Max wallis
Cardiff University, VC, Emeritus
The Fokker-Planck equation for small stochastic changes to particles in Kepler orbits has to be formulated in terms of the integrals of motion. We generalize the modelling of proton and electron collisional perturbations to gas particles... more
The Fokker-Planck equation for small stochastic changes to particles in Kepler orbits has to be formulated in terms of the integrals of motion. We generalize the modelling of proton and electron collisional perturbations to gas particles on trajectories through the solar system in order to include both spatial and velocity diffusion. The general solution is obtained in terms of a 4-dimensional normal distribution. Treatment of the singularity in the Fokker-Planck operator reduces the dimensionality by one. In addition to extending earlier results for anisotropic collisional heating in the thermal approximation, the present formulation gives the changes in density due to the mean repulsive force and to perturbations of trajectories (spatial diffusion). The net diffusion is almost everywhere towards the sun and the density increase is significant in the downstream hydrogen wake, particularly where destructive depletion is strong and gravitational focussing weak.
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Research Interests: Geology and Astrobiology
Observations of the distribution and evolution of a number of the major constituents of the neutral coma (CN, C2, CH, O, H, Na) of Comet Halley were made during two observing periods, each of 3 weeks duration, from the Table Mountain... more
Observations of the distribution and evolution of a number of the major constituents of the neutral coma (CN, C2, CH, O, H, Na) of Comet Halley were made during two observing periods, each of 3 weeks duration, from the Table Mountain Observatory, California. The first period was pre-perihelion, in late November/December 1985. The second period, from Feb 28 to March 22 1986, covered the five close spacecraft encounters with Halley, and when ICE flew some 20 M Km upstream of Halley. Sodium emission was recorded in early Dec 1985 from the near-nuclear region at a heliocentric distance of 1.4 AU, an observation confirmed with the UCL Doppler Imaging system. The CN coma could be detected to an outer diameter of more than 4M Km in Dec 1985, and 5 – 6M Km in early March 1986, allowing the production of heavy cometary pick-up ions to be estimated. Observations of the cometary ion coma (H2O+ and CO+ ions) showed considerable variability from day to day, particularly during the period of the spacecraft encounters. These observations have been used, in conjuction with the neutral coma data, to map the flow field of cometary ions. In early Dec. 1985, Halley developed a traditional “type I” ion tail, which persisted until late April 1986. It has also been possible to evaluate the ion flow fields within the narrow core of the ion tail, and in the surrounding diffuse, low density, regions populated by pick-up and extracted cometary ions, and by slowed solar wind ions. Tail disconnection events were observed on several occasions, particularly between the VEGA 2 and GIOTTO encounters, and with a highly spectacular event on March 19 1986.
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The Viking measurement of15N enrichment on Mars has been interpreted as setting low limits on the original complement of volatiles, which seems incompatible with estimates around 0.5–3 km depth of crustal H2O. A re-examination of... more
The Viking measurement of15N enrichment on Mars has been interpreted as setting low limits on the original complement of volatiles, which seems incompatible with estimates around 0.5–3 km depth of crustal H2O. A re-examination of mechanisms losing nitrogen to space shows that currently operating chemical processes alone give a fractionation ratio for15N :14N of 0.69–0.75: combining this with the diffusive separation gives the ratio of escape rates as 0.53–0.62. If there has been no interchange with the crust, this implies under 1 mb initial complement of nitrogen. Alternatively, the low (62 ± 16%) enrichment of15N is explicable as resulting from continuous outgassing from the martian surface together with the current loss processes. This is supported by the “ordinary” values of N2 : inert gases in SNC meteorites and is compatible with a proportionate initial complement of N2 lost via physical or chemical processes early in the planet's evolution. Persistence to the present epoch of abundant, kilometre-deep H2O is thus acceptable. As diffusive separation and chemical loss processes for oxygen give a fractionation ratio for18O :16O of ∼ 0.75, the observed enrichment by ≲ 10% suggests interchange with the large reservoir of crustal H2O, probably polar ice, is dominant.13C :12C fractionation is a little stronger, but escape rates two orders of magnitude lower, so enrichment by 3–6% implies much less interchange with the surface. The martian atmosphere as occluded in SNC meteorites during the last 1.3 Ga would be a little lighter isotopically in C and O but potentially heavier in N than the current atmosphere.
