## Faculty Research Work

### Analysis of the frequency dependence of the AC loss in MgB2 based on the eddy current model

#### College

College of Science

Physics

#### Document Type

Conference Proceeding

#### Source Title

Proceedings of the 19th Philippine Physics Congress

2001

#### Abstract

The frequency dependence of the AC loss peak in x"(T) of MgB2 is analyzed using the eddy current model. In this model, eddy current loops are induced in the grain of a superconductor subject to small AC fields. This current, which generates lhe loss peak, is proportional to the area enclosed by the loops and inversely proportional to the resislance of the loops. The AC loss peak is a result of the competition between the rapidly diminishing resistance of the material below Tc and the decreasing area where the hannonic field can thread as lhe penetralion depth λ decreases in the superconducting state [1]. Utilizing equations for temperature dependent penetration depth and electrical resistance, a fitting function for x"(T) which is proportional to i(T)/Bac is obtained. A circular grain of radius r is assumed. For a particular λ, the area where the field can penelrates is equal to A(T) =πr2 -(r -λ(T))2 (2)

The temperature dependence of the penetration depth is chosen such that A(T) attains a zero value at low temperatures. The resulting eddy current equation is

(2)

At Tc, A.=lo and is very large compared to the grain radius; r. At temperatures 􀃎here r is less than λ, the penetrated area is maintained at A (T) = πr2 . lc is a fitting parameter that describes the rate of decrease of λ(T). R0 is the value of the electrical resistance at Tc. R0 is constant for all measurement since the material is in a region where the magnetization varies linearly with field. An increase in R0 indicates a nonlinear magnetization. b is a fitting parameter that describes the rale of decrease of R(T). The superimposed plots of the experimental data and the resulting curve employing the eddy current model are shown in the figure. The corresponding model fit show satisfactory agreement with the experimental X"(T) measurements.

As the frequency is increased from 200 to 3200Hz, 1c decreases. This means that λ decreases faster at a higher frequency and the flux penetrated area attain the zero value faster. Thus. the penetration depth decreases with increasing frequency. On the other hand, the fitting parameter b, increases as the frequency is increased from 200 to 3200Hz. This equivalently means that the rate of change of R(T) is decreased with increased frequency. Thus, the resislance increases with frequency. This behavior is similar to the behavior of metals in the presence of AC field. Thus, indicating that MgB2 indeed a highly metallic material as previously observed.

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Physics

#### Keywords

Annealing of crystals; Liquid phase epitaxy; Superconductors