K. Rypdal

Blow-up in Nonlinear Schroedinger Equations-I A General Review

The general properties of a class of nonlinear Schroedinger equations: iut + p:∇∇u + f(|u|2)u = 0 are reviewed. Conditions for existence, uniqueness, and stability of solitary wave solutions are presented, along with conditions for blow-up and global existence for the Cauchy problem.

Electric probes for plasmas: The link between theory and instrument

Electric probe methods for diagnostics of plasmas are reviewed with emphasis on the link between the appropriate probe theories and the instrumental design. The starting point is an elementary discussion of the working principles and a discussion of the physical quantities that can be measured by the probe method. This is followed by a systematic classification of the various regimes of probe operation and a summary of theories and methods for measurements of charged particle distributions. Application of a single probe and probe clusters for measurements of fluid observables is discussed. Probe clusters permit both instantaneous and time-averaged measurements without sweeping the probe voltage. Two classes of applications are presented as illustrations of the methods reviewed. These are measurements of cross sections and collision frequencies (plasma electron spectroscopy), and measurements of fluctuations and anomalous transport in magnetized plasma.

A thermal oscillating two‐stream instability

A theory for the oscillating two‐stream instability, in which the Ohmic heating of the electrons constitutes the nonlinearity, is developed for an inhomogeneous and magnetized plasma. Its possible role in explaining short‐scale, field‐aligned irregularities observed in ionospheric heating experiments is emphasized. The theory predicts that the initial growth of such irregularities is centered around the level of upper hybrid resonance. Furthermore, plane disturbances nearly parallel to the magnetic meridian plane have the largest growth rates. Expressions for threshold, growth rate, and transverse scale of maximum growth are obtained. Special attention is paid to the transport theory, since the physical picture depends heavily on the kind of electron collisions which dominate. This is due to the velocity dependence of collison frequencies, which gives rise to the thermal forces.

Sharper criteria for the wave collapse

Abstract Sharper criteria for three-dimensional wave collapse described by the Nonlinear Schrodinger Equation (NLSE) are derived. The collapse threshold corresponds to the ground state soliton which is known to be unstable. Thus, for nonprefocusing distributions this represents the separatrix between collapsing and noncollapsing sectors. Numerical results support the theoretical results. Generalizations of the criteria for the NLSE with arbitrary power nonlinearity are also presented.

Confinement and turbulent transport in a plasma torus with no rotational transform

In the BLAAMANN device a weakly ionized hydrogen plasma is produced by electrons accelerated from a hot, negatively biased tungsten filament and confined in a toroidal magnetic field of strength up to 0.4 T. The plasma is turbulent, with relative fluctuation levels in ne, phi and Te of 10% or more. The time-averaged state exhibits nested toroidal surfaces of constant potential and pressure, which requires an anomalous cross-field current to remove the space-charge injected by the cathode and the charge accumulated due to the Del B- and curvature drifts. Typical plasma parameters are ne approximately 1016 m-3, Te approximately 1-20 eV, Ti approximately 1 eV. The cross-field diffusion coefficient is typically Dperpendicular to approximately 30 m2 s

Hypervelocity dust impacts in FTU scrape-off layer

-1 approximately 104*Dperpendicular to classical approximately 101*Dperpendicular to Bohm. Evidence is presented in support of the hypothesis that the plasma goes turbulent because it needs to develop an anomalous current channel, and this turbulence in turn determines the plasma transport and the time-averaged state.

Probe measurements of electron energy distributions in a strongly magnetized low-pressure helium plasma

The first evidence of dust-impact ionization processes in the scrape-off layer of the Frascati tokamak upgrade (FTU) was reported in Nucl. Fusion 47 L5 (2007). In this work an extended data analysis (both of electrostatic probe signals and probe surface analysis) is presented, using results of empirical studies of hypervelocity impacts. Within the accuracy and limits of application of such results to tokamak plasma environment, the data are shown to be consistent with occurrence of impacts by micrometre size iron particles at velocities of the order of 10 km s −1 .

Stability of solitary structures in the nonlinear Schrödinger equation

Electron energy distributions (EED) in strongly magnetized (∼0.3 T), low-pressure (∼0.2 Pa) helium plasmas of the toroidal device “Blaamann” [K. Rypdal et al., Plasma Phys. Controlled Fusion 36, 1099 (1994)] have been measured. In the analysis of measurements, one applies a simplified expression for the limit of a strongly magnetized plasma relating the electron energy distribution to the first derivative of electron probe current with respect to the probe potential. It is shown that for the conditions investigated this approximation gives the same electron densities and slightly lower temperatures (up to 10%) as the kinetic theory for arbitrary magnetic field strength. Cylindrical probes, which are oriented along and perpendicular to the magnetic field, are used in the measurements. It is shown that these probes give nearly identical results. However, the probe that is oriented perpendicular to the magnetic field can give the electron energy distribution in a wider energy range and with better accuracy. ...

Long-memory effects in linear response models of Earth's temperature and implications for future global warming

The transverse stability of solitary wave structures to the equation iψt + ψxx + sψyy + p|ψ|2ψ = 0 is studied for the four cases; (p = 1, s = 1), (p = 1, s = −1), (p = −1, s = −1) and (p = −1, s = 1). Solitary waves in the x-direction are envelopes ψ = √2 sech(x) exp (it), for p = 1, and they are kinks; ψ = √2 tanh(x) exp (– 2it), for p = −1. For s = 1 an energy principle can be invoked, and instability for the envelope occurs in the range 0 < k2 < 3, and for the kink in the range 0 < k2 < 1. Here k is the wavenumber of the perturbation in the y-direction. Growth rates are estimated very simply by means of a Rayleigh-Ritz method. For s = −1, we review existing results for the envelope. It is unstable in a range 0 < k2 ≤ 1.17 where the upper limit must be determined numerically. For the kink, we find a continuum of unstable, non-local perturbations covering the whole range 0 < k2 < ∞. On both sides of the kink structure (|x| 1) these perturbations are oblique, purely growing plane waves. We conclude that both envelopes and kinks are transversely unstable for all signs of p and s.

Confinement and bursty transport in a flux-driven convection model with sheared flows

AbstractA linearized energy-balance model for global temperature is formulated, featuring a scale-invariant long-range memory (LRM) response and stochastic forcing representing the influence on the ocean heat reservoir from atmospheric weather systems. The model is parameterized by an effective response strength, the stochastic forcing strength, and the memory exponent. The instrumental global surface temperature record and the deterministic component of the forcing are used to estimate these parameters by means of the maximum-likelihood method. The residual obtained by subtracting the deterministic solution from the observed record is analyzed as a noise process and shown to be consistent with a long-memory time series model and inconsistent with a short-memory model. By decomposing the forcing record in contributions from solar, volcanic, and anthropogenic activity one can estimate the contribution of each to twentieth-century global warming. The LRM model is applied with a reconstruction of the forcing...