Yoshiomi Kondoh

Numerical study of an ion acceleration in a z‐pinch type plasma focus

Motions of ions in the plasma focus are investigated theoretically using a model for a z‐pinch type plasma focus. Macroscopic radial motions of plasma are calculated numerically using the snowplow model, the Leontovich–Osovets’ equation, and a circuit equation. The equations of motion of ions are solved in the presence of fields induced in the pinched phase of the macroscopic motion. It is found that in the collapse phase there appears a betatron‐like acceleration process of ions with negligible drift velocity. It is also shown that a strong free‐streaming acceleration process leading to high, axial velocity of ions in the direction of current flow appears in the expansion phase.

Stable equilibrium configuration of reversed-field pinch with the partially-relaxed-state condition jp = αBp/μ0

The stability of a partially-relaxed-state model of the reversed-field pinch (RFP) with the condition jp = αBp/μ0 is investigated numerically. An F-θ stability diagram obtained here suggests that, to obtain a stable high-β RFP plasma experimentally, it is necessary to operate the RFP with a relatively high field reversal ratio, F, and a medium pinch parameter, θ, e.g. F − 1 and θ 2.0. It is also suggested that, to confine a stable RFP plasma for long periods, the state of the RFP plasma should be kept inside a stable region in the F-θ stability diagram by field control. Numerical results on the influence of toroidal effects on stability show that the βax–value of the marginally stable configuration with F = 0 with respect to the high-m localized modes decreases with increasing inverse aspect ratio , e.g. βax at = 1/3 is about 70% of that at = 0 (i.e. a cylindrical plasma).

An Energy Principle for Axisymmetric Toroidal Plasmas

It is proved that both the global invariant with respect to helicity given by Taylor and that with respect to helical flux given by Kadomtsev are included in a generalized fundamental global invariant composed of poloidal and toroidal magnetic fluxes, which brings about the well-known force-free equilibria µ 0 j =λ 0 B as the minimum-magnetic-energy state. By implicating the plasma-wall interaction in the global constraint, we can obtain the minimum-energy state which satisfies the experimental boundary condition of j =0 at the wall. Formulation of an energy principle including the edge plasma effects for slightly resistive MHD plasmas is presented. Two typical numerical results of the Tokamak-like equilibria and the reversed-field-pinch equilibria are shown.

Evolution of reversed-field-pinch plasma through partially relaxed states

It is shown that two typical kinds of experimental evolution of a re versed-field-pinch plasma (RFP plasma) can be interpreted fairly well by using a partially-relaxed-state model. The RFP plasma tends to evolve along the curve of constant beta on axis in the F — θ diagram. A proposal of how to achieve a stable RFP plasma with a higher β-value by using an F — θ stability diagram is presented.

Partially Relaxed Minimum Energy States of Reversed-Field-Pinch Plasma

An energy principle is formulated for construction of toroidal equilibria in partially relaxed minimum energy states. It is shown that additional global constraint yields an additional condition on the force-free current term of the MHD equilibrium equation. It is clarified that the partially relaxed state model (PRSM) for toroidal plasmas, such as the tokamak plasma and the reversed-field-pinch plasma (RFP plasma), represents the minimum-energy states with finite β-values under global invariants. Comparisons of numerical results by the PRSM for the RFP plasma with two typical experimental data indicate that RFP configurations close to the PRSM are realized in the two RFP experiments. The most advanced partially relaxed state with finite β-values is also discussed.

Power deposition by neutral beam injected fast ions in field-reversed configurations

