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The equilibrium and stability of a fully ionized, dense, rapidly rotating, magnetized plasma is analysed in terms of a simple model: (i) An equivalent beta value βc is defined, being related to the centrifugal force and the corresponding azimuthal plasma current, as well as the associated radial "expansion" of the frozen-in magnetic field lines. (ii) A steady-state plasma balance exists only at beta values below a certain maximum, being either due to an equilibrium limit at βc = 2/3 or to a stability limit at βc < 2/3. (iii) The stability limit is due to the onset of a "centrifugal expansion instability" being similar to the mirror mode, but with the centrifugal force replacing the perpendicular pressure as driving mechanism. (iv) Plasma structures which are strongly elongated in the magnetic field direction depend critically on the beta limitation. Such structures exist both in cosmos and in the laboratory. (v) The theory gives a possible explanation of earlier experiments on voltage limitation with the devices FI and FIII, in terms of a velocity limitation of the former and a beta limitation of the latter.

It is likely that the velocity limitation observed in some types of rotating plasma devices is caused by an enhanced plasma-neutral gas interaction at the end walls bounding the plasma in the magnetic field direction. If the mechanism underlying the interaction is due to some process which forms anomalous azimuthal electric fields, a short-circuit of the latter would eliminate the velocity limitation If these predictions are true, new possibilities will open up in the use of rotating plasmas. In particular, the power losses due to ions and electrons escaping from a hot isotropic plasma through the magnetic mirror ends can then be kept small enough to balance the thermonuclear power at technically realizable beta values, plasma densities, and magnetic field strengths. At the same time such a strong confinement can only be achieved by very large centrifugal forces, rotational velocities and applied voltages, the technical feasibility of which has to be further examined.

An experimental and theoretical analysis is performed of a fully ionized, magnetized, quasi-steady plasma being separated from a surrounding neutral gas blanket by partially ionized boundary regions: (i) For rotating as well as high-frequency heated plasmas there exists a sharply defined minimum heating power Pm and temperature T0m below which a steady fully ionized state cannot be maintained. At laboratory dimensions and ion densities of about 1021 m-3, these parameters become Pm 0.5 MW and T0m 2 × 104 K. This "minimum-P effect" is important both to the processes of creating and maintaining laboratory plasmas in fusion research and to the studies of certain cosmical plasmas. (ii) The theoretically predicted behaviour of the plasma is roughly in agreement with the experiments in the power range close to the minimum value.

The pressure gradient dp/dr of a steady-state magnetized thermonuclear plasma column is determined by the Nernst effect, the emitted neutron flux, the ionization rate in regions containing neutral gas, externally imposed plasma sources and sinks, and by the pinch effect of an axial current. When the temperature gradient dT/dr

Experiments on rotating plasmas provide methods for studying part of the important problems of plasma equilibrium and stability at high beta values. This report describes investigations on high-density plasmas being performed by means of probe and Rogowski coil recordings: (i) Appreciable forces can be generated in the plasma, corresponding to equivalent beta values as high as about 20%. The magnetic field lines are in some cases "pushed out" radially by a considerable fraction of the distance from the axis of symmetry. (ii) The observed plasma behaviour agrees roughly with that predicted by a simple classical model. (iii) The plasma is at least macroscopically stable in respect to flute and ballooning modes, and has an outer boundary being sharply defined by the conditions imposed by a limiter and a surrounding neutral gas blanket.

The behavior of an ionized gas in cosmical observations and laboratory experiments is examined by means of dimensionless parameters. The deviations of experimental from theoretical calculations on electric neutrality and "creep diffusion" are estimated. The coupling between plasma and neutral gas is investigated by the basic equations for a partially ionized gas, This was found to give a dispersion relation for plane disturbances of small amplitudes. The effective electrical conductivity can be deduced from the corresponding damplng distance. Agreement was obtained with the conclusions of Piddington and Cowling regarding the increased dissipation of magneto-hydrodynamic waves in the solar chromosphere and of magnetic fields in cool interstellar clouds. It was determined that magnetohydrodynamic oscillations with wave lengths comparable to the thickness of the ionospheric F/sub 1/ region and with periods comparable to those of "giant pulsations" are damped moderately only if the ionization degree is about a hundred times greater inside than outside of the auroral zones. As an experimental illustration of the theory, torsional oscillations in a cylindrical "magnetohydrodynamic wave guide" are discussed. It was found that Alfvon waves will exist In an ionized gas in the laboratory only in a high-current discharge of relatively large dimensions. The dlffusion processesmore » which take place in a plasma column situated in a longitudinal magnetic field are discussed, Experimental data on the electric potential drop were found to agree well with the collision diffusion theory in a range of magnetic fields up to a centain critical value. Above this value a marked change occurs which can be interpreted as a sudden and rapid increase in the diffusion coefficient with a simultaneous rise in the noise level, These results support the "drain" diffusion mechanism proposed by Bohm, Burhop, Massey, and Williams-particle dlffusion across the magnetic field is accelerated by the action of transverse electric fields.« less

