An analytic determination of beta poloidal and internal inductance in an elongated tokamak from magnetic probe measurements
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Analytic calculations of the magnetic fields available to magnetic diagnostics are performed for tokamaks with circular and elliptical cross sections. The explicit dependence of the magnetic fields on the poloidal beta and internal inductances is sought. For tokamaks with circular cross sections, Shafranov`s results are reproduced and extended. To first order in the inverse aspect ratio expansion of the magnetic fields, only a specific combination of beta poloidal and internal inductance is found to be measurable. To second order in the expansion, the measurements of beta poloidal and the internal inductance are demonstrated to be separable but excessively sensitive to experimental error. For tokamaks with elliptical cross sections, magnetic measurements are found to determine beta poloidal and the internal inductance separately. A second harmonic component of the zeroth order field in combination with the dc harmonic of the zeroth order field specifies the internal inductance. The internal inductance in hand, measurement of the first order, first harmonic component of the magnetic field then determined beta poloidal. The degeneracy implicit in Shafranov`s result (i.e. that only a combination of beta poloidal and internal inductance is measurable for a circular plasma cross section) reasserts itself as the elliptic results are collapsed to their circular limits.
- Research Organization:
- Massachusetts Inst. of Tech., Cambridge, MA (United States). Plasma Fusion Center
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- FG02-91ER54109
- OSTI ID:
- 10158210
- Report Number(s):
- DOE/ER/54109-T3; PFC/RR-92-6; ON: DE92016294
- Resource Relation:
- Other Information: TH: Thesis (M.S.); PBD: Feb 1992
- Country of Publication:
- United States
- Language:
- English
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