Physica C 165 ( 1990) 397-403 North-Holland INVESTIGATION OF THE INTERACTION BETWEEN A MAGNET AND A TYPE-II SUPERCONDUCTOR BY VIBRATION METHODS Z.J. YANG, T.H. JOHANSEN, H. BRATSBERG, G. HELGESEN and A.T. SKJELTORP a Department of Physics, University of Oslo, Oslo, Norway a Institute for Energy Technology, N-2007 KJ.eNer, Norway Received 24 November 1989 Vibration methods are used to investigate the interaction between a magnet and a type-II superconductor on the basis of a dipole-dipole interaction model. For this purpose, a compound pendulum was constructed for studying the interaction between a magnet and a high-T, superconductor. The experiments show that the damping of the pendulum is much larger when the motion is parallel to the direction of the magnetic moment than when it is perpendicular. This novel result is discussed in relation to the model and movements of flux lines. 1. Introduction In connection with the application of levitation in superconducting systems, it is very important to un- derstand the interaction between a magnet and a su- perconductor [ l-41. The interaction between a magnet and a type-1 superconductor is well under- stood by means of perfect diamagnetism of the su- perconductor in the Meissner state. A dipole-dipole model is very good to describe the interaction [ l- 51: the potential energy V-Z-~ and force zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB F-Z-~ with z the distance between the magnet and super- conductor. However, due to the flux pinning of type- II superconductors when H>H,, (H,, =lower criti- cal field), the interaction between a magnet and a type-II superconductor is, to our knowledge, not clear so far [ 11. Hellman and co-workers [ 2 ] have sug- gested a flux pinning model, which yields, in the range of H,, <H-c H,,(H,, =upper critical field) and un- der certain conditions, V-z-’ and F-z-=. Moon et al. and Marshall et al. [ 31 have reported experimental investigations of the force in this range, but they did not investigate the power law behaviour of the interaction. In an earlier paper we reported [4] the investigations of the force between a per- manent magnetic sphere and an oxide superconduc- tor as a function of separation z. We employed a power law to describe the force, F-Z-~(‘), with y(z) satisfying 0 < y(z) < 4. Based on these experimental results, we studied the vibrations of a magnet levi- tated over a flat superconductor using a Lagrangian dynamical method [ 61. The purpose of this letter is to suggest a vibration method based on a dipole-dipole interaction model, developed from our previous research [ 61, to in- vestigate the interaction between a magnetic system and a type-II superconductor. 2. Description of the methods Consider a permanent magnetic sphere with mo- ment M over a flat superconductor as shown in fig. 1. For type-1 superconductors, (or when H-c H,, for type-II superconductors), we can use a dipole-di- pole model and the image method to deal with it. The interaction between a dipole and an infinite super- conducting plane can thus be expressed by: v=& M’*M [ 3(M’*n)(M*n) -- 4x (2z)3 (2z)3 zyxwvutsrqponmlkjihgfedcbaZYXW 1 PO IMIIM’ I = 4x (2z)3 [cos(a+a’)+3 sin (Ysin a’] (1) where M’ is the image dipole of the dipole M and 0921-4534/90/$03.50 0 Elsevier Science Publishers B.V. ( North-Holland )