Energy Coupling Function Research Articles

Establishment and Application of an Interplanetary Disturbance Index Based on the Solar Wind–Magnetosphere Energy Coupling Function and the Spectral Whitening Method

We develop a preliminary interplanetary disturbance index (J sW ) by applying the spectral whitening method to an energy coupling function with solar wind measurements during the years 1998–2014 as the input, which can be used as an indicator of perturbations in the near-Earth solar wind. The correlation and temporal variation between J sW and the geomagnetic disturbance index (J pG ) constructed from the same method have been analyzed in detail for 167 geomagnetic storms with the minimum D st index less than or equal to −50 nT. The time delay between J sW and J pG is clearly observable and varies for different events, according to which J sW is shifted backward with respect to J pG . We obtain a fairly good negative correlation between the shifted J sW and the J pG indices for the majority of events, and the significance level for 88% of the events (i.e., 147 events) does not exceed 0.05. A statistical analysis of the shifted J sW and the J pG indices for 147 selected events reveals that larger values of J sW and smaller magnitudes of J pG are commonly accompanied by enhanced southward magnetic fields, which implies that more solar wind energy is entering the magnetosphere and thus causing strong geomagnetic storms. Furthermore, a linear fit of the two indices suggests that the evolution of J pG can be predicted about 2 hr in advance based on J sW , indicating that J sW can provide early warnings of possible disturbances in the geomagnetic fields, which is crucial for space weather monitoring and operational forecasting.

Passivity and underactuated modeling-based load energy coupling control for three-dimensional overhead crane systems

The conventional control strategies and methods with the three-dimensional model of overhead crane system are excessively dependent on model parameters and lead to the controllers design complex on position and anti-swing of overhead crane systems. With analysis on the coupling relationship among various state variables of overhead crane, the three-dimensional dynamic model of overhead crane based on mechanical virtual displacement and Lagrangian equation is constructed. A novel control strategy based on load energy coupling is designed to realize system positioning and eliminate the problem of residual load swing. The passivity of the three-dimensional overhead crane system is judged, and the energy composition of the system is deduced. The energy coupling function based on load displacement and swing angle is built. The control strategy of three-dimensional overhead crane system based on load energy coupling is designed by the Lyapunov stability theory and function construction method. The stability of the system is verified by the Lasalle invariance principle. With the experimental and programming, the proposed method is compared with different control methods. The results show that this method can realize the accurate positioning of the trolley more quickly and restrain the load swing more effectively.

Различия в отклике на геомагнитные возмущения, вызванные КВМ и ОКВ

Utilizing 1-minute resolution data on the geomagnetic indices SYM-H, AE, solar wind parameters (velocity Vsw and density Np), and z-component Bz of the interplanetary magnetic field (IMF) during solar cycles 23 and 24, we have statistically analyzed the correlations between geomagnetic activity (storms and substorms), Vsw, Np, Bz, and energy coupling functions of solar wind and Earth’s magnetosphere. For the selected 131 CME-driven storms, SYM-H stronger depends on Vsw and B than other parameters, whereas the selected 161 CIR-driven storms have nearly the same dependence on the solar wind electric field, the rate of open magnetic flux dφ/dt, and the reconnection electric field Ekl. Thus, the solar wind electric field and the dayside magnetic reconnection are likely to have different contributions for storms of the two types. During storms of different types, the substorm intensity AE relies mainly on the IMF Bz, rate of open magnetic flux and reconnection electric field.

Differences in the response to CME and CIR drivers of geomagnetic disturbances

Utilizing 1-minute resolution data on the geomagnetic indices SYM-H, AE, solar wind parameters (velocity Vsw and density Np), and z-component Bz of the interplanetary magnetic field (IMF) during solar cycles 23 and 24, we have statistically analyzed the correlations between geomagnetic activity (storms and substorms), Vsw, Np, Bz, and energy coupling functions of solar wind and Earth’s magnetosphere. For the selected 131 CME-driven storms, SYM-H stronger depends on Vsw and B than other parameters, whereas the selected 161 CIR-driven storms have nearly the same dependence on the solar wind electric field, the rate of open magnetic flux dφ/dt, and the reconnection electric field Ekl. Thus, the solar wind electric field and the dayside magnetic reconnection are likely to have different contributions for storms of the two types. During storms of different types, the substorm intensity AE relies mainly on the IMF Bz, rate of open magnetic flux and reconnection electric field.

