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For the next step in the investigation of reversed-field pinches, the HBTX machine is being converted to have an advanced first wall with a low Z smooth surface and a close-fitting, thick conducting shell. The new wall is the logical extrapolation of previous work where the loop voltage has been reduced about five fold by lowering field errors, improving the equilibrium, and removing the limiters. These steps reduce the magnetic flux intersecting the wall and the advanced first wall will further reduce this flux by suppressing magnetic fluctuations. The engineering design and construction of the new experiment are described. >

Investigations of HBTX1B (R/a = 0.8/0.26 m, I = 0.2 MA) edge phenomena are reported. Calculations show that the 160 small graphite limiters intercept half of PΩ = 10 MW and photography shows strong and intermittent heating of edges exposed to the poloidal electron current. Experiments and simulation are described of density maintenance by preloading the vessel with gas to achieve RFP with low I/N ≤ 5 × 10−14 A m (N = 2π∝nerdr). A movable limiter probe collects large spikes of electron current ≲ 500 A and the average current is much larger than that required for RFP equilibrium. The conserving ion current to the wall will produce jrBθ forces on the plasma. From energy and potential measurements we infer that the SOL is collisionless and because of the low magnetic field is less than a few ion gyro radii thick.

Experimental and numerical results on plasma heating in a theta pinch at low azimuthal electric fields, Eθ 200 V cm−1, are presented. Energy losses due to partial ionization of the initial plasma, and impurities, are shown to govern the final temperatures obtained. In particular, partial ionization results in a critical value of Eθ below which no effective heating occurs. This effect can be overcome by the use of negative bias fields, which increase the initial ionization and allow additional dissipative heating. At larger values of Eθ the initial heating rate is found to scale with

Theoretical and experimental research in the reversed-field pinch (RFP) is reviewed. In this system, Bθ ~ B, q 10% has been observed. Following a historical review of pinch research, the basic theoretical properties of the RFP are established including the equilibrium, toroidal displacement, diffusion and confinement; studies of ideal and dissipative MHD stability theory are then described. Experimental and theoretical work on relaxation and self-reversal, the process whereby an RFP distribution can be set up spontaneously and subsequently sustained, is presented and discussed. There follows a general account of RFP experiments. These are divided into 'fast experiments', which utilize small-bore insulating tori in which the distribution is usually set up by fast programming on microsecond timescales, and 'slow experiments', carried out in large metal-walled tori in which the field configuration is set up slowly by self-reversal on millisecond timescales. A brief account of RFP reactor studies and of new and future experiments is then given, followed finally by a general discussion in which the main conclusions are presented.

Experiments on the motion of a deuterium plasma in a theta pinch and a screw pinch in the presence of local perturbing magnetic fields are described. Small coils outside the vacuum vessel were used to superimpose a dipole field on the theta pinch, and a transverse field on the screw pinch, and measurements were made of the resulting plasma motion. Experiments were performed using a 350-cm long theta-pinch coil which produced plasmas with an average beta up to 0.45 and an average temperature up to 65 eV. Perturbing fields of ~5% of the main axial field of 17.5 kG produced local displacements of ~ 1 cm, which propagated along the plasma with a velocity of about 20 cm μs−1. The displacement was proportional to the perturbing field, and was spatially damped with an e-folding length of about 20 cm. Screw-pinch experiments were performed by superimposing an axial current of 10 kA on the theta pinch; this produced instability growth rates of about 0.5 × 106 s−1. A transverse field of ~2 kG excited plasma displacements of ~1 cm. This displacement was found to be proportional to both the axial plasma current and the perturbing field. In all cases the plasma column remained intact and no additional instabilities or rapid diffusion were observed. Predictions of plasma displacement were made using a simple model and good agreement with the experimental results was obtained.

A method for avoiding rapid current termination and associated machine damage in RFP is described. During current decay an externally applied voltage removes toroidal flux giving constant θ, hence maintaining field reversal and ideal MHD stability.

