Electromagnetic induction in conductors accelerated in magnetic fields amplified by flux compression

The initial boundary-value problem for the electromagnetic induction in a conducting slab ats(t)≦x≦s(t)+a resulting from its accelerated motionv={s(t), 0, 0} across a transverse magnetic fieldB={0,B(x,t), 0} is treated, when the latter is amplified by orders-of-magnitude with respect to its initial valueB(x,t=0)=B ₀(x) by flux compression in the gap between the moving conductor surfacex=s(t) and an ideal resting conductor atx=0. Two initial (t=0) configurations are considered, assuming that (I)B ₀ (step-shaped) has not yet and (II)B ₀ (uniform) has completely diffused into the conductor atx=s(t=0). By means of a time-dependent coordinate transformation ξ=x ? s(t)]/a and Fourier series expansions, the electromagnetic fields in the moving conductor are represented as integralfunctionals of the magnetic fieldB ₁ (t) in the gap 0≦x≦s(t).B ₁ (t) is given analytically as solution of a singular Volterra integro-differential equation. The theory is valid for arbitrary (nonrelativistic) speeds.(t) and accelerationss(t)) of the moving conductor. Applications to explosion driven electric induction generators and magnetic flux experiments are discussed briefly.