Does Adding Solar Wind Poynting Flux Improve the Optimum Solar Wind‐Magnetosphere Coupling Function?

AbstractWe study the contribution of the solar wind Poynting flux to the total power input into the magnetosphere. The dominant power delivered by the solar wind is the kinetic energy flux of the particles, which is larger than Ssw by a factor of order , where MA is the Alfvén Mach number. The currents flowing in the bow shock and magnetosheath and the electric field of the solar wind give regions where , which are sources of Poynting flux, generated from the kinetic energy flux. For southward interplanetary magnetic field, is duskward and the currents in the high‐latitude tail magnetopause are also sources of Poynting flux. We show transfer of kinetic energy into the magnetosphere is less efficient than direct entry of by a factor MA. Because MA is typically of order 10, this means that although the power density in the solar wind due to is typically only 1%, it is responsible for of order 10% of the energy input to the magnetosphere. To investigate the effect of this, we add a term to the solar wind‐magnetosphere energy coupling function that allows for and that increases the correlation with the geomagnetic am index for 1995–2017 (inclusive) from 0.908 to 0.924 for 1‐day averages and from 0.978 to 0.979 for annual means. The increase for means on daily or smaller timescales is a small improvement but is significant (at over the 3σ level), whereas the improvement for annual or Carrington rotation means is not significant.

An SOC Approach to Study the Solar Wind‐Magnetosphere Energy Coupling

AbstractSolar wind‐magnetosphere interaction and the injection of large quantity of plasma particles into the Earth's magnetosphere are the primary reasons behind geomagnetic storm, auroral effects, and, in general, all the fluctuations observed in the terrestrial magnetic field. In this paper, we analyzed the perturbed magnetosphere as a sandpile‐like cellular automata model based on the concept of self‐organized criticality and many‐body interactive system and proposed a solar wind‐magnetosphere energy coupling function in terms of interplanetary magnetic field BZ, the zth component of interplanetary magnetic field. The function determines the cusp width W depending on the intensity of (−BZ − BTh) where BTh is the threshold value. The model generates two output series, which are the numerical representation of the real‐time Dst index and AE index series, respectively. For our study, the range of years 1997–2007 of the 23rd solar cycle had been considered here. The threshold value BTh plays a significant role in the analysis and exhibits a proportional relationship with the yearly mean total number of sunspots for each year of the range 1997–2007 of the 23rd solar cycle. For each year, the two resultant output time series of the model display high‐correlation coefficients with the real‐time Dst and AE indexes, respectively, which denotes the acceptability of the proposed energy coupling function and its relation with the solar activities.

New Diagnosis for Energy Flow From Solar Wind to Ionosphere During Substorm: Global MHD Simulation

AbstractTo investigate the energy involved by a substorm, we performed global magnetohydrodynamics simulation for different solar wind conditions. The intensity of the auroral electrojet increases with the southward component of interplanetary magnetic field (IMF) and the solar wind velocity, which is consistent with observations. To evaluate the energy that enters the magnetosphere, we first defined a solar wind effective cross‐sectional area in which all the Poynting fluxes entering the magnetosphere pass through. We found that the solar wind magnetic energy is insufficient to provide the magnetic energy entering the magnetosphere (intake magnetic energy) for southward IMF. About 33–88% of the intake magnetic energy is converted from the solar wind kinetic energy. About 2–7% of the solar wind kinetic energy (passing through the effective area) is converted to the magnetic energy that enters the magnetosphere. Significant contribution from the solar wind kinetic energy makes the energy coupling function complicated. The effective area also depends on the solar wind parameters, also making it complicated. An interesting point is that the rates of energy stored and released in the lobe also depend on the solar wind parameters. The ionospheric Joule heating rate is well correlated with the intake magnetic energy at onset, and during the substorm expansion. The correlation coefficients between them are better than that of the ε parameter. These results imply that both the directly driven process (manifested by intake magnetic energy) and loading‐unloading process (manifested by stored/released energy in the lobe) are largely regulated by the solar wind condition.

