Pinch Oscillations in Electron-Hole Plasmas. I. Theory

The Drummond—Ancker-Johnson magnetothermal pinch theory which describes the oscillations in electron-hole plasmas is extended. The theory is based on only two fundamental equations, the power-balance equation in the inner region of the pinch and the particle-conservation equation in the outer region of the pinch. By perturbing the two fundamental equations from their quasiequilibrium states, a dispersion relation is obtained which predicts oscillations in the electric field strength, provided specific conditions are satisfied. When the experimental dependencies of the frequency on current and time are incorporated into the equations, a theoretically determined inner current $I_i$ and outer temperature $T_0$ are obtained. These values of $I_i$ and $T_0$ are uniquely defined, and their behavior is consistent with the observed dependence of the oscillation amplitude on current and time. These results are also consistent with the known thermal conductance of InSb. The theory predicts that the pinch radius expands somewhat as time progresses. Although the theory invokes several simplifying assumptions, it agrees well with the observed properties of the pinch oscillations. On the basis of this agreement, it is concluded that the theory is basically correct.