The mechanism of magnetization reversal by simple rotation has been discussed by a number of authors, but a completely general analysis (applicable to a single-domain ferromagnetic body of any type of anisotropy, with an applied field in an arbitrary direction) has not been given. The purpose of this paper is to present such an analysis. General differential equations are derived which can be used to describe the rotation process in any body for which demagnetization and anisotropy factors can be written. These equations are then applied to a sphere, a cylinder, and a thin sheet. Both uniaxial and cubic anisotropy are considered for the sphere and cylinder; only uniaxial anisotropy (the kind observed in deposited films) is considered for the thin sheet. The resulting differential equations can be solved numerically to obtain output voltages, switching times, and switching constants.

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In a fast pinch the plasma particles are forced to move with a velocity the same order of magnitude as that of the piston itself. Since in the simple models we have considered here instabilities can propagate and grow only via the motions of the particles, we might expect that the instability times for these models would be of the order of the pinch time itself.We have shown that the free particle model and the shock wave model predict instabilities and we have found that indeed an initially small perturbation becomes large in times comparable to the pinch time. The snowplow model predicts stability for the initial stages of the pinch, although in stabilities probably develop later on. VI. ACKNOWLEDGMENTSeveral theoretical analyses of the process of magnetization reversal in thin films by coherent rotation of the magnetization vector have been published. However, these analyses suffer from the use of questionable assumptions and from a lack of generality. This paper presents results obtained by employing an electronic digital computer to solve differential equations of greater accuracy and generality than those previously used. These results show how the optimum damping factor (which, as defined herein, differs slightly from the critical damping factor), the peak output voltage, and the reversal time vary with the magnitude and direction of a field applied to a thin ferromagnetic film with uniaxial anisotropy. The results for a particular direction of applied field show that the optimum damping factor and the peak voltage increase and the reversal time decreases with increasing magnitude of the field; and that a plot of reciprocal reversal time versus field magnitude is a parabola if the damping factor is always equal to its optimum value, but a hyperbola if the damping factor is a constant.