Oblate Field-reversed Configuration Research Articles

Stability and confinement improvement of an oblate field-reversed configuration by using neutral beam injection

A low-energy, high-current neutral beam injection (NBI) was applied to an oblate field-reversed configuration (FRC) for the first time. The NB fast ions reduce growth rates of low-n modes dangerous for the oblate FRC, extending the FRC lifetime by a factor of 1.2. The reduced loss power of 5 MW is much higher than the NBI power of 0.5 MW, indicating that the NBI not only heats the FRC plasma but also improves its stability and transport properties. The NBI also maintains higher pressure and current density profiles of the FRC, improving its flux and energy decay times by a factor of 2.

Inductive sustainment of oblate field-reversed configurations with the assistance of magnetic diffusion, shaping, and finite-Larmor radius stabilization

Oblate field-reversed configurations (FRCs) have been sustained for >300μs, or >15 magnetic diffusion times, through the use of an inductive solenoid. These argon FRCs can have their poloidal flux sustained or increased, depending on the timing and strength of the induction. An inward pinch is observed during sustainment, leading to a peaking of the pressure profile and maintenance of the FRC equilibrium. The good stability observed in argon (and krypton) does not transfer to lighter gases, which develop terminal co-interchange instabilities. The stability in argon and krypton is attributed to a combination of external field shaping, magnetic diffusion, and finite-Larmor radius effects.

Inductive Sustainment of a Field-Reversed Configuration Stabilized by Shaping, Magnetic Diffusion, and Finite-Larmor-Radius Effects

Oblate field-reversed configuration (FRC) plasmas are sustained for up to 350 micros, or approximately 15 poloidal flux-confinement times, in the magnetic reconnection experiment. The diamagnetic equilibrium is maintained in argon plasmas as a balance of an inward pinch and outward diffusion. Numerical and analytic models show that the observed stability is provided by a combination of plasma shaping, magnetic diffusion, and finite-Larmor radius effects. FRCs formed with lighter ions, which benefit less from these stabilizing effects, succumb to rapid instability and cannot be sustained.

Merging formation and current amplification of field‐reversed configuration

AbstractThe merging formation of the field‐reversed configuration (FRC) has been developed in the TS‐3 merging experiment, leading us to a new scenario of FRC slow formation, heating and current amplification. Two force‐free spheromaks with opposing toroidal fields were merged together in the axial direction to form a high‐β FRC with higher efficiency than the conventional field‐reversed theta‐pinch method. This unique relaxation from the force‐free (β ∼ 0.05 − 0.1) spheromaks to the high‐β (β ∼ 0.7 − 1) FRC is attributed to the conversion of toroidal magnetic energy into ion thermal energy through the reconnection outflow. A central ohmic heating (OH) coil worked successfully to amplify the FRC plasma current by a factor of 2. Toroidal mode analysis of magnetic structure indicated that the tilting stability of the oblate FRC was provided by an ion kinetic effect. This oblate FRC is also useful as an initial equilibrium to produce a high‐βp spherical tokamak (ST) with diamagnetic toroidal magnetic field, suggesting the close relationship between FRCs and high‐βp STs in the second stable region of the ballooning mode. © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Equilibrium and stability studies of oblate field-reversed configurations in the Magnetic Reconnection Experiment

The equilibrium and stability of oblate field-reversed configurations (FRCs) have been studied in the Magnetic Reconnection Experiment [M. Yamada et al., Phys. Plasmas 4, 1936 (1997)]. In the absence of a passive stabilization, tilt and shift instabilities often become unstable, with the tilt in particular limiting the plasma lifetime. The tilt instability can be mitigated by either including a passive stabilizing conductor, or by forming very oblate plasmas. Large perturbations (n=2 and 3) may still remain after passive stabilization is applied. These perturbations have the characteristics of co-interchange modes, which have never been observed, and can lead to the early termination of the plasma. The co-interchange modes can be minimized through the formation of plasmas with a very oblate shape, leading to the maximum FRC lifetime. A code has been developed to calculate equilibria for these plasmas. A rigid-body model explains the improved stability of oblate plasmas to n=1 tilt modes. Numerical calculations indicate improved stability to n⩾2 co-interchange modes for the very oblate plasma shapes.

