The angular velocity Ωc of the impurity ions (CV) is measured spectroscopically for the FRC (Field-Reversed-Configuration) plasmas confined in the θ-pinch region and translated into the confinement region with magnetic mirror field. The FRC plasma confined in the θ-pinch region becomes unstable due to the n=2 rotational instability which can be suppressed by the multipole magnetic field. The ion rotation in the stabilized plasma is almost equal to the velocity in the unstabilized case, suggesting that the multipole field acts on the plasma surface due to the skin effect and suppresses the instability without changing the field configuration within the separatrix radius. The FRC plasma translated in the confinement region is stable without destructive instability. The ion rotation in such a plasma indicates that a suppression mechanism of the n=2 instability exists, which is excited by the rotation in the confinement region.

In order to obtain a detailed density profile of a field-reversed configuration (FRC) plasma, fast-response multichannel heterodyne quadrature interferometers are constructed. Using these interferometers and assuming a rigid-body radial shift motion of the plasma, a spatially fine-grained line integrated density (∫ n dl) profile at its axial midplane is measured. A radial density profile n(r) is reduced from spline fitting of ∫ n dl. The n(r) is found to be nearly an even function of u(=r2/R2−1, R is the magnetic axis radius) as expected. The n(r) is also obtained by the fitting of a line integral of a model n(r) consisting of a modified rigid rotor (RR) profile which can describe the density steepening near the separatrix of the FRC plasma. When the plasma is fat (xs =separatrix radius/coil inner radius=0.63), the density profile is very near to the RR profile itself given by sech2 (Ku), where K is a constant. When the plasma is slender (xs =0.43), the modification is somewhat pronounced. In both cases n(r) at r=R is flatter but near to the RR profile, and the scale length of the density gradient at the separatrix is about twice the ion gyroradius. Detailed error analyses of the fitting parameters are done to show the range of allowed profiles. Although the fitting is accomplished very well (root-mean-square excursion of the fitted ∫ n dl from the measured one is from 1.9% to 2.5%), much variation of n(r) is still possible.

Electrical resistivity at the magnetic axis η(R) and at the separatrix η(rs) of a field-reversed configuration (FRC) plasma produced by theta pinch machines are estimated from detailed interferometric measurements, assuming that the temperature is uniform within the separatrix. The ratio f0[=η(R)/η(rs)] increases with the beta value at the separatrix βs, which is consistent with the fact that f0 decreases when xs (separatrix radius normalized by the inner radius of a theta pinch coil) increases [Phys. Fluids 28, 888 (1985)]. This tendency is a natural consequence of the transport properties of the FRC plasma when the particle confinement time is nearly equal to the decay time of the trapped reversed magnetic flux, as is normally the case. Theoretical expectations of the anomaly of η(rs) over the classical resistivity η0 increases and decreases slightly with βs for the case of the lower hybrid drift and the low-frequency drift instability, respectively. On the other hand, the observed η(rs)/η0 decreases substantially with βs. [The value of η(rs)/η0 changes from about 15 to 5 as βs changes from 0.45 to 0.6.]

The ion rotational angular velocity Ω and the ion temperature Ti of a translated field-reversed configuration (FRC) plasma are measured using neutral beam probe spectroscopy. The value of Ω is ∼(1.0∼1.2)×Ω* at the onset time of the n=2 rotational instability, where Ω* is the ion diamagnetic frequency for a rigid-rotor equilibrium. The ion rotational direction is the same as the ion diamagnetic direction. The value of Ω is smaller than the angular frequency ωre of the n=2 instability, which can yield experimental evidence of the ion kinetic effects on the n=2 instability in the FRC plasma. When the octupole field is applied to the plasma in order to suppress the n=2 deformation, Ω is slightly reduced. The ion temperature Ti is ∼70 eV at the onset time of the n=2 instability.

A numerical algorithm for the time-independent Stefan problem is presented. The heat conducting plate is assumed to be infinitely broad and the heat source of constant intensity is assumed to move with a constant velocity in the plate.The shape of molten pool is determined by correcting successively the provisional shape of the molten pool given beforehand until it satisfies the Stefan condition. The isotherms showing the temperature field are determined successively by starting from the obtained fusion boundary. The algorithm is given for the two-dimensional case and for the axi-symmetric three-dimensional case. Some examples of the results are given for the case of a linear heat source and a point heat source of various intensities.

A compact and pulsed atomic-hydrogen beam source was constructed for the advanced spectroscopic technique of ion-temperature measurements. The mean energy and the equivalent current of the beam were ∼400 eV and ∼13 A/cm2. In this energy region, most of the charge-transferred neutrals in a hydrogen plasma are in the ground state and they emit spectral lines through an electron impact excitation process. The behavior of the neutrals generated by beam probing was analyzed by a Monte-Carlo simulation to study the relation between the temperatures of the plasma ions and the neutrals. The measured temperature of a plasma was 100 eV and its rotation energy 20 eV.

