The Stellarator Concept
TL;DR: In this article, the basic concepts of the controlled thermonuclear program at Project Matterhorn, Princeton University are discussed, the theory of confinement of a fully ionized gas in the magnetic configuration of the stellarator is given, the theories of heating are outlined, and the bearing of observational results on these theories is described.
Abstract: The basic concepts of the controlled thermonuclear program at Project Matterhorn, Princeton University are discussed. In particular, the theory of confinement of a fully ionized gas in the magnetic configuration of the stellarator is given, the theories of heating are outlined, and the bearing of observational results on these theories is described.Magnetic confinement in the stellarator is based on a strong magnetic field produced by solenoidal coils encircling a toroidal tube. The configuration is characterized by a ``rotational transform,'' such that a single line of magnetic force, followed around the system, intersects a cross‐sectional plane in points which successively rotate about the magnetic axis. A theorem by Kruskal is used to prove that each line of force in such a system generates a toroidal surface; ideally the wall is such a surface. A rotational transform may be generated either by a solenoidal field in a twisted, or figure‐eight shaped, tube, or by the use of an additional transverse multipolar helical field, with helical symmetry.Plasma confinement in a stellarator is analyzed from both the macroscopic and the microscopic points of view. The macroscopic equations, derived with certain simplifying assumptions, are used to show the existence of an equilibrium situation, and to discuss the limitations on material pressure in these solutions. The single‐particle, or microscopic, picture shows that particles moving along the lines of force remain inside the stellarator tube to the same approximation as do the lines of force. Other particles are presumably confined by the action of the radial electric field that may be anticipated.Theory predicts and observation confirms that initial breakdown, complete ionization, and heating of a hydrogen or helium gas to about 106 degrees K are possible by means of a current parallel to the magnetic field (ohmic heating). Flow of impurities from the tube walls into the heated gas, during the discharge, may be sharply reduced by use of an ultra‐high vacuum system; some improvement is also obtained with a divertor, which diverts the outer shell of magnetic flux away from the discharge. Experiments with ohmic heating verify the presence of a hydromagnetic instability predicted by Kruskal for plasma currents greater than a certain critical value and also indicate the presence of other cooperative phenomena. Heating to very much higher temperatures can be achieved by use of a pulsating magnetic field. Heating at the positive‐ion cyclotron resonance frequency has been proposed theoretically and confirmed observationally by Stix. In addition, an appreciable energy input to the positive ions should be possible, in principle, if the pulsation period is near the time between ion‐ion collisions or the time required for a positive ion to pass through the heating section (magnetic pumping).
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TL;DR: In this article, the authors review the underlying physical processes and the existing experimental database of plasma-material interactions both in tokamaks and laboratory simulation facilities for conditions of direct relevance to next-step fusion reactors.
Abstract: The major increase in discharge duration and plasma energy in a next step DT fusion reactor will give rise to important plasma-material effects that will critically influence its operation, safety and performance. Erosion will increase to a scale of several centimetres from being barely measurable at a micron scale in today's tokamaks. Tritium co-deposited with carbon will strongly affect the operation of machines with carbon plasma facing components. Controlling plasma-wall interactions is critical to achieving high performance in present day tokamaks, and this is likely to continue to be the case in the approach to practical fusion reactors. Recognition of the important consequences of these phenomena stimulated an internationally co-ordinated effort in the field of plasma-surface interactions supporting the Engineering Design Activities of the International Thermonuclear Experimental Reactor project (ITER), and significant progress has been made in better understanding these issues. The paper reviews the underlying physical processes and the existing experimental database of plasma-material interactions both in tokamaks and laboratory simulation facilities for conditions of direct relevance to next step fusion reactors. Two main topical groups of interaction are considered: (i) erosion/redeposition from plasma sputtering and disruptions, including dust and flake generation and (ii) tritium retention and removal. The use of modelling tools to interpret the experimental results and make projections for conditions expected in future devices is explained. Outstanding technical issues and specific recommendations on potential R&D avenues for their resolution are presented.
1,187 citations
TL;DR: In this paper, a variety of properties are derived satisfied by any static equilibrium of a plasma governed by the well-known magnetostatic equations, and a variational principle for such equilibria is derived.
Abstract: A variety of properties are derived satisfied by any static equilibrium of a plasma governed by the well‐known magnetostatic equations. Some of these are local and quite trivial. Others involve integrals over surfaces of constant pressure, which are shown to be topologically toroidal under fairly general assumptions.A variational principle for such equilibria is derived. One of its consequences is to provide a characterization of equilibria by their values of certain invariants.Finally, conditions are obtained additional to the magnetostatic equations appropriate to the steady state of a plasma slowly diffusing across a magnetic field out of a topologically toroidal region.
419 citations
TL;DR: In this article, it was shown that the Poisson bracket of φ with J is an integral integral of the system and that φ is unity, both to all orders.