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Interstellar gas streaming through the solar system undergoes both elastic collisions with solar wind ions and destructive, ionizing processes. The Boltzmann equation is set up, with linear Fokker-Planck terms describing the glancing... more
Interstellar gas streaming through the solar system undergoes both elastic collisions with solar wind ions and destructive, ionizing processes. The Boltzmann equation is set up, with linear Fokker-Planck terms describing the glancing elastic collisions. Solutions combining the dynamical effects of the central force field and the diffusion in velocity space are derived, appropriate to cool gas.For the He component of the streaming gas, if initially at 100 K, the collisional heating dominates inside 2 a.u. upstream and 5 a.u. downstream. A modified formula is given for the density in the downstream wake, as enhanced by gravitational focussing. Calculations of the helium resonant radiation backscatter require substantial modification.
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Energetic neutrals in dissociative recombinations near or above the exobase provide an important component of exospheric density and escape fluxes. Plasma thermal velocities provide the main contribution to the velocity spread and an... more
Energetic neutrals in dissociative recombinations near or above the exobase provide an important component of exospheric density and escape fluxes. Plasma thermal velocities provide the main contribution to the velocity spread and an exact integral for the escape flux applicable in marginal cases is found for a simple atmosphere and collisional cut-off. Atomic fragments from recombination of diatomic oxygen and nitrogen ions in the Venus and Mars atmospheres are examined and density integrals derived. The oxygen escape flux on Mars is half that previously estimated and there is very little isotope preference supplementing diffusive separation. However, escape of the heavier 15N isotope is low by a factor two. Reinterpretation of its 75% enrichment as detected by Viking leads to a range 0.4–1.4 mbar for the primeval nitrogen content on Mars.
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The observations of comet Halley from International Ultraviolet Explorer (IUE) satellite from March 9 to 16, 1986 allow a comprehensive study of gas and dust production by comet in the week during which the fleet of six spacecraft from... more
The observations of comet Halley from International Ultraviolet Explorer (IUE) satellite from March 9 to 16, 1986 allow a comprehensive study of gas and dust production by comet in the week during which the fleet of six spacecraft from four space agencies encountered the comet. The gaseous output of the nucleus was found to vary over timescales of the order
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The dust impact detection system (DIDSY) carried by the Giotto spacecraft has measured the density and mass spectrum (in the range 10 -20 −10 -8 kg) of the dust near comet Halley. Profiles of the dust spectrum obtained at a distance of... more
The dust impact detection system (DIDSY) carried by the Giotto spacecraft has measured the density and mass spectrum (in the range 10 -20 −10 -8 kg) of the dust near comet Halley. Profiles of the dust spectrum obtained at a distance of 291,000 km from the Halley nucleus show a ...
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The thermal description of interplanetary helium gas flow in the solar gravitational and radiation fields is used to construct expected line profiles from resonant scattering of solar 584 A radiation, ignoring collisional heating and... more
The thermal description of interplanetary helium gas flow in the solar gravitational and radiation fields is used to construct expected line profiles from resonant scattering of solar 584 A radiation, ignoring collisional heating and photon multiple scattering. Profiles from 1 AU in anti-solar directions are shown to agree closely with results from full computations, except for the minor secondary peaks. The analytic formula derived for cold gas is accurate for 1000 K helium. Total intensities are generally given with surprising accuracy by the thermal model, though further checks are desirable on the density formula in the gravitationally-focused tail and on integrals along lines-of-sight passing well inside 1 AU.
