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Notes: Exact three-dimensional volume current solutions of the magnetohydrodynamic (MHD) equations are presented. The configurations are infinitely extended along a straight axis and have neither cylindrical nor helical nor mirror symmetry. All field lines lie in planes orthogonal to the axis and are closed around it. The surfaces of constant pressure have elliptical cross sections, whose ellipticity and orientation are arbitrary functions along the axis. © 1995 American Institute of Physics.

Notes: In this paper the inverse problem of the existence of surface current magnetohydrodynamic (MHD) equilibria in toroidal geometry with vanishing magnetic field inside is addressed. Inverse means that the plasma–vacuum interface rather than the external wall or conductors is given, and the latter remain to be determined. This makes a reformulation of the problem possible in geometric terms: what toroidal surfaces with analytic parametrization allow a simple analytic covering by geodesics? If such a covering by geodesics (field lines) exists, their orthogonal trajectories (current lines) also form a simple covering, and are described by a function satisfying a nonlinear partial differential equation of the Hamilton–Jacobi type, whose coefficients are combinations of the metric elements of the surface. All known equilibria—equilibria with zero and infinite rotational transform and the symmetric ones in the case of finite rotational transform—turn out to be solutions of separable cases of that equation, and allow a unified description if the toroidal surface is parametrized in the moving trihedral associated with a closed curve. Analogously to volume current equilibria, the only continuous symmetries compatible with separability are plane, helical, and axial symmetry. In the nonseparable case numerical evidence is presented for cases with chaotic behavior of geodesics, thus restricting possible equilibria for these surfaces. For weak deviation from axisymmetry, Kolmogorov–Arnold–Moser (KAM)-type behavior is observed, i.e., destruction of geodesic coverings with a low rational rotational transform and preservation of those with irrational rotational transform. A previous attempt to establish three-dimensional surface current equilibria on the basis of the KAM theorem is rejected as incomplete, and a complete proof of the existence of equilibria in the weakly nonaxisymmetric case, based on the twist theorem for mappings, is given. Finally, for a certain class of strong deviations from axisymmetry, an analytic criterion is formulated that rules out equilibria for these surfaces.

Notes: The present work explores the existence of nonaxisymmetric toroidal magnetohydrodynamic equilibria when all lines of force of the magnetic field close after a single revolution about a given magnetic axis. It is assumed that the magnetic axis is a closed curve with arbitrary curvature and zero torsion, implying that it is constrained to lie in a plane surface. In addition, it is assumed that the closed magnetic field lines lie in planes that are orthogonal to the magnetic axis. Subject to these conditions, the existence of toroidal magnetic surfaces, F(r)=const, is explored. The governing equilibrium equations of magnetohydrodynamics place a constraint on the function F(r) in the form of two nonlinear partial differential equations that must be simultaneously satisfied. It is demonstrated that this is not always possible without axisymmetry. Two specific cases where toroidal magnetic surfaces do not exist are identified: (I) isodynamic configurations, which implies that the magnetic field strength is constant on each magnetic surface, and (II) configurations with "bumpy'' surfaces, which implies that the size but not the geometrical shape of the poloidal section containing the closed field lines depends on s. © 1995 American Institute of Physics.

