Parker Model Research Articles

Solar cycle variations of heliospheric magnetic flux

We extend previous studies of BR, the radial component of the heliospheric magnetic field and a measure of heliospheric magnetic flux, to include the maximum in cycle 23 so that most of 4 cycles are covered. Solar rotation averages reveal that BR systematically increases from a minimum value at sunspot minimum to a maximum value during the declining phase. This increase is interrupted by a temporary decrease associated with the disappearance and reversal of the Sun's polar cap fields. We examine variations in BR and field strength, B, and find a close correspondence consistent with the Parker model when allowance is made for the ever‐present fluctuations in the heliospheric magnetic field. The solar cycle variation in BR and B is consistent with the widely accepted model of the solar field in which bipolar sunspot fields emerging at solar maximum are responsible for the erosion and reversal of the polar cap fields. Although the solar cycle change in heliospheric magnetic flux is less than a factor of 2, it is very large compared with the average flux transported into the heliosphere by an interplanetary coronal mass ejection (ICME). If the increases in B and BR at solar maximum are attributed to closed ICME fields, several hundred ICMEs must connect to the Sun for about two solar rotations before disconnecting, consistent with a recent model that attributes the increase in heliospheric flux at solar maximum to ICMEs. Future studies must distinguish between the open and closed topologies in order to evaluate their relative contributions.

Nonlinear dynamical modeling of solar cycles using dynamo formulation with turbulent magnetic helicity

Variations of the sunspot number are important indicators of the solar activity cycles. The sunspot formation is a result of a dynamo process inside the Sun, which is far from being understood. We use simple dynamical models of the dynamo process to simulate the magnetic field evolution and investigate general properties of the sunspot number variations during the solar cycles. We have found that the classical Parker's model in this formulation with a standard kinetic helicity quenching cannot represent the typical profiles of the solar cycle variations of the sunspot number, and also does not give chaotic solutions. For modeling of the solar cycle properties we use a nonlinear dynamo model of Kleeorin and Ruzmaikin (Dynamics of the mean turbulent helicity in magnetic field. Magnetohydrodynamics, 1982, 18, 116–122), which takes into account the dynamics of the turbulent magnetic helicity. We have obtained a series of periodic and chaotic solutions for different layers of the convective zone. The solutions qualitatively reproduce some basic observational features of the solar cycle properties, in particular, the relationship between the growth time and the cycle amplitude. Also, on the longer time scale the dynamo model with the magnetic helicity has intermittent solutions, which may be important for modeling long-term variations of the solar cycles.

Bidirectional jet formation during driven magnetic reconnection in two-beam laser–plasma interactions

Measurements of the bidirectional plasma jets that form at the surface of a solid target during a laser-generated driven magnetic reconnection are presented. Resistivity enhancement of at least 25× the classical Spitzer value is required when applying the Sweet–Parker model of reconnection to reconcile the experimentally observed reconnection time scale. Analytic calculations show that a fast reconnection model, which includes a priori the effects of microturbulent resistivity enhancement, better reproduces the experimental observations.

The overall configuration of the interplanetary magnetic field upstream of Saturn as revealed by Cassini observations

The Cassini spacecraft approached Saturn during the declining phase of the solar cycle, at a time when the heliosphere was highly structured by compressions and rarefactions associated with corotating interaction regions (CIRs). We examine in detail the hourly averaged interplanetary magnetic field (IMF) data prior to Saturn Orbit Insertion and during one subsequent orbit of Cassini closer to solar minimum, where the spacecraft spent several months in the solar wind. We observe the effects of CIRs on IMF structure and show examples of where this structure is disturbed by the passage of strong coronal mass ejections and by solar cycle effects. We examine the field directions and find that in general, they correspond well to the predictions of the Parker model, but with several notable deviations, which we discuss.

Comparison of alternative upscaled model formulations for simulating DNAPL source dissolution and biodecay