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The depletion by charge exchange of energetic cometary ions picked up in the solar wind flow into Halley's coma is calculated to coincide with the upstream extension of its cometopause, detected by the comet probes. It relates to the... more
The depletion by charge exchange of energetic cometary ions picked up in the solar wind flow into Halley's coma is calculated to coincide with the upstream extension of its cometopause, detected by the comet probes. It relates to the cometary plasma structures observed telescopically. The field-free ionospheric cavity and the cometosheath regions of Halley's plasma must in some way connect to the comet's tail. The origin of the cometosheath-envelope is argued to be due to charge-exchange cooling, this mechanism determining the source and variability of the main tail rays. The ionosphere connects to a denser tail core. The sunward part of the charge-exchange dominated cometosheath is identified on an IPD image of Halley by depletion in CO(+) ions. Where traversed by the comet probes, however, the cometosheath was twice as far out. Pressure-driven expansion occurs there and the sheath's main signature is a change in the flow direction.
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ABSTRACT
Research Interests: Pharmacology, Biochemistry, Bioinformatics, Evolutionary Biology, Genetics, and 42 moreMarine Biology, Neuroscience, Environmental Science, Geophysics, Physics, Materials Science, Quantum Physics, Developmental Biology, Immunology, Climate Change, Molecular Biology, Structural Biology, Genomics, RNA, Computational Biology, Transcriptomics, Biotechnology, Systems Biology, Cancer, Biology, Metabolomics, Cell Cycle, Proteomics, Ecology, Drug Discovery, Evolution, Nanotechnology, Astrophysics, Neurobiology, Medicine, Multidisciplinary, Palaeobiology, Functional Genomics, Nature, Signal Transduction, Astronomy, DNA, Cell Signalling, Medical Research, Solar Wind, Ionizing Radiation, and Earth Science
The abundances of diatomic molecules seen in the UV both give clues to the parent compounds and help unravel the gas and ion mass spectrometry. From IUE spectra of comet Halley, the authors find limits on SH and CS+column densities, and... more
The abundances of diatomic molecules seen in the UV both give clues to the parent compounds and help unravel the gas and ion mass spectrometry. From IUE spectra of comet Halley, the authors find limits on SH and CS+column densities, and estimates of probable NO, S2 and SO. In particular, judged from the 226 nm y-band, NO was relatively abundant at 2 - 8×1013cm-2 on 9 - 14 March. The production rate of S2 was around 1×1027molecules/s at that time, but both showed day-to-day variability by 2 - 3 times.
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Environmental nongovernment organisations (ENGOs) in Europe have been hardly involved in AIRNET, in part because the technicalities deter access. However, ENGOs should be seen as representing the public as well as acting as stakeholders... more
Environmental nongovernment organisations (ENGOs) in Europe have been hardly involved in AIRNET, in part because the technicalities deter access. However, ENGOs should be seen as representing the public as well as acting as stakeholders in their own right. ENGOs can be intimately involved in assessing the public information, as in the UK example criticized here, and can spotlight an issue like ultrafine particulate pollution that is being avoided for reasons of institutional inertia and special interests. For risk analysis and integrating a precautionary approach, ENGO participation within a stakeholder process is vital. Policies designed to combat air pollutants have to change profoundly how people live, travel, and work (Maynard et al., 2003), yet policymakers tend to duck the hard choices. Winning the public to make such changes requires enrolling the major campaigning ENGOs as allies, in the context of effective stakeholder communication and accountability in public information and policy setting.
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Research Interests: Geology and Astrobiology
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Heating processes are expected to strongly affect the structure and dynamics of cometary comas. A radial expansion velocity of less than 1 km/sec in the inner coma is quite compatible with a few km/sec in the outer regions of large comets.
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The mass-loading concept is discussed in relation to the dynamics of magnetoplasma streaming through rarefied background gas. Changes in energy and momentum flux (generally losses) can outweigh the increases in mass flux. Suprathermal ion... more
The mass-loading concept is discussed in relation to the dynamics of magnetoplasma streaming through rarefied background gas. Changes in energy and momentum flux (generally losses) can outweigh the increases in mass flux. Suprathermal ion components cannot be simply described in fluid terms: as shown by the probes to comet Halley, the main cometary ions are depleted by interaction with the background gas faster than they are scattered and thermalized by plasma turbulence. MHD instabilities tend to isotropize pitch angles but do not thermalize the ions, while wave steepening into a bow shock occurs outside positions expected from mass-loading. In the strongly-loaded subsonic region, charge exchange of suprathermal ions causes energy losses that can be more significant than further increases of mass. Non-parallel pick-up of new implanted ions, large gyroradii and finite spatial scales also limit the validity of fluid models.
