Search

The KArlsruhe TRItium Neutrino (KATRIN) experiment, which aims to make a direct and model-independent determination of the absolute neutrino mass scale, is a complex experiment with many components. More than 15 years ago, we published a technical design report (TDR) [https://publikationen.bibliothek.kit.edu/270060419] to describe the hardware design and requirements to achieve our sensitivity goal of 0.2 eV at 90% C.L. on the neutrino mass. Since then there has been considerable progress, culminating in the publication of first neutrino mass results with the entire beamline operating [arXiv:1909.06048]. In this paper, we document the current state of all completed beamline components (as of the first neutrino mass measurement campaign), demonstrate our ability to reliably and stably control them over long times, and present details on their respective commissioning campaigns., Comment: Added missing acknowledgement, corrected performance statement in chapter 4.2.5, updated author list and references

A light beam of high photon density and spatially limited cross-section is analysed with respect to its boundary conditions and angular momentum ( spin). For Maxwell's equations in a vacuum state o ...

Several important questions regarding the photon wave and particle concepts have so far not been fully settled by means of conventional theory which is based on Maxwell's equations. This concerns the problems of the angular momentum and the divergence of the obtained solutions in vacuum space. In attempts to tackle these and other unclear points, a number of extended non-Maxwellian theories have been elaborated. The present analysis is due to one of these approaches, as being based on a nonzero electric field divergence in the vacuum state, under the condition of Lorentz invariance. This theory leads to models for the individual photon being based on axisymmetric wave packet solutions with imposed relevant quantum conditions. Such solutions can be confined to a limited volume in vacuum space, thereby giving rise to a nonzero angular momentum, as required for a boson particle. Two wave packed modes are obtained which have limited characteristic diameters in the direction being perpendicular to that of the propagation. For one of the modes the diameter even becomes comparable to atomic dimensions. This provides the possibility for an efficient photon-electron interaction in the widely discussed but not fully understood photoionization effect. Both modes further have features in common with an earlier theory by de Broglie, where the photon is represented by a propagating pilot wave with a superimposed particle-like part having a very small rest mass. A proposal is finally made for the photon to appear in different quantum states, and where rapid transitions can take place between these states in the form of photon oscillations.

Steady axisymmetric equilibria of an earlier developed extended electromagnetic theory are considered. as based on a nonzero electric field divergence in the vacuum state and Lorentz invariance. Th ...

It is shown that if the Lorentz condition is discarded, the Maxwell–Heaviside field equations become the Lehnert equations, indicating the presence of charge density and current density in the vacuum. The Lehnert equations are a subset of the O(3) Yang–Mills field equations. Charge and current density in the vacuum are defined straightforwardly in terms of the vector potential and scalar potential, and are conceptually similar to Maxwell's displacement current, which also occurs in the classical vacuum. A demonstration is made of the existence of a time dependent classical vacuum polarization which appears if the Lorentz condition is discarded. Vacuum charge and current appear phenomenologically in the Lehnert equations but fundamentally in the O(3) Yang–Mills theory of classical electrodynamics. The latter also allows for the possibility of the existence of vacuum topological magnetic charge density and topological magnetic current density. Both O(3) and Lehnert equations are superior to the Maxwell–Heaviside equations in being able to describe phenomena not amenable to the latter. In theory, devices can be made to extract the energy associated with vacuum charge and current.

It is shown that the Maxwell–Heaviside theory is incomplete and limited, for example, it is unable to describe the Sagnac effect, either with platform at rest or in motion. An electrodynamical theory based on a physical internal O(3) gauge space is shown to provide the correct explanation in classical electrodynamics for the Sagnac effect, and for interferometry in general, for example Sagnac and Michelson interferometry. The U(1) sector of unified field theory must therefore be replaced by an SU(2) sector broken to O(3). This has numerous consequences for unified field theory.

It is shown that higher symmetry (O(3)) electrodynamical considerations lead to a straightforward explanation of the Sagnac effect in terms of the topological phase and Aharonov Bohm effect. The method is extended to interferometry and physical optics in general, using the Sagnac, Michelson and Young interferometers as examples.