This paper compares the performance of analytical and numerical approaches for modeling DNAPL dissolution with biodecay. A solution derived from a 1-D advective transport formulation (“Parker” model) is shown to agree very closely with high resolution numerical solutions. A simple lumped source mass balance solution in which with decay is assumed proportional to DNAPL mass (“Falta1” model) over- or underpredicts aqueous phase biodecay depending on the magnitude of the exponential factor governing the relationship between dissolution rate and DNAPL mass. A modification of the Falta model that assumes decay proportional to the source exit concentration is capable of accurately simulating source behavior with strong aqueous phase biodecay if model parameters are appropriately selected or calibrated (“Falta2” model). However, parameters in the lumped models exhibit complex interdependencies that cannot be quantified without consideration of transport processes within the source zone. Combining the Falta2 solution with relationships derived from the Parker model was found to resolve these limitations and track the numerical model results. A method is presented to generalize the analytical solutions to enable simulation of partial mass removal with changes in source parameters over time due to various remedial actions. The algorithm is verified by comparison with numerical simulation results. An example application is presented that demonstrates the interactions of partial mass removal, enhanced biodecay, enhanced mass transfer and source zone flow reduction applied at various time periods on contaminant flux reduction. Increasing errors that arise in numerical solutions with coarse discretization and high decay rates are shown to be controlled by using an adjusted decay coefficient derived from the Parker analytical solution.

On professional accounting body complaints procedures

PurposeThe purpose of this paper is to examine the operation of the Institute of Chartered Accountants in Ireland's (ICAI) complaint process from the complainant's perspective. The findings are interpreted drawing on key elements of Parker's private interest model of professional accounting ethics, particularly the private interest roles of professional authority and professional insulation.Design/methodology/approachThe primary evidence used is drawn from numerous sources. These include: extensive “private” documentation comprising original correspondence between the complainant in the case examined (or his advisors) and various representatives of the ICAI spanning a five‐year period; detailed supporting documentation included with this correspondence; Independent Experts' Reports on the complaints submitted; and in‐depth interviews with the complainant prior to, during, and post the examination of the documentary evidence.FindingsThe paper reveals how high levels of professional authority and professional insulation worked in tandem to prevent complaints entering the complaint process and deny the complainant reasons for decisions taken. It demonstrates how a key structural barrier in the complaint process, the screening role of the professional accounting body's secretary, created a complainant impression of a process concerned primarily with protecting members' interests. Subsequent to complaint process changes, an erosion of professional insulation is unveiled. However, this proves fleeting and, in response to persistent complainant challenges to heightened demonstrations of professional authority, the degree of professional insulation intensifies further.Research limitations/implicationsThe paper focuses on a specific case where the complainant was dissatisfied with the ICAI's procedures. It reveals the extent to which complainants using professional body complaints procedures may, often by virtue of the structures in place, feel that profession protection motives are overriding purported concerns for society protection.Originality/valueThe paper extends and advances the literature examining professional accounting body disciplinary and complaint procedures. Prior research investigating the operation of these procedures has neglected to examine complaint processes in depth to inform their evaluations, particularly from the perspective of potential users of these processes.

Solar Grand Minima and Random Fluctuations in Dynamo Parameters

We consider to what extent the long-term dynamics of cyclic solar activity in the form of Grand Minima can be associated with random fluctuations of the parameters governing the solar dynamo. We consider fluctuations of the alpha-coefficient in the conventional Parker migratory dynamo, and also in slightly more sophisticated dynamo models, and demonstrate that they can mimic the gross features of the phenomenon of the occurrence of Grand Minima over a suitable parameter range. The temporal distribution of these Grand Minima appears chaotic, with a more or less exponential waiting time distribution, typical of Poisson processes. In contrast however, the available reconstruction of Grand Minima statistics based on cosmogenic isotope data demonstrates substantial deviations from this exponential law. We were unable to reproduce the non-Poissonic tail of the waiting time distribution either in the framework of a simple alpha-quenched Parker model, or in its straightforward generalization, nor in simple models with feedback on the differential rotation. We suggest that the disagreement may only be apparent and is plausibly related to the limited observational data, and that the observations and results of numerical modeling can be consistent and represent physically similar dynamo regimes.

A Gravito‐electrostatic Sheath Model for Surface Origin of Subsonic Solar Wind Plasma

Parker's model prediction of an unbounded solution for the supersonic solar wind plasma (SWP) requires a subsonic origin at the solar surface. The transition to supersonic SWP flow is well understood by analogy with the de Laval nozzle. The basic physics, however, of the self-consistent solar surface emission of subsonic SWP is still not very clear. We propose a theoretical model based on a gravito-electrostatic plasma sheath (GES) to investigate the surface emission mechanism of the quasi-neutral SWP. The basic equations for the interior steady state description are solved numerically as an initial-value problem under spherical geometry. A bounded solution for the solar self-gravity distribution is found to exist, meaning that a global quasi-hydrostatic equilibrium is formed at some distance from the heliocentric origin. This defines the solar surface boundary in our model, which lies at radius ξ ~ 3.5 (in units of the Jeans length). A minimum speed of ~3.0 cm s-1, corresponding to Mach number ~10-7, is obtained at this location. Consequently, a subsonic origin of the solar interior plasma flowing radially outward becomes a physical reality. Our model requires a mean electron temperature Te ~ 107 K (=1 keV) for the numerical results to match the standard solar values. The boundary is found to be negatively biased, with a normalized value of the electrostatic potential θs ~ -1 (=1 kV). It is conjectured that our model provides an interesting new physical basis for understanding the collective dynamical coupling processes of solar interior and exterior (heliosphere) regions through local, as well as global, modes of GES-induced collective waves, instabilities, and oscillations.