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The parameters and location of the weak bow shocks detected by the spaceprobes are compared with gas dynamical calculations. No shock is identifiable at times, indicating that it is not dominant over temporal changes and not very... more
The parameters and location of the weak bow shocks detected by the spaceprobes are compared with gas dynamical calculations. No shock is identifiable at times, indicating that it is not dominant over temporal changes and not very significant in enhancing intrinsic dissipation and phase mixing proceses. The location at comet Halley was closer than predicted on the mass-loading model, indicating inefficient pick-up of implanted ions. Flaring of the shock limbs was also lower at the Giotto encounter, closer to the minimum level induced by strong cooling in the inner coma. The suprathermal cometary ions' disappearance in the ionospheath outside the magnetopause discontinuity confirms this. Flow deviation and shock strength need closer modelling, but the thick shock in the protons is evidence for an ion-ion instability mechanism, apart from the upstream Fermi process.
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The quasi-one-dimensional continuum description of the solar wind's ionizing interaction with neutral atmospheres is employed to describe the transsonic flow upstream of the body. The subsonic flow is approximated by assuming constant... more
The quasi-one-dimensional continuum description of the solar wind's ionizing interaction with neutral atmospheres is employed to describe the transsonic flow upstream of the body. The subsonic flow is approximated by assuming constant total energy density. Weakly-shocked solutions are found to mass-accreting flows, and they pass continuously over to shock-free solutions for low spatial gradients in the ionization rate. Flow computations currently in progress at Munich are in good agreement with these solutions. Cometary shocks are subcritically weak, and probably heat the electrons, but only moderately. These shocks occur inside the ionization region, close to the innermost position for strictly one-dimensional mass-accreting flows. These features conflict with the earlier flow calculations, which are in error as the authors (Biermann et al., 1967) now recognize. The previous computational method is judged to be invalid. The shocks ahead of Venus and Mars can also be subcritical if the relevant density gradient is provided by a supra-thermal atmospheric component, or if charge exchange interactions effect rapid cooling of the plasma. Now at Mathematical Institute, St Giles, Oxford, England.
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Energy and momentum arguments lead to useful bounds on the effective impulse of dust grains impacting the high velocity space probes passing through Comet Halley's dust coma. Impulse enhancement by a factor of 8-10 above the impacting... more
Energy and momentum arguments lead to useful bounds on the effective impulse of dust grains impacting the high velocity space probes passing through Comet Halley's dust coma. Impulse enhancement by a factor of 8-10 above the impacting momentum is favored, while the marginal mass for dust grain penetration of the Giotto bumper shield is 4-5 micrograms. The reduced impulse to the bumper from grains that penetrate it is assessed, in relation to interpretation of data from the Giotto DIDSY momentum sensors.
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It is hypothesized that Triton's geysers are analogous to the remnant activity of Comet Halley, whose outbursts producing a particulate coma are persisting out beyond 12 AU Halley's outbursts are understood as resulting from inward... more
It is hypothesized that Triton's geysers are analogous to the remnant activity of Comet Halley, whose outbursts producing a particulate coma are persisting out beyond 12 AU Halley's outbursts are understood as resulting from inward freezing of a subsurface lake or sea that's maintained at greater than 10 m depth via metabolic energy release. Cracking of the ice due to thermal expansion forces generates sporadic emissions of H2O and other gases. Analogous activity on Triton is a manifestation of internal freezing of an interior sea under a km or so of ice. This sea at the present epoch is quite separate from the interior liquid ocean, expected to be maintained at greater than 100 km deep by radiogenic heating. The near-surface sea is maintained also by chemical or metabolic energy and sporadically emits gases and condensates through cracks induced during its freezing. Emissions through the ice cover on both comets and Triton would drive surface geology, thus enabling access to new nutrients and trace elements that may be vital for subterranean biology. Triton's biology would be a relic from its tidal heating phase, when the interior was liquid below a 1-2 km frozen lithosphere.