Two experiments are described on the inhibition of convection in a magnetic field. In the first experiment a layer of mercury is placed in an inhomogeneous magnetic field and heated from below. Photographs show convection where the field is weak, but indicate no motion where the field is strong. The boundary between these two regions corresponds to a critical magnetic field in agreement with current theory. The boundary is well defined showing that the onset of convection is sensitive to variations in the magnetic field. In the second experiment with a homogeneous field, varied in direction from vertical to horizontal, it is the vertical component which controls the onset of motion. A strong horizontal field does not inhibit convection but causes motion in narrow cells elongated in the direction of the field. DOI: 10.1111/j.2153-3490.1957.tb01856.x

A review is given of the experimental evidence and evaluation of macro- and micro-instabilities in a gaseous plasma. The paper briefly describes the physical mechanisms of the instabilities and the experimental methods used in their detection. The present state of research is summarized and discussed in connexion with thermonuclear and cosmic problems, with special emphasis on recently obtained results. An extensive list of references on the experimental work is included.

Recent research on magneto-hydrodynamics has indicated the existence of a great number of situations where a magnetic field stabilizes the state of motion of an electrically conducting liquid. Examples have been given by Hartmann & Lazarus (1937), Murgatroyd (1953 a,b ), Shercliff (1953), and Stuart (1954) for viscous flow between parallel planes and in pipes, by Chandrasekhar (1953) and Lehnert (1952 a ) for viscous flow between rotating cylinders, by Chandrasekhar & Fermi (1953) for problems of gravitational stability and by Chandrasekhar (1952) and Nakagawa (1955) for the inhibition of convection in a fluid layer.

The Second European Conference on Controlled Fusion and Plasma Physics was held at the Royal Institute of Technology in Stockholm, Sweden, from the 14th to the 18th of August 1967. A total number of 249 participants from 21 countries attended. The present report summarizes the conference proceedings and includes the abstracts of papers presented.

The motion and equilibrium is investigated of a plasma confined by an arbitrary magnetic field where the lines of force are either closed inside the confinement volume or form a bottle between two magnetic mirrors, (a) Stationary states are treated for which macroscopic fluid motions are allowed to take place in the plasma. Such states represent a larger class of equilibria than the static ones where the plasma is assumed to be at rest all over space, (b) For a hot plasma confined i n a closed magnetic bottl e the fluid motions decay at essentially the same rate as the pressure gradients and the electric currents, (c) A modified deduction is presented of the average guiding centre drifts from field line to field line in the αβ space defined by the magnetic field. The drifts include contributions from the electric field and the magnetic gradient, (d) The contribution to the macroscopic particle flux from the gyro motion is averaged along the field lines to form a corresponding flux in αβ space. An average macroscopic fluid velocity is further obtained by superimposing the contributions from the guiding centre drifts and the gyro motion, (e) The mechanisms producing density changes and charge separation phenomena are treated in terms of the average macroscopic fluid velocity. They are found to be due to the average guiding centre drifts only, (f) An analysis is performed in terms of the velocities in αβ space of equilibria for which local fluid velocities are allowed to exist in the plasma. For a particular class of such states an electric field can be set up which, on the average, keeps the plasma at rest on each field line, (g ) The results indicate that plasma confinement should becom e possible in ring-current configurations with magnetically screened supports, provided that the plasma remains stable and that there are no excessive losses in the small weak field regions close to the leads where this analysis is inapplicable.

The partially ionized plasma centrifuge contains a neutral gas mixture of isotopes or elements, the motion of which is driven by a small amount of rotating plasma. The plasma motion is, in its turn, controlled by externally imposed electric and magnetic fields. In this report earlier investigations of the centrifuge are extended by an analysis of its operation conditions. It is shown that high rotational velocities, large separation degrees, and stable velocity profiles can be achieved at comparatively small power losses, within certain ranges of the parameters involved.

