By W. B. Thompson (Auth.)

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3(a). Structure of the positive column. Measured and theoretical values of the potential as a function of radius for short mean free path, where ions diffuse. and the plasma is held positive with respect to the wall by the sheath poten tial. If the potential of a small section of the wall is made less negative with respect to the plasma then an excess of electrons will reach the wall, while the ion current is only slightly altered. The electron current will be ~ ^(kT) exp(eF/&T); hence by plotting the log of the current against V, the probe potential, a straight line of slope (e/JcT_) should be obtained.

LANGMUIR, I. and TONKS, L. (1929). Phys. Rev. 34, 874. LANGMUIR, I . a n d TONK:S, L. (1926). Phys. Rev. 28, 104. THONEMANN, P . C. and COWHIG, W. T. (1951). Proc. Phys. Soc. B64, 345. K A R F E L D , B . (1941). J. Phys. , 5, 135. KARELINA, N . A. (1942). J. Phys. , 6, 218. TONKS, L. (1939). Phys. Rev. 56, 360 (an early b u t full discussion of the effect of mag netic fields on the arc). G-UTHRiE, A. and WAKIERLING, R. K. ) (1949). The Characteristics of Electrical Discharges in Magnetic Fields Chapter 3.

Dolder, op. ). MAGNETOHYDRODYNAMICS 4. 1) If the pressure is a scalar, there are severe restrictions on the magnetic field. Since clearly B . Vp = 0 and j . Vp = 0, the magnetic field lines and the currents must lie in surfaces of constant pressure and the magnetic field must form a set of magnetic surfaces. ) = - c u r l I —V J52 ( B . V)B L87T 4π J 47Γ The complete properties of the solutions to this complex non-linear partial differential equation are not known, however some simple systems have been studied.