Modeling of the Heliospheric Interface, Magnetic Field, and Cosmic‐Ray Transport

Magnetized flow and cosmic-ray transport in the local astrosphere are studied. A hybrid numerical model is used to calculate the heliospheric interface, the heliospheric magnetic field, and cosmic-ray modulation. Assuming that the transport parameters scale inversely proportional to the magnetic field, the amplification of the field in the inner heliosheath results in a sudden decrease of these parameters over the shock. This, together with our model calculations showing the compressed and heated solar wind flow is not divergence-free in the postshock region, results in effective adiabatic acceleration of cosmic-ray particles in the heliosheath. In particular, the peak of the computed anomalous particles is not at the shock but some distance into the inner heliosheath, where this region becomes populated with relatively high intensities of heated anomalous particles. However, this effect is largely dependent on the values of the transport parameters in the heliosheath. It is also shown that an improvement in the kinematically transported heliospheric magnetic field leads to a significantly different spatial distribution of cosmic rays compared to a Parker model.

Role of Dynamic Flow in Relationships between Suction Head and Degree of Saturation

This paper presents results of the relationship between the degree of saturation and the matric suction head at static equilibrium and during dynamic flow of water using a Buchner funnel and a fully instrumented two-dimensional tank, respectively. The major influences of the dynamic flow on the relationships between the suction head and the degree of saturation are highlighted and discussed. The experimental results show that dynamic flow of water strongly affects the volume of entrapped air. The results also reveal that any scanning curve can be described as two parts, namely, transition and coinciding. The transition curve starts from the recent reversal degree of saturation and continues up to the previous reversal degree of saturation. The shape of the transition curve and the amount of hysteresis are not only a function of the reversal degree of saturation but are also a function of the saturation path history. The experimental results are used to examine the validity of the proposed analytical model by Parker and Lenhard in 1987 for describing the relationships between the degree of saturation and the matric suction head. It was found that Parker and Lenhard's model provides a good prediction of the relations provided that care should be taken for the value of the reversal degree of saturation at zero suction head.

Reply to comment on ‘A novel hysteresis model in unsaturated soil’ by A. D. Werner and D. A. Lockington

Werner and Lockington (2006) have raised comments on our paper (Huang et al., 2005). They have reminded us that the inclusion of hysteresis effects and elimination of pumping errors are critical to model the movement of soil moisture in the vadose zone. If the soil-moisture model fails to eliminate the artificial pumping effect, the cumulative errors associated with the generation of hysteresis scanning curves are significant and lead to unrealistic simulated results. Several studies have developed empirical hysteresis models (e.g. Gillham et al., 1979; Jaynes, 1984; Scott et al., 1983; Kool and Parker, 1987; Parker and Lenhard, 1987; Lenhard et al., 1991; Simunek et al., 1999) and a systematic evaluation of the accuracy and convenience of these models is required. Our hysteresis model (Huang et al., 2005) is developed on the basis of the van Genuchten soil-moisture relation (van Genuchten, 1980) and modified from the Kool and Parker (1987) model, hereafter called KP model, to describe soil-moisture retention curves and eliminate the pumping effect. Parker and Lenhard (1987) had carried out a similar treatment, which is referred to as PL model here. Our model yields a series of closed-form relationships in which two shape factors, and , are determined from the main drying and wetting curves. Experimental data and data from the literature were used to compare the accuracy of the proposed model, KP model and Scott model (Scott et al., 1983). The three models have equal accuracy for estimation of the primary scanning curve. However, the Scott and KP models yield an erroneous pumping effect in the secondary and higher order scanning curves. Our model is simple, accurate and effective in constructing the series of wetting and drying scanning curves. It eliminates the pumping effect and has a perfect closure at the reversal points of the scanning curve. Several studies (e.g. Bomba and Miller, 1967;

Crossing the Termination Shock into the Heliosheath: Magnetic Fields

Magnetic fields measured by Voyager 1 show that the spacecraft crossed or was crossed by the termination shock on about 16 December 2004 at 94.0 astronomical units. An estimate of the compression ratio of the magnetic field strength B (+/- standard error of the mean) across the shock is B2/B1 = 3.05 +/- 0.04, but ratios in the range from 2 to 4 are admissible. The average B in the heliosheath from day 1 through day 110 of 2005 was 0.136 +/- 0.035 nanoteslas, approximately 4.2 times that predicted by Parker's model for B. The magnetic field in the heliosheath from day 361 of 2004 through day 110 of 2005 was pointing away from the Sun along the Parker spiral. The probability distribution of hourly averages of B in the heliosheath is a Gaussian distribution. The cosmic ray intensity increased when B was relatively large in the heliosheath.