In magneto-hydrodynamics conservation of energy leads to the adiabatic relation, du = pd?/? 2 , between the internal energy u per unit mass, the pressure p , and the density ?. The relation is valid for arbitrary amplitudes in a non-dissipative medium. The Hall current modifies the properties of magneto-hydrodynamic waves in an ionized gas. The compressive modes and the Alfven mode earlier discussed by van de Hulst are shown to be coupled by means of the Hall current. The dissipation of slightly damped waves is expressed in terms of the effective conductivity s? 3 = s? 1 + s? 3 2 /s? 1 earlier introduced by Cowling. The theory is applied to magneto-hydrodynamic oscillations in the layers of the ionosphere. The possible periods of the waves are consistent with the periods of “giant pulsations” which have been observed as a type of perturbation in the earth's magnetic field in the auroral zone. The results indicate that magneto-hydrodynamic waves in the E -, F 1 -, and F 2 -layers may explain the existence of giant pulsations as well as the occurrence of rapid vibrations in the terrestrial magnetic field. DOI: 10.1111/j.2153-3490.1956.tb01217.x

The balance of forces is investigated for a rotating plasma contained in a long cylindrical vessel and placed in an axial magnetic field. A relation is deduced between the voltage which arises in a radial direction in the plasma and the electric charge being transmitted through the system from an external source. It is found that the equivalent capacity, which describes the electrical behaviour of the plasma, depends upon the transmitted charge and upon the constitution of the vessel wall. An explanation is suggested for the voltage limiting effect earlier observed in the Ixion device.

The final period of decay of magneto-turbulence in an external, homogeneous magnetic field is considered and it is shown that it develops pronounced axisymmetric properties, turbulence elements with finite wave numbers in the direction of the field being damped strongly under normal physical conditions. The turbulence consists of aperiodic motions as well as wave motions. An introduction of an angular velocity, inclined to the field, destroys the axisymmetry and modifies the damping effects and periodicity. The influence of the magnetic field on the damping is counteracted by the Coriolis force. A linear stationary theory on the action of the field gives results consistent with those of the theory of decay. From the results of both theories an explanation is given of the observed inhibition of turbulence in mercury by a magnetic field.

Two examples are given of non-laminar motion in an electrically conducting liquid in the presence of an external magnetic field.DOI: 10.1111/j.2153-3490.1952.tb00989.x

Comparisons are made between magneto-hydrodynamics on cosmical and on laboratory scale. Magneto-hydrodynamic waves, turbulence, the generation of magnetic fields and thermal convection are discussed and a review is given of earlier experimental investigations. The possibilities are examined of realizing cosmical phenomena of this type in the laboratory.

Previous investigations on the confinement of a plasma in the magnetic field from one or several ring-shaped magnetic coils are extended in this paper. The energy losses are analysed for a number of magnetically screened leads which support the coils situated inside the plasma volume. Under thermonuclear conditions it is found that the losses due to the leads become negligible compared to the thermonuclear power of the DD and DT reactions when the main magnetic field is purely poloidal. In a sheared field the same losses are larger, but still negligible for the DT reaction, and it should in any case be possible to make them less than the thermonuclear power of the DD reaction. In connexion with the present type of configuration some further comments are made on the problems of stability, plasma generation and heating, the experimental analysis of the confinement, and on some of the engineering problems.

The field from one or several ring-shaped coils can be used as a magnetic bottle for plasma confinement. In stationary operation as a fusion device the coils have to be suspended. A possible method is provided by magnetically screened leads. Earlier investigations by the author on this problem are extended by the following results: In the confinement volume defined by field lines encircling one or several ring-shaped coils a static plasma equilibrium should be possible even in the presence of the magnetic field from the leads. The particle losses introduced by the leads are mainly non-adiabatic. They are partly due to deviations from the constancy of the equivalent magnetic moment in some very small regions where the field is weak, partly to deviations from the constancy of the longitudinal invariant which arise when a particle passes the lead region repeatedly and in finite steps. These effects produce a scattering which displaces a particle randomly across the magnetic field by about one Larmor radius for each complete lead passage. It is equivalent to a kind of ambipolar diffusion across the magnetic field.