Field-reversed configurations (FRC) and theta pinches with trapped reversed bias field are essentially the same magnetic confinement systems using closed magnetic field lines inside an open-ended magnetic flux tube. A simple model of joule heating and parallel electron thermal conduction along the open flux lines to an external heat sink gives the electron temperature as Te(eV) 0.05 B2/3(G) L1/3(cm), where B is the magnetic field and L is the coil length. This model appears to agree with measurements from present FRC experiments and past theta-pinch experiments which cover a range of 40?900 eV. The energy balance in the model is dominated by (a) parallel electron thermal conduction along the open field lines which has a steep temperature dependence, , and (b) the assumed rapid perpendicular transport in the plasma bulk which, in experiments to date, may be due to the small number of ion gyroradii across the plasma.

Simulation du comportement dependant du temps du plasma d'une striction a champ inverse, couple a un circuit electrique. L'application principale concerne la conception du circuit, mais le code sert aussi a l'etude du comportement du plasma pour une tension externe directement appliquee au plasma

The horizontal position of the plasma in the HBTX1C reversed field pinch has been controlled to ± 1 mm by a feedback circuit. The plasma is moved to the desired position by momentarily closing either one of two semiconductor switches which alter the way in which current is shared by the parallel-connected field windings. Equilibrium control was added without the need for additional power supplies or additional field coils.

We investigated the radial implosion of a deuterium plasma in a theta pinch in which the initial level of ionization was controlled. Measurements of the diamagnetism of the plasma during the implosion were related to the mass of gas in motion. The latter depends on the interaction between the ions and the neutral atoms. The effective cross-section for momentum transfer from ions to neutrals is 4 × 10−15 cm2, close to the charge exchange cross-section for protons and hydrogen atoms.

A high-speed framing camera has been used to photograph deuterium and helium discharges in which flute instabilities are driven by the inertial force of a radial acceleration. The wavelength of the instability increases with decreasing initial pressure, suggesting the damping effect of viscosity; in some cases this damping apparently prevents the growth of flutes entirely. A simple theory of viscous damping is in qualitative agreement with the observations. An instability due to the radial acceleration accompanying a rotation of the plasma appears at about peak field.

Measurements made in the mid-plane of a theta pinch plasma indicate a sudden decrease in line density. This is interpreted as the arrival of a rarefaction wave due to axial plasma loss. Detailed predictions of density, and β given by an axial MHD computation, are in good agreement with the observations.

The electrical characteristics of discharges with high and low initial rates of current rise are briefly described and the electrical measurements are used to determine the work done on the plasma by rapid compression. The particle and the magnetic energy in the discharge are discussed for both high and low initial rates of current rise (dl/dt(0)) and for discharges with and without an axial magneticfield (Hz). It is shown that the gas is heated much more efficiently both with and without Hz at high dl/dt(0). For dl/dt(0) ~ 1.5× 1012 amps/sec (Hz = 0) 15% of the initial bank energy goes into heating the gas and 10% into the magneticfieldat the first maximum contraction; for dl/dt ~ 1011 amps/sec (Hz = 0) 11% goes into the field and only 6.5% into the gas at this time. The energy input to the gas is found to become limited well before peak current, and the initial implosion is not followed by much of the subsequent isentropic compression heating which might be expected, so that the temperature never exceeds about 300 eV; it follows that most of the observed neutron yield (~ 106) is not thermonuclear. Data obtained from the electrical waveforms and from high-speed photographs are presented and analysed, and it is shown that large currents build up outside the central plasma column after the first maximum contraction. Further evidence suggests that these currentsflowin wall material boiled off by radiation from the central column. These wall effects account for the absence of further isentropic compression heating and also contaminate the central plasma column; they are such as to prevent any significant gain in heating by increasing the power input to the discharge. It is concluded that similar effects probably account for the failure to achieve a thermonuclear temperature in many high power pinch experiments.

