Double-probe theory for a continuum low-density plasma

Abstract

A theoretical treatment is given for the double-probe method in an electron/positive-ion plasma having mean free path <or=probe size<or=Debye length i.e. under conditions in which neither the collisionless theory of Johnson and Malter (1950) for Kojima and Takayama (1950), nor continuum theories based on either the work of Su and Lam (1963) or that of Cohen (1963) are applicable. The theory applies to any probe geometry, including spheres and finite cylinders. Applications to plasma diagnostics are developed in detail.

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“…The double probe has been studied, both theoretically and experimentally, under various conditions (Johnson and Malter 1950, Cozens and von Engel 1965, Bradley and Mathews 1967, Bradley and Ibrahim 1973, Dote and Kaneda 1974, Chang and Laframboise 1976b. In some experimental situations, the two arms of a double probe may be located in regions of unequal number density, associated with gradients in the plasma.…”

“…In the limiting case of one current being much greater than the other, the characteristics are equivalent to single probe characteristics obtained using an inadequate reference electrode (Szuszczewicz 1972, Chang 1973. Floating single probe measurements, made using an inadequate surface area reference electrode, are equivalent to the double probe case of equal area probe arms located in regions of different plasma density, when the probe currents are proportional to number density and the potential dependence is not a function of the probe shape, as in the case of the continuum large-Debye-length theory of Chang and Laframboise (1976a).…”

“…In this paper the continuum large-Debye-length probe theory of Chang and Laframboise (1976a) is combined with the electron emission current relationship, derived by Langmuir (1931), to examine the effects of electron emission on double probe characteristics. Theoretical characteristics are generated, assuming unequal arm currents at space potential, to see how the measurement of plasma parameters is altered from that predicted by the ideal double probe theory of Chang and Laframboise (1976b).…”

“…Theoretical characteristics are generated, assuming unequal arm currents at space potential, to see how the measurement of plasma parameters is altered from that predicted by the ideal double probe theory of Chang and Laframboise (1976b).…”

“…The current to a probe in the continuum large-Debye-length limit has been given by Chang and Laframboise (1976a) as where ip is the current non-dimensionalised by dividing by its value, Z, , at space potential, ti is the ratio of ion to electron temperatures, TJT~, zis = -Zis/Zes, q is the non-dimensionalised potential qV/kT,, q is the magnitude of the electron charge, k is Boltzmann's constant and the subscripts i, S and e denote ion, space potential and electron respectively. This relationship is valid for any probe geometry.…”