Interaction of a Modulated Electron Beam with a Plasma

The results of a theoretical and experimental investigation of the high-frequency interaction of an electron beam with a plasma are reported. An electron beam, modulated at a microwave frequency, passes through a uniform region of a mercury arc discharge after which it is demodulated. Exponentially growing wave amplification along the electron beam was experimentally observed for the first time at a microwave frequency equal to the plasma frequency. Approximate theories of the effects of 1) plasma-electron collision frequencies, 2) plasma-electron thermal velocities and 3) finite beam diameter, are given. In a second experiment the interaction between a modulated electron beam and a slow electrostatic wave on a plasma column has been studied. A strong interaction occurs when the velocity of the electron beam is approximately equal to the velocity of the wave and the interaction is essentially the same as that which occurs in traveling-wave amplifiers, except that here the plasma colum replaces the usual helical slow-wave circuit. The theory predicting rates of growth is presented and compared with the experimental results

Observation of b2_2 symmetry vibrational levels of the SO2_2 \tilde{\mbox{C}} 1^1B2_2 state: Vibrational level staggering, Coriolis interactions, and rotation-vibration constants

The $\mathrm{\tilde{C}}$ $^1$B$_2$ state of SO$_2$ has a double-minimum potential in the antisymmetric stretch coordinate, such that the minimum energy geometry has nonequivalent SO bond lengths. However, low-lying levels with odd quanta of antisymmetric stretch (b$_2$ vibrational symmetry) have not previously been observed because transitions into these levels from the zero-point level of the $\mathrm{\tilde{X}}$ state are vibronically forbidden. We use IR-UV double resonance to observe the b$_2$ vibrational levels of the $\mathrm{\tilde{C}}$ state below 1600 cm$^{-1}$ of vibrational excitation. This enables a direct characterization of the vibrational level staggering that results from the double-minimum potential. In addition, it allows us to deperturb the strong $c$-axis Coriolis interactions between levels of a$_1$ and b$_2$ vibrational symmetry, and to determine accurately the vibrational dependence of the rotational constants in the distorted $\mathrm{\tilde{C}}$ electronic state

Edgeworth expansions for slow-fast systems with finite time scale separation

We derive Edgeworth expansions that describe corrections to the Gaussian limiting behaviour of slow-fast systems. The Edgeworth expansion is achieved using a semi-group formalism for the transfer operator, where a Duhamel-Dyson series is used to asymptotically determine the corrections at any desired order of the time scale parameter ε. The corrections involve integrals over higher-order auto-correlation functions. We develop a diagrammatic representation of the series to control the combinatorial wealth of the asymptotic expansion in ε and provide explicit expressions for the first two orders. At a formal level, the expressions derived are valid in the case when the fast dynamics is stochastic as well as when the fast dynamics is entirely deterministic. We corroborate our analytical results with numerical simulations and show that our method provides an improvement on the classical homogenization limit which is restricted to the limit of infinite time scale separation

Transition to subcritical turbulence in a tokamak plasma

Tokamak turbulence, driven by the ion-temperature gradient and occurring in the presence of flow shear, is investigated by means of local, ion-scale, electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A parameter scan in the local values of the ion-temperature gradient and flow shear is performed. It is demonstrated that the experimentally observed state is near the stability threshold and that this stability threshold is nonlinear: sheared turbulence is subcritical, i.e. the system is formally stable to small perturbations, but, given a large enough initial perturbation, it transitions to a turbulent state. A scenario for such a transition is proposed and supported by numerical results: close to threshold, the nonlinear saturated state and the associated anomalous heat transport are dominated by long-lived coherent structures, which drift across the domain, have finite amplitudes, but are not volume filling; as the system is taken away from the threshold into the more unstable regime, the number of these structures increases until they overlap and a more conventional chaotic state emerges. Whereas this appears to represent a new scenario for transition to turbulence in tokamak plasmas, it is reminiscent of the behaviour of other subcritically turbulent systems, e.g. pipe flows and Keplerian magnetorotational accretion flows.Comment: 16 pages, 5 figures, accepted to Journal of Plasma Physic

Near-Infrared Spectroscopy of Molecular Hydrogen Emission in Four Reflection Nebulae: NGC 1333, NGC 2023, NGC 2068, and NGC 7023

We present near-infrared spectroscopy of fluorescent molecular hydrogen (H_2) emission from NGC 1333, NGC 2023, NGC 2068, and NGC 7023 and derive the physical properties of the molecular material in these reflection nebulae. Our observations of NGC 2023 and NGC 7023 and the physical parameters we derive for these nebulae are in good agreement with previous studies. Both NGC 1333 and NGC 2068 have no previously-published analysis of near-infrared spectra. Our study reveals that the rotational-vibrational states of molecular hydrogen in NGC 1333 are populated quite differently from NGC 2023 and NGC 7023. We determine that the relatively weak UV field illuminating NGC 1333 is the primary cause of the difference. Further, we find that the density of the emitting material in NGC 1333 is of much lower density, with n ~ 10^2 - 10^4 cm^-3. NGC 2068 has molecular hydrogen line ratios more similar to those of NGC 7023 and NGC 2023. Our model fits to this nebula show that the bright, H_2-emitting material may have a density as high as n ~ 10^5 cm^-3, similar to what we find for NGC 2023 and NGC 7023. Our spectra of NGC 2023 and NGC 7023 show significant changes in both the near-infrared continuum and H_2 intensity along the slit and offsets between the peaks of the H_2 and continuum emission. We find that these brightness changes may correspond to real changes in the density and temperatures of the emitting region, although uncertainties in the total column of emitting material along a given line of sight complicates the interpretation. The spatial difference in the peak of the H_2 and near-infrared continuum peaks in NGC 2023 and NGC 7023 shows that the near-infrared continuum is due to a material which can survive closer to the star than H_2 can.Comment: Submitted for publication in ApJ. 34 pages including 12 embedded postscript figures. Also available at http://www.astronomy.ohio-state.edu/~martini/pub

Construction of Integrals of Higher-Order Mappings

We find that certain higher-order mappings arise as reductions of the integrable discrete A-type KP (AKP) and B-type KP (BKP) equations. We find conservation laws for the AKP and BKP equations, then we use these conservation laws to derive integrals of the associated reduced maps.Comment: appear to Journal of the Physical Society of Japa