1. Vortex avalanches in superconductors: Size distribution and Mechanism Daniel Shantsev Tom Johansen andYuri Galperin AMCS group Department of Physics, University of Oslo A. V. Bobyl A. F. Ioffe Institute, St. Petersburg, Russia

2. T c Temperature T c Mixed state (vortex matter) Meissner state Normal state H c1 H c2 Type II Vortex lattice A.A. Abrikosov (published 1957) 2003 Vortices in Superconductors

3. Critical state Vortices : driven inside due to applied field get pinned by tiny inhomogeneities => Metastable critical state

4. Critical state in a superconductor YBaCuO film, picture from R.Wijngarden Distribution of flux density Sandpile Critical currentCritical angle picture from E.Altshuler Avalanches ???

5. Motivation to study vortex avalanches The slope of the vortex pile - the critical current density J c – is the key parameter for many applications of superconductors JcJc Trapped field magnets Record trapped field: 17 Tesla ~100 times better than Cu wire High-current cables

6. H Hall probe YBCO Measuring avalanches Size distribution or SOC

7. Peaked or Power Law (dep. on H & T) Internal Hall probe arrang. Nb film Planar Behnia et al PRB (2000) Exp or Power law (dep. on T & t) Off the edge SQUID BSCCO crystal Planar Aegerter PRE (1998) Peaked or Power law (dep. on T) Off the edge & internal 2 Hall probes Nb film Ring Nowak et al PRB (1997) Peaked Internal 1 Hall probe YBCO crystal Planar Zieve et al PRB (1996) Power law (slow ramps) Off the edge CoilNb-Ti Hollow cylinder Field et al PRL (1995) Exponential Off the edge CoilPb-In Hollow cylinder Heiden & Rochlin PRL (1968) Avalanche distribution Avalanche type SensorMaterialGeometryReference Statistics of vortex avalanches Why peaked?

8.  T 0   J c     Q   T >  T 0 1) Flux motion releases heat 2) T rise weakens flux pinning Thermal effects Can it also affect the statistics of small avalanches? and in what way? The thermal instability can lead to catastrophic avalanches with thermal runaways (flux jumps) and sometimes remarkable flux patterns 1 mm Magneto-optical movie of flux penetration in MgB2 film

9. Linearly polarized light Faraday-active crystal Magnetic field H  (H)(H) F Magneto-optical Imaging Square YBaCuO film

10. Down to small scales... 5 mm 100  m Flux penetration on small scales : in space: highly non-uniform in time: gradual or abrupt ??? B a rise MgB 2 film

11. number of vortices 50 - 50000 Analyzing difference images 7.15 mT 7.40 mT linear ramp of B a 15 MO images T=3.6K = MO image (7.165mT) — MO image (7.150mT)  B a = 0.015mT,  t=2.5 sec local increase of flux density - avalanche 2300  0 1100  0 250  0

12. 20  0 2.500.000  0 Avalanche size 1.Typical size exists 2.It grows with B a

13. B a = 13.6 mT the flux pattern almost repeats itself Irreproducibility B(r)  B(r) is irreproducible! The final pattern is the same but the sequences of avalanches are different MOI(8.7mT) - MOI(8.5mT)  B(r) T=3.6K

14. Adiabatic approach Heat stays where it has been released OK if thermal diffusion is much slower than flux diffusion D T <<D M Originally used by Swartz &Bean in 1968

15. Adiabatic : All energy released by flux motion is absorbed Flux that has passed through “x” during avalanche Biot-Savart Adiabatic critical state for a thin strip is given by a set of equations: Critical state

16. temperature T th Intermediate result: the adiabatic instability field for a thin strip Demonstrates existence of a threshold T (above which jumps do not occur no matter how large field is applied)

17. x B, T - profiles film edge 31,000  0 7,500  0

18. We fit B fj ~ 2 mT T th ~ 10 K  (B a ) dependence using only one parameter: T=0.1T c 0.3T c Thermal origin of avalanches

19. Conclusions Flux avalanches are observed in superconducting films using magneto-optical imaging They have a charactristic size (~1000  0 ) that grows with B a Adiabatic model for the size of thermal flux avalanche in a thin film is developed Agreement with experiment (the thershold B a, threshold T, size(B a )-dependence) Thermal mechanism can be responsible for microscopic avalanches (not only catastrophic jumps) and leads to a peaked size distribution Thermal effects contribute to formation of the critical state (and modify J c ) without destroying it Phys. Rev. B 72, 024541 (2005) http://www.fys.uio.no/super/ Trivial conclusions: Deep conclusions:

21.  B dA = h/2e =  0 Flux quantum:  J B(r) normal core The vortex core interacts with tiny inhomogeneities (  nanometers) => vortices get pinned (don’t want to move)

22. We want to understand how the critical state is formed because: it determines the critical current density J c – the key parameter for most applications of superconductors (high-current cables, trapped-field magnets) to test models, e.g. self-organized criticality, for applicability to vortices (that move in a disordered landscape and don’t have inertia)

23. local flux density calculated from local intensity of MO image; each point on the curve corresponds to one MO image No long-range correlation between the jumps Frequent jumps at the same place 5 x 5  m 2 linear ramp 6  T/s Evolution of local flux density 7mT7.4mT7.9mT

24. Why small and big jumps ? Nb films: also 2 types of jumps, big and small: James et al., Phys.C 2000 Nowak et al, PRB 1997 Both types of jumps have the same threshold T=10K the same mechanism

25.  all jumps  i  final  initial = ? < 100% Fraction of flux arrived via jumps: Distribution functions of jump sizes Dendritic 10% 50% 90% Some flux penetrates into the sample via very small jumps or without jumps at all resolution limit