Joule heating hot spot at high latitudes in the afternoon sector

AbstractThe afternoon Joule heating hot spot has been studied statistically by using the EISCAT Svalbard Radar (ESR) measurements at 75.4° Corrected Geomagnetic latitude (CGMLAT) and the OMNI solar wind data base. For a small subset of events, the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) field‐aligned current distributions have been available. The main results are as follows. Afternoon Joule heating hot spots are associated with high values of ionospheric electric fields and slightly enhanced Pedersen conductances. The Joule heating hot spot values are larger in summer than in winter, which can be explained by the higher Pedersen conductances during summer than winter. The afternoon Joule heating hot spots are located close to the reversals of the large‐scale field‐aligned current systems. The most common location is close to the Region 1/Region 2 boundary and those events are associated with sunward convecting F region plasma. In a few cases, the hot spots take place close to the Region 1/Region 0 boundary and then the ionospheric plasma is convecting antisunward. The hot spots may occur both during slow (<450 km/s) and high (>450 km/s) speed solar wind conditions. During slow‐speed solar wind events, the dominant interplanetary magnetic field (IMF) direction is southward, which is the general requirement for the low‐latitude magnetic merging at the dayside magnetopause. During high‐speed solar wind, also northward IMF conditions appear, but those are associated with large values of the IMF |By| component, making again the dayside magnetopause merging possible. Finally, the measured afternoon hot spot Joule heating rates are not a linear function of the solar wind energy coupling function.

New model fit functions of the plasmapause location determined using THEMIS observations during the ascending phase of Solar Cycle 24

AbstractIt is well known that the plasmapause is influenced by the solar wind and magnetospheric conditions. Empirical models of its location have been previously developed such as those by O'Brien and Moldwin (2003) and Larsen et al. (2006). In this study, we identified the locations of the plasmapause using the plasma density data obtained from the Time History of Events and Macroscale Interactions during Substorms (THEMIS) satellites. We used the data for the period (2008–2012) corresponding to the ascending phase of Solar Cycle 24. Our database includes data from over a year of unusually weak solar wind conditions, correspondingly covering the plasmapause locations in a wider L range than those in previous studies. It also contains many coronal hole stream intervals during which the plasmasphere is eroded and recovers over a timescale of several days. The plasmapause was rigorously determined by requiring a density gradient by a factor of 15 within a radial distance of 0.5 L. We first determined the statistical correlation of the plasmapause locations with several solar wind parameters as well as geomagnetic indices. We found that the plasmapause locations are well correlated with the solar wind speed and the interplanetary magnetic field Bz, therefore the y component of the convective electric field, and some energy coupling functions such as the well‐known Akasofu's epsilon parameter. The plasmapause locations are also highly correlated with the geomagnetic indices, Dst, AE, and Kp, as recognized previously. Finally, we suggest new model fit functions for the plasmapause locations in terms of the solar wind parameters and geomagnetic indices. When applied to a new data interval outside the model training interval, our model fit functions work better than existing ones. The new model fit functions developed here extend the range of conditions from those used in previous works.