The hypothesis of a non-zero divergence of the electric field in vacuo and an associated extended Lorentz invariant formulation of Maxwell's equations provide steady-state solutions of the electromagnetic field. Among the solutions there are those of axisymmetric configurations having integrated field quantities which represent an equivalent electric charge q0, magnetic moment M0, mass m0, and angular momentum s0. All these quantities become finite and non-zero, at the same time as the corresponding characteristic radius can be allowed to shrink indefinitely, to correspond to the property of a "point charge". The present theoretical model includes relevant quantum conditions, and a condition of equipartition between electric and magnetic energy. The question is raised whether the obtained results could have a bearing on the physics of charged leptons, such as the electron. In comparison with observed electron data, the present approach thus yields correct signs of the quantities q0, M0, m0 and s0, the ratio M0 m0/q0 s0 is predicted to be of the order of unity as for measured data, a "point charge" of very small radial extension can be obtained, and a minimum charge |q0| 1.60 × 10−19 Coulomb is deduced from a simple iteration process, thereby differing at most by about one percent from the measured value of the electronic charge. This suggests that the electronic charge is not an independent constant of nature, but is a typical quantum number determined by the speed of light and Planck's constant. The present theory also fits the muon data, at least within one percent accuracy.

A search for the radiative neutrinoless double electron capture with single \gray\ emission has been performed in $^{58}$Ni. Gamma radiation from a 7286 g nickel sample in natural isotope composition was measured for 58.3 d with an ultra low background HPGe detector in the Felsenkeller underground laboratory in Dresden, Germany. A new lower half-life limit of $2.1 \times 10^{21}$ yr (90% CL) was obtained for this decay mode. This half-life limit is two orders of magnitude higher than the existing limit for $^{58}$Ni and among the best half-life limits for neutrinoless double electron capture decays.

The GERDA experiment searches for neutrinoless double beta ($0\nu\beta\beta$) decay in $^{76}$Ge using an array of high purity germanium (HPGe) detectors immersed in liquid argon (LAr). Phase II of the experiment uses 30 new broad energy germanium (BEGe) detectors with superior pulse shape discrimination capabilities compared to the previously used semi-coaxial detector design. By far the largest background component for BEGe detectors in GERDA are n$^+$-surface events from $^{42}$K $\beta$ decays which are intrinsic in LAr. The $\beta$ particles with up to 3.5 MeV can traverse the 0.5 to 0.9 mm thick electrode and deposit energy within the region of interest for the $0\nu\beta\beta$ decay. However, those events have particular pulse shape features allowing for a strong discrimination. The understanding and simulation of this background, showing a reduction by up to a factor 145 with pulse shape discrimination alone, is presented in this work., Comment: Proceeding TAUP 2015

International audience; Borexino is a liquid scintillator detector primary designed to observe solar neutrinos. Due to its low background level as well as its position in a nuclear free country, Italy, Borexino is also sensitive to geo-neutrinos. Borexino is leading this interdisciplinary field of neutrino geoscience by studying electron antineutrinos which are emitted from the decay of radioactive isotopes present in the crust and the mantle of the Earth. With 2056 days of data taken between December 2007 and March 2015, Borexino observed 77 antineutrino candidates. If we assume a chondritic Th/U mass ratio of 3.9, the number of geo-neutrino events is found to be 23.7(+6.5) (-5.7)(stat) (+0.9)(-0.6) (syst). With this measurement, Borexino alone is able to reject the null geo-neutrino signal at 5.9σ, to claim a geo-neutrino signal from the mantle at 98% C.L. and to restrict the radiogenic heat production for U and Th between 23 and 36 TW.

International audience; The new limit on the electron lifetime is obtained from data of the Borexino experiment. The expected signal from the e → γν decay mode is a 256 keV photon detected in liquid scintillator. Because of the extremely low radioactive background level in the Borexino detector it was possible to improve the previous measurement by two orders of magnitude.

The present analysis concerns a plasma confined in a magnetic field, which consists of one part due to the plasma current density and one part due to steady currents in fixed external conductors. Unrestricted free-boundary displacements are studied that lead to an unbalanced pressure force at the plasma boundary and to a corresponding change in potential energy. Thus the total change in energy is due to two factors: (i) the work done against the plasma volume forces, and (ii) the work done against the unbalanced pressure forces at the plasma boundary. As a consequence, the conventional extended energy principle has to be reconsidered. This reconsideration applies in particular to its final formulation, where unrestricted displacements are made to replace restricted ones in an expression for the potential energy change deduced from the work of the plasma volume force only. The conventional MHD analysis on perturbed plasmas thus has to be revised, by taking induced surface currents properly into account. This applies to all plasmas in inhomogeneous externally applied magnetic fields.

