A Variable-Flavour Number Scheme for NNLO

At NNLO it is particularly important to have a Variable-Flavour Number Scheme (VFNS) to deal with heavy quarks because there are major problems with both the zero mass variable-flavour number scheme and the fixed-flavour number scheme. I illustrate these problems and present a general formulation of a Variable-Flavour Number Scheme (VFNS)for heavy quarks that is explicitly implemented up to NNLO in the strong coupling constant alpha_S, and may be used in NNLO global fits for parton distributions. The procedure combines elements of the ACOT(chi) scheme and the Thorne-Roberts scheme. Despite the fact that at NNLO the parton distributions are discontinuous as one changes the number of active quark flavours, all physical quantities are continuous at flavour transitions and the comparison with data is successful.Comment: 17 pages, 5 figures included as .ps files, uses axodraw. One additional explanatory sentence after eq. (25). Correction of typos and updated references. To be published in Phys. Rev.

Locating the magnetospheric ring current

Protons are studied in the global depression of the earth's horizontal magnetic field. It is shown that 10 to 100 keV protons dominate ring current energetics in two preferred regions of cyclotron instability, which serve as stable trapping boundaries for ring current protons. The only apparent means of removing this stably trapped belt of particles are considered to be by charge exchange interactions, or by outward expansion of the plasmapause to erode the ring current. Both of these processes require about two days, which is the characteristic decay period of the main phase depression. Questions whose answers are necessary to formulate a quantitative theory of geomagnetic storms which relates main phase depression to solar wind parameters are included

Unstable growth of unducted whistlers propagating at an angle to the geomagnetic field

Unstable growth rate of unducted whistler waves propagating at angle to geomagnetic fiel

Magnetospheric electrons

Coupling of source, transport, and sink processes produces a fairly accurate model for the macroscopic structure and dynamics of magnetospheric electrons. Auroral electrons are controlled by convective transport from a plasma sheet source coupled with a precipitation loss due to whistler and electrostatic plasma turbulence. Outer and inner zone electrons are governed by radial diffusion transport from convection and acceleration sources external to the plasmapause and by parasitic precipitation losses arising from cyclotron and Landau interactions with whistler and ion cyclotron turbulence

A unified theory of stable auroral red arc formation at the plasmapause

A theory is proposed that SAR-arcs are generated at the plasmapause as a consequence of the turbulent dissipation of ring current energy. During the recovery phase of a geomagnetic storm, the plasmapause expands outward into the symmetric ring current. When the cold plasma densities reach about 100/cu cm, ring current protons become unstable and generate intense ion cyclotron wave turbulence in a narrow region 1/2 earth radius wide (just inside the plasmapause). Approximately one-half of the ring current energy is dissipated into wave turbulence which in turn is absorbed through a Landau resonant interaction with plasma spheric electrons. The combined thermal heat flux to the ionosphere due to Landau absorption of the wave energy and proton-electron Coulomb dissipation is sufficient to drive SAR-arcs at the observed intensities. It is predicted that the arcs should be localized to a narrow latitudinal range just within the stormtime plasmapause. They should occur at all local times and persist for the 10 to 20 hour duration of the plasma-pause expansion

Complex Wave Numbers in the Vicinity of the Schwarzschild Event Horizon

This paper is devoted to investigate the cold plasma wave properties outside the event horizon of the Schwarzschild planar analogue. The dispersion relations are obtained from the corresponding Fourier analyzed equations for non-rotating and rotating, non-magnetized and magnetized backgrounds. These dispersion relations provide complex wave numbers. The wave numbers are shown in graphs to discuss the nature and behavior of waves and the properties of plasma lying in the vicinity of the Schwarzschild event horizon.Comment: 21 pages, 9 figures, accepted for publication Int. J. Mod. Phys.

Lead-tellurium oxysalts from Otto Mountain near Baker, California: IV. Markcooperite, Pb(UO_2)Te^(6+)O_6, the first natural uranyl tellurate

