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The energy of the residual flow and magnetic field in a maintained shear flow has source $S=-a{T}_{xy}$, where $T_{xy}=\rho v_x{v}_y-B_x{B}_y/{\mu }_0$. The kinetic and magnetic stresses can exchange energy with the imposed background. The source vanishes when their off-diagonal contributions cancel.

In a homentropic flow, the cross-helicity conservation law givesConsequently cross-helicity density is conserved along each trajectory exactly when the right-hand side vanishes. In a steady state, mass conservation gives $\nabla \cdot \mathbf{u}=-\mathbf{u}\cdot \nabla \log \rho$, so the criterion becomesThe absence of an entropy source in a conservation law does not alone make its density an advected scalar: compression and transport along the magnetic field still change that density.

A mean-field dynamo evolves a slowly varying spatially averaged magnetic field. Correlations of fluctuating velocity and magnetic field supply a mean-field electromotive force. Its local linear response includes the alpha effect; gradients of the mean field can contribute additional transport terms. The distinction between a uniform test field used to measure a response coefficient and a spatially varying mean field used to obtain growth is essential.

Motional electromotive force is the contribution caused by a conductor moving through a magnetic field. The magnetic part of the Lorentz force separates charges within the conductor. For a bar of length $L$ moving at velocity $v$ perpendicular to a uniform field, its magnitude is $BL|v|$; the sign follows the chosen circuit orientation. Together with the electric-field contribution it enters Faraday's law for moving circuits.

A finite-amplitude ideal-MHD Alfvén wave can rotate the transverse magnetic field at constant magnitude, with constant mass density, pressure and longitudinal components. Its transverse velocity obeys ${\mathbf{u}}_{\perp }=\mathbf{C}-s{\mathbf{B}}_{\perp }/\sqrt{{\mu }_0\rho }$ and its speed is constant along the wave. The constant magnetic pressure prevents compressive acceleration.

A cataclysmic variable whose white dwarf magnetic field does not dominate the large-scale accretion flow. It normally supports an accretion disk fed through Roche-lobe overflow. The term does not rule out a magnetized donor star or magnetic braking of a binary star.

A normal-field wall imposes zero tangential magnetic field: $\mathbf{B}\times \mathbf{n}=0$ for the wall unit normal $\mathbf{n}$. In a channel with imposed normal field $B_0\hat{\mathbf{z}}$, an induced tangential component $b(z)\hat{\mathbf{x}}$ therefore satisfies $b=0$ on each wall. This condition is distinct from the no-slip boundary condition on fluid velocity.

Parker instability is an undular magnetic buoyancy instability of a gravitationally stratified atmosphere supported partly by magnetic pressure. A bent horizontal magnetic field can permit gas to drain along its magnetic field lines, leaving buoyant rising regions. Magnetic tension resists bending, so wavelengths and boundary conditions affect the instability threshold. For a magnetized isothermal atmosphere, the unrestricted-wavevector threshold is given by the magnetic buoyancy energy criterion.