It has been observed that populations of human cervical carcinoma cells (strain HeLa) may be induced to undergo parasynchronous division by chilling of the cell culture for a short period. Replicate cultures of HeLa cells were incubated at 37 °C for 24 hours after subculture and then placed at 4 °C for 1 hour. Samples were taken for cell counts at intervals after replacement at 37 °C. Growth curves based on these estimations of cell number show that little or no cell division occurred for 17 hours after chilling; at this time as many as 95 per cent of the cells then divided within 1 hour. No further cell division was observed in the following 18 hours, after which most of the cells again underwent division. Cytological observations of the cells at various stages during those growth cycles have been made to determine the frequency of mitosis. The results of those studies indicate that following chilling of the cells there is a gradual decrease in the number of cells in mitosis until at 10 hours this figure reaches a minimum. There is then a rapid increase in the mitotic index which achieves a maximum value just before the increase in cell numbers is observed. Maximum values of the prophase, metaphase, anaphase indices are observed in succession. The nucleic acid content of these dividing cells has been determined. Synthesis of DNA is inhibited for about 14 hours after chilling, the DNA content of the cells then increases rapidly before cell division occurs. During the second cycle of cell division DNA synthesis occurs during early and late interphase. The total nucleic acid in each culture increases throughout the period when cell numbers are not increasing but at the time just prior to cell division there is a fall in the amount estimated. This has not been explained. These results are discussed and it is concluded that although these cultures do not exhibit a complete synchrony of the events of mitosis, the time of cell division is restricted to a very small portion of the total growth cycle. For this reason the term parasynchronous division has been employed.

Predictions from a simple analytical theory were compared with results from six theta-pinch experiments. Data were selected for a time during each experiment after the implosion but before axial electron thermal conduction became significant. Thus the measured plasma properties were determined only in the formation stage. Density distribution data are shown.

Local perturbing magnetic fields are used to excite motion of a 3.5 m long plasma column. A screw pinch, showing gross instability, is perturbed by a transverse field. Displacements are observed which propagate along the column. A ‘string’ model is used to interpret the results. The significance of these studies for feedback stabilisation is discussed.

Previously reported results obtained from Zeta at current approaching 1 MA, with rise times varied by a factor of 3 and with sustained current pulses of 0.02 sec total duration show that stable pinches are readily obtained in these conditions.

Observations of the generation of enhanced axial flux leading to the self reversal of toroidal magnetic field in three different experiments, HBTX, FRSX and ZETA, are summarised and compared with theoretical predictions.

Publisher Summary This chapter discusses unbounded invariant curves for flows in three-dimensional space. The chapter presents an assumption where a vector field X, of class C2 on some Rn (n ≥ 2) and with all first-order partials uniformly bounded on Rn are given. It is known from the established theory of linear differential equations that there will exist three linearly independent solutions that may be expressed symptotically by means of normal series. Until some convergent method of computing connection coefficients is devised, the solution of the problem in the large cannot be considered as solved.

The neutral atom velocity distribution of a 60kA Stabilized Z pinch is found to have a Maxwellian component (temperature 15eV) and a high energy tail associated with instabilities. Measurements of total radiated power from Reversed field pinches show that radiation is an important source of energy loss only in discharges with peak currents below 50kA. Neutral atoms leaving the pinch do not represent a significant energy loss.

In this paper we describe the HBTX1B torus where a GRP bobbin is used to support the coil system wound with commercial cable. HBTX1C (under construction) is of similar design and includes a stabilising “shell” of copper gauze sheets moulded in GRP.

A 3.3 μm helium–neon laser and 2.25 and 8.6 mm microwave interferometer systems have been used to measure electron densities over the range 1.8 × 1015 to 8 × 1011 electrons/cm3 in a decaying helium plasma without a confining magnetic field at gas pressures ranging from 82 mtorr to 1.2 torr. Collisional radiative recombination is considered to be the dominant mechanism of electron removal above a pressure of 700 mtorr.

An experimental and theoretical study has been made of the hydromagnetic instability of an axisymmetric bulged region in the midplane of a theta pinch 8 m long. The bulged region was generated adiabatically after the initial implosion in such a way that it fulfilled most of the assumptions of the theoretical model; in particular, it was free of end effects for the time of observation. At a filling pressure of 20 m Torr D 2 and with a peak magnetic field of 20 kG the plasma, which was collision dominated, had values of temperature, density, and beta on the axis of 120 eV, 3 × 10 16 cm −3 , and 0.7 ± 0.2 . The predicted m = 1 instability was observed and for a range of bulge amplitudes its measured growth and propagation along the column agreed to within a factor of less than 2 with the theoretical values. It is concluded that the m = 1 instability of such bulged plasmas is well described by ideal hydro‐magnetic theory. Modes with m ≥ 2 were not observed during the m = 1 growth and their absence is attributed to finite Larmor radius stabilization.