density (3 × 1015 to 1018 m?3), probe bias (10?400V) and probe/plasma relative velocity (3?40m/s). Under these conditions, the sheath surrounding the probe is thin and the probe current is a function of the probe/plasma velocity. In consequence, the static continuum probe theory of Su and Lam, and the motionally dependent thick-sheath theory of Clemenets and Smy are both found to be in error by at least an order of magnitude. A thin relationship has been derived for the spherical probe which shows excellent agreement with the experimental data: I=12.13(??0)1/4(neevf)3/4V1/2rp5/4 where I = probe current, ? = ionic mobility, ?0 = permittivity of free space, ne = ionisation density, e = electron charge, vf = flow velocity, V = probe bias and rp = probe radius (all in MKS units)

Anomalous currents to a spherical electrostatic probe in a flame plasma

By following the same line of reasoning which the authors used in a previous paper, concerned with cylindrical probes, the ion current Ii to a spherical probe (radius rp, bias voltage V) immersed in a collision-dominated flowing plasma of subsonic velocity vf has been calculated to beIMG1where ne is the electron density, μi the ion mobility, e the electronic charge and ϵ0 the permittivity of free space. This theory is only valid for conditions where the plasma sheath diameter r0>>rp.A propane-air flame with a moving probe was used to investigate the above relationship. Reasonable agreement (considering the approximations made in deriving the theoretical relationship) was obtained between measured and theoretical ion currents.

Dielectric properties of thin films of aluminium oxide and silicon oxide

Measurements are reported of the loss tangent and permittivity of vacuum- baked dielectric films of anodized aluminium oxide and evaporated silicon oxide, in the frequency range 10 -2–10 7 Hz and temperature range 77–600 °K. At low frequencies two types of dispersion mechanisms are found: an interfacial process known as type “B” present in both materials, and an orientation polarization known as type “A” depending on the deposition rate and only found in silicon oxide. The activation energy for these processes is in the range 0.5-0.8 eV. At higher frequencies, a square-law dependence of conductivity on frequency is observed in both oxides, with a much lower activation energy, and is interpreted in terms of hopping conduction.

Triple Resonance Phenomenon in Plasmas

INTERACTIONS between electromagnetic waves and weakly ionized plasmas in the presence of a steady magnetic field have been widely investigated1. The Appleton–Hartree formula for the equivalent complex dielectric constant of the plasma is partially reproduced in graphical form in Figs. 1 and 2. These graphs are restricted to the case that the propagation vector and E-polarization of the electromagnetic wave are both perpendicular to the direction of a uniform steady magnetic field. With these restrictions, the relative dielectric constant can be written: in which where ω is the radian frequency of the wave, ν is the collision frequency, ωb = eB/m is the cyclotron frequency, ωp = √(ne2/mɛ0) is the plasma frequency, e and m are the charge and mass of an electron. B is the strength of the steady magnetic field, n is the volume density of free electrons in the plasma, and ɛ0 is the permittivity of free space. A dependence on time of ejωt has been assumed.

Induction Flowmeter

According to Faraday's law of induction an electric field will be induced in a medium moving relative to a magnetic field. This induced electric field is proportional to the intensity of the magnetic field and to the relative velocity of the moving medium. When applied to media of arbitrary electrical conductivity and dielectric constant, it is seen that any potential difference that arises in connection with the induced electric field is attenuated by the shunting effect of the permittivity of free space. For most media this shunting effect is negligible; for media of extremely low conductivity, however, the effect is appreciable. Finally the effect of the electrical properties of the containing pipe is investigated.