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Greenhouse gas emissions can be reduced via supply-side changes — gas turbine generation and domestic fuelling by natural gas being favoured at present — or via energy efficiency and emission reduction measures. Methane emissions from... more
Greenhouse gas emissions can be reduced via supply-side changes — gas turbine generation and domestic fuelling by natural gas being favoured at present — or via energy efficiency and emission reduction measures. Methane emissions from leaky gas supply systems and from coal mining are significant in the greenhouse equation. Renewal of leaky gas mains, domestic boilers fired by gas or coal and domestic energy efficiency measures are found to all rank higher in the UK context than building new gas-fired power stations, contrary to earlier claims. Speeding the replacement of aged cast-iron gas mains and service pipes is calculated to be very economic in greenhouse abatement.
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The abundances of diatomic molecules seen in the UV both give clues to the parent compounds and help unravel the gas and ion mass spectrometry. From IUE spectra of comet Halley, the authors find upper limits on SH and CS+ column... more
The abundances of diatomic molecules seen in the UV both give clues to the parent compounds and help unravel the gas and ion mass spectrometry. From IUE spectra of comet Halley, the authors find upper limits on SH and CS+ column densities, and estimates of probable NO, S2, and SO. In particular, judged from the 226 nm γ-band, NO was relatively abundant at 2 - 8×1013cm-2 on March 9 - 14. The production rate of S2 was around 1027 molecules s-1 at that time, but both showed day-to-day variability by 2 - 3 times.
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Comet Bradfield 1987s and Comet P/Borrelly 1987p were observed between December 14 and December 22, 1987. The large-scale and near-nucleus CN profiles for both comets were fit to a simple radial outflow model with decay. At 1 AU, parent... more
Comet Bradfield 1987s and Comet P/Borrelly 1987p were observed between December 14 and December 22, 1987. The large-scale and near-nucleus CN profiles for both comets were fit to a simple radial outflow model with decay. At 1 AU, parent scalelengths of (2.3 + or - 0.2) x 10 to the 4th for CN and (2.1 + or - 0.2) x 10 to the 4th km for C2 were found. It is suggested that these short parent scalelengths could correspond to the scale for release from CHON grains. Although a proportion of the C2 in P/Borrelly is expected to be a produced by the CHON grains, the results suggest a second source which is noncentral.
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Results are presented of observations of Comet Halley and other cometary targets performed between August 1985 to May 1990. Near-nucleus studies were carried out using 1-m and 24-in telescopes, and large-scale structures were investigated... more
Results are presented of observations of Comet Halley and other cometary targets performed between August 1985 to May 1990. Near-nucleus studies were carried out using 1-m and 24-in telescopes, and large-scale structures were investigated by means of wide-angle camera lenses. The CN parent scalelength was approximately two times larger during solar minimum conditions than during solar maximum conditions and scaled approximately as the heliocentric distance in both cases. During solar maximum conditions the C2 parent scalelength scaled as the heliocentric distance raised to the power of 1.75. During solar maximum conditions, the CN scalelength scaled as the square of the heliocentric distance, confirming the usual assumption that the destruction of the CN radical is controlled by the solar flux of radiation. During solar maximum conditions, for Comet Austin, the CN scalelength appeared to scale as the square root of the heliocentric distance. Evidence for a significant heliolatitude dependence of the CN scalelength is inferred from this anomalous result.
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Narrow-band spectral images of a number of the constituents of the neutral coma (CN, C2, CH, O, H, Na), and of the ion coma and tail formation of comet P/Halley were obtained during four observing periods between late Nov 1985 and... more
Narrow-band spectral images of a number of the constituents of the neutral coma (CN, C2, CH, O, H, Na), and of the ion coma and tail formation of comet P/Halley were obtained during four observing periods between late Nov 1985 and mid-June 1986. The CN coma was detectable to a distance of more than 4 Mkm in Dec 1985, and 5 - 6 Mkm in early March 1986. The inner (assumed parent) and outer (assumed daughter) Haser scale lengths of the CN2 coma were found to each have a dependence on (R)2. A narrow, tail-like, feature in CN emission, occasionally extending 10 Mkm anti-sunward, may be due to sputtering of dust grains sometimes present within the ion tail core.