Diffusion processes in the positive column in a longitudinal magnetic field

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The motion of a charged particle in a magnetic field may be described as the sum of a gyration around the field lines, a drift motion across the same lines and a motion parallel the field. External force fields, magnetic field inhomogeneities and inertia forces are responsible for the drift motion in this single-particle picture. In an ionized gas the picture has be modified by particle interactions, such as collisions and phenomena caused by space charges. Only encounters between nonidentical particles produce a diffusion in first order across the magnetic field.» The macroscopic correspondence a situation where the transverse drift due particle interactions and inertia forces can be neglected and where the motions are relatively slow is an ionized gas nearly frozen to the magnetic field lines. This strong coupling between ionized matter and magnetic fields is of great importance, not only in astrophysics but also for the problem of producing controlled thermonuclear energy in a plasma confined by a magnetic field. However, it has been emphasized by Bohm, Burhop, Massey and Williams that random fluctuations of charge density and plasma oscillations may produce electric fields which in their turn give rise drift motions across the magnetic field lines. This ' drain diffusion provides an additional mechanism for ionized matter slip across a magnetic field and may, when it dominates over collision diffusion, introduce considerable difficulties into the physics of a plasma in a magnetic field. Bohm and collaborators performed experiments with an arc plasma in a magnetic field and came the conclusion that the diffusion was not consistent with collision phenomena but could be explained by drain. This interpretation was criticized by Simon, who pointed out that the transverse diffusion of the plasma is not necessarily ambipolar. Thus, in the arc experiment, space-charge neutralization can be maintained by the conducting end walls which produce an electron short-circuit across the magnetic field. With this new interpretation Simon was able show that the arc experiments did not conflict with the binary collision theory. The purpose of the present investigation is study diffusion across a magnetic field in a configuration which is free from short-circuiting effects such as those described by Simon. It provides the possibility of deciding whether collision or drain diffusion is operative. For the purpose a long cylindrical plasma column with a homogeneous magnetic field along the axis has been chosen as described in Section 5. The theoretical treatment is given in Sections 2 4. On the basis of the collision diffusion theory Tonks, Rokhlin, Cummings and Tonks and Fataliev have pointed out that a longitudinal magnetic field will reduce the losses of particles the walls. Consequently, when the magnetic field is present, a lower electron temperature and a smaller potential drop along the plasma column should be required sustain a certain ion density. The same conclusions have recently been drawn by Bickertonf and by Bickerton and von Engel in theoretical and experimental investigations which also include probe measurements in a magnetic field. In the range of the apparatus used by these authors the positive column was found behave in good agreement with the collision theory. In the absence of a magnetic field the behaviour of the column was consistent with the theory of Tonks and Langmuir, and when the field was present a modified Schottky theory was applicable (next section). The present experiment forms an extension of that of Bickerton and von Engel into a range where the Schottky theory is applicable in the absence of a magnetic field and where the applied magnetic field is still made strong enough influence the electron temperature.