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Phys. Plasmas 21, 032507 (2014)
present. The result is a net plasma rotation and a plasma cur- rent predominantly due to the ions, at least initially during formation. Electrons present in this region remain as a neutralizing-background fluid. However, once r B becomes large, that is, after a closed-field line configuration has been established, the electrons contribute to the total current.
The simulations presented here show that the applied- magnetic field is modified early, upon formation, and that complete field-reversal is established by 50 ls. By this time most of the plasma is swept-up into the FRC core region, establishing a rigid-rotor equilibrium. The ion-rotational ve- locity reaches a maximum value Vih 1⁄4 3.0 107 cm/s by 20 ls, then decays to 2.0 107 cm/s and remains fairly con- stant until 50 ls. After 50 ls, it decays slowly for the dura- tion of the simulation period, up to 150 ls. After 100 ls, the rotating plasma is confined as a stationary FRC configura- tion, except for some radial and axial compression. The max- imum ion temperature at 150 ls reaches Ti 1⁄4 60 eV and the density ni 1⁄4 1.5 1014 cm 3.
Using these values for n and T and assuming the plasma is unity beta allows the outer magnetic field to be estimated as Bz 1⁄4 600 G, which agrees with the simulations. The total current density integrated over the entire region of FRC gives a total current of Ip 1⁄4 28 kA, consistent with the experiments.
The radial profiles for ni and Bz also agree with the experimentally measured profiles. The only difference is in the measured magnetic field near the outer boundary, which is 3–4 times higher in the simulation than in experiment. This may be due to the higher temperature of the simulated plasma, compared to that measured in the experimental plasma. In the above simulations, the plasma temperature reaches to about 60 eV, whereas the measured value is about 6 eV. The simulations consider deuterium as the only plasma component, whereas impurities are not only added but also exist as contaminants in the experiment, producing a lower temperature, by radiative cooling, and a narrower radial pro- file for the density and a compressed magnetic field between the FRC and the outer boundary of the simulation.
V. CONCLUSIONS
A hybrid MHD model is used to simulate the accelera- tion, formation, evolution, and equilibrium of a flux-coil pro- duced FRC. The simulation retains the MHD equations for the radial and axial components, and a two-fluid description for the azimuthal component. The model is two dimensional and is applied to a magnetized plasma, where the ion- Larmor radius is comparable to the dimensions of the simu- lation boundaries for the confinement vessel, and the electron-Larmor radius is small. The inductive-electric field accelerates ions, producing an azimuthal current and a rigid- rotor-like, quasi-equilibrium state. The simulation produces results similar to experimental measurements. These results may be relevant to other FRC experiments produced in a reversed-field H-pinch, where plasma spin-up is observed in
the azimuthal direction, reversing direction outside the FRC near the separatrix.
This hybrid-simulation approach may also be of interest to space-plasma magnetic-reconnection processes, for exam- ple, those in the earth’s magnetotail and in solar flares, where magnetized plasmas and strong electric fields may also exist. The usual approach to magnetic-reconnection assumes that the magnetic energy is converted into particle energy, due to a resistive- or Hall type- processes. A clear mechanism lead- ing to the formation of solar flares and geomagnetic storms has yet to be established. The present approach may provide a means to convert magnetic energy into particle energy, by properly taking into account the ion motion; as previously suggested.5–7
ACKNOWLEDGMENTS
We acknowledge the gracious and insightful contribu- tions of Dr. Deepak Gupta (TAE) and (the late) Professor P. K. Shukla.
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