An extended analysis is presented of the earlier investigated induced surface current effects which arise in a magnetized plasma when the confining field has an imposed inhomogeneous part generated by currents in external conductors. The electromagnetic induction law requires a corresponding contribution from these effects to be added to the formulation of the energy principle for plasma MHD stability. For a plasma with a free boundary, conventional theory therefore holds in a strict sense only when there is a homogeneous external magnetic field. An illustration is given by two-dimensional straight Extrap geometry with a peaked current distribution, subject to a combined translational and ballooning-like displacement. In this case there are strong restoring forces, leading to stable oscillations around the plasma equilibrium position.

Anisotropic resistivity causes paramagnetic effects (Bz'(r) 1 are unattainable. Diamagnetism caused by radial particle diffusion and the Nernst effect is also discussed. In a tokamak or reactor plasma, diamagnetism is shown to be negligible, whereas it may contribute in present ultra-low q, Extrap and RFP experiments. A basic relation is derived for the coupling between the poloidal and axial magnetic field components with the above effects included. Of specific importance to the Extrap programme is the result that plasma current limitation can arise due to the lack of equilibrium when the plasma radius tends to exceed its upper limit, which is defined by a magnetic or material limiter. Comparisons are made with stability limits depending on the safety factor, the number of contained ion Larmor radii and the line density.

Two neutrino double beta decay of $^{76}$Ge to excited states of $^{76}$Se has been studied using data from Phase I of the GERDA experiment. An array composed of up to 14 germanium detectors including detectors that have been isotopically enriched in $^{76}$Ge was deployed in liquid argon. The analysis of various possible transitions to excited final states is based on coincidence events between pairs of detectors where a de-excitation $\gamma$ ray is detected in one detector and the two electrons in the other. No signal has been observed and an event counting profile likelihood analysis has been used to determine Frequentist 90\,\% C.L. bounds for three transitions: ${0^+_{\rm g.s.}-2^+_1}$: $T^{2\nu}_{1/2}>$1.6$\cdot10^{23}$ yr, ${0^+_{\rm g.s.}-0^+_1}$: $T^{2\nu}_{1/2}>$3.7$\cdot10^{23}$ yr and ${0^+_{\rm g.s.}-2^+_2}$: $T^{2\nu}_{1/2}>$2.3$\cdot10^{23}$ yr. These bounds are more than two orders of magnitude larger than those reported previously. Bayesian 90\,\% credibility bounds were extracted and used to exclude several models for the ${0^+_{\rm g.s.}-0^+_1}$ transition.

Silicon photosensors represent a viable alternative to standard photomultipliers in fields such as communications and medical imaging. We explored the interesting possibility of using these sensors in combination with liquid argon (LAr) for astroparticle physics applications such as neutrino, dark matter and double beta decay experiments. In fact, silicon photosensors have detection efficiencies comparable with those of the highest performance PMTs and can be manufactured with high level of radiopurity. In particular within the on-going R&D activity of the SILENT project (Low background and low noise techniques for double beta decay physics funded by ASPERA) a large area SiPM (Silicon PhotoMultiplier - Hamamatsu S11828-3344M - 1.7 cm2 area) has been installed in a LAr scintillation chamber of 0.5 liters volume together with a cryogenic photomultiplier tube (Hamamatsu R11065) used as a reference. The liquid argon chamber has been exposed to many gamma sources of different energies and single photoelectron response and light yield for the SiPM and PMT have been measured and compared. In this contribution the results of the tests, and the ongoing R&D to optimize the SiPM for cryogenic and for ultralow background applications, are reported, as well as the possible application in the GERDA experiment on Double Beta Decay Searches of 76Ge.

Electrostatic perturbations are considered in a model where a plasma is situated in a homogeneous magnetic field and is subject to an equivalent gravitation force representing the magnetic inhomogeneity effects. The perturbations are strongly affected by large Larmor radius (LLR) effects when their wavelength becomes comparable to the ion Larmor radius. In the case of a dilute plasma, two time-dependent constants of he motion are found from which a solution can be deduced for the perturbations. The LLR effects are show to 'chop up' the time development of the macroscopic density and electric field perturbations into a pulse-shaped periodic patterns. The latter is repeated at every half of a gyro period and becomes strongly damped between a set of arising narrow peaks. The LR effects have been demonstrated in a simple special case, but similar results are likely to be obtained in more complicated situations, such as in denser plasmas where the electric field from the space charges affects particle dynamics. Consequently, the fine structure of a number of plasma perturbation is expected to become strongly distorted by LLR effects, and this becomes important to plasma stability.

