**PROGRESS IN HELIOSPHERIC
PHYSICS*******

FENG Xueshang

Center for Space Science and Applied Research, Chinese
Academy of Sciences, Beijing 100080, China.

ABSTRACTHere is an overview for the progress of heliospheric physics made in China in the period of 1999 to 2002. The report is focused on theoretical study, modelling and observational analysis of interplanetary physical phenomena. This overview is divided into five parts: acceleration and heating of solar wind, corona structure, coronal mass ejections, magnetic reconnection phenomena, interplanetary transient phenomena. The main achievements made recently by Chinese scientists in related area are simply listed in corresponding sections without any priority, only certain editorial consideration.Key words:Solar wind acceleration, Coronal mass ejection, Interplanetary, Transient phenomena

I. ACCELERATION AND HEATING OF SOLAR WINDHu et al. (1999a; 1999b) presented a solar wind model with resonant heating and acceleration by dispersive parallel-propagating left-hand-polarized ion cyclotron waves. The Alfvén wave spectrum equation is generalized to a multi-ion plasma. A Kolmogorov type of cascade function is then introduced to transfer energy from the low-frequency Alfvén waves to the high-frequency ion cyclotron waves, which are assumed to be entirely dissipated by the wave-particle interaction. The dissipated wave energy is assumed to be distributed among different ions according to the quasi-linear theory of the wave-particle interaction with the cold plasma dispersion relation and a power law spectrum of the ion cyclotron waves, of which the spectral index is assumed to be a free parameter of the model. The solutions of the set of three-fluid solar wind equations and the Alfvén wave spectrum equation show that the effect of the alpha particles on the dispersion relation has a significant influence on the preferential acceleration and heating of the alphas. With this effect included, the alpha particles can be accelerated to a bulk flow speed faster than the protons by a few hundred kilometers per second and heated by the resonant cyclotron interaction to more than mass-proportional temperature values at several solar radii.

Hu (1999c) presented a two-fluid model to study the turbulence cascade processes in the corona and in the solar wind. The fluid equation and a power spectrum equation for Alfvén waves were solved simultaneously in a self-consistent manner. Both Kolmogorov like and Kraichnen cascade functions were considered. It is found that the Kolmogorov process produces a stronger cascade effect than the Kraichnen process and seems more relevant for Alfvén waves in the fast solar wind.

Tu et al. (1999a; 1999b) suggested a two-step model describing systematically both the heating of the protons and oxygen ions based on the quasi-linear theory. First the heavy ions absorb almost all the energy of the waves and are preferentially accelerated. Then, because of the Doppler shift and dependence of the resonant frequency of the heavy ions upon their drift speed, these heavy ions become resonant with cyclotron waves at higher wave numbers, at which a considerable number of the protons is also resonant with the waves.

By using characteristics and structures of solar wind of recent spacecraft observations and analytical solutions to MHD flow in trumpet-like open magnetic field, the acceleration and the location of energy supplying are discussed qualitatively (Wei, Pan and Feng, 2000). The main results are as follows: the energy for high-speed wind in the polar region abide by exponent law, the main energy supply location is situated at lower coronal region (1-3)

R, the energy needed decreases rapidly beyond (6-7)_{S}R. The most efficient region of solar wind acceleration is located at about_{S}_{ }, not beyond (6-7)R._{S}Song, Xiao and Feng (2000) show that Landau damping of dynamic Alfvén wave with high frequency can accelerate efficiently the solar wind and heat the corona when it travels along magnetic field in coronal holes. Theoretical computation displays that dissipative form and length of energy flux are consistent with those given by empirical models.

Tu (2000) gives a review on the progress about the origin and formation of solar wind with emphasis on the recent observational results from SOHO and Ulysses, including some related theoretical models such as cyclotron resonant heating and high frequency Alfvén wave solar wind models.