Under certain conditions, plasma may be contained by a transversal magnetic field. If the plasma pressure is low with respect to the energy density of the magnetic field, the field is the same in the presence of plasma and in vacuum. A transversal motion of the plasma is theoretically impossible but other types of motion, not accompanied by a change of the magnetic field, may ultimately result in the escape of the plasma. Such cases, involving flute and screw instabilities were more closely examined; mechanisms involved in the formation of spatial charges, such as the gravitation-induced drift, centrifugal forces, inertia forces generated by magnetic pinch, and the effect of the Larmor radius. The results of the calculations indicated a strong interaction between the mechanisms corresponding to the flute and screw instabilities; these mechanisms are able to create instabilities in both partially and completely ionized gases. The theory developed is based on the equations of the macroscopic motion of the gas, as defined by the Boltzmann equation. (TTT)

A self-sustained thermonuclear fusion reaction requires a high degree of particle confinement. A ring-shaped solid conductor placed in the interior of the reaction volume produces a strong poloidal magnetic field which traps particles completely, at least at low gas densities. The leads which supply current to the conductor can be arranged in a way such as to prevent particle losses out of the confinement volume. Modifications and improvements of the magnetic field configuration by the addition of auxiliary coils are discussed. Injection of ions into the confinement volume is discussed briefly as well as a number of other possible heating mechanisms. A short consideration of the stability problem is also given at the end of the present paper.

The accessible voltage levels have been determined for a rotating plasma device in which the confinement region surrounds a ring-shaped coil that is suspended by a single rod. (i) There exists a sharply defined critical voltage and a corresponding velocity limit which cannot be exceeded by a moderately large power input. This is clearly shown with the present apparatus where the plasma voltage slowly approaches the critical level from below and where the insulator consists only of a narrow rod. (ii) The critical voltage increases with the mean radial ratio r 0/r w in the plasma. This ratio is defined by a magnetic field line which intersects the midplane of the device at a radial distance r 0 from the axis of symmetry, and cuts the end insulator at the corresponding distance r w. (iii) The results can be explained by an interaction between the plasma and a neutral gas layer at the insulator surface that limits the velocity to the critical value v c earlier introduced by Alfvén. As a consequence, the velocity limit becomes (r 0/r w)v c in the equatorial plane. Deductions of the corresponding voltage limit agree with the experiments, (iv) The plasma is heavily disturbed even by a very small obstacle which is introduced in the equatorial plane. This indicates that the losses of the system are small under normal operation, (v) So far the stability, is not influenced by the fact that most of the field lines pass freely around the confinement region and do not end upon an insulator surface.

Experimental studies have been performed of a fully ionized magnetized plasma generated in a poloidal magnetic field by a transverse electric field applied between two electrodes and being surrounded by a neutral gas blanket: (i)The rotating plasma which has been generated in the crossed fields is released from its energy source and its rotation is being stopped. The plasma decay is then studied in the absence of macroscopic motions, with the exception of those from a slow diffusion process. The state of ionization is determined by suddenly giving the plasma a small pulse of angular momentum which, after a short time is recovered as a current pulse being extracted by means of a short-circuit between the electodes. The pulse becomes a measure of the state of ionization and shows that the rate of penetration of neutral gas into the plasma is strongly delayed at high plasma densities, in agreement with theory. (ii)The velocity field of a quasi-stationary, rotating plasma has been investigated spectroscopically by observing the Doppler shifts of various spectral lines. The results agree with theoretical perdictions of the velocity and temperature distributions within the plasma region. The results also support the prediction that the interior of the plasma should be screened from the surrounding neutral gas.

Liquid sodium, because of its higher electrical conductivity and lower density, is more suitable than mercury for magneto-hydrodynamic experiments. Torsional waves in liquid sodium have been generated in a cylindrical vessel with the axis parallel to a homogeneous magnetic field, and resonance phenomena have been investigated at constant frequency and variable magnetic field strength. The agreement between theory and experiment is satisfactory. It is shown that even with sodium, damping plays an important role under laboratory conditions. The calculations of this paper are also used to improve the results of earlier investigations with mercury.