This paper draws attention to some mechanisms which can contribute to the understanding of particle transport in Tokamaks and similar systems. First, it is demonstrated that, even when there are highly anomalous heat losses due to electron heat conduction, the particle losses do not necessarily have to become strongly anomalous but can remain nearly neoclassical. Second, plasma-neutral gas interaction is shown to have a number of important effects on plasma equilibrium, transport and profile shaping, even in Tokamaks where the boundary layer only contains a small fraction of neutral particles. Thus, under rather general conditions of strong recycling, the characteristic plasma pressure gradient in the boundary layer becomes independent of the rate of particle transport. On the other hand, the ratio between the average electron density and the neutral density at the plasma edge provides a measure of the plasma particle loss rate. Finally, in Tokamaks near the density limit, the heat losses due to plasma-neutral gas interaction affect the energy confinement time. The present analysis appears to be consistent with experiments, as far as orders of magnitude are concerned.

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.

The particle and energy balance is considered of plasmas which are permeable to neutral gas: (i) There exist two subclasses of permeable plasmas. The first includes 'dilute' plasmas being penetrated by slow neutrals of wall temperature. The second includes 'non-dilute' plasmas being penetrated only by fast neutrals having a temperature comparable to that of the ions. (ii) The energy and particle balance of dilute plasmas are strongly affected by plasma-neutral gas and plasma-wall interaction, as well as by the vacuum conditions, especially at long particle and energy containment times such as in the Spherator. (iii) Earlier experiments with the Spherator can be explained by classical theory including plasma-neutral gas interaction, and need not be interpreted in terms of anomalous diffusion. Thus, the possibilities of the Spherator as a magnetic bottle have to be reconsidered.

A number of technological problems concerning the coils in internal conductor systems is investigated, with an efficient plasma confinement imposed as a working hypothesis: (i) At technically feasible power levels and linear dimensions, the Ohmic power losses can, under optimized conditions, be made much smaller than the thermonuclear reaction power, even with ordinary metal windings at temperatures of some hundred degrees centrigrade. Thus, superconducting coils should not become necessary in these systems, (ii) The mechanical stresses can be kept well below the limits of tensile strength of possible coil materials. In addition, both the internal coils and their magnetically shielded supports can be made magnetically force-free in certain cases, (iii) These results are due to the fact that high beta values are,in principle, available in systems with a main poloidal field, and that only a fraction of the total magnetic field energy originates from the internal conductors. This provides an important advantage over systems with a main toroidal field where, at a given plasma pressure, the Ohmic power losses and mechanical stresses become between one and two orders larger than those of poloidal field systems, (iv) The coil supports can be made large enough to provide cooling ducts for the internal conductor system.

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.

In a hot magnetized plasma large ion excursions can take place along the magnetic field lines, thereby introducing kinetic effects which cannot be treated in terms of a macroscopic fluid model. These effects are studied for transverse wave motions of ions and electrons in a homogeneous thermal plasma which is immersed in a homogeneous magnetic field. Strong kinetic wave damping is found to occur when the product kui of the wave number k and the ion thermal velocity ui exceeds the ion gyro frequency omega i. The physical mechanism of this damping originates from the ion excursions and differs from that of Landau and cyclotron damping. For plasmas having a comparatively low beta value, such as in Tokamak experiments, the present results indicate that kinetic damping becomes important only at small wave lengths, as compared to the dimensions of the plasma body. However, in high-beta systems, such as the Z-pinch, wave lengths in a large range become affected by kinetic damping, in some cases even those which are comparable to the characteristic macroscopic dimensions. This also affects the conditions of plasma stability and plasma high-frequency heating.

Under the conditions of the quasi-steady tokamak experiments near the density limit performed so far, the plasma pressure gradient in the outer layers of the plasma body becomes determined mainly by the plasma-neutral gas balance. A combination of this balance with the results of MHD stability theory leads to a corresponding restriction in plasma density, being closely related with the empirical Murakami limit.

