摘要:

Probe and recombination‐radiation spectrum measurements were used to measure the electron number density and temperature profiles in front of a flat disc in a supersonic seeded‐gas plasma. The region of interest extended several body diameters upstream of the disc and through the shock wave. The experiment covered a free stream electron density range of 4 × 1011to 1.6 × 1012cm−3and an electron temperature range of 0.06 to 0.1 eV. The region of reduced luminosity upstream of the shock wave is shown to be associated with electron heating at constant electron density. The electron thermal conductivity is derived from measurements in the upstream region and gives reasonable agreement with the Spitzer formula. Measurements are made of the electron temperature change across the heavy‐particle shock wave and of the over‐all electron temperature ratio across the entire process. It is shown that the over‐all electron‐temperature ratio could not be predicted on the basis of an adiabatic one‐demensional flow process in this experiment.

ISSN:0031-9171    

DOI:10.1063/1.1762080

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Previously [P.N.Hu, Phys. Fluids9, 89 (1966)], a universal monotonic profile was found for a weak plasma shock propagating perpendicular to a magnetic field using an elaborate set of moment equations which included electron and ion viscosity, coupled electron and ion heat conduction, thermal diffusion, and resistivity, together with distinct Hall terms for the resistivity, stress, and heat flow. Inclusion of an additional term related to electron inertia now gives a one‐parameter family of profiles which spans the entire range from collision dominated monotonic profiles to damped oscillatory profiles and the limiting collisionless case of purely oscillatory and solitary wave profiles.

ISSN:0031-9171    

DOI:10.1063/1.1762081

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The use of truncated Wiener‐Hermite functional expansions as a basis for the theory of turbulence is critically examined. An account is given of the application of such expansions to Burgers' model equation. The nature of Wiener‐Hermite expansions is such that certain important consistency requirements, such as realizability, follow immediately. In order to gain insight into other aspects of the predicted turbulence dynamics, a simpler model problem in which there are only three interacting modes is first studied. It is shown that Wiener‐Hermite closures do not faithfully represent the dynamics for this latter model. Then, the analysis is extended to Burgers' equation. It is shown that Wiener‐Hermite closures do not preserve fundamental properties of the exact dynamics in equilibrium. Inviscid equipartition solutions do not survive in the closures. In addition, it is shown that these closures do not treat the effects of large scales on small scales properly. Numerical calculations be extended to the corresponding theory of Navier‐Stokes turbulence. We conclude that truncated Wiener‐Hermite expansions are unsuitable for the theory of high Reynolds‐number turbulence.

ISSN:0031-9171    

DOI:10.1063/1.1762082

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A purely deductive approximation theory for incompressible fluid turbulence is presented, based exclusively on the Hopf characteristic functional space‐time formulation and without any additive statistical postulate. Certain real symmetric solenoidal tensors called ``stationary functionalities'' are defined in terms of the characteristic functional by functional integration, quantities which vanish in the neighborhood of anexactphysical characteristic functional, hence, for anapproximatephysical characteristic functional. By explicit functional integration, the first and second tensorial rank stationary functionalities are evaluated with a zero‐mean velocity field Gaussian approximation for the characteristic functional. Equating the resulting expressions to zero produces a subsidiary equation and a dynamical equation for the two‐point velocity correlation tensor, equations which are identical to the Navier‐Stokes expectation value equation for a zero‐mean velocity field and to a specific two‐point Navier‐Stokes expectation value equation with a zero‐mean velocity field probability distribution such that the fourth‐order velocity field product expectation values are related to lower‐order product expectation values in the same way as for a zero‐mean Gaussian probability distribution. Specialized forms of the nonlinear integrodifferential dynamical equation are worked out for the cases of homogeneous and isotropic homogeneous turbulence.

ISSN:0031-9171    

DOI:10.1063/1.1762083

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The behavior of charged particles in an electromagnetic field composed of two parts is treated. The first is an unperturbed part, for which the solution of the Vlasov equation is assumed to be known; the second part is a perturbation which is assumed to be random and of small amplitude. Such a ``stochastic'' or ``turbulent'' electromagnetic field leads to diffusion, pitch‐angle scattering, and acceleration. Equations governing these processes may be derived by test‐particle calculations. The problem is first posed in a general way, and solved by a method similar to that used in quasi‐linear theory. The connection of this method with the Fokker‐Planck formulation is discussed. The case which is analyzed in detail is that of relativistic particles moving in a uniform magnetic field under the influence of a steady homogeneous spectrum of electromagnetic fluctuations. Results are given which are valid for any (weak) fluctuation spectrum and for finite test‐particle gyroradii. The physical meaning of the results is discussed, and it is shown that in certain limits there is agreement with earlier, less general analyses.

ISSN:0031-9171    

DOI:10.1063/1.1762084

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The quasi‐linear development of the instability of two counter‐streaming electron beams is discussed from a hydrodynamic point of view. While it turns out that the closure assumptions for the system of moment equations have an appreciable influence on the time asymptotic result, the nonresonant diffusion mechanism allows a number of interesting interpretations in the fluid picture.

ISSN:0031-9171    

DOI:10.1063/1.1762085

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The fast (right‐handed) hydromagnetic wave is generated by a Stix coil installed on the Model C stellarator. Maximum wave generation and heating occurs, as expected, under conditions such that the wavelength of the propagating wave equals the wavelength of the coil structure. Measurements of diamagnetic pressure determine the efficiency for conversion of rf power into thermal energy. Theoretical calculations of heating rates shows that plasma resistivity and Landau damping are insufficient to account for the observed heating rates if only the body wave is considered. Introduction of surface waves associated with finite electron mass results in increasedEzfields which enhance the heating rate.

ISSN:0031-9171    

DOI:10.1063/1.1762086

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Dispersion relation for transverse waves in a fully ionized plasma in the presence of a spatially uniform fieldE0cosvthas been obtained and the possibility of instabilities has been discussed. It has been shown that the analysis also gives the Dawson‐Oberman formula for the force of an ion on the electrons for the uncoupled longitudinal field.

ISSN:0031-9171    

DOI:10.1063/1.1762087

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Instabilities of a ballooning type were observed in the ∮dl/Bstable region of a linear quadrupole device. The amplitude distribution of the fluctuation along a field line behaved like a standing wave that had a node where ▿B2· ▿p< 0 and was peaked where ▿B2· ▿p> 0. The quantityk∥&lgr;mfpewas typically 5–10. The observed fluctuation is in qualitative agreement with the theory of collisionless drift waves modified to take into account the change of field curvature and field strength along the field line. The threshold for the instability appears to be strongly dependent on the ratio of the plasma radius to connection length. The plasma confinement was not sensitive to the presence of the ballooning instability.

ISSN:0031-9171    

DOI:10.1063/1.1762088

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The discussion of the motion of single particles in stellarators is simplified by identifying three distinct groups of particles. The drift equations are used to treat these groups by analytical and numerical methods. It is shown that, unlike an axisymmetric system the region of a stellarator with surfaces closed about a magnetic axis need not form a perfect trap. In fact, unless the toroidal curvature is very small, particles in one of the groups, those mirrored between maxima in a single period of the helical field, will drift out beyond the separatrix no matter how large the magnetic field strength.

ISSN:0031-9171    

DOI:10.1063/1.1762089

出版商:AIP    

年代:1967

数据来源: AIP