The ion temperature and the energy of gross drift motion of a fully ionized hydrogen plasma with a field-reversed configuration are measured from the observed Doppler profile of the Hβ line from charge exchange neutrals which are generated by a pulsed intense hydrogen beam with energy ∼400 eV. At the beam energy, the generated neutrals are almost hydrogen atoms in the ground state and they emit spectral lines via electron impact excitation. A Monte Carlo analysis shows that the obtained Doppler temperature of the charge exchange neutrals agree with the ion temperature within 6% accuracy. The measured ion temperature and drift energy of the plasma are typically 100 and 10 eV, respectively.

A theoretical analysis based on the magnetohydrodynamic approximation is carried out on the effect of multipole-field suppression of the rotational instabilities excited in a high-β plasma column. The multipole field is assumed not to penetrate into the plasma column but to exert magnetic pressure on its boundary surface in order to suppress the distortion of the plasma column. Analytical theory, which takes into account only the effects of the fundamental wave, gives the stability criterion for the n=2 mode as Bs≥Bs,c= 1/2 (m−1)−1/2rs‖Ω‖(μ0 ρ0)1/2, where rs, ρ0, and Ω are the radius, mass density, and rotational angular velocity of the plasma column, respectively, 2m the order of the multipole field, Bs the field strength at radius rs in the vacuum state, and μ0 the permeability of vacuum. Numerical calculations including the effects of the waves parasitic to the fundamental wave support the stability criterion for hexapole (m=3) and octopole (m=4) fields. For quadrupole (m=2) fields, it is shown that the stable range of Bs is limited between 0.841 Bs,c and 0.856 Bs,c, where Bs,c is the analytical threshold for m=2.

Importance of plasma diagnostics as well as of diagnosticians is addressed by quoting the Langmuir probe with some remarks on its application and topics on the diagnostics for very first z-pinch experiment at Osaka University.

A fast response frequency-modulated interferometric polarimeter was designed and constructed with a single 28 μm H2O laser for high density plasma diagnostics. This newly developed modulation system employs an electro-magnetically driven movable mirror to achieve the modulation frequency beyound 1 MHz for about 100 μs duration. The movable mirror performance is studied experimentally in detail. The determination of the Faraday rotation angle is based on the zero-crossing method for the observed beat signals produced by two kinds of rotating plane-polarized waves. The feasibility of the polarimeter constructed was verified in experiments of a field-reversed thetapinch plasma.

The $n=2$ rotational instability is the most dangerous gross instability in a field-reversed theta pinch. It is demonstrated for the first time that the instability is completely suppressed by superposing a quadrupole field which is much smaller than the axial confinement field at the separatrix. The experimental threshold intensity of the field for stabilization is about 2.5 times less than that predicted by theoretical stability analysis.

Two-dimensional equilibria of field-reversed configuration with subsidiary coils are computed by integrating the ideal magnetohydrodynamic equilibrium equation. The mirror coils have an effect to compress the plasma appreciably in the axial direction and hence sustain the compact torus. The cusp coils enlarge the plasma and consequently make the gradient of plasma density relaxed in the radial direction.

A method of determining plasma ion density by spectroscopic measurement of line emission from a probing neutral beam, attenuated by resonance charge transfer interaction with plasma ions, is proposed and tested. A hydrogen plasma produced by an R.F. discharge was used as the subject of the test. The parameters of the hydrogen probing beam in the region of observation were ∼400 eV average energy, ∼3×1012 cm-3 peak density and ∼2 µs pulse width. The beam was produced by a z-pinch-gun, a neutral beam source. From the attenuation rate of Hβ emission and the known cross-section of the interaction, the ion density was determined when it was in the range from 2×1014 cm-3 to 5×1014 cm-3. The value determined agreed well with the electron density measured with an He–Ne laser interferometer.

A z-pinch gun with a gas puffer was studied as a pulsed neutral particle source for active plasma diagnostics. Typical thermal and drift energies of the gun plasma were 120 eV and 140 eV, respectively. The peak density of fast neutral particles converted from the gun plasma was 6.2×1011cm-3 with an energy of 400 eV at a distance of 1.8 m from the gun. The pulse width was about 4 µsec. It is suggested that this kind of particle source with these values can be used for measuring the spatially-resolved ion temperature of plasmas. The experimental results are analyzed by a collisionless free-expansion model.

A high-power CW 27.972 μm water-vapor laser has been developed for interferometric and polarimetric measurements of plasmas. The maximum output power and the power density in the cavity of the laser with 2.0 cm bore and 220 cm length reach 85 mW and 109 μW/cm3, respectively. An interferometer using this laser is constructed and its performance is examined as a study on polarimetric method of magnetic field measurement. Preliminary interferometric experiments are also carried out on a compact toroidal plasma with field-reversal configuration.