J. E. Allen

The expansion of a plasma into a vacuum

This paper reports calculations of the collision-free expansion of a semi-infinite plasma. It is shown that the ion front is accelerated to velocities comparable with the thermal velocity of the electrons.

Boundaries and probes in electronegative plasmas

A criterion for the positive-ion velocity at the boundary of an electronegative plasma is discussed. The case considered is that in which the negative-ion density obeys the Boltzmann relation. The appropriate physical solution is determined in circumstances where a triple-valued mathematical solution is found. The work has much in common with models of two-electron-temperature plasmas. Under conditions where the theory is valid, the ratio of negative-ion density to positive-ion density can be determined from Langmuir probe characteristics.

Study of the 3D plasma cluster environment by emission spectroscopy

Three-dimensional (3D) plasma clusters were formed inside a quasi-neutral plasma of very small size (38?mm3) obtained by applying a radio frequency (rf) to a small electrode at the edge of a main plasma. In order to find the density of such a plasma, spectroscopic analysis at three wavelengths was performed. The emission structure of the small plasma as well as of the whole discharge was obtained with a resolution of 0.5?mm. The optical thickness of the plasma allowed us to apply the steady-state corona model for the calculation of the plasma density. The density was estimated to be 2.8?1016?m?3 in the small plasma, one order higher than in the main plasma volume.

On the orbital motion limited theory for a small body at floating potential in a Maxwellian plasma

The condition for the validity of the orbital motion limited (OML) theory is reviewed, with reference to the calculation of the floating potential attained by a spherical body immersed in a plasma. It is shown that the OML theory is never satisfied in Maxwellian plasmas, even in the case of very small bodies, i.e. those with radii much smaller than the plasma Debye length. The case considered is that where the ion temperature is less than or equal to the electron temperature. The results are relevant to the theory of dusty plasmas, where the OML theory has been much employed.

A note on ion rarefaction waves

A theory is given of an ion rarefaction wave in a low pressure plasma under conditions where ionization processes are unimportant.

The collection of positive ions by spherical and cylindrical probes in an electronegative plasma

The collection of positive ions by spherical and cylindrical probes is investigated for electronegative plasmas in collisionless, unmagnetized and non-flowing regimes as a function of the ratio of negative ion density to positive ion density. The pre-sheath is given by a solution assuming quasineutrality. The potential in the sheath and the current-voltage characteristics are obtained by solving Poissons equation with the initial value given by the pre-sheath solution. The calculations are mostly based on the radial motion theory but the orbital motion theory is also considered to take the finite ion temperature effect into account. Particularly, the thin sheath model is considered for the latter case. A method for diagnostics in negative ion plasmas is suggested.

The plasma?sheath boundary: its history and Langmuir's definition of the sheath edge

The introduction of the terms sheath in 1923 and plasma in 1928 by Langmuir is described, followed by their use in the Tonks and Langmuir theory of the positive column at low pressures in 1929. Attention is drawn to the development of Langmuirs ideas during the period from 1923 to 1929. The well-known Bohm criterion for sheath formation, published in 1949, is shown to be closely related to the earlier work of Tonks and Langmuir. The much-used version of the Bohm criterion with the equality sign is obtained by employing the two-scale theory of the plasma and sheath, for the case where λD/L → 0.A generalized Bohm criterion is obtained by introducing the ion velocity distribution; the resulting expression can be understood by considering the propagation of ion-acoustic waves. The plasma–sheath boundary is found to be a sonic surface. Other generalizations of the Bohm criterion are given, including a mixture of positive ions, the presence of negative ions and a non-Maxwellian electron velocity distribution.

Free expansion of a plasma with two electron temperatures

A theory for the free expansion of a plasma with two electron temperatures is presented. It is shown that in the case of a laser-produced plasma expansion the ions separate into a fast and a slow component, and that the number of fast ions is particularly sensitive to the hot to cold electron temperature ratio. If the electron temperature ratio is ≳ 10 then the quasi-neutral self-similar solution breaks down. The regions in the rarefaction expansion where the quasi-neutrality assumption fails are discussed.

Ion currents to cylindrical Langmuir probes in RF plasmas

The positive ion current collected by cylindrical Langmuir probes has been measured in an RF argon plasma. The current-voltage characteristics were measured using an RF compensation technique whereby the probe was forced to follow the RF fluctuation in the local plasma potential. The I-V curves from probes of different radii and material show an ion current which is always greater than that predicted by the orbital motion theory and that agrees well with the radial motion theory. This is because the ions travel to the probe from a distance which is limited by the vessel geometry or by the collisional mean free path. The role of the possible collisions, ion-ion and ion-neutral, in the ion trajectories is analysed. It is suggested that the criterion for the application of the orbital motion theory should be tested whenever this theory is used for the determination of the charged particle density.

Identification of plasma‐sheath resonances in a parallel‐plate plasma reactor

A new, unexpected resonance has been observed in radio frequency, parallel plate plasma reactors. It has been explained using a linear model by analogy with the series resonance of probes. This discovery may be used in different ways; as a diagnostic, to measure the plasma density with high accuracy and, possibly, in improving the plasma performance in the low‐pressure range.