It is known that quasi-linear theory predicts that ions in resonance with transverse ion cyclotron waves suffer merely pitch angle diffusion while conserving their total kinetic energy in the frame moving with the wave phase speed. For the first time, direct observational evidence from Helios plasma data is shown by Marsch and Tu (2001a) for the occurrence of this pitch angle diffusion of solar wind protons, induced by resonance with parallel ion cyclotron waves propagating away from the sun. Parts of the isodensity contours in velocity space are well outlined by a sequence of segments of circles centered at the adapted wave phase speed, which is assumed to vary slightly and to be due to dispersion smaller than the local Alfvén speed. This observation confirms the validity of basic concepts of resonant wave particle interactions as described by quasi-linear theory. The solar wind proton velocity distributions show a plateau defined by a vanishing pitch angle gradient in the resonant regime, implying marginal stability of the distribution function. These results also give new ideas and further motivation to study the interaction between the ions and Alfvén/ion cyclotron waves in coronal holes and the associated fast solar wind.

On the basis of quasi-linear theory, the parallel and perpendicular wave heating and acceleration rates for gyrotropic particle velocity distribution functions are derived by Marsch and Tu (2001b). These rates can be used in anisotropic multicomponent fluid equations, in order to describe the wave-particle interactions of ions with, for example, kinetic Alfvén and electromagnetic or electrostatic ion cyclotron, respectively, magnetosonic waves propagating along or obliquely to the mean magnetic field. The waves of coronal origin propagating away from the sun into the interplanetary medium can resonantly heat the solar wind ions and accelerate minor ions preferentially with respect to the protons. Such processes are required in order to explain and understand the measured characteristics of ion velocity distributions in the solar wind and to interpret the recent spectroscopic evidence obtained from EUV emission line measurements made by SOHO spacecraft, which indicate cyclotron-resonance-related line broadenings and shifts.

The preferential heating and acceleration of O

^{+5}ions, as observed by Ultraviolet Coronagraph Spectrometer (UVCS) on Solar and Heliospheric Observatory (SOHO) in the solar coronal holes have been interpreted and modeled by invoking wave-particle cyclotron resonance before. However, in the previous models the assumption of a rigid slope of the wave spectrum was made in calculating the wave energy absorption by the different ion species. It is shown (Tu and Marsch, 2001) that that a self-consistent treatment of the wave damping and absorption is necessary and leads to substantially different results. On the basis of quasi-linear theory, the interaction between the ions and the ion-cyclotron waves is studied. The total energy conservation equation, including the kinetic energy of the resonant particles and the wave energy, is derived and discussed in detail. The spectral evolution equation for cyclotron waves, when being controlled by the wave growth/damping rate and WKB effects, is solved self-consistently together with the full set of anisotropic multifluid equations for the ions including the cyclotron-resonance wave heating and acceleration rates. From the numerical results Tu and Marsch (2001) reach the following conclusions: (1) It is physically questionable to use a spectrum with a fixed spectral slope near the cyclotron resonance when one calculates the partition of wave energy among the different ionic species and the kinetic degrees of freedom parallel and perpendicular to the magnetic field. This assumption neglects the important effects of wave absorption and the concurrent reshaping of the wave spectrum, and thus leads in the dissipation domain to extremely low amplitudes of the waves and to difficulties in supplying enough energy to balance the wave absorption at the cyclotron resonances. (2) if the spectrum is allowed to evolve self-consistently and concurrently with the particles' heating and acceleration through wave absorption, such as a high perpendicular temperature and corresponding large temperature anisotropy as observed by UVCS do not occur or can not be maintained. The authors conclude that the UVCS oxygen ion observations can not be explained satisfactorily by the cyclotron-resonance theory.The four-fluid model with O

