MAGNETIZATION OF TYPE-II SUPERCONDUCTORS IN THE MODIFIED BEAN MODEL

Within the construct of the modified Bean model which takes into consi deration the surface barrier Delta H and a nonzero value of the lower critical field H-cl, we have calculated the initial magnetization curv es and full hysteresis loops of type-II superconductors immersed in an external field H = H-dc + H-ac cos(omega t), where H-dc (greater than or equal to 0) is a de bias field and H-ac (> 0) is an ac field ampli tude. We denote the maximum and minimum values of H by H-A(= H-dc + H- ac) and H-B(= H-dc - H-ac). We consider an infinitely long cylinder wi th radius a, and the applied field along the cylinder axis. Magnetizat ion equations M(H) for full hysteresis loops are derived for four diff erent ranges of H-A: 0 < H-A less than or equal to H-cl + Delta H, H-c l + Delta H less than or equal to H-A less than or equal to H-cl + Del ta H + H-p, H-cl + Delta H + H-p less than or equal to H-A less than o r equal to H-cl + Delta H + 2H(p), H-cl + Delta H + 2H(p) less than or equal to H-A. Here H-P is the field for full penetration. Each of the se four cases is further classified for several ranges of H-B. To desc ribe completely the descending and ascending branches of full hysteres is loops for all cases, 83 stages of H are considered. To verify the p resent derivations, all the equations were confirmed to be continuous at their end points. Some typical hysteresis loops computed using the appropriate magnetization equations are demonstrated. From the results , we recognize the role of Delta H and H-cl on the hysteresis loops. D elta H does not cause any essential deformation of the M(H) curves, bu t merely expands them up and down with the increase of Delta H. On the contrary, H-cl introduces a step-like feature into the hysteresis loo ps, resulting in drastic change in their shape. Present derivations wo uld be a useful tool for analyses of the magnetization curves of type- II superconductors.