Notes: The inverse problem of the existence of magnetohydrostatic equilibria in toroidal geometry with surface currents and vanishing magnetic field inside is considered. The inverse formulation (plasma–vacuum interface given, external wall or conductors to be determined) allows a purely geometric characterization of the problem: Toroidal surfaces with analytic parametrization are admissible plasma–vacuum interfaces if they allow a simple analytic covering by geodesics (field lines) or, equivalently, by equidistant lines (current lines). On the basis of this approach it was shown in a recent publication [Phys. Plasmas 1, 281 (1994)] that equilibria with sufficiently irrational rotational transform exist for configurations with arbitrary but weak deviations from axisymmetry. The present paper completes this work by demonstrating that this result, essentially, cannot be sharpened. More precisely, it is shown that for every rational rotational transform ι there exists a (arbitrarily weak) deformation of the axisymmetric circular torus (with sufficiently large aspect ratio) such that an equilibrium with that toroidal surface as plasma–vacuum interface and that ι does not exist. This does not mean that there are no three-dimensional equilibria with rational ι at all. In fact, in the special case of infinite rotational transform, i.e., field lines are simply closed in the poloidal direction, it is demonstrated that, depending on the type of perturbation, equilibria may survive arbitrarily strong deviations from axisymmetry or may immediately be destroyed. Toroidal surfaces of the former type are the so-called canal surfaces, which are generated by the nonrotating transport of a poloidal section along an arbitrary closed space curve, whereas examples of the latter type are "bumpy'' tori, where the poloidal section may vary in magnitude but not in shape along the generating curve. If the poloidal section rotates along the generating curve ("helical'' torus) so that the rotation velocity vanishes somewhere, the surface is also of the latter type.

Notes: An enhanced supersonic carbon source produces carbon atoms in their C(3Pj) electronic ground states via laser ablation of graphite at 266 nm. The 30 Hz (40±2) mJ output of a Nd-YAG laser is focused onto a rotating graphite rod with a 1000 mm focal length UV-grade fused silica plano-convex lens to a spot of (0.5±0.05) mm diameter. Ablated carbon atoms are subsequently seeded into helium or neon carrier gas yielding intensities up to 1013 C atoms cm−3 in the interaction region of a universal crossed beam apparatus. The greatly enhanced number density and duty cycle shift the limit of feasible crossed beam experiments down to rate constants as low as 10−11–10−12 cm3 s−1. Carbon beam velocities between 3300 and 1100 m s−1, with speed ratios ranging from 2.8 to 7.2, are continuously tunable on-line and in situ without changing carrier gases by varying the time delay between the laser pulse, the pulsed valve, and a chopper wheel located 40 mm after the laser ablation. Neither electronically excited carbon atoms nor ions could be detected within the error limits of a quadrupole-mass spectrometric detector. Carbon clusters are restricted to ∼10% C2 and C3 in helium, minimized by multiphoton dissociation, and eliminating the postablation nozzle region. © 1995 American Institute of Physics.

Notes: In our laboratory a novel and convenient technique has been developed to generate an intense pulsed cyano radical beam to be employed in crossed molecular beam experiments investigating the chemical dynamics of bimolecular reactions. CN radicals in their ground electronic state 2Σ+ are produced in situ via laser ablation of a graphite rod at 266 nm and 30 mJ output power and subsequent reaction of the ablated species with molecular nitrogen, which acts also as a seeding gas. A chopper wheel located after the ablation source and before the collision center selects a 9 μs segment of the beam. By changing the delay time between the pulsed valve and the choppper wheel, we can select a section of the pulsed CN(X2Σ+) beam choosing different velocities in the range of 900–1920 ms−1 with speed ratios from 4 to 8. A high-stability analog oscillator drives the motor of the chopper wheel (deviations less than 100 ppm of the period), and a high-precision reversible motor driver is interfaced to the rotating carbon rod. Both units are essential to ensure a stable cyanogen radical beam with velocity fluctuations of less than 3%. The high intensity of the pulsed supersonic CN beam of about 2–3×1011 cm−3 is three orders of magnitude higher than supersonic cyano radical beams employed in previous crossed molecular beams experiments. This data together with the tunable velocity range clearly demonstrate the unique power of our newly developed in situ production of a supersonic CN radical beam. This versatile concept is extendible to generate other intense, pulsed supersonic beams of highly unstable diatomic radicals, among them BC, BN, BO, BS, CS, SiC, SiN, SiO, and SiS, which are expected to play a crucial role in interstellar chemistry, chemistry in the solar system, and/or combustion processes. © 1999 American Institute of Physics.