The potentialities and properties are discussed of a recently suggested axially symmetric, quasi-steady, closed, high-beta magnetic confinement system. A toroidal pinch of non-circular cross section is immersed in the strong, inhomogeneous polodial vacuum field from a set of ring-shaped conductors, all carrying currents in the opposite direction of the plasma current. This "EXTRAP" concept is expected to have some important advantages, as compared to magnetic bottles based on a main torodial field component. Concerning plasma equilibrium, there are closed local and average guiding centre orbits, beta values of order unity should become available, there is no magnetic surface splitting limit, cyclotron radiation should be kept at a comparatively low level, and bootstrap operation may become possible. Concerning plasma stability, the system should not become sensitive to magnetic island formation and asymmetries, and the short magnetic connection lengths as well as the strong vacuum field gradients should favour stabilization of flute-type, kink, and other magnetohydrodynamic modes. Concerning reactor technology, high power densities are expected to be reached, superconducting coils should not become necessary, the coil stresses are moderate, and repair and replacement are facilitated by the coil geometry. Before a final judgement can be made on this concept, however, extensive experiments and further theoretical analysis are needed.

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.

Neutral gas which penetrates into a hot plasma of characteristic dimension L b, average density n̄, and temperature T, consists mainly of a slow and fast component of densities nns, nnf and temperatures T ns≪T, T nf ≃ T, respectively. These components have the penetration lengths L ns = 1/σcsn̄ and L nf = 1σcfn̄ defining the critical densities ncs = 1/σcs L b and n cf = 1σcf L b where 1/σcf ≃ 100/σcs ≃ 5×1018m-2 for hydrogen in the range 106 < T < 107 K. Thus, hot plasmas can be divided into the classes of permeable dilute, permeable non-dilute, and impermeable systems defined by n̄ ≲ n cs≪ncf,ncs≪n̄ ≲ ncf and ncs≪ncf≪n̄ respectively: (i) These classes have different equilibrium and stability properties, depending on the relative concentrations, spatial distributions, and transport processes of the neutral gas. (ii) The density of the neutral gas immersed in a quasi-steady permeable plasma becomes a measure of the plasma particle loss rate. (iii) The ratio between the neutral gas "blanket" density and the average plasma density increases when transitions are made from the permeable dilute to the permeable non-dilute state, and further to the impermeable state. (iv) The spatial distributions and relaxation times of the plasma. The pressure gradient, which acts as a driving force of instabilities, reaches a maximum value when the transition is made from a permeable to an impermeable state.

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.

During recent investigations on plasma confinement by internal ring systems with magnetically shielded supports some authors have arrived at contradictory conclusions. This paper reconsiders support shielding in terms of the problems of plasma cut-off at the support surfaces, the plasma equilibrium in presence of the support field, non-adiabatic effects on transit and trapped particles, and magnetic field misalignment in the weak-field regions.

Neutral gas which penetrates into a hot plasma body, of characteristic dimension Lb, average density and temperature T, consists mainly of a slow and a fast component, of densities nns, nnf and temperatures TnsT, TnfT, respectively. These components have the penetration lengths Lns = l/σcs and Lnf= 1/σcf, corresponding to the critical densities ncs=1/σcsLb and ncf=l/σcfLb where l/σcflOO/σcs5 × 1018 m−2 for hydrogen in the range 106 < T < 107 K. Thus, hot plasmas can be divided into the classes of permeable dilute, permeable non-dilute, and impermeable systems defined by ncsncf, ncsncf, and ncs ncf , respectively.Concerning tokamaks, an analysis of the plasma-neutral gas interaction leads to the following conclusions: So far, all reported tokamak experiments have been conducted in the permeable density range and have been limited by instabilities in the transition region close to = ncf. Full-scale tokamak reactors should, on the other hand, operate far inside the impermeable density range. The driving force of instabilities due to the pressure gradient is expected to reach its maximum value when approachesthe density limit ncf from below, i.e. at the transition to the impermeable state. The experimentally observed parameter values at the instability limit agree with those calculated from the theory on collisionless ballooning modes driven by the pressure gradient.

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.

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.

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.

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.

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.

The axially symmetric equilibrium of a magnetically confined plasma is reconsidered, with the special purpose of studying high-beta schemes with a purely poloidal magnetic field. A number of special solutions of the pressure and magnetic flux functions are shown to exist.

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.

Flute-type disturbances are investigated by normal mode analysis in the case of a low-beta plasma being confined in the field from a straight line current. A dispersion relation and stability criterion are derived including the joint effects of the plasma pressure, the finite ion Larmor radius and frequency, and of an imposed radial gravitation field. The results, which may also illustrate the general plasma behaviour in more complicated field geometries, indicate that the stability domain is enlarged substantially by finite Larmor radius effects, especially for small-scale disturbances. Also the centrifugal force in rotating plasmas should have a stabilizing effect under certain conditions. In combination with the stabilizing mechanisms in the boundary regions of impermeable plasmas, the present results provide an alternative to the method of minimum-average-B stabilization.

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.