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Some features of neutron emission from dense plasma focus suggest that the participating deuterons have energy in the range of 105 eV and have a directionality of toroidal motion. Theoretical models of these devices assume that the plasma evolves through a purely irrotational flow and thus fail to predict such solenoidal flow on the scale of the plasma dimensions. Predictions of a relaxation theory are consistent with experimental data [S K H Auluck, Physics of Plasmas, 18, 032508 (2011)], but the assumptions upon which it is based are not compatible with known features of these devices. There is thus no satisfactory theoretical construct which provides the necessity for solenoidal flow in these devices. This paper proposes such theoretical construct, namely, the principle of constrained dynamics, and describes an experiment which provides support for this idea. The experiment consisted of low-inductance self-breaking spark discharge in helium at a pressure ~ 100 hPa between two pointed electrodes separated by 30-50-mm distance kept inside a vacuum chamber mounted on a low-inductance high-voltage capacitor. The current derivative signal showed reproducible sharp dips at all of the extrema of the damped sinusoidal discharge. A planar diamagnetic loop centered with and perpendicular to the discharge axis consistently showed a signal representing rate of change of axial magnetic flux. The discharge plasma was very weakly ionized. Its acceleration was constrained by viscous drag of the neutrals, pressure gradient was constrained by heat conduction by neutrals, and at the same time, the axial current density and azimuthal magnetic field were constrained to follow an oscillatory temporal profile. Under these conditions, radial momentum balance equation cannot be satisfied unless the plasma possesses a degree of freedom, which supplies the shortfall in momentum balance. Azimuthal symmetry of the plasma allows azimuthal current density to provide such degree of - reedom. A qualitative explanation of observed phenomena is obtained using a simple model.