Under laboratory conditions particle losses from a magnetized plasma will produce a neutral particle flux reentering from the surrounding vessel walls into the plasma region. Even at very high temperatures, where the plasma is almost fully ionized, this gives rise to interactions between charged and neutral particles which cannot always be neglected. Three types of interactions are discussed: ionization, charge exchange, and elastic collisions with neutrals. The conservation laws of mass, charge, momentum, and energy are reconsidered for a two-fluid system with ionization, charge exchange, and elastic scattering of neutral particles taken into account. It is found not necessary to derive the energy equation in terms of the joint action of electromagnetic and mechanical changes of state. It has earlier been concluded from the motion of a single particle that a very strong confinement can be obtained in a rotating plasma situated in the magnetic field of a current loop (Bonnevier and Lehneat). These results are verified in a macroscopic theory including the energy balance of stationary motion. It is found that the main part of the heating of the plasma and the scattering of ions are not provided by coulomb collisions, but by collisions with reentering neutral particles. Twomore » special cases are treated in detail, one with vanishing heat conductivity and one with infinite heat conductivity in the direction along the magnetic field. For the latter, which is more likely to occur in a high temperature plasma, the energy loss by escaping particles is deduced. The theory predicts that this loss should be several orders of magnitude less in the current loop configuration than in earlier described homopolar machines. Finally, some comments are given on the nonexistence of interchange instabilities in systems with volume currents.« less

A new scheme for steady-state magnetic plasma confinement is suggested, consisting of a superposition of two poloidal magnetic field components. The first arises from the unidirectional currents flowing in a number of ring-shaped external conductors. The second is produced by an oppositely directed azimuthal current in the plasma. Whenever being necessary, an additional toroidal magnetic field component can be introduced. The scheme differs from those having passive guard conductors surrounding the plasma, in the sense that given currents are fed into the rings from external sources. This scheme provides a closed axisymmetric magnetic bottle with closed guiding-centre drift orbits of the plasma particles, as well as possibilities of "bootstrap" operation. The problems are considered of stabilizing electrostatic modes by means of minimum-average-Bgeometry, and of stabilizing electromagnetic modes by means of the mutual forces between the currents in the plasma and those in the external conductors.

The confinement and energy balance of rotating plasmas are studied by means of a device whose configurations may be changed to resemble the homopolar, Ixion, and current loop types of plasma generators. The effects of particle losses along the magnetic field lines to a nonconducting wall are examined. For the three configurations studied, the voltage and current characteristics, light intensities, gas production, and wall deterioration effects are determined using H and N gas. The plasma contains a considerable amount of energy for as long as 0.7 msec. (T.F.H.)

Electric current is sent through a hollow jet of mercury which is flowing over the surface of a glass tube. The jet is broken up by the action of the electrodynamic force. However, if at the same time a strong current is sent through a central conductor placed inside the glass tube, the jet can be stabilized. This occurs when the currents are parallel. Sausage instabilities have not been observed in the present experiment.

Balance equations of the partially ionized boundary layer of a dense plasma surrounded by a neutral gas blanket are discussed. The plasma-blanket pressure ratio and pressure and density limitations are described. (MOW)

Confinement of charged particles by axially symmetrical, stationary magnetic fields and electric fields is discussed. It is shown that if the coil connections are made as small as possible and if the magnetic field, in the neighborhood of the connections, from the supply current predominates over the field from the coil, particles will be reflected and will not be absorbed by the connections. The field from the supply current gives an additional drift in planes through the z axis, but since the connections carry current in opposite radial directions, a cancellation of the drift takes place for particles passing around the z axis repeatedly. (J.S.R.)

The possibility of trapping a plasma in a magnetic field generated by a ring-shaped solid conductor was investigated using a hollow mercury jet as a liquid-conductor model. The jet was formed around a glass-tube sheathed copper rod. It was found that if a sufficiently large current I/sub 0/ is sent through the central rod in the same direction as the current I in the jet, there is no sign of instability. The transition between stability and instability becomes sharper for strong currents and large electrodynamic forces than for weak currents. The transition for currents of 200 to 400 amp seems to occur at I/sub 0/ = 1.37 I. It is not possible to draw conclusions about the stability of a highly ionized plasma from the present results. This is because mercury has a comparatively low electric conductivity and the situation is very far from that of frozen field lines. (B.O.G.)

A physical interpretation of the theory of the screw instability in plasma is presented. It is shown that if a screw configuration exists in the plasma, the axial electric field tends to shift the electron component with respect to the positive ion component. The resultant charge separation causes a radial electric field to form, which drives the particles outward and destabilizes the plasma. Conditions under which the screw configuration is stable are discussed. (T.F.H.)

