摘要:

Kinetic theory for a spatially homogeneous plasma with Coulomb interaction is considered within the framework of the adiabatic approximation or secular perturbation theory. Time dependent solutions are obtained for the pair correlation function, multiple time distribution functions, etc. Auto correlation functions and spectral densities for fluctuating quantities are defined and obtained for a stable or unstable plasma. The results show that the plasma behaves as though it consisted of statistically independent quasiparticles. The relationship between test‐particle problems and the more general kinetic theory is clarified. Physical interpretation of each term in the Fokker‐Planck equation is provided in terms of spontaneous emission, induced emission, and absorption.

ISSN:0031-9171    

DOI:10.1063/1.1711227

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A test particle of coordinatesX= (x, v) is surrounded by a shield cloud of field particles of coordinatesX′ characterized by a conditional probability functionP(X|X′t). A relationship has been found between this function, the one‐particle functionf(X, t) and the two‐particle correlation functionG(X, X′;t). It isG(X, X′;t)=f(Xt)P(X | X′t)+f(X′t)P(X′ | Xt)+ndX″ f(X″,t)P(X″ | Xt)P(X″ | X′t).The first two terms indicate that each of the two particles involved is a test particle as well as part of the shield cloud of the other particle. The last term corresponds to the two particles shielding a third particle. This relation has been established without solving explicitly for anything and has none of the usual restrictions such as spatial homogeneity, adiabatic time behavior, etc., usually necessary for obtaining explicit solutions. It is useful because the problem of kinetic theory is reduced to determiningPwhich involves only the Vlasov equation. In addition, superposition principles for fluctuations, etc., are apparent at the outset.

ISSN:0031-9171    

DOI:10.1063/1.1711228

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

Formal conditions are derived for the stability of a velocity discontinuity at a plane interface between two perfectly conducting, inviscid, compressible fluids, in the presence of uniform magnetic fields. Certain special cases, in which the stability conditions can be simplified, are discussed in detail. Previous results for incompressible fluids are rederived and it is shown that the introduction of a slight compressibility always reduces the stabilizing effect of magnetic fields. It is further shown that in two special cases the magnetic field required to stabilize an interface continues to increase with the introduction of more compressibility until it reaches a limiting value that is about twice as large as the value appropriate to incompressible fluids.

ISSN:0031-9171    

DOI:10.1063/1.1711229

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A calculational method of determining the boundary surface between a plasma and a magnetic field is described. The method consists of neglecting the curvature of the surface and approximating the magnetic field adjacent to the boundary by a sum of the field due to thelocalsurface current and the plasma‐independent magnetic field source. This field is used in the boundary equations to compute the boundary surface. The resulting surface is then used to compute the magnetic field due to the curvature of the surface and the computation of the boundary surface is repeated. Reiteration of the calculational steps is continued until a self‐consistent solution is obtained in which the magnetic field resulting from the curvature of the previous surface is used to obtain a surface whose shape does not differ from the previous surface by more than the imprecision of the calculation of the magnetic field. The method is illustrated by application to three simple problems of (1) a line dipole immersed in a plasma exerting a constant pressure on the boundary, (2) a point dipole immersed in plasma exerting constant pressure, and (3) a line dipole in a plasma stream exerting a pressure in only one direction (parallel to the stream velocity).

ISSN:0031-9171    

DOI:10.1063/1.1711230

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The coupling between ion oscillations and electric currents introduced by collisional effects was studied. A growth of ion acoustic waves is found which extrapolates to the Vlasov gas value as the collision mean free path and wavelength become comparable. The damping of ion acoustic waves is calculated from the fluid equations. For a plasma confined by a strong magnetic field, convective oscillations can be excited by an electron drift along the magnetic field lines. The growth rate and frequency of these oscillations is compared to stellarator experiments.

ISSN:0031-9171    

DOI:10.1063/1.1711231

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

Calculations are presented for the influence of small impurity concentrations on the energy balance and electron temperature during the magnetic compression of a deuterium plasma. The rate equations which describe the ionization are based on the Corona Plasma Model in much the same way as has been done earlier for a plasma assumed to be homogeneous.Despite the comparatively high electron densities (≳1016cm−3) in these plasmas, this model should be applicable because of the high ionic charge at temperatures over ∼10 eV. The radial temperature and density distributions were obtained numerically by coupling the Hain‐Roberts two‐fluid, hydromagnetic equations to the Corona equations. The ionization of up to four different impurities, i.e., C, N, O, Ne, can be taken into account. Radiation losses were included in the electron energy‐balance equation, but the influence of impurity ionization on the electron density and electrical conductivity was neglected. Therefore, only small impurity concentrations can be considered. However, only a few percent impurities have a drastic effect on the electron temperature so that the present calculations may be meaningful in the interpretation of certain experiments.

ISSN:0031-9171    

DOI:10.1063/1.1711232

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A method for measuring local atom or ion densities, based on the scattering of resonance line radiation, is discussed for the case of an optically thin barium plasma confined by a strong magnetic field. The anisotropy of the flux of scattered resonance radiation due to anisotropic illumination and the presence of a magnetic field is examined. Barium ion density measurements on a laboratory plasma are described. It is noteworthy that this method is capable of high spatial resolution, and that light intensity ratio measurements suffice to obtain absolute ion densities. No absolute photometric measurements are required.

ISSN:0031-9171    

DOI:10.1063/1.1711233

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A study was made of the motion of a single charged particle in the magnetic induction generated by an axisymmetric current sheet, the current of which was sinusoidally modulated along the axis. Several adiabatically invariant quantities were investigated, and it was found thatM4= |v×B|2/|B|3varied least along a given trajectory. A particle was considered to be adiabatic ifM4varied by less than 5% during a single interaction with the magnetic barrier. An averaging process was found which made it possible to predict the relations between particle mass and energy, and the magnetic induction strength and geometry, which causeM4to vary by more than 5% during a single interaction with the magnetic barrier.Experimental apparatus was constructed which made it possible to study a single interaction of a beam of charged particles with a magnetic barrier under steady‐state conditions. An experimental procedure was developed which made it possible to detect the transition from adiabatic to nonadiabatic reflection of the ion beam, and the results were compared with the results of the numerical computation.

ISSN:0031-9171    

DOI:10.1063/1.1711234

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A convenient method for the accurate measurement of Doppler temperatures as a function of time has been developed and applied to the C Stellarator. General agreement between Doppler and other temperature measures has been found when the plasma is quiescent. Late in the period of plasma containment however, the ion‐Doppler temperatures begin to fall appreciably below the electron temperature. This is shown to be explainable in terms of an influx of cold gas which tends to overcome the heating by the electrons.

ISSN:0031-9171    

DOI:10.1063/1.1711235

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

Drift surfaces of guiding centers in the Bumpy Torus static magnetic field have been located and analyzed for various torus parameters by making use of the transverse adiabatic invariant &mgr; =p⊥2/Band the longitudinal adiabatic invariantJ= ∮p∥dl.In addition, the drift equations (for which &mgr; is an invariant) have been solved numerically to investigate limitations on the application of the invariance ofJ. In general,Jis an invariant for the drift equations under adiabatic conditions; however, some special guiding‐center trajectories are presented for which the drift per longitudinal period is sufficiently large that the assumption of the invariance ofJis not valid. Closed surfaces of constantU= ∮B−1dlhave been found. These are also surfaces of constant plasma pressure under static equilibrium conditions at low &bgr; for a hydromagnetic model. The stability of the equilibrium is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1711236

出版商:AIP    

年代:1964

数据来源: AIP