A Model of the Thermal Expansion of the Solar Corona with Allowance for Radiation

The Parker model is modified to describe a rapid temperature increase from the region of temperature minimum to the coronal base and to relate the electron density in the region of the temperature minimum (∼0.85×1011 cm−3 according to the modified model) to that at the orbit of the Earth (∼7.42 cm−3 according to the model). The coronal temperature reaches its maximum (1.8×106 K) at the Parker critical point; physical processes at this point are left beyond the scope of the model. It is suggested to consider the expanding solar corona as a self-heating system in which heating of the solar corona is related to the transonic regime of its expansion, which is maintained by the high coronal temperature.

Coalescence of two magnetic flux ropes via collisional magnetic reconnection

Quasi-two-dimensional coalescence of two parallel cylindrical flux ropes and the development of three-dimensional merged structures are observed and studied in the reconnection scaling experiment [Furno et al., Rev. Sci. Instrum. 74, 2324 (2003)]. These experiments were conducted in a collisional regime with very strong guide magnetic field (Bguide⪢Breconnection), which can be adjusted independently of plasma density, current density, and temperature. During initial coalescence, a reconnection current sheet forms between the two flux ropes, and the direction of the current is opposite to the flux rope currents. The measured current sheet thickness is larger than the electron skin depth but smaller than the ion skin depth. Furthermore, the thickness does not vary for three different values of the strong external guide field. It is shown that the geometry of the observed current sheet is consistent with the Sweet–Parker model using a parallel Spitzer resistivity. The flux ropes eventually become kink unstable due to increasing current and fast-gated camera images show the development of three-dimensional merged structures.

Solar rotation and solar wind–magnetosphere coupling

This paper deals with three characteristics of the interplanetary magnetic field (IMF), important for solar wind–magnetosphere coupling and related to solar rotation: the IMF azimuthal component, the IMF total magnitude, and the handedness or the sense of rotation of magnetic clouds. The IMF configuration is described by Parker's Archimedian spiral model (Astrophys. J. 128 (1958) 664) under the assumptions of a purely radial solar wind with a constant velocity emanating from a uniformly rotating Sun. In situ measurements confirmed this general picture, but a systematic deviation from the predicted IMF winding angle was found, supposedly exhibiting a 11-year periodicity. We account for the non-uniform solar rotation and compare the observed IMF azimuthal component to the one calculated from Parker's formula with the measured equatorial solar rotation rate. We find that the differences between the calculated and measured IMF azimuthal component and the winding angle have a clear 22-year dependence on the solar polarity cycle, matching the 22-year periodicity in solar rotation rate rather than on the 11-year sunspot cycle. Our results are an observational confirmation of the validity of the model of Fisk (J. Geophys. Res. 101 (1996) 15547) for heliospheric magnetic field with footpoint motions due to solar differential rotation. Solar differential rotation is also an important element of the solar dynamo which is responsible for the generation of the solar magnetic field. We compare the different periodicities in the variations in the latitudinal rotation gradient of the two solar hemispheres and show that the IMF which is an extension of the solar coronal field, is related to the differential rotation in the more active solar hemisphere. Another feature related to solar differential rotation that is persistently different in the two solar hemispheres is the prevailing magnetic helicity, which is carried to the Earth by magnetic clouds preserving the helicity of the source region of their origin. The reaction of the magnetosphere to magnetic clouds is determined mainly by the presence or absence of a prolonged period of southward IMF component. We show that it also depends on the helicity of the clouds, and compare the effects of right- and left-handed magnetic clouds on geomagnetic activity.

