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The diffusion phenomena in plasmas with low charged-particle densities, in which the quasi-neutrality condition cannot be applied, are investigated with the aid of diffusion equations and the Poisson equation. From the asymptotic analysis in the limits of high and low densities, it is found that the transition between the ambipolar diffusion and the free diffusion is classified into three types. In each type, numerical solutions are obtained and the variations of the column thickness, the wall potential, the leak current to the wall, etc. with the change of the electron density are shown. When ions diffuse faster than electrons in a strong magnetic field, it is found that the electron diffusion is most enhanced in the transitional state. It is also shown that this phenomenon has influence upon the relation between the longitudinal current and field in discharge column.

A theta pinch gun is operated to get a plasma stream in a longitudinal magnetic field which is uniform over a region of 1 m in length. Plasma parameters such as density, temperature and traveling velocity can be controlled by changing the charging voltage of the capacitor bank for the gun and the strength of the uniform field. The loss rate of the transverse energy of a plasma stream is proportional to the so called Bohm diffusion rate for both deuterium and helium plasmas.

The diffusion waves in a plasma are analyzed for the ion-neutral collision frequency greater than the ion plasma frequency. It is, then, observed that with the increase in frequency, the diffusion wave tends to a mode governed by an electron free diffusion rather than the ion acoustic mode. The experiment has been mode in an axially decaying helium plasma produced by r.f. discharge at the pressures of 2.0 and 4.0 Torr. The interferometer patterns of the diffusion waves are well explained by the theory proposed here.

A general theory is presented for the diffusion of a multi-ion species plasma across magnetic field due to electrostatic fluctuations. It is shown that the diffusion flux due to wave-particle interactions is not necessarily proportional to the density gradient of the particle species of interest. The result is applied to the impurity diffusion due to those drift waves which exist in a single ion-species plasma. The dominant nonlinear effect is the induced scattering of waves on ions and the resulting diffusion constant of the host ions is given by the Kadomtsev formula, D ∼γ 2 / k 2 ω, where γ, ω and k are respectively the growth rate, frequency and wavenumber of the drift wave. The impurity diffusion constant is positive (or negative) if the impurity Larmour radius is smaller (or greater) than the host-ion Larmour radius, and becomes greater than the host diffusion constant if the spectrum is localized to the unstable region.

Cross field heat and particle transport due to the thermally excited convective cell mode is investigated both by theoretical work and by particle simulations. It is shown that there is a parameter range where the heat diffusion coefficient D H is considerably less than the particle diffusion coefficient D P . This results from the fact that high energy particles in a velocity distribution diffuse much more slowly than the low energy particles because the fluctuating electric fields are averaged over their finite Larmor radii. The magnetic field scaling of D H / D P is also discussed. The results imply that ions in a thermonuclear reactor should be less affected by turbulence than are electrons as appears to be the case.

The effects of magnetic field and pressure on the radial distribution of plasma density are investigated experimentally for an energetic arc of 10 14 cm -3 density and 2×10 5 °K temperature in relation to the diffusion phenomena of plasma. Experiments are made in argon at pressures ranging from 3×10 -2 to 3×10 -5 torr and 1000∼4000 gauss of the magnetic field strength. Classical and Bohm type's diffusion coefficients were examined for two different states of plasma: One is with low ionization degree ( 98%). The experimental results show that the e-folding length of the exponentially varying density-profile is inversely proportional to the magnetic field strength at 3×10 -3 torr pressure, whereas to the square root of the strength at 3×10 -5 torr pressure. This suggests that some types of turbulence would be produced in the fully ionized plasma of energetic arc.

Diffusion rate of a plasma across a magnetic field lower than the critical field for screw instability is measured and is compared with Simon's diffusion theory which states that the diffusion of the plasma across the longitudinal magnetic field is not ambipolar in short discharge tubes. Mathematical treatment of the plasma state equation shows that the short circuit path to neutralize space charge pointed by Simon can not be made up in the plasma. A new measuring method by means of the voltage-current relation of the discharge tube in the magnetic field is introduced to determine the diffusion rate across the magnetic field quantitatively. According to the present investigations, there is no diffusion mechanism due to so called “short circuit effect,” and the diffusion is ambipolar independent of the tube dimension.

Effect of electric field on the diffusion of a plasma across a magnetic field is analytically investigated for the purpose of the calculation of the power generation from the potential energy. The results are compared with experiment. The friction and the diffusion coefficient are obtained as a function of the electric field caused by the diffusion of the ions. It is found that, in the direction of the electric field, the diffusion increases while it decreases in the opposite direction. A measurement of potential distribution and plasma density in a cylindrical plasma produced by electron beam is performed and these agree qualitatively with the theory.

A cylinder of collision-free plasma in a strong, uniform magnetic field parallel to its axis is studied theoretically. A plasma of cylindrical symmetry in equilibrium is assumed to have a current due to the electron velocity distribution of a shifted Maxwellian type. Drift instability is discussed for the density profile n ( r )= N 0 (1- r 2 / a 2 ), N 0 being the density on the axis. The drift waves are shown to grow to form a nonlinear equilibrium spectrum and to generate an anomalous diffusion, whose coefficient is about one-tenth of Bohm's in magnitude.