Spontaneous and artificial generation of sheared-flow in oblate FRCs in TS-3 and 4 FRC Experiments

Spontaneous formation of toroidal flow was measured for the first time in oblate field-reversed configurations (FRCs) produced in TS-3 and TS-4 experiments. The toroidal ion flow (Vi ≈ 10 km s−1) was found to peak around the magnetic axis, indicating that the FRC had a peaked ion current in sharp contrast to its hollow electric current. The peaked ion flow also indicated the formation of high flow shear inside the separatrix. The toroidal flow was observed to deform the magnetic field lines of the FRC, producing bipolar toroidal field profile. In high-s FRC (averaged number of ion gyro-radii in the separatrix: `s' = 4.5) with slow flow, its n = 1 mode kept growing, causing collapse of the whole configuration. However, in low-s FRC (s = 3) with fast flow, the rotating n = 2 mode (saturated) became dominant after n = 1 mode saturation. The spontaneous formation of flow-shear possibly transformed the n = 1 mode into the n = 2 mode, suggesting a new sheared-flow stabilization of the n = 1 mode. The flow-shear was also generated artificially using the `sling shot' effect of the counterhelicity reconnection. The n = 1 and 2 mode amplitudes were reduced to (1/5)–(1/10) due to the generated flow-shear. A new method for continuous sheared-flow generation was proposed for stabilization and heating of FRC by the use of intermittent merging of spheromaks with opposing toroidal field.

Numerical study of global stability of oblate field-reversed configurations

Global stability of the oblate (small elongation, E<1) Field-Reversed Configuration (FRC) has been investigated numerically using both three-dimensional magnetohydrodynamic (MHD) and hybrid (fluid electrons and kinetic ions) simulations. For every nonzero value of the toroidal mode number n, there are three MHD modes that must be stabilized. For n=1, these are the interchange, the tilt and the radial shift; while for n>1 these are the interchange and two co-interchange modes with different polarization. It is shown that the n=1 tilt mode becomes an external mode when E<1, and it can be effectively stabilized by close-fitting conducting shells, even in the small Larmor radii (MHD) regime. The tilt mode stability improves with increasing oblateness, however at sufficiently small elongations the radial shift mode becomes more unstable than the tilt mode. The interchange mode stability is strongly profile dependent, and all n⩾1 interchange modes can be stabilized for a class of pressure profile with separatrix beta larger than 0.035. Our results show that all three n=1 modes can be stabilized in the MHD regime, but the stabilization of the n>1 co-interchange modes still remains an open question.

Ultra-high-beta spherical tokamak formation by use of an oblate field-reversed configuration

A new slow formation of oblate field-reversed configuration (FRC) has been developed in the Tokyo University Spherical Torus No. 3 (TS-3) merging experiment using two merging spheromaks with opposing toroidal field. This unique technique was extended to a novel formation of ultra-high-beta (50%–70%) spherical tokamak (ST) by applying an external toroidal field Bt,ext to the FRC so produced. The high-beta ST was found to have a diamagnetic toroidal field in sharp contrast with low-beta STs with strong paramagnetic toroidal fields. High-beta properties of FRCs including their hollow current profile were maintained during the equilibrium transition, suggesting a close relationship between FRCs and high-beta STs in the second stability regime.

Full magnetohydrodynamic simulation of the tilting instability in a field-reversed configuration

Nonlinear evolution of the tilting instability in a field-reversed configuration (FRC) is investigated by means of a three-dimensional full magnetohydrodynamic simulation. Three types of plasma model are considered, i.e., case (a) where the plasma is confined by a uniform external field, case (b) where the plasma is confined by a mirror external field, and case (c) where the plasma rotates around the major axis. For the prolate FRC the internal tilt mode cannot stay at a low amplitude but keeps growing irrespective of whether the mirror field exists or not. When the initial configuration is substantially deformed, the instability triggers an external mode at the plasma–vacuum boundary because of the pressure imbalance. The outgoing flow driven by the external mode tears the plasma into two pieces, and the torn pieces move away toward the axial edges. The growth time is nearly equal to the transit time for the Alfvén wave to propagate over the plasma length. When the plasma is driven to spin with the Mach number of M=1.5, the growth rate is halved compared to the nonrotating case. The spin stabilization is expected to be complete for M>2.5. It is also found that the oblate FRC plasma is linearly unstable against the external tilt mode.