Das Vektorpotentialfeld stromumflossener Toroide

The magnetic toroidal sector as a broad-band electron–positron pair spectrometer I. lepton trajectories

“…The fact that surfaces of constant  are toroids makes toroidal coordinates very appropriate for investigation of magnetic fields generated by coils configured in toroidal geometry [99][100][101][102].…”

“…for the future calculation of the lepton trajectories in classical Hamiltonian equations of motion, one has accordingly to evaluate the vector potential for 0.7 (see appendix 1). Note, that in toroidal coordinates the magnetic vector potential has only one non-vanishing component A≠0, whereas A=A=0 [101].…”

“…The corresponding vector potential A may either be approximated by analytical models or may be derived directly from given current density distributions, preferably in toroidal coordinates [100][101][102]141],but see also Appenix 1.…”

“…It was shown that corresponding numerical evaluations of expansion coefficients in toroidal coordinates may be performed significantly faster than standard Biot-Savart techniques [99,[100][101][102][119][120][121][122]141] which is of relevance as guidance for further analytical analysis, e.g. for Hamilton equations of motion, is desirable.…”

Magnetic Energy of Surface Currents on a Torus

“…However, the problem has also technological import in, e.g., plasma fusion research and astrophysics. In the past, the work on toroids has focused on the vector potential and magnetic fields of such currents [3][4][5][6][7][8][9][10][11][12][13][14][15], on their inductance and energy [16][17][18][19][20][21][22], as well as on force free configurations of such currents [23][24][25][26][27]. In particular the problem of surface currents, either due to skin effect, or due to superconductivity or perfect conductivity of the tori, has been investigated [28][29][30][31][32][33][34].…”