Solar wind‐magnetosphere energy coupling function fitting: Results from a global MHD simulation

AbstractQuantitatively estimating the energy input from the solar wind into the magnetosphere on a global scale is still an observational challenge. We perform three‐dimensional magnetohydrodynamic (MHD) simulations to derive the energy coupling function. Based on 240 numerical test runs, the energy coupling function is given by. We study the correlations between the energy coupling function and a wide variety of magnetospheric activity, such as the indices ofDst,Kp,ap,AE,AU,AL, the polar cap index, and the hemispheric auroral power. The results indicate that this energy coupling function gives better correlations than theεfunction. This result is also applied to a storm event under northward interplanetary magnetic field conditions. About 13% of the solar wind kinetic energy is transferred into the magnetosphere and about 35% of the input energy is dissipated in the ionosphere, consistent with previous studies.

Energy transfer and flow in the solar wind‐magnetosphere‐ionosphere system: A new coupling function

In this paper we describe and quantify the energy transfer, flow, and distribution. Our high‐resolution data set covers 13 years of OMNI, SuperMAG, and Kyoto data. We employ what we consider to be the best estimates for energy sinks and relate these to SuperMAG indices for better coverage and spatial resolution. For the energy input, we have used the method of dimensional analysis that is presented in unit power and makes it appropriate for energy analysis. A cross‐correlation analysis parameterizes the magnetospheric response on the solar wind parameters during a wide range of conditions, ranging from substorms and storms up to a decade. The determined functional form is then evaluated and scaled using superposed epoch analysis of geomagnetic storms, revealing that the effective area of interaction cannot be considered static. Instead, we present a dynamic area which depends to the first order on the cube of the interplanetary magnetic field Bz component. Also, we find that for longer time periods, this area must be increased compared to the area used for geomagnetic storms. We argue that some of the terms in the energy coupling function are contributory to describing magnetosheath conditions and discuss how our coupling function can be related to Maxwell stress components. Also, we quantify the relative importance of the different energy sinks during substorms, geomagnetic storms, and long time series and present the coupling efficiency of the solar wind. Our energy coupling functions are compared with the ε parameter and perform better for almost any event.

Apposite of atmospheric electric parameters with the energy coupling function ( ε) during geomagnetic storms at high latitude

In this paper we are concerned with the variation of the atmospheric electric field and the air–earth current due to the excessive power generated by the solar wind-magnetosphere dynamo during geomagnetic storms, recorded at Maitri in Antarctica during 2004. A major part of the power generated by the solar wind-magnetosphere dynamo is used in the formation of the ring current and the rest is utilized for Joule heating and auroral particle precipitation. The method adopted by Frank-Kamenetsky et al. [Frank-Kamenetsky A.V., Troshichev O.A., Burns G.B., Papitashvili V.O., 2001. Variations of atmospheric electric field in the near-pole region related to the interplanetary magnetic field. J. Geophys. Res. 106, A1, 179–190.] was utilized to delineate the variations due to the signatures of tropical thunderstorm activity from the geoelectric data; while statistical methods used in our earlier studies were used to delimit variation due to the constant buffeting of the solar wind. We find that the solar wind-magnetosphere energy coupling function ( ε) to be well correlated with the atmospheric electric parameters during the onset of geomagnetic disturbances. However the correlation breaks down during minor storms and sub-storm events.

Energy balance during intense and super-intense magnetic storms using an Akasofu ε parameter corrected by the solar wind dynamic pressure

