摘要:

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 106degrees 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).

ISSN:0031-9171    

DOI:10.1063/1.1705883

出版商:AIP    

年代:1958

数据来源: AIP

摘要:

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.

ISSN:0031-9171    

DOI:10.1063/1.1705884

出版商:AIP    

年代:1958

数据来源: AIP

摘要:

Criteria useful for the investigation of the stability of a system of charged particles are derived from the Boltzmann equation in the smallm/elimit. These criteria are obtained from the examination of the variation of the energy due to a perturbation, when subject to the general constraint that all regular, time‐independent constants of the motion (including the energy) have their equilibrium values.The first‐order variation of the energy vanishes trivially, and the second‐order variation yields a quadratic form in the displacement variable &xgr; (which may be introduced because of the well‐known properties of this limit). The positive‐definiteness of this form is a sufficient condition for stability.Several theorems are stated comparing stability under the present theory with that under conventional hydromagnetic fluid theories where heat flow along magnetic lines of force is neglected. Generalizations can be made to systems where the effect of collisions is included.

ISSN:0031-9171    

DOI:10.1063/1.1705885

出版商:AIP    

年代:1958

数据来源: AIP

摘要:

Hydromagnetic equilibria are obtained for a variety of situations which differ little from that of a zero pressure uniform axial magnetic field. Criteria for ascertaining the stability of these equilibria are found by means of an energy principle. In particular, if helically invariant fields are present, stable equilibria with nonzero pressure and net axial current can be found.

ISSN:0031-9171    

DOI:10.1063/1.1705886

出版商:AIP    

年代:1958

数据来源: AIP

摘要:

A method which is used for the ionization and heating of helium plasmas in various stellarator models consists of inducing an approximately constant electric field along the main axial confining magnetic field. In this paper we present the details and results of various calculations pertaining to this method. The gas is assumed initially to be 10&percent; ionized and at a temperature of a few electron volts.The major approximations on which the calculations are based are (1) Maxwellian velocity distributions for the particles and (2) negligible charged particle loss across the confining magnetic field. The equations for the power balance and number balance were integrated in time numerically for a variety of initial conditions. The results indicate that temperatures of a few hundred electron volts are attainable within milliseconds with an applied field of the order 0.1 volt per cm at densities of 3 × 1013particles per cm3. It was found that the maximum temperature is limited by power loss in bremsstrahlung radiation.

ISSN:0031-9171    

DOI:10.1063/1.1705887

出版商:AIP    

年代:1958

数据来源: AIP

摘要:

There are two ways of heating a plasma confined by a strong axial magnetic field. In the first of these the electric field is parallel to the magnetic field, the situation that obtains in ohmic heating. In the second of these, the electric field is perpendicular to the main axial magnetic field. In this paper we consider the second case only and consider the electric field to be produced by an externally imposed oscillation of the axial field. This method of heating is often called magnetic pumping.It is found that as far as the heating of the plasma is concerned, there are four characteristic times which play a fundamental role. These four times are: (1) the collision time, (2) the period of the oscillating field, (3) the time of transit of a typical ion through the heating region, and (4) the cyclotron period of an ion. If these four characteristic times are all of comparable order, the theoretical analysis is exceedingly complex. Therefore, four cases were considered in which these were taken to be of different orders. The heating mechanism differs in each of these four cases since the period of the externally produced electric field is chosen to be comparable to one of the characteristic times in the analysis. In each of the four cases configurations were found which led theoretically, at least, to efficient heating of the plasma.In those cases where the energy imparted to the plasma appears in the form of wave motion, the subsequent damping of these waves is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1705888

出版商:AIP    

年代:1958

数据来源: AIP

摘要:

Generation of hydromagnetic and ion cyclotron waves by an induction coil is considered for a cylindrical plasma in a uniform confining magnetic field. Resonance widths are calculated and power absorption is calculated and compared to ohmic losses in the induction coil. Rapid thermalization of transverse plasma waves occurs when appreciable numbers of ions stream through the periodic perturbation with velocities such that, in their own rest frames, these ions ``feel'' the perturbation at their own cyclotron frequency. This effect, termed cyclotron damping, makes possible an efficient plasma heating scheme for thermonuclear reactors. Radio‐frequency power can be transferred from an induction coil into ion cyclotron waves with an efficiency typically greater than 65&percent;. The wave energy can be quickly transformed into energy of effectively random transverse ion motion by causing the ion cyclotron wave to travel along a magnetic field which decreases slowly with distance.