The instability of a plasma supported under gravity by a magnetic field is considered in terms of fluid equations. Mathematical derivations are presented. (L.N.N.)

In combination with transverse density gradients the finite Larmor radius produces space‐charge effects both in the interior and at the boundaries of a magnetized plasma. In a thermal plasma having moderately large density gradients, electric quasi‐neutrality can be preserved by a smoothly varying electric potential of limited amplitude. It is not obvious that a plasma containing groups of nonthermal ions will behave in a similar way when there are steep density gradients. An example is given here where a strongly oscillating potential of sheath‐like structure arises from nonthermal ions which are peaked at a singular velocity. Whenever nonthermal effects of this or a similar kind occur, they should introduce fundamental changes in the plasma behavior which cannot be described by elementary plasma theory. Possible applications are given by the motion of a plasma through a neutral gas, where groups of nonthermal ions arise from charge exchange and ionizing collisions. The electric fields generated by the nonthermal particles may affect the ionization process and become connected with the mechanisms of ionizing waves and with the observed voltage limitation in rotating plasmas and in certain types of plasma guns.

Charge separation caused by ion and electron clouds drifting with different velocities in the x direction is discussed. It is shown that a plasma region(1) of constunt density n(1- theta ) is initially divided from another region(2) of constant density n by a sharp sinusoidal boundary. The density gradient is then involved in the parameter 1- theta which vanishes in the earlier theory. For cases where theta 1/4, whereas the amplitude is limited for gamma < 1/4. Consequently, a strong magnetic field gradientmore » provides a scrambling mechanism which smooths out the electric field drift and may stabilize the system, at least for small disturbances. (N.W.R.)« less

WITH their admirable experimental technique, Babcock and Babcock have been able to measure certain very small line displacements in the Sun's spectrum, from which they deduce a general magnetic field of the order of −1 gauss. In order to draw this conclusion they use (although implicitly) two theories: (1) the theory of the Zeeman effect, connecting the line displacements with the magnetic field in a small homogeneous volume of gas; (2) the theory of magneto-turbulence in the photosphere, which, as Babcock's ‘point’ measurements include many thousand granulae, is necessary for computing the average.

In several experiments on a magnetically confined plasma and under certain conditions of a fusion reactor in stationary operation, neutral gas will be present in the regions surrounding the plasma. The inflow of neutrals and the outflow of plasma by diffusion or free streaming is studied in this paper, both for closed and open-ended systems: In a closed bottle neutral gas will not be able to penetrate through the cool boundary layers into the hot core of a high-density plasma. At plasma densities above 1021 m−3 the energy losses from interaction with the neutrals become negligible compared to the thermonuclear power production, but not at densities below 1019 m−3. This is due to the fact that the penetration depth of the neutrals depends on the ionization rate and becomes about 10−3 and 0.1 m at the densities 1021 and 1019 m−3. Further, the neutral gas inflow will be delayed by diffusion through a cool boundary region of sufficiently high density. In stationary operation the plasma density will be determined by the magnetic field strength and the density of the surrounding neutral gas. A condition for stable heat balance in a boundary region of finite thickness is deduced in this paper. As an alternative to a fusion device where the plasma is surrounded by an ultra-high vacuum region, it is therefore possible to surround a high-density plasma by a neutral gas blanket. The latter should be dense enough for released wall impurities to diffuse only slowly towards the plasma boundary. With a superimposed stream of neutral gas along the plasma boundary, the impurities can then be removed before reaching the plasma. In an open-ended system, thin layers of neutral gas are formed by plasma particles which escape along the magnetic field and recombine at the end walls. The theory agrees with measurements of the density of a fully ionized plasma as a function of the applied magnetic field and the density of the surrounding neutral gas. It also suggests that Bohm diffusion has not been present in earlier experiments with rotating plasmas where the density was found to decay at a very slow rate during free-wheeling.

A plasma boundary is defined by magnetic field lines which are tangent to a conducting wall. For a sufficiently good contact between the outermost layers of the plasma and the wall, the boundary will become an equipotential surface. The joint effect of line‐tying at the boundary and a finite ion Larmor radius then produces a stabilization of flute disturbances which is stronger than that arising from the finite Larmor radius alone. This effect is especially pronounced when the density increases steeply in a narrow boundary region and is nearly constant within the plasma interior. The present mechanism should have a marked influence on rotating plasma devices, but should hardly affect the rotational instability of theta pinches. An additional stabilization is provided by a velocity field which is sheared in the equilibrium state.