Geomagnetic storms are large disturbances in the Earth's magnetosphere caused by enhanced solar wind–magnetosphere energy transfer. One of the main manifestations of a geomagnetic storm is the ring current enhancement. It is responsible for the decrease in the geomagnetic field observed at ground stations. In this work, we study the ring current dynamics during two different levels of magnetic storms. Thirty-three events are selected during the period 1981–2004. Eighteen out of 33 events are very intense (or super-intense) magnetic storms ( Dst ⩽−250 nT) and the remaining are intense magnetic storms (−250< Dst ⩽−100 nT). Interplanetary data from spacecraft in the solar wind near Earth's orbit (ACE, IMP-8, ISEE-3) and geomagnetic indices ( Dst and Sym-H) are analyzed. Our aim is to evaluate the interplanetary characteristics (interplanetary dawn–dusk electric field, interplanetary magnetic field component B S), the ε parameter, and the total energy input into the magnetosphere ( Wε) for these two classes of magnetic storms. Two corrections on the ε energy coupling function are made: the first one is an already known correction in the magnetopause radius to take into account the variation in the solar wind pressure. The second correction on the Akasofu parameter, first proposed in this work, accounts for the reconnection efficiency as a function of the solar wind ram pressure. Geomagnetic data/indices are also employed to study the ring current dynamics and to search for the differences in the storm evolution during these events. Our corrected ε parameter is shown to be more adequate to explain storm energy balance because the energy input and the energy dissipated in the ring current are in better agreement with modern estimates as compared with previous works. For super-intense storms, the correction of the Akasofu ε is on average a scaling factor of 3.7, whilst for intense events, this scaling factor is on average 3.4. The injected energy during the main phase using corrected ε can be considered a criterion to separate intense from very intense storms. Other possibilities of cutoff values based on the energy input are also investigated. A threshold value for the input energy is much more clear when a new classification on Dst=−165 nT is considered. It was found that the energy input during storms with Dst<−165 nT is double of the energy for storms with Dst>−165 nT.

Theoretical study of the CS2+ dication

The potential energy and spin-orbit coupling functions of 11 lowest electronic states of CS(2+) dication have been calculated using internally contracted multireference configuration method. Using these functions, the positions and widths of the corresponding vibronic levels have been evaluated by means of the stabilization and log-phase-amplitude methods. The states governing the second step in the sequential pathway CS2(3+)-->S++CS2+-->S++C++S+ of the overall three-body Coulomb explosion of CS(2)3+ have been determined.

Computed lifetimes of metastable states of CO2+

Highly correlated internally contracted multireference configuration interaction wave functions are used to calculate the potential energy and spin-orbit coupling functions for the lowest electronic states of CO2+ dication. Using these functions, the positions and lifetimes of the corresponding vibronic states are evaluated by means of log-phase-amplitude, stabilization, and complex-scaling methods within the framework of a multichannel Schrodinger analysis. For the first time in the literature, the calculated lifetimes are in good agreement with the experiment, thereby proving the reliability of the predicted characteristics and adequacy of the used theory for a theoretical study of other molecular dications.

Influence of the interplanetary magnetic field on the ring current injection rate

Abstract In order to check the validity of Akasofu’s ε parameter and of the Vasyliunas et al. (1982) general formula, we examine the dependence of the ring current injection rate, calculated from the Dst index for the period of 1965–1990, on the interplanetary magnetic field (IMF). We compare the influence of the Bz component with the influence of the combination of sin(θ/2), where θ is the IMF clock angle, and the IMF magnitude, B, (or the transverse component of the IMF, BT = (By2 + Bz2)1/2) by using the regression analysis in a power law form. The main results are as follows: (1) the exponent for Bz shows higher consistency than that for sin(θ/2); (2) we never obtain B 2 sin4(θ/2) or B T 2 sin4(θ/2), which is the IMF dependence expected from the ε parameter; and (3) the ring current injection rate has a very low correlation with the Alfven Mach number, from which the IMF dependence of the Vasyliunas et al. general formula is assumed to arise. On the basis of the above results we conclude that the ε parameter and the Vasyliunas et al. general formula are less appropriate than a function of Bz, and that the energy coupling function between the solar wind and the Earth’s magnetosphere is described better by Bz than by the combination of B (or B T) and sin(θ/2). The above results and conclusions are the same as those obtained by Aoki (2005) through the analysis of the AL index.