^{5+ }replaced by one of_{ }ions respectively is adopted (Shu, Chen and Tu, 2001). The bulk velocity and temperature of the heavy ions are obtained and compared with the SUMER observation data. Chen, Ruth and Hu (2002) presented a theoretical model for O^{5+}(O^{7+}) ions as test particles in the fast solar wind using a previous turbulence-driven four-fluid model to establish the background solar wind, which consists of electrons, protons, alpha particles, and O^{6+}ions. The O^{5+}(O^{7+}) ions in our model and the O^{6+}ions in the background are driven by the same mechanism, say, the resonant cyclotron interaction or an exponential heating addition. The ionization and recombination processes of O ions are taken into account. It is shown that the differential flow speeds between O^{6+}and O^{5+}or O^{7+}, which are found to be in the range of 0.3－2, play very different roles in the formation of O charge states. This is due to discrepancy between the freezing-in distances of the two ion species. O^{7+}forms predominantly below 1.2 Rs too close to the Sun to develop a differential streaming between O ions. O^{5+}, on the other hand, freezes-in at about 1.8 Rs where differential flows are well developed and therefore important for the formation of O^{5+}ions.By using a one-dimensional, four-fluid turbulence driven solar wind model, Hu, Esser and Habbal (2000) extend the cascade model of Alfvén fluctuations from electron-proton plasma to multi-ion plasma (including electrons, alpha particles, protons, and one species of minor ions) and solve the solar wind equations and the wave spectrum equation simultaneously in order to explain the preferential acceleration and heating of heavy ions near the sun. The numerical results show that the heavy ions can be accelerated to a bulk flow speed faster than the protons by a few kilometers per second and heated to a temperature more than mass-proportional values at several solar radii by the resonant cyclotron interaction, which agree with the SOHO observations.

A two-dimensional, Alfvén-wave-driven solar wind model is proposed by Chen and Hu (2002) by assuming the wave energy to cascade from the low-frequency Alfvén waves to high-frequency ion cyclotron waves and to be transferred to the solar wind protons by cyclotron resonance at the Kolmogorov rate. A typical structure in the meridional plane consisting of a coronal streamer near the sun, a fast wind in high latitudes, and a slow wind across the heliospheric current sheet is found. The fast wind obtained in the polar region is essentially similar to that derived by previous one-dimensional flow-tube models, and its density profile in the vicinity of the sun roughly matches relevant observations. The proton conditions at 1 AU are also consistent with observations for both the fast and slow winds. The Alfvén waves appear in the fast and slow wind regions simultaneously and have comparable amplitudes, which agree with Helios observations. The acceleration and heating of the solar wind by the Alfvén waves are found to occur mainly in the near-sun region. It is demonstrated in terms of one-dimensional calculations that the distinct properties of the fast and slow winds are mainly attributed to different geometries of the flow tubes associated with the two sorts of winds. In addition, the 2-D and 1-D simulations give essentially the same results for both the fast and slow winds.

Tu, Wang and Marsch (2002) suggested a new mechanism to explain the formation of proton beam velocity distributions in high-speed streams of the solar wind. The proton beam is a well-known kinetic phenomenon, which was already found in the early days of solar wind in situ measurements. Observationally, proton beams move faster than the core part of the proton distribution by more than the Alfvén speed. The beam has a higher temperature than the core, but the thermal anisotropy is usually smaller. Until today none of the major properties of the observed beams have been adequately explained. The basic difficulty faced by precious investigations is that in a proton-electron plasma, hardly any cyclotron waves are found to be in resonance with the beam protons. However, when considering a proton-alpha-electron plasma, we find a second dispersion branch of outward propagating RHP and LHP waves. This branch is mainly determined by the alpha particles drifting at the Alfvén speed. The associated waves can resonate with the beam protons, and the resulting cyclotron-resonance-induced diffusion produces a beam velocity distribution. The time-dependent two-dimensional diffusion equation, as determined from the quasi-linear theory of ion cyclotron-wave resonance, is solved numerically. A proton beam distribution is shown to form, by diffusion in the wave field, out of an initial shuttle-like bi-Maxwellian velocity distribution function. The drift velocity of the model beam is about the Alfvén speed. The perpendicular thermal speed is about 44 km/s, and the thermal anisotropy of the beam is much less than the core anisotropy.