On the roles of magnetization and topography in the scaling behaviour of magnetic-anomaly fields

SUMMARY There is lack of agreement on the underlying cause of widely observed power-law scaling behaviour of magnetic-anomaly fields. Some workers ascribe this behaviour to intrinsic 3-D fractal distributions of magnetization in the crust of the Earth; others point to a power-law exponent β∼ 3, expected for a random ensemble of statistically independent magnetized prisms: the classic Spector & Grant model (SG model). We apply a perturbation approach to the Parker model to derive expressions for the power spectra of magnetic-anomaly fields in the presence of laterally varying magnetization and/or topography at the top of magnetic basement. Under appropriate assumptions, our modified Parker model reduces to either an SG model or a 2-D fractal model. In the case of fractal magnetization without topography, the power-law slope of the magnetic-anomaly field (after depth correction) is equal to the power-law slope for the magnetization distribution. In the case of fractal basement topography alone, the power-law slope is reduced by 2. Where both the magnetization and topography are fractal, the effects of magnetization tend to dominate the power-law behaviour of the associated magnetic-anomaly field. Two real-data examples from the Canadian Shield exhibit power-law exponents of 2.02 ± 0.02 and 1.42 ± 0.01, within a wavelength band of 2 to 100 km. These slopes are significantly different from previously cited values of ∼3, casting doubt on the general applicability of the β∼ 3 slope that is inherent to SG models at high wavenumber.

Azimuthal Magnetic Field Disturbances and Spiral Structure of Interplanetary Magnetic Field

AbstractA 2.5 dimensional, ideal MHD model in spherical coordinates is used to numerically simulate the propagation of azimuthal magnetic field disturbances with emphasis upon its influence on the spiral angle of the interplanetary magnetic field (IMF). The observed fact that the IMF spiral angle is larger than that predicted by the Parker model is attributed to a ceaseless launching of azimuthal magnetic field disturbances of the same sign from the solar surface. The differential rotation of the Sun induces an azimuthal magnetic field inside the Sun, providing a source for these disturbances. The simulation results show that azimuthal magnetic field disturbances of the same sign which have a duration of one tenth of the period and an amplitude of order of 103 nT is capable of increasing the IMF spiral angle at 1AU by 2° so as to match with relevant observations. The results also indicate that the azimuthal magnetic field disturbances mentioned above have little effect on the solar wind properties and the magnetic configuration in the heliospheric meridional plane.

Diamagnetic effects of heliospheric Pick-up ions and magnetic fluxes in the outer heliosphere

For a long time it has been suggested that at larger solar distances the interplanetary field may not be behaving as predicted by Parker's Archimedian spiral field model. This phenomenon, partly identified as the magnetic flux deficit paradox, appears as deficits in the azimuthal field components connected with underwound fields, though the pick-up ion decelerated solar wind should rather lead to excesses. Up to now no satisfactory explanation for this phenomenon has been presented. In this paper we study for the first time the diamagnetic effect of pick-up ions which system- atically load the solar wind with suprathermal ions at its expansion to larger distances and diamagnetize the plasma. We shall demonstrate that such ions mainly reduce the azimuthal field component by their diamagnetic action. As we can show the field deficits can easily theoretically be explained by this effect. Also some new light is now shed on the problem of the field jump to be expected at the termination shock.

Morphologies of silicon crystals solidified on a chill plate

Electromagnetically levitated liquid droplets of pure Si or a Si-Ge alloy were cooled to different temperatures and then dropped onto a chill plate of Cu. Droplet oscillations mark the solid/liquid interface during solidification and permit the different crystal morphologies of silicon to be observed on the quenched surface by scanning electron microscopy (SEM). A spherical morphology found on the quenched surface represents the initial stage of crystal growth. Further growth leads to octahedral crystals bounded by {111} faces near equilibrium and to other polyhedra or even faceted dendrites further from equilibrium. The spherical growth can be observed only when the initial melt undercooling is moderately high. The critical size at which spherical crystals start to develop dendritic growth is much bigger than that calculated from the Mullins and Sekerka model, and is bigger than the Coriell and Parker model when kinetic undercooling is taken into account.

The solar wind in the outer heliosphere

We review recent plasma and magnetic field results stemming from Voyager 1 and 2 observations of the solar wind in the outer heliosphere. The solar wind speed profiles in 2002 are dominated by shock-related speed increases followed by long ramps of decreasing speed. Significant variability in the density and temperature are seen on all time scales. Transient events near solar maxima drive the formation of MIRs which are increasingly important at large radial distances. Both the density and magnetic field magnitude are consistent with the predictions of Parker's solar wind model. The solar wind pressure changes at all latitudes over the solar cycle, resulting in an oscillation of the heliospheric boundary positions. As the Voyagers move farther out, the effect of the interstellar medium on the solar wind increases. Observed speeds at Voyager 2 are about 60 km/s lower than those in the inner heliosphere due to interaction with the interstellar neutrals.