Finite Amplitude Instability of a Plasma Column

A weakly ionized cylindrical plasma column is investigated in a longitudinal magnetic field larger than the critical field which makes the column unstable to small perturbations. The restriction of small perturbations is removed by superimposing a finite amplitude helix upon the steady state density and potential. The stability of this system is investigated and conditions for marginal stability are found as a function of the amplitudes of the superimposed helix. Results of numerical calculations of electric field, wavelength, and frequency as functions of the magnetic field are given for the helical (m = 1) mode for different values of the amplitude parameter. Two sets of solutions are found. One set is singled out and combined with the energy balance theory of the positive column. The results given in plots are compared with experimental data and found to be in qualitative agreement with measurements of electric field, wavelength, and frequency. A hysteresis effect is predicted, and the paramagnetism of the positive column above a certain gas pressure is verified.