The effects of Coulomb collisions on neutral beam (NB) injected fast ions into field-reversed configuration (FRC) plasmas are investigated by calculating the single particle orbits, where the ions are subject to the slowing-down and pitch-angle collisions. The Monte Carlo method is used for the pitch-angle scattering, and the friction term is added to the equation of motion to show the effects of the slowing-down collision, such as the deposited power profile. The calculation parameters used are relevant to the NB injection on the FRC injection experiment device [T. Asai, Y. Suzuki, T. Yoneda, F. Kodera, M. Okubo, and S. Goto, Phys. Plasmas 7, 2294 (2000)]. It is found that the dominant local power deposition occurs in the open field region between the X point and the mirror point because of a concentration of fast ions and a longer duration travel at the mirror reflection point. In the present calculation, the maximum deposited power to the FRC plasma is about 10% of the injected power. Although the pitch-angle scattering by Coulomb collision destroys the mirror confinement of NB injected fast ions, this effect is found to be negligible. The loss mechanism due to nonadiabatic fast ion motion, which is intrinsic in nonuniform FRC plasmas, has a much greater effect than the pitch-angle scattering by Coulomb collision.The effects of Coulomb collisions on neutral beam (NB) injected fast ions into field-reversed configuration (FRC) plasmas are investigated by calculating the single particle orbits, where the ions are subject to the slowing-down and pitch-angle collisions. The Monte Carlo method is used for the pitch-angle scattering, and the friction term is added to the equation of motion to show the effects of the slowing-down collision, such as the deposited power profile. The calculation parameters used are relevant to the NB injection on the FRC injection experiment device [T. Asai, Y. Suzuki, T. Yoneda, F. Kodera, M. Okubo, and S. Goto, Phys. Plasmas 7, 2294 (2000)]. It is found that the dominant local power deposition occurs in the open field region between the X point and the mirror point because of a concentration of fast ions and a longer duration travel at the mirror reflection point. In the present calculation, the maximum deposited power to the FRC plasma is about 10% of the injected power. Although the pitc...

Losses of neutral beam injected fast ions due to adiabaticity breaking processes in a field-reversed configuration

Losses of neutral beam (NB) injected fast ions from the confinement region of a field-reversed configuration (FRC) with a strong magnetic mirror are numerically analyzed for parameters relevant to NB injection experiments on the FIX (FRC injection experiment) device [T. Asai et al., Phys. Plasmas 7, 2294 (2000)]. Ionization processes of beam particles are calculated by the Monte Carlo method. The confinement of beam ions is discussed with the concept of accessible regions that restrict the ion excursion and are determined from two constants of motion, the kinetic energy and canonical angular momentum, in the case of an axisymmetric and a steady state FRC without an electrostatic field. From the calculation of the accessible regions, it is found that all the fast ions suffer from the orbit loss on the wall surface and/or the end loss. Single particle orbits are also calculated to find a difference of confinement properties from the results by employing the accessible regions. The magnetic moment is observe...

Experimental Study on Favorable Properties of Compound RF Discharge Plasmas with a Tapered Shape Hollow Cathode Compared with a Plane Cathode

An experimental investigation on the characteristics of compound RF discharge plasmas with a tapered shape hollow-cathode (HC) compared with a plane cathode is presented for the development of processing plasma. Dense plasmas are shown to be generated in the wide range of working pressures, 3< p<90 Pa. It is clarified that the higher RF power yields the greater HC effect to increase the ratio of electron density with the HC to that without it. The HC effect is shown to work well for decreasing the self-bias potential compared with the plane cathode. It is clarified that the dense plasma with relatively low electron temperature produced by the compound RF discharge results from the synergetic effect of the lowered input RF power density and the effective increased discharge area due to the HC effect.

Uniform RF Discharge Plasmas Produced by a Square Hollow Cathode with Tapered Shape

A square hollow cathode with a tapered shape (square HCT) is developed in order to produce highly uniform and dense plasmas (density ~ 6×1010 cm-3) with a wide range of operating pressures. It is shown experimentally that the plasma density produced by the HCT is higher than that produced by a plane cathode from 0.02 Torr to 0.2 Torr. It is demonstrated experimentally that uniform plasmas can be produced by modifying the structure of the HCT for different operating pressures. It is shown that an additional outer hollow cathode is useful to compensate the nonuniformity of plasmas due to edge effects. With the use of the outer hollow cathode for the modified HCT, highly uniform plasmas are produced within almost the entire surface of the grounded square electrode.

Stability conditions for perturbations with a singularity derived from the energy principle

The stability conditions of an equilibrium plasma for perturbations with a singularity are derived from the energy principle for a non-ideal MHD plasma. The stability conditions are shown to include a stability criterion for the helical resistive tearing mode that is equivalent to the stability condition derived from conventional tearing mode theory. The effects of the resistive wall on stability are also discussed briefly.