Reduction of core-resonant mϭ1 magnetic fluctuations and improved confinement in the Madison Symmetric Torus ͓Dexter et al., Fusion Technol. 19, 131 ͑1991͔͒ reversed-field pinch have been routinely achieved through control of the surface poloidal electric field, but it is now known that the achieved confinement has been limited in part by edge-resonant mϭ0 magnetic fluctuations. Now, through refined poloidal electric field control, plus control of the toroidal electric field, it is possible to reduce simultaneously the mϭ0 and mϭ1 fluctuations. This has allowed confinement of high-energy runaway electrons, possibly indicative of flux-surface restoration in the usually stochastic plasma core. The electron temperature profile steepens in the outer region of the plasma, and the central electron temperature increases substantially, reaching nearly 1.3 keV at high toroidal plasma current ͑500 kA͒. At low current ͑200 kA͒, the total beta reaches 15% with an estimated energy confinement time of 10 ms, a tenfold increase over the standard value which for the first time substantially exceeds the constant-beta confinement scaling that has characterized most reversed-field-pinch plasmas.
A hot stable field-reversed configuration (FRC) has been produced in the C-2 experiment by colliding and merging two high-β plasmoids preformed by the dynamic version of field-reversed θ-pinch technology. The merging process exhibits the highest poloidal flux amplification obtained in a magnetic confinement system (over tenfold increase). Most of the kinetic energy is converted into thermal energy with total temperature (T{i}+T{e}) exceeding 0.5 keV. The final FRC state exhibits a record FRC lifetime with flux confinement approaching classical values. These findings should have significant implications for fusion research and the physics of magnetic reconnection.
Several of the known solutions of the Einstein field equations are re-examined and it is shown that these solutions are special cases of more general solutions of the field equations. The explicit solution of the field equations in terms of known functions is also found for the case of Volkoff's massive spheres. In the last section of this paper a mathematical procedure for generating solutions of the field equations is outlined.
Energy confinement comparable with tokamak quality is achieved in the Madison Symmetric Torus (MST) reversed field pinch (RFP) at a high beta and low toroidal magnetic field. Magnetic fluctuations normally present in the RFP are reduced via parallel current drive in the outer region of the plasma. In response, the electron temperature nearly triples and beta doubles. The confinement time increases tenfold (to ∼10 ms), which is comparable with Land H-mode scaling values for a tokamak with the same plasma current, density, heating power, size and shape. Runaway electron confinement is evidenced by a 100-fold increase in hard x-ray bremsstrahlung. Fokker-Planck modelling of the x-ray energy spectrum reveals that the high energy electron diffusion is independent of the parallel velocity, uncharacteristic of magnetic transport and more like that for electrostatic turbulence. The high core electron temperature correlates strongly with a broadband reduction of resonant modes at mid-radius where the stochasticity is normally most intense. To extend profile control and add auxiliary heating, rf current drive and neutral beam heating are in development. Low power lower-hybrid and electron Bernstein wave injection experiments are underway. Dc current sustainment via ac helicity injection (sinusoidal inductive loop voltages) is also being tested. Low power neutral beam injection shows that fast ions are well-confined, even in the presence of relatively large magnetic fluctuations.
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