Solar causes of the long‐term increase in geomagnetic activity

We analyze the causes of the century‐long increase in geomagnetic activity, quantified by annual means of the aa index, using observations of interplanetary space, galactic cosmic rays, the ionosphere, and the auroral electrojet, made during the last three solar cycles. The effects of changes in ionospheric conductivity, the Earth's dipole tilt, and magnetic moment are shown to be small; only changes in near‐Earth interplanetary space make a significant contribution to the long‐term increase in activity. We study the effects of the interplanetary medium by applying dimensional analysis to generate the optimum solar wind‐magnetosphere energy coupling function, having an unprecedentedly high correlation coefficient of 0.97. Analysis of the terms of the coupling function shows that the largest contributions to the drift in activity over solar cycles 20–22 originate from rises in the average interplanetary magnetic field (IMF) strength, solar wind concentration, and speed; average IMF orientation has grown somewhat less propitious for causing geomagnetic activity. The combination of these factors explains almost all of the 39% rise in aa observed over the last three solar cycles. Whereas the IMF strength varies approximately in phase with sunspot numbers, neither its orientation nor the solar wind density shows any coherent solar cycle variation. The solar wind speed peaks strongly in the declining phase of even‐numbered cycles and can be identified as the chief cause of the phase shift between the sunspot numbers and the aa index. The rise in the IMF magnitude, the largest single contributor to the drift in geomagnetic activity, is shown to be caused by a rise in the solar coronal magnetic field, consistent with a rise in the coronal source field, modeled from photospheric observations, and an observed decay in cosmic ray fluxes.

Ionospheric response to magnetic forcing: Magnetic cloud passage of October 18–20, 1995

On October 18–20, 1995 a magnetic cloud was observed, first by the WIND spacecraft upstream in the solar wind, then at the Earth. Inside the cloud, plasma density, velocity and temperature, and magnetic field strength were relatively steady for almost 24 hrs. However, the magnetic field direction rotated slowly from −Z to −Y and finally to +Z (GSE coordinates). This magnetic cloud passage allows us to study the solar wind‐magnetosphere‐ionosphere interaction under nearly ideal slowly‐varying conditions. This paper reports on the nightside ionospheric response to a long interval with Bz &lt;0 in the interplanetary medium. Temporal variations in the integrated energy deposited in the nightside auroral zone within 3 hrs of local midnight are similar to variations in ϵ, the energy coupling function, and dissimilar to auroral magnetograms. While substorm effects are observed in the ionospheric electron flux, the integrated energy is dominated by diffuse precipitation at low latitudes. We also find that the integrated energy curve lags the ϵ parameter by 1–2 hrs. This delay represents the time required for convective electric fields to heat particles adiabatically in the plasma sheet.

Multi-Partitioning QDPT and Difference-Dedicated CI Calculations of Non-Adiabatic Couplings: Application to Charge Transfer in LiF System

Potential energy and non-adiabatic coupling functions for the two lowest 1 Σ + states of LiF were calculated using the recently proposed perturbative approach, based on the multiple partitioning of the full Hamiltonian, and the difference-dedicated CI method. The results are compared with MRDCI and available full CI data for the same AO basis set. A high accuracy was achieved with a semiempirical perturbative scheme combining the direct calculations at second order with an approximate estimation of higher-order local contributions.

The response of the quiet-time auroral configuration to short- and long-term interplanetary magnetic field variations

Observations from the IMP-8 satellite of the interplanetary magnetic field (IMF) are compared with areas of the polar region bounded by the aurora as observed by the Viking spacecraft during quiet-time conditions (IMF Bz northward). A variety of energy-coupling functions are investigated and it is determined that the auroral distribution can be best described by the inclusion of azimuthal terms in addition to standard energy-coupling functions. The auroral distributions for Bz northward support antiparallel merging as a mechanism whereby energy is transferred to the magnetosphere from the solar wind. As well, however, when the polar angle is small the region bounded by the auroras expands and may be controlled more by wave interaction at the magnetopause. Observations by the Viking spacecraft indicate a dominance of dusk sector polar arcs in the spring time and dawn sector arcs in the fall (post equinox). Two alternative mechanisms can explain the observations. One involves the ordering of the IMF in a solar equatorial coordinate system while the other involves the Sun's polarity and the traversal of the Earth's orbit through different heliographic latitudes. A test is proposed whereby the two hypotheses can be investigated during the next solar cycle.