ISSN:0031-9171    

DOI:10.1063/1.1705889

出版商:AIP    

年代:1958

数据来源: AIP

摘要:

The half‐range method of solution of the Boltzmann equation is used to give a kinetic theory treatment of the Rayleigh problem. In contrast to the Navier‐Stokes or Grad theories, the method yields exact results for the initial stress and slip velocity at the boundary. It also indicates corrections to the classical Rayleigh results, even at long times compared to the collision periods of the gas molecules. The corrections are shown to be related to the usual slip boundary conditions of hydrodynamics plus an additional part arising from boundary layer effects. The half‐range method predicts corrections to the standard methods of between 10&percent;–25&percent; for all values of the time.

ISSN:0031-9171    

DOI:10.1063/1.1705890

出版商:AIP    

年代:1958

数据来源: AIP

摘要:

The compressibility of a sample of very pure methane has been measured with high precision from 0°C to 150°C and over a pressure range of about 20 to 230 atmos. The precision attained is of the order of 1 part in 104. Small but consistent discrepancies exist between the present results and earlier measurements, and it is believed these discrepancies are the result of a small impurity of ethane in the methane used earlier. The virial coefficients of methane are redetermined from the present measurements, and the intermolecular forces of methane are calculated from the second virial coefficient for several forms of force laws. These force laws are then used to calculate the third virial coefficient, the crystal properties at 0°K, and the viscosity for comparison with experiment. All the force laws fit the second virial coefficient very well, but some can be eliminated on the basis of the other properties.

ISSN:0031-9171    

DOI:10.1063/1.1705891

出版商:AIP    

年代:1958

数据来源: AIP

摘要:

A general method is developed for calculating theadditionalmechanical energy dissipation incurred by the presence of solid particles suspended in an incompressible viscous fluid in laminar flow. The development is applicable to flow in any apparatus within which the steady motion of a homogeneous fluid can be described by omitting the inertial terms in the Navier‐Stokes equations or in which the motion occurs in concentric circles. The validity of the results obtained is limited to situations in which the particle dimensions are small compared to those of the apparatus in which the motion is occurring.The technique, based largely upon a reciprocal theorem for the inertialess flow of viscous fluids, is employed to calculate the permanent pressure drop accompanying the passage of liquid through a bed of fluidized solids. When the particles are uniformly distributed throughout the bed, this pressure diminution is equal to the bed weight (corrected for buoyancy) per unit area of duct—in agreement with experimental data on systems in a state of particulate fluidization. Calculations are also presented for the permanent pressure arising from the passage of fluid past an immobilized spherical particle within a cylindrical duct.Einstein's formula for the apparent viscosity of a dilute suspension of spherical particles is also deduced. By means of a new definition of suspension viscosity the heretofore different points of view advanced by Einstein, Jeffery, and Burgers are seen to be consistent with one another. Einstein's result is shown to be independent of the type of viscometer employed provided that the motion of a homogeneous fluid within the device fulfills the previous criteria.In the case of nonspherical particles it is demonstrated that the constant in Einstein's viscosity equation (which has a value of 2.5 for spheres) can never be less than unity, whatever the shape of the rigid particles or their orientation with respect to the axes of the apparatus.

ISSN:0031-9171    

DOI:10.1063/1.1705892

出版商:AIP    

年代:1958

数据来源: AIP