Theory of Magnetic Effects in the Plasma of an Arc

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Abstract
The equations governing electron drift in the presence of a magnetic field are applied to the low pressure uniform positive column plasma. (1) An exponential variation of electron concentration with distance across an arc in a transverse magnetic field, found experimentally, is accounted for quantitatively. (2) A longitudinal magnetic field leaves the point-to-point concentration of electrons unchanged and does not alter the relative potentials in the cross section although transverse potential differences in the plasma decrease everywhere in proportion as the magnetic field increases. The transverse plasma fields vanish or even reverse slightly for large enough fields. (3) The plasma exhibits a diamagnetic susceptibility for longitudinal fields, which is proportional to the electron current density to the tube walls. With nonconducting walls electron wall current is automatically adjusted to the ion wall current. The magnetic polarization then increases oppositely to the magnetic field at first, reaches a maximum and then decreases hyperbolically to zero, so that beyond the maximum the plasma is paramagnetic for small variations in the field. Qualitatively this is the same behavior predicted by a previous erroneous theory which was itself checked only qualitatively by experiment. The present theory predicts that the diamagnetic polarization shall be directly proportional to the electron current to the tube wall and the magnetic field. (4) The magnetic field of the arc itself has a concentrating pinch effect which would cause the axial concentration of electrons to become infinite at a finite arc current if other limitations did not intervene. This may be the cause of rapidly increasing arc gradients in the neighborhood of certain critical currents in large mercury arc rectifiers. Larger diameter arc columns and higher pressures favor the magnetic pinch effect as a cause of current limitation over a blowout effect due to the outward-moving positive ions driving the gas before them.

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