Statistische Theorie der Haftkraft von Flußliniensystemen in harten Supraleitern. I. Eigenschaften des statistischen Kraftfeldes

Abstract

This paper is concerned with the mathematical properties of the random field of force Fp( T ) acting on a single line element of a fluxline due to a statistical distribution of the defects. With the assumption of a linear interaction between fluxlines and defects it follows from the central limit theorem that F p ( r ) corresponds t o a Gaussian distribution. I n this case the complete statistical information on F p ( r ) is contained in the correlation matrix B(a), from which we obtain the wavelength, the mean amplitude, and the anisotropy of the random field F p ( r ) . These quantities are determined for edge dislocations parallel to the fluxlines. The dislocation-fluxline interaction used is the socalled volume effect. For sufficiently high dislocation densities (e 2 l/p) the wavelength l p is shown to be independent of e (Zp e 2n l), while the mean amplitude (dispersion) is proportional to 15.

The Flux‐Line Lattice in Type‐II Superconductors

“…Some of the later work is quoted in the following. Stochastic force fields are treated in [87]. A statistical summation of point pins is performed in [88] by considering "bundelling" of FLs.…”

Dielastic interaction of the flux line lattice with internal stresses of crystal imperfections. II. Second-order interaction force between flux lines and crystal dislocations

“…Choosing the coordinate origin at the FL center (rF = 0), the interaction potential is given by (6) Here AG denotes the Fourier transform (FT) of the shear modulus change AG(r), defined by A~3~(k) = (1/27r)//AG(r) exp (-ik. r)dZr (7) ./ ,d Analogously, ez~ is the FT of the square of the strain component of the screw dislocation. In the second integral in (6), the convolution theorem has been applied.…”

Die Fließspannung des Flußliniengitters in supraleitern zweiter art

“…gilt (Kornfeld und Kronmuller 1971) Fur die mittlere WellenlBnge I,, In (29) und (32) wurde die Kraft pro Lgngeneinheit auf die FLV in den auf die Kristallversetzung bezogenen Koordinaten x , und x3 angegeben (siehe Fig. 9).…”