Abstract: Consider a system of N ordinary first‐order differential equations in N dependent variables, and let the independent variable s not appear explicitly. Let the system depend on a small parameter e and possess a formal infinite power series expansion in e, and suppose that the limiting system for e = 0 exists and has only periodic solutions. Then a formal solution can be constructed involving infinite power series in e and satisfying the equations over large domains of s (of order 1/e). The true solutions of the system exist over such domains and are asymptotically represented as e→0 by the formal solutions. The construction is based on the standard type of formal series solution of a ``reduced'' system of N − 1 equations in N − 1 dependent variables and with the new independent variable σ = e s; the omitted variable is essentially an angle variable φ describing the phase around the simple, closed curves. If the original system is Hamiltonian, then one can define the usual action integral J = ∫ p·dq to all orders; the integral is taken around the phase ring. It is proved that J is an integral of the system and that the Poisson bracket of φ with J is unity, both to all orders. The usefulness of this particular integral is that it is computable locally. The reduced system, after elimination of another dependent variable by means of the constancy of J, can itself be put in Hamiltonian form; if its solutions are nearly periodic, the whole procedure can be reapplied. The present theory encompasses previous proofs of adiabatic invariance to all orders for particular systems such as the harmonic oscillator, the nonlinear oscillator, the charged particle gyrating tightly in a given electromagnetic field, and the longitudinal back‐and‐forth motion of such a particle trapped between two ``magnetic mirrors'' in a weak electric field. There are many other applications.
404 citations
TL;DR: In this article, Ideal magnetohydrodynamic theory and its application to magnetic fusion systems are reviewed and the stability properties of such equilibria are investigated, including general stability properties and applications to those concepts of current fusion interest.
Abstract: Ideal magnetohydrodynamic theory and its application to magnetic fusion systems are reviewed. The review begins with a description and derivation of the model as well as a discussion of the region of validity. Next, the general properties are derived. These are valid for arbitrary geometry and demonstrate the inherently sound physical foundation of the model. The equilibrium behavior of the currently most promising toroidal magnetic fusion concepts are then discussed in detail. Finally, the stability of such equilibria is investigated. Included are discussions of the general stability properties of arbitrary magnetic geometries and of detailed applications to those concepts of current fusion interest.
380 citations
TL;DR: In this paper, the authors reviewed the physics of diveror in tokamaks from an experimental point of view, although where possible simple analytic modelling is included, and provided a framework for comparison of the experimental results with simply derived expectations.
Abstract: The physics of divertors in tokamaks is reviewed, primarily from an experimental point of view, although where possible simple analytic modelling is included. The paper covers the four main subject areas at issue in divertor research: (1) the wide dispersal of plasma power exhausted from the main plasma, (2) the production of sufficiently high gas pressures in the vicinity of pump ducts to enable the removal of fuel and helium (`ash') gas from the system, (3) the elimination or reduction of impurity production and (4) the screening of impurities produced, or intentionally added, at the plasma boundary from the plasma core. A simple analytic model, the `two-point' model, is introduced early in the paper and provides a framework for comparison of the experimental results, drawn from many machines, with simply derived expectations. Conclusions regarding the direction of future research priorities are made.
362 citations
Cites background from "The Stellarator Concept"
...The divertor was first suggested by Spitzer in an early report (Spitzer 1951) and discussed in the open literature in connection with the stellarator concept (Spitzer 1958, Burnett et al 1958)....
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References
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TL;DR: In this paper, an attempt is made to obtain one-fluid hydromagnetic equations by expanding in the ion mass to charge ratio, but the results show that the electron degrees of freedom can be replaced by a macroscopic current, but true hydrodynamics still does not result unless some special circumstance suppresses the transport of pressure along magnetic lines of force.
Abstract: Starting from the Boltzmann equation for a completely ionized dilute gas with no interparticle collision term but a strong Lorentz force, an attempt is made to obtain one-fluid hydromagnetic equations by expanding in the ion mass to charge ratio. It is shown that the electron degrees of freedom can be replaced by a macroscopic current, but true hydrodynamics still does not result unless some special circumstance suppresses the transport of pressure along magnetic lines of force. If the longitudinal transport of pressure is ignored, a set of self-contained one-fluid hydromagnetic equations can be found even though the pressure is not a scalar.
1,324 citations
TL;DR: In this paper, the stability of static, highly conducting, fully ionized plasmas is investigated by means of an energy principle developed from one introduced by Lundquist, and the derivation of the principle and the conditions under which it applies are given.
Abstract: The problem of the stability of static, highly conducting, fully ionized plasmas is investigated by means of an energy principle developed from one introduced by Lundquist. The derivation of the principle and the conditions under which it applies are given. The method is applied to find complete stability criteria for two types of equilibrium situations. The first concerns plasmas which are completely separated from the magnetic field by an interface. The second is the general axisymmetric system.
1,146 citations
Book•
01 Jan 1903
TL;DR: In this paper, the authors studied the conduction of electricity through a gas containing ions and determined the ratio of the charge to the mass of an ion, and the charge carried by the negative ion.
Abstract: 1. Electrical conductivity of gases in a normal state 2. Properties of a gas when in a conducting state 3. Mobility of ions 4. Mathematical theory of the conduction of electricity through a gas containing ions 5. Effect produced by a magnetic field on the motion of the ions 6. Determination of the ratio of the charge to the mass of an ion 7. Determination of the charge carried by the negative ion 8. On some physical properties of gaseous ions 9. Ionisation by incandescent solids 10. Ionisation in gases from flames 11. Ionisation by light. Photo-electric effects Name index Subject index.
636 citations