Notes: The cosmic ray simulator consists of a 50 l cylindrical stainless steel chamber. A rotable cold finger milled of a silver (111) monocrystal optimizes heat conductivity and is connected to a programmable, closed cycle helium refrigerator allowing temperature control of an attached silver wafer between 10 and 340 K (±0.5 K). Oil-free ultrahigh vacuum (UHV) conditions of ≈10−10 mbar are provided by a membrane, drag, and cryopump, hence guaranteeing a vacuum system free of any contamination. Ice layers of defined crystal structures and reproducible thickness of (5±1) μm are achieved by depositing gases, e.g., CH4, CD4, CD4/O2, and CH4/O2, with a computer-assisted thermovalve on the cooled wafer. These frosts are irradiated at 10 and 50 K with 7.3 MeV protons and 9 MeV α particles of the compact cyclotron CV28 in Forschungszentrum Jülich up to doses of 150 eV per molecule, i.e., simulating the distribution maximum of galactic cosmic ray particles interacting with primordial matter in space during 0.7×109 yr. During the experiments, gas phase and solid state are monitored for the first time quantitatively on line and in situ by a quadrupole mass spectrometer (QMS) via matrix interval arithmetic and a Fourier transform infrared spectrometer (FTIR) in an absorption-reflection mode at 62.5°.For the first time, a cosmic ray simulator allows detailed and reproducible mechanistic studies on the interaction of cosmic ray particles with frozen gases in space based on pressure conditions (hydrocarbon free UHV conditions, the limitation of condensations of residual gases during an experiment to less than one monolayer), temperature regime (the use of silver monocrystals, FTIR in reflection, optimized ion currents, and target thicknesses 〈5 μm restrict temperature increasing to 14 K), and defined target systems. In combination with two on line and in situ analyses techniques, i.e., FTIR and QMS, the machine yields unprecedented options such as computing the heating of the ice surfaces directly exposed to the ion beam by a calibrated QMS and a complete quantification of product distribution. Preliminary results indicate a strong temperature-dependent component of the reaction mechanisms in the frosts: surface layers are heated by impinging ions to (14±1) K and yield (70%–100%) of higher molecular weight species, such as C11D24, whereas 10 K regions produce majority of simpler hydrocarbons, e.g., C3D8. Second, O2 contaminations influence the experiments dramatically by trapping of diffusive H atoms as O2H and, thus, yield oxygen-containing yellow to brown residues after heating to 293 K. Irradiation of pure methane targets, however, produce no residues. But an increasing concentration of H atoms exceeding (6%±3%) leads to ejection of up to 90% of the frosts into vacuum. © 1995 American Institute of Physics.

Notes: A novel, efficient technique to identify and quantify complex gas mixtures is described. This approach can be applied on line and in situ and is extendible to samples with reactive and thermally labile species. Complex hydrocarbon mixtures are prepared in test experiments by irradiating frozen methane targets with 9 MeV α particles in an ultrahigh vacuum chamber and releasing them during successive heating of the solid samples from 10 to 293 K after each ion bombardment. A quadrupole mass spectrometer monitors time-dependent ion currents of selected m/z values, which are proportional to partial pressures in the case of a nonoverlapping fragmentation pattern. Predominantly, parent molecules and fragments of different molecular species add to a specific m/z value, i.e., C2H+4, N+2, and CO+ contribute to m/z=28. Programmed m/z ratios are chosen to result in an inhomogeneous system of linear equations including the measured ion current (right-hand vector), partial pressures (unknown quantity), and the calibration factors of fragments of individual gases determined in separate experiments. Since all quantities are provided with experimental errors, matrix interval algebra, i.e., an IBM high accuracy arithmetic subroutine defining experimental uncertainties as intervals, is incorporated in the computations to extract individual, calibrated components of complex gas mixtures. This proceeding enables the quantitative sampling of calibrated hydrocarbons, and, especially, H2 and D2 without further time-consuming preseparation devices on line and in situ, hence justifying the use of this approach in space missions to elucidate the chemical composition of, e.g., planetary atmospheres without payload wasting gas chromatographs. © 1995 American Institute of Physics.