Markcooperite, Pb_2(UO_2)Te^(6+)O_6, is a new tellurate from Otto Mountain near Baker, California, named in honor of Mark A. Cooper of the University of Manitoba for his contributions to mineralogy. The new mineral occurs on fracture surfaces and in small vugs in brecciated quartz veins. Markcooperite is directly associated with bromian chlorargyrite, iodargyrite, khinite-4O, wulfenite, and four other new tellurates: housleyite, thorneite, ottoite, and timroseite. Various other secondary minerals occur in the veins, including two other new secondary tellurium minerals: paratimroseite and telluroperite. Markcooperite is monoclinic, space group P2_1/c, a = 5.722(2), b = 7.7478(2), c = 7.889(2) Å, β = 90.833(5)°, V = 349.7(2) Å^3, and Z = 2. It occurs as pseudotetragonal prisms to 0.2 mm with the forms {100} and {011} and as botryoidal intergrowths to 0.3 mm in diameter; no twinning was observed. Markcooperite is orange and transparent, with a light orange streak and adamantine luster, and is non-fluorescent. Mohs hardness is estimated at 3. The mineral is brittle, with an irregular fracture and perfect {100} cleavage. The calculated density is 8.496 g/cm3 based on the empirical formula. Markcooperite is biaxial (+), with indices of refraction α= 2.11, β = 2.12, γ= 2.29 calculated using the Gladstone-Dale relationship, measured α-β birefringence of 0.01 and measured 2V of 30(5)°. The optical orientation is X = c, Y = b, Z = a. The mineral is slightly pleochroic in shades of orange, with absorption: X > Y = Z. No dispersion was observed. Electron microprobe analysis provided PbO 50.07, TeO_3 22.64, UO_3 25.01, Cl 0.03, O≡Cl –0.01, total 97.74 wt%; the empirical formula (based on O+Cl = 8) is Pb_(2.05)U_(0.80)Te^(6+)_(1.18)O_(7.99)Cl_(0.01). The strongest powder X-ray diffraction lines are [d_(obs) in Å (hkl) I]: 3.235 (120, 102, 1[overbar]02) 100, 2.873 (200) 40, 2.985 (1[overbar]21, 112, 121) 37, 2.774 (022) 30, 3.501 (021, 012) 29, 2.220 (221, 2[overbar]21, 212) 23, 1.990 (222, 2[overbar]22) 21, and 1.715 (320) 22. The crystal structure (R_1 = 0.052) is based on sheets of corner-sharing uranyl square bipyramids and tellurate octahedra, with Pb atoms between the sheets. Markcooperite is the first compound to show Te^(6+) substitution for U^(6+) within the same crystallographic site. Markcooperite is structurally related to synthetic Pb(UO_2)O_2

Lead-tellurium oxysalts from Otto Mountain near Baker, California: V. Timroseite, Pb_2Cu_5^(2+)(Te^(6+)O_6)_2(OH)_2, and paratimroseite, Pb_2Cu_4^(2+)(Te^(6+)O_6)_2(H_2O)_2, two new tellurates with Te-Cu polyhedral sheets

Timroseite, Pb_2Cu_5^(2+)(Te^(6+)O_6)_2(OH)_2, and paratimroseite, Pb_2Cu_4^(2+)(Te^(6+)O_6)_2(H_2O)_2, are two new tellurates from Otto Mountain near Baker, California. Timroseite is named in honor of Timothy (Tim) P. Rose and paratimroseite is named for its relationship to timroseite. Both new minerals occur on fracture surfaces and in small vugs in brecciated quartz veins. Timroseite is directly associated with acanthite, cerussite, bromine-rich chlorargyrite, chrysocolla, gold, housleyite, iodargyrite, khinite-4O, markcooperite, ottoite, paratimroseite, thorneite, vauquelinite, and wulfenite. Paratimroseite is directly associated with calcite, cerussite, housleyite, khinite-4O, markcooperite, and timroseite. Timroseite is orthorhombic, space group P2_1nm, a = 5.2000(2), b = 9.6225(4), c = 11.5340(5) Å, V = 577.13(4) Å^3, and Z = 2. Paratimroseite is orthorhombic, space group P2_12_12_1, a = 5.1943(4), b = 9.6198(10), c = 11.6746(11) Å, V = 583.35(9) Å^3, and Z = 2. Timroseite commonly occurs as olive to lime green, irregular, rounded masses and rarely in crystals as dark olive green, equant rhombs, and diamond-shaped plates in subparallel sheaf-like aggregates. It has a very pale yellowish green streak, dull to adamantine luster, a hardness of about 2 1/2 (Mohs), brittle tenacity, irregular fracture, no cleavage, and a calculated density of 6.981 g/cm^3. Paratimroseite occurs as vibrant "neon" green blades typically intergrown in irregular clusters and as lime green botryoids. It has a very pale green streak, dull to adamantine luster, a hardness of about 3 (Mohs), brittle tenacity, irregular fracture, good {001} cleavage, and a calculated density of 6.556 g/cm^3. Timroseite is biaxial (+) with a large 2V, indices of refraction > 2, orientation X = b, Y = a, Z = c and pleochroism: X = greenish yellow, Y = yellowish green, Z = dark green (Z > Y > X). Paratimroseite is biaxial (–) with a large 2V, indices of refraction > 2, orientation X = c, Y = b, Z = a and pleochroism: X = light green, Y = green, Z = green (Y = Z >> X). Electron microprobe analysis of timroseite provided PbO 35.85, CuO 29.57, TeO_3 27.75, Cl 0.04, H_2O 1.38 (structure), O≡Cl –0.01, total 94.58 wt%; the empirical formula (based on O+Cl = 14) is Pb_(2.07) Cu^(2+)_(4.80)Te^(6+)_(2.04)O_(12)(OH)_(1.98)Cl_(0.02). Electron microprobe analysis of paratimroseite provided PbO 36.11, CuO 26.27, TeO_3 29.80, Cl 0.04, H_2O 3.01 (structure), O≡Cl –0.01, total 95.22 wt%; the empirical formula (based on O+Cl = 14) is Pb_(1.94)Cu^(2+)_(3.96)Te^(6+)_(2.03)O_(12)(H_2O)_(1.99)Cl_(0.01). The strongest powder X-ray diffraction lines for timroseite are [d_(obs) in Å (hkl) I]: 3.693 (022) 43, 3.578 (112) 44, 3.008 (023) 84, 2.950 (113) 88, 2.732 (130) 100, 1.785 (multiple) 33, 1.475 (332) 36; and for paratimroseite 4.771 (101) 76, 4.463 (021) 32, 3.544 (120) 44, 3.029 (023,122) 100, 2.973 (113) 48, 2.665 (131) 41, 2.469 (114) 40, 2.246 (221) 34. The crystal structures of timroseite (R_1 = 0.029) and paratimroseite (R_1 = 0.039) are very closely related. The structures are based upon edge- and corner-sharing sheets of Te and Cu polyhedra parallel to (001) and the sheets in both structures are identical in topology and virtually identical in geometry. In timroseite, the sheets are joined to one another along c by sharing the apical O atoms of Cu octahedra, as well as by sharing edges and corners with an additional CuO_5 square pyramid located between the sheets. The sheets in paratimroseite are joined only via Pb-O and H bonds

