Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Geophysical fluid dynamics.

Review of Charged Particle Dynamics. Beam Optics and Focusing Systems Without Space Charge. Linear Beam Optics with Space Charge. Self-Consistent Theory of Beams. Emittance Variation. Beam Physics Research from 1993 to 2007. Appendices. List of Frequently Used Symbols. Bibliography. Index.

Theory and Design of Charged Particle Beams

Ion acceleration driven by superintense laser pulses is attracting an impressive and steadily increasing effort. Motivations can be found in the applicative potential and in the perspective to investigate novel regimes as available laser intensities will be increasing. Experiments have demonstrated, over a wide range of laser and target parameters, the generation of multi-MeV proton and ion beams with unique properties such as ultrashort duration, high brilliance, and low emittance. An overview is given of the state of the art of ion acceleration by laser pulses as well as an outlook on its future development and perspectives. The main features observed in the experiments, the observed scaling with laser and plasma parameters, and the main models used both to interpret experimental data and to suggest new research directions are described.

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Ion acceleration by superintense laser-plasma interaction

第12次 아시아ㆍ太平洋 矯政局長會議 參加記

Stix's treatment of zero-damped electrostatic waves in a Maxwellian plasma is extended to the nonlinear regime. Stationary Bernstein-Greene-Krusk almodes which propagate with ion acoustic speed are constructed. This subclass consists of solitary, snoidal (=periodical waves, like ocean waves, which can be written in terms of Jacobian elliptic functions) and sinusoidal waves. A discrimination of those waves can be given by a single parameter, the steepness parameter, which contains nonlinearity, trapping of particles and dispersion. It turns out that Sadgeev's soliton represents a special case of the class solitons having the largest width and the lowest velocity. Hence a modified Korteweg-de-Vries equation must exist with a stronger nonlinearity.

https://iopscience.iop.org/article/10.1088/0032-1028/14/10/002/pdf

Stationary solitary, snoidal and sinusoidal ion acoustic waves

The dependence of the asymptotic behaviour of small ion-acoustic waves on the number of resonant electrons is investigated by assuming an electron equation of state corresponding to the observed flat-topped electron distribution functions. The result is a modified Korteweg-de Vries equation with a stronger nonlinearity.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002237780000756X

A modified Korteweg-de Vries equation for ion acoustic wavess due to resonant electrons

Electron holes, ion holes and double layers: Electrostatic phase space structures in theory and experiment

A unified description of weak hole equilibria in collisionless plasmas is given. Two approaches, relying on the potential method rather than on the Bernstein, Greene, Kruskal method and associated with electron and ion holes, respectively, are shown to be equivalent. A traveling wave solution is thereby uniquely characterized by the nonlinear dispersion relation and the “classical” potential V(φ), which determine the phase velocity and the spectral decomposition of the wave structure, respectively. A new energy expression for a hole carrying plasma is found. It is dominated by a trapped particle contribution occurring one order earlier in the expansion scheme than the leading term in conventional schemes based on a truncation of Vlasov’s equation. Linear wave theory— reconsidered by taking the infinitesimal amplitude limit—is found to be deficient, as well. Neither Landau nor van Kampen modes and their general superpositions can adequately describe these trapped particle modes due to an incorrect treatmen...

Hole equilibria in Vlasov-Poisson systems: A challenge to wave theories of ideal plasmas

We present analytical solutions for the electron holes discovered recently and for the `Gould-Trivelpiece-Soliton'. Based on appropriate electron distribution functions, stationary solutions of the Vlasov-Poisson-system adopted to finite geometry are constructed. It is shown that the electron hole found experimentally and by numerical simulations is well described by this solution. It represents a nonlinear version of the slow-electron acoustic mode and exists due to a distortion of the electron distribution in the resonant region, forming a hollow vortex in phase space. Its importance for studying nonlinear diffusion processes in phase space is emphasized.

Hans Schamel

Papers

Stationary solitary, snoidal and sinusoidal ion acoustic waves

A modified Korteweg-de Vries equation for ion acoustic wavess due to resonant electrons

Electron holes, ion holes and double layers: Electrostatic phase space structures in theory and experiment

Hole equilibria in Vlasov-Poisson systems: A challenge to wave theories of ideal plasmas

Theory of Electron Holes