A new technique for calculating toroidal harmonic coefficients for curl-free magnetic fields in helical toroidal devices
✍ Scribed by E Thomas Jr.; G.E Sasser; S.F Knowlton; J.D Hanson; R.F Gandy
- Book ID
- 104109654
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 786 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0010-4655
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✦ Synopsis
In a curl-free toroidai magnetic system, the vector magnetic field may be derived from a scalar magnetic pozer~ expressed as a series of toroidal harmonic functions. A new method of computing the coefficients of the torokla| harmonics of the magnetic scalar potential is presented in this paper. The method uses Fourier integrals performed over the po~k~ and toroidal angles on a closed toroidal sorface. The integraud includes the component of the magnetic field normal to ~he toroidal surface and a muqiplying factor chosen to create a set of simple equations which are |i,'rear in the coeffic/eB~s. set of equations is then inverted to obtai,'l the toroidal harmonic coefficients. The magnetic fields calculated using ff~e magnetic scalar potential with these coefficients are found to agree well with the original magnetic fiekt even for a sm~| number of coefficients. For a small number of coefficients used in the scalar potential, the time required to cak:ulate the magnetic field is reduced by up to a factor of five from standard Biot-Savart methods.