Hamilton's principle for quasigeostrophic motion

We show that the equation of quasigeostrophic (QG) potential vorticity conservation in geophysical fluid dynamics follows from Hamilton's principle for stationary variations of an action for geodesic motion in the f-plane case or its prolongation in the beta-plane case. This implies a new momentum equation and an associated Kelvin circulation theorem for QG motion. We treat the barotropic and two-layer baroclinic cases, as well as the continuously stratified case.Comment: 16 pages, LATeX, no figure

A Note on QED with Magnetic Field and Chemical Potentia

Using a generalized proper-time method, we obtain expressions for the fermion density and the QED effective Lagrangian for an external magnetic field at finite chemical potential. The effective Lagrangian and the density are here written in terms of elementary functions, summed over a finite number of filled Landau levels.Comment: 11 pages (postscript figure file appended at the end), FIAN/TD/94-01, G\"oteborg ITP 94-1

Magnetic-field Induced Screening Effect and Collective Excitations

We explicitly construct the fermion propagator in a magnetic field background B to take the lowest Landau-level approximation. We analyze the energy and momentum dependence in the polarization tensor and discuss the collective excitations. We find there appear two branches of collective modes in one of two transverse gauge particles; one represents a massive and attenuated gauge particle and the other behaves similar to the zero sound at finite density.Comment: 5 pages, 3 figures; references on the zero sound added and typos correcte

Update on Radiation Dose From Galactic and Solar Protons at the Moon Using the LRO/CRaTER Microdosimeter

The NASA Lunar Reconnaissance Orbiter (LRO) has been exploring the lunar surface and radiation environment since June 2009. In Mazur et al. [2011] we discussed the first 6 months of mission data from a microdosimeter that is housed within the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) instrument onboard LRO. The CRaTER microdosimeter is an early version of what is now a commercially available hybrid that accurately measures total ionizing radiation dose in a silicon target (http://www.teledynemicro.com/product/radiation-dosimeter). This brief report updates the transition from a deep solar minimum radiation environment to the current weak solar maximum as witnessed with the microdosimeter

Explicit Lie-Poisson integration and the Euler equations

We give a wide class of Lie-Poisson systems for which explicit, Lie-Poisson integrators, preserving all Casimirs, can be constructed. The integrators are extremely simple. Examples are the rigid body, a moment truncation, and a new, fast algorithm for the sine-bracket truncation of the 2D Euler equations.Comment: 7 pages, compile with AMSTEX; 2 figures available from autho

Measurements of galactic cosmic ray shielding with the CRaTER instrument

[1] The Cosmic Ray Telescope for the Effects of Radiation (CRaTER) instrument aboard the Lunar Reconnaissance Orbiter has been measuring energetic charged particles from the galactic cosmic rays (GCRs) and solar particle events in lunar orbit since 2009. CRaTER includes three pairs of silicon detectors, separated by pieces of tissue-equivalent plastic that shield two of the three pairs from particles incident at the zenith-facing end of the telescope. Heavy-ion beams studied in previous ground-based work have been shown to be reasonable proxies for the GCRs when their energies are sufficiently high. That work, which included GCR simulations, led to predictions for the amount of dose reduction that would be observed by CRaTER. Those predictions are compared to flight data obtained by CRaTER in 2010–2011

On the Quantum Inverse Problem for the Closed Toda Chain

We reconstruct the canonical operators $p_i,q_i$ of the quantum closed Toda chain in terms of Sklyanin's separated variables.Comment: 16 page

Quantization of the N=2 Supersymmetric KdV Hierarchy

We continue the study of the quantization of supersymmetric integrable KdV hierarchies. We consider the N=2 KdV model based on the $sl^{(1)}(2|1)$ affine algebra but with a new algebraic construction for the L-operator, different from the standard Drinfeld-Sokolov reduction. We construct the quantum monodromy matrix satisfying a special version of the reflection equation and show that in the classical limit, this object gives the monodromy matrix of N=2 supersymmetric KdV system. We also show that at both the classical and the quantum levels, the trace of the monodromy matrix (transfer matrix) is invariant under two supersymmetry transformations and the zero mode of the associated U(1) current.Comment: LaTeX2e, 12 page

Planar Dirac Electron in Coulomb and Magnetic Fields

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong magnetic fields, we present the exact recursion relations that determine the coefficients of the series expansion of wave functions, the possible energies and the magnetic fields. It is found that analytic solutions are possible for a denumerably infinite set of magnetic field strengths. This system thus furnishes an example of the so-called quasi-exactly solvable models. A distinctive feature in the Dirac case is that, depending on the strength of the Coulomb field, not all total angular momentum quantum number allow exact solutions with wavefunctions in reasonable polynomial forms. Solutions in the nonrelativistic limit with both attractive and repulsive Coulomb fields are briefly discussed by means of the method of factorization.Comment: 18 pages, RevTex, no figure

The first cosmic ray albedo proton map of the Moon

[1] Neutrons emitted from the Moon are produced by the impact of galactic cosmic rays (GCRs) within the regolith. GCRs are high-energy particles capable of smashing atomic nuclei in the lunar regolith and producing a shower of energetic protons, neutrons and other subatomic particles. Secondary particles that are ejected out of the regolith become “albedo” particles. The neutron albedo has been used to study the hydrogen content of the lunar regolith, which motivates our study of albedo protons. In principle, the albedo protons should vary as a function of the input GCR source and possibly as a result of surface composition and properties. During the LRO mission, the total detection rate of albedo protons between 60 MeV and 150 MeV has been declining since 2009 in parallel with the decline in the galactic cosmic ray flux, which validates the concept of an albedo proton source. On the other hand, the average yield of albedo protons has been increasing as the galactic cosmic ray spectrum has been hardening, consistent with a disproportionately stronger modulation of lower energy GCRs as solar activity increases. We construct the first map of the normalized albedo proton emission rate from the lunar surface to look for any albedo variation that correlates with surface features. The map is consistent with a spatially uniform albedo proton yield to within statistical uncertainties