## Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes

## Abstract

Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various nonellipsoidal shapes. The procedure is based on calculating the total magnetic moment by integrating the magnetic induction obtained from a full three-dimensional (3D) solution of the Maxwell equations using an adaptive mesh. The results are relevant for superconductors (and conductors in ac fields) when the London penetration depth (or the skin depth) is much smaller than the sample size. In conclusion, simple but reasonably accurate approximate formulas are given for practical shapes including rectangular cuboids, finite cylinders in axial and transverse fields, as well as infinite rectangular and elliptical cross-section strips.

- Authors:

- Ames Lab. and Iowa State Univ., Ames, IA (United States). Dept. of Physics & Astronomy
- Ames Lab., Ames, IA (United States)

- Publication Date:

- Research Org.:
- Ames Laboratory (AMES), Ames, IA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE

- OSTI Identifier:
- 1464479

- Alternate Identifier(s):
- OSTI ID: 1461931

- Report Number(s):
- IS-J-9726

Journal ID: ISSN 2331-7019; PRAHB2; TRN: US1902390

- Grant/Contract Number:
- AC02-07CH11358

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review Applied

- Additional Journal Information:
- Journal Volume: 10; Journal Issue: 1; Journal ID: ISSN 2331-7019

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Prozorov, R., and Kogan, V. G. Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes. United States: N. p., 2018.
Web. doi:10.1103/PhysRevApplied.10.014030.
```

```
Prozorov, R., & Kogan, V. G. Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes. United States. doi:10.1103/PhysRevApplied.10.014030.
```

```
Prozorov, R., and Kogan, V. G. Sun .
"Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes". United States. doi:10.1103/PhysRevApplied.10.014030. https://www.osti.gov/servlets/purl/1464479.
```

```
@article{osti_1464479,
```

title = {Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes},

author = {Prozorov, R. and Kogan, V. G.},

abstractNote = {Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various nonellipsoidal shapes. The procedure is based on calculating the total magnetic moment by integrating the magnetic induction obtained from a full three-dimensional (3D) solution of the Maxwell equations using an adaptive mesh. The results are relevant for superconductors (and conductors in ac fields) when the London penetration depth (or the skin depth) is much smaller than the sample size. In conclusion, simple but reasonably accurate approximate formulas are given for practical shapes including rectangular cuboids, finite cylinders in axial and transverse fields, as well as infinite rectangular and elliptical cross-section strips.},

doi = {10.1103/PhysRevApplied.10.014030},

journal = {Physical Review Applied},

number = 1,

volume = 10,

place = {United States},

year = {2018},

month = {7}

}

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