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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 42, NO. 10, OCTOBER 2014
predominantly due to the ions during formation. Electrons that are present in this region will remain as a neutralizing- background fluid. Once ∇ × B becomes large, after a closed- field line configuration has been established, electron flow will commence and contribute to the total current.
Simulations show that the applied-magnetic field is modified early and that complete reversal is established by 60 μs. Much of the plasma is swept into the FRC core region, establishing a rigid-rotor equilibrium. The ion-rotational velocity reaches a value, Viθ = 2.5 × 107 cm/s and remains fairly constant for the duration of the simulation period, up to 150 μs. After 100 μs, the rotating plasma is confined as a stationary FRC, except for some slow radial and axial compression. The maximum ion temperature at 150 μs reaches Ti = 50 eV and density, ni = 1.5 × 1014 cm−3 . The net integrated current density over the entire region of FRC gives a total current of ∼30 kA. These parameters are consistent with experimental measurements.
V. CONCLUSION
A hybrid MHD model is used to study the formation, evo- lution, and equilibrium of a FRC, when an inductive-electric field is applied. The approach retains the MHD equations for the radial and axial directions, and a two-fluid description for the azimuthal direction. The model is 2-D and is applied to a magnetized plasma, where the ion-Larmor radius is comparable with the scale radius of the confinement vessel and the electron-Larmor radius is small. The inductive-electric field accelerates ions, producing an azimuthal current and a rigid-rotor equilibrium.
The results of the simulations are supported by previous experiments and may have relevance to FRC experiments where toroidal plasma spin-up is observed. This hybrid model may also be relevant to space-plasma, magnetic-reconnection processes, for example, those occurring in the magnetotail and in solar flares, where a similar class of plasma conditions are believed to exist. The usual approach to magnetic-reconnection
is that the magnetic energy is converted into particle energy, due to a resistive, or Hall process. A clear mechanism leading to the formation of solar flares and geomagnetic storms has yet to be established. The present model may provide a simple, self-consistent method to convert magnetic energy into particle energy, by properly taking the ion motion into account.
ACKNOWLEDGMENT
The authors would like to thank Prof. P. K. Shukla (deceased) and Dr. D. Gupta at Tri Alpha Energy, Inc., Rancho Santa Margarita, CA, USA, for their helpful and stimulating contributions.
REFERENCES
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