ALBERT

Notes: Abstract We investigate the state on the Fermion algebra which gives rise to the thermodynamic limit of the Gibbs ensemble in the two-dimensional Ising model on a half lattice with nearest neighbour interaction. It is shown that the operatorP ∞ − in the GNS space, which performs the essential functions of the renormalized transfer matrix, has a quasi-particle structure.

Notes: Long wavelength density fluctuations can be observed by scattering even with a probe beam of much shorter wavelength provided the scattering angle is small enough. This paper is concerned with experiments in which the scattering angle is comparable with the probe beam divergence so the scattered and incident radiation never achieve spatial separation. Under these circumstances, the role of diffraction is preeminent and Fourier optics methods are used to describe the propagation of the beam, which is taken to be TEM00 mode Gaussian. Interaction between the probe beam and the plasma disturbance is described by refraction and no appeal is made to explicit scattering theory. Analysis of the effect of a monochromatic wave disturbance confined to a plane perpendicular to the probe beam (a plane grating in effect) reveals oscillations at the wave frequency induced on the probe with an intensity varying over the beam profile in a regular pattern symmetric about the beam axis. Detail of the pattern depends on the wavelength of the disturbance, its direction, and its axial position relative to a local beam waist. These oscillations are readily identified as due to radiation scattered by the plasma wave into diffraction orders, beating with the unperturbed part of the beam. Indeed, it can be shown1 that Fourier optics plus refraction produce almost the same result as conventional scattering theory,2 the small discrepancy being traceable to the neglect in the latter of incident beam wavefront curvature. The results of the two approaches coincide in the Fraunhofer limit. Computations of this sort have been confirmed by experiments using transducer-driven waves in air3 and by plasma experiments where the same regular patterns are observed from spontaneous plasma waves.4,5 Calculation suggests and experiments have demonstrated6 that additional information, such as the absolute direction of wave propagation, can be deduced from phase, measured with a multichannel detector array.Asymmetric profiles are frequently encountered in far forward scattering experiments in plasma, and they are attributed either to (1) the volume effect, that is, the finite width of a plasma wave, or (2) a pair of counter-propagating waves, such as poloidal waves in a torus met twice by a probe beam traversing a minor diameter. The first explanation rests on the difference between the multiple order scattering of a two-dimensional grating (Raman–Nath) and the single-order scattering of a three-dimensional crystal (Bragg). In a regime intermediate between these extremes, both +1 and −1 orders are present, but of unequal intensity, therefore giving rise to asymmetry in the beam profile. The Fourier optics treatment can be extended to describe a wave of arbitrary interaction length L, and a controlling parameter Q=κ2L/k (κ and k being wave numbers of the plasma wave and the probe radiation, respectively) which is (very-much-less-than)1 for Raman–Nath and (very-much-greater-than)1 for Bragg, determines the precise regime that prevails.7 Calculations describing the counter-propagating waves model have been performed and verified experimentally, again using transducer-driven waves in air.8 Profiles based on this model are currently providing best fits to data recently recorded from tokamak plasmas in TOSCA. A preliminary inspection of the results of these measurements reveals, from the orientation of the beam profile pattern, predominantly poloidal waves. Their maximum intensity is near 100 kHz and they fall away towards higher frequencies as ν−2.5. Evidence for coherent gross modes at lower frequencies is also seen. Wave numbers are in the range 1 cm−1〈κ⊥〈30 cm−1, bracketing the neighborhood where κ⊥ρi∼1. The strength of the relative density fluctuation ñe/n¯e of a few per cent is consistent with diffusion coefficients D⊥∼104 cm2 s−1, and there is evidence for inverse correlation between ñe/n¯e and confinement time τE.

Notes: [Auszug] ANALYTICAL gas chromatography has been studied extensively during the past few years and is now used very widely. In this Department1-5, gas chromatography has been applied also on a preparative scale (1-10 gm.) for the isolation of pure compounds from volatile mixtures which are difficult to ...

Notes: [Auszug] With FabryPerot spacings of 2.78 cm and 4.05 cm, giving free spectral ranges of 0.18 cm1 and 0.12 cm1 respectively, we obtained fringe patterns (Fig. 1) which typically fill between 1/2 and 2/3 of an order. They are composed of several lines, usually 4 or 5 although occasionally 3 or 6 have been ...

Notes: The experimental observation of spatially asymmetric scattering on the TOSCA tokamak has led to the identification of two distinct mechanisms responsible for such effects. The first is the influence of the plasma interaction length L on the scattered field (volume effect). When L is small, the plasma behaves like a thin phase grating and equal-amplitude positive and negative diffraction orders are generated (Raman–Nath scattering). As L increases, however, the scattering takes on three-dimensional properties similar to x-ray diffraction from a crystal; only one diffraction order can occur, and then only if the Bragg condition is satisfied (Bragg scattering). The second effect occurs whenever the scattering volume is large enough to contain counterpropagating waves. In this case, constructive/destructive interference can affect the measured intensity of the scattered light.

Notes: Understanding of the RFP plasma will be materially advanced by a knowledge of its magnetic field or current density profiles. A nonintrusive means of measuring these is offered by Thomson scattering, which, to demonstrate the principle, has been performed at 90° in the poloidal plane of HBTX at three locations: the center, and ±16 cm either side of center along a horizontal diameter. Laser light scattered at any one of these locations is dispersed into two broad wavebands whose intensity ratio depends on Te and on the poloidal component of the electron drift velocity vθ, so a pair of measurements, one at each of the eccentric positions, is needed to determine Te and vθ independently. Typical results for constant current 200-kA plasmas for which average jz ∼1 MA m−2 are, 1.5 ms after initiation of the current: Te =255 eV, vθ =0.55 m/μs, and using ne ∼1.5×1019 m−3, jθ =2.1 MA m−2. At 2.5 ms, Te =455 eV, vθ =2 m/μs, ne ∼1×1019 m−3, and jθ =3.2 MA m−2. At 4.0 ms, Te =475 eV, vθ =1.1 m/μs, ne ∼0.9×1019 m−3, and jθ =1.5 MA m−2. The direction of jθ deduced from scattering agrees with that known for the prevailing HBTX wiring configuration.

Notes: [Auszug] IT is now well known that the illumination of a plasma by a monochromatic uni-directional light beam results in a spectral distribution of scattered light the shape of which depends on the ratio, a, of the scale length for scattering to the plasma Debye length. It has been shown theoretically1 that ...

Notes: Thomson scattering is proposed for the direct measurement of magnetic field fluctuations in a tokamak. The analysis is based on the electron fluid equations. The ordering λ(very-much-less-than)λturb(very-much-less-than)a, where λ and λturb are the incident and turbulence wavelengths, respectively, and a is the torus minor radius, is suggested by spectral information from observations on the TEXT tokamak, as well as general theoretical arguments. With this ordering, temperature effects are unimportant and an expression is derived for probe radiation-induced plasma polarization that depends upon density and magnetic fluctuations only. By choosing the incident probe beam to have its plane of polarization parallel to the local mean magnetic field B0, and observing the scattered power in the plane of polarization perpendicular to B0, it is shown that contributions from density fluctuations are automatically excluded. Faraday rotation is shown to have negligible influence on the scattered signal, which is accordingly determined by magnetic field fluctuations alone.