Lead-tellurium oxysalts from Otto Mountain near Baker, California: VI. Telluroperite, Pb_3Te^(4+)O_4Cl_2, the Te analog of perite and nadorite

Telluroperite, Pb_3Te^(4+)O_4Cl_2, is a new tellurite from Otto Mountain near Baker, California. The new mineral occurs on fracture surfaces and in small vugs in brecciated quartz veins in direct association with acanthite, bromine-rich chlorargyrite, caledonite, cerussite, galena, goethite, and linarite. Various other secondary minerals occur in the veins, including six new tellurates, housleyite, markcooperite, paratimroseite, ottoite, thorneite, and timroseite. Telluroperite is orthorhombic, space group Bmmb, a = 5.5649(6), b = 5.5565(6), c = 12.4750(14) Å, V = 386.37(7) Å^3, and Z = 2. The new mineral occurs as rounded square tablets and flakes up to 0.25 mm on edge and 0.02 mm thick. The form {001} is prominent and is probably bounded by {100}, {010}, and {110}. It is bluish-green and transparent, with a pale bluish-green streak and adamantine luster. The mineral is non-fluorescent. Mohs hardness is estimated to be between 2 and 3. The mineral is brittle, with a curved fracture and perfect {001} cleavage. The calculated density based on the empirical formula is 7.323 g/cm^3. Telluroperite is biaxial (–), with very small 2V (~10°). The average index of refraction is 2.219 calculated by the Gladstone-Dale relationship. The optical orientation is X = c and the mineral exhibits moderate bluish-green pleochrosim; absorption: X < Y = Z. Electron microprobe analysis provided PbO 72.70, TeO_2 19.26, Cl 9.44, O≡Cl –2.31, total 99.27 wt%. The empirical formula (based on O+Cl = 6) is Pb_(2.79)Te_(1.03)^(4+)O_(3.72)Cl_(2.28). The six strongest powder X-ray diffraction lines are [d_(obs) in Å (hkl) I]: 3.750 (111) 58, 2.857 (113) 100, 2.781 (020, 200) 43, 2.075 (024, 204) 31, 1.966 (220) 30, and 1.620 (117, 313, 133) 52. The crystal structure (R_1 = 0.056) is based on the Sillén X_1 structure-type and consists of a three-dimensional structural topology with lead-oxide halide polyhedra linked to tellurium/lead oxide groups. The mineral is named for the relationship to perite and the dominance of Te (with Pb) in the Bi site of perite