Earlier results, by Lehnert, on the diffusion processes in the positive column in a longitudinal magnetic field have been confirmed in a new series of measurements over a wide range of data. Experiments with helium, argon, krypton, nitrogen, and hydrogen are described. In the case of helium good agreement is obtained between the collision diffusion theory and the experiment up to a certain critical magnetic field. For stronger fields the potential drop along the column indicates a much higher diffusion rate across the magnetic field than that expected from the binary collision theory. Account is taken, in the theory, of the presence of molecular ions and of charge exchange collisions. Abnormal voltage characteristics indicating an increased diffusion rate above a certain magnetic field strength have also been investigated in argon, krypton, nitrogen, and hydrogen. The transition from the normal to the abnormal branch of the characteristics seems to depend neither on the length of the discharge tube nor on the length of the magnetic field, provided that these lengths exceed some fifty tube diameters. On the other hand, the transition depends upon the gas density, the nature of the gas, the tube radius, and, also slightly, upon the discharge current. The transition is also indicated by an increasing noise level above the transition point. Finally, the product of the magnetic field strength and the tube radius seems to be constant at this point.

The problem of flute instabilities earlier discussed by Rosenbluth and Longmire and by the author is reconsidered. The theory is extended to include the influence of a mass velocity in the unperturbed state as well as compression and expansion effects arising from the inhomogeneity of the magnetic field. According to the latter effects, surfaces of constant density will not move with the fluid velocity. A description of the dynamics of density perturbations is made in terms of the fluid equations under the assumption of negligible Ohmic and viscous dissipation. Adiabatic and isothermal changes of state are discussed for a plasma with adiabatic and isothermal distributions of pressure and density in the unperturbed state. The plasma is found to be stable against flute disturbances of any wavelength, not only for cusped geometry, but also for mirror geometry under certain conditions. This is the case when the characteristic length B/|∇B| of the magnetic field is less than twice the characteristic length N/|∇N| of the unperturbed density distribution. The approximations of the present theory exclude a treatment of perturbations which extend across the whole plasma body. The compression mechanism which is responsible for the stabilization is a zero‐order effect which is independent of the assumptions of isotropy and of the special forms of the unperturbed density and pressure distributions.

The stability of a plasma confined by a magnetic field has been discussed by Rosenbluth and Longmire in terms of particle orbits and the results applied to a plasma separated from vacuum by a sharp boundary which is rippled by a sinusoidal perturbation. This earlier theory is reconsidered and extended to include the effects of a finite density gradient. Drift motions along the boundary are also discussed for displacements comparable to and exceeding the wavelength of the perturbation. For small wavelengths it is found that the plasma is stable against small flute deformations not only for a magnetic field which is convex towards the plasma but also for a field which is concave towards the plasma, provided that the latter has a sufficiently strong gradient and that the density distribution is not too steep. Even in the unstable case the growth rate is reduced very much compared to the situation studied by Rosenbluth and Longmire. The result provides a possible explanation of the observed stability of the Van Allen radiation belts and in experiments with magnetic mirrors and rotating plasma devices.

It is shown that so far there is no experimental proof that magnetic guarding is ineffective, contrary to conclusions drawn from a strongly restricted plane model.

The ionization due to thermal electrons is discussed. Earlier theories on the voltage characteristics of a partially ionized homopolar cell are reconsidered. It is found that the results obtained from the theory on thermal ionization do not agree with experiments within the range of neutral gas densities studied so far, but a better agreement is expected at higher densities. In several cases the ionization rates estimated from experiments suggest that there exists a more powerful ionization mechanism than that provided by thermal electrons. Such a mechanism is probably associated with a highly nonthermal distribution of electron velocities within considerable parts of the plasma volume.

In order to study the instubilities of a pinched gas discharge, a liquid scale model of the discharge column is constructed. The model consists of a freely fulling vertical, cylindrical stream of mercury. The stream is carrying a direct current, and its stability to electromagnetic disturbances is studied. Different types of instability are found in cases with and without a longitudinal magnetic field. A 3000 frames per second high speed camera is used, and the films taken show the growth of sausage'' and lateral instabilities. A possible analogy with gas discharge pinch intstabilities is discussed. (auth)