The normal zone acceleration in superconductor with changing current

The quench propagation in superconductors with changing current I(t) and/or placed into varying magnetic field B(t) is studied. The perturbations induced by I˙,B˙ may result in the thermomagnetical instability at quench current I_q(I˙,B˙)<I_s, where I_s is the critical current. It is shown that the interaction between the instability and the propagating normal zone leads to the acceleration of normal zone. The quench propagation velocity v increases sharply and the quench energy e_c tends to zero at I~I_q or with increase of I˙,B˙. The effects of current sharing and the nonuniformities of superconductor on quench process are discussed. Analytical dependencies of v and e_c on I˙,B˙ are found and compared with the experiments