The velocity distribution functions (VDFs) of protons measured by Helios in fast solar wind are analyzed by Tu and Marsch (2002) in the framework of quasi-linear theory (QLT). Evidence is presented that the shape of the central isodensity contours in velocity space and the temperature anisotropy of the core part of the VDFs can be explained by wave-induced plateau formation according to QLT. The plateau is formed by protons that are in resonance with cyclotron waves, which are assumed to propagate both outwardly and inwardly at phase speeds following from the plasma dispersion relation. For the proton VDFs measured near 0.3 AU in fast low-beta solar wind, the theoretical predictions of QLT, using the cold plasma dispersion relation, agree well with the in situ observations. For the proton VDFs measured near 1AU in fast high-beta wind, the predictions of QLT, using again the cold plasma dispersion relation, only give an upper limit for the anisotropy. Yet, considering thermal effects in the dispersion relation, a better agreement between the theory based on resonant ion diffusion and the observations is obtained. For nondispersive waves a simple relation between the ion thermal speed parallel to the magnetic field and the ion-temperature anisotropy is derived, which is shown to be consistent with the anisotropy of the heavy O

^{+5}ion as observed on the Solar and Heliospheric Observatory (SOHO), as well as with the anisotropy predicted numerically by a hybrid simulation of the ion-temperature regulation by waves.A new mechanism for explanation of

_{ }-particles acceleration is presented by Song and Xiao (2002), by using kinetic Alfvén wave theory. The basic idea is that moving along the open magnetic field from the corona holes towards the direction in which the solar wind was accelerated by the gradient of thermal pressure, the heavy ions move slower than the mean solar wind speed just a little near Alfvén point because its mass is heavy. When the solar wind speed is up to the Alfvén speed_{ }, namely near the Alfvén point, a new kinetic Alfvén wave will be excited. When the wave is excited, the heavy ions staying near the excited point in velocity space will be captured by the wave field, that is nearly all the heavy ions participate in the wave excitation. Due to the excitated source of wave in the solar wind, the new excited wave propagates forward at the speed of_{ }, so the trapped heavy ions taking part in the excitation have the velocity of_{ }. Parts of protons also take part in the excitation and are trapped, so these protons will form the beam stream with the velocity_{ }. Substantially, the new excitated kinetic Alfvén wave will evolve into Alfvén solitary wave due to the nonlinear interaction and dispersion influence of kinetic Alfvén wave. It is most possible that the heavy ions and parts of protons are trapped in the Alfvén solitary wave and obtain the velocity of_{ }. This scenario model can explain the observation and give the conditions of wave excited and ions trapped.The turbulent excitation of torsional Alfvén waves was presented by Luo, Wei and Feng (2002) on the basis of Lighthill-Stein theory. Due to the special properties of torsional modes, we can apply the theory to the inhomogeneous magnetic flux tube embedded in the solar photosphere, to evaluate the wave energy generated from the turbulent source in the convection zone. Torsional wave spectrum distribution along the

rcoordinate is achieved. In order to estimate the net wave energy transported to the chromosphere, they investigated the wave propagation and dissipation in the photospheric flux tube by simple phase mixing due to the inhomogeneity. Results for several cases with different model parameters are compared. Conclusions are drawn on the significant role of the energy carried by torsional Alfvén waves in the chromospheric and coronal heating, and the wave spectrum may be helpful in understanding the problem of footpoint azimuthal motion of coronal loops.

II. CORONA STRUCTUREThe study of coronal structure is an important topic in space physics and solar physics. It has been shown by observations that in most cases the corona has a variety of asymmetric multi-streamer structures. Since CMEs must pass the low coronal environment before moving into interplanetary space, the study of coronal structure is fundamentally important, especially for quantitatively understanding the changes in space weather. There have been a great number of numerical works devoted to the study of the steady structure of the corona and CMEs. Due to the lack of measurement of coronal magnetic field, it is a very interesting problem how to construct the coronal structure (including the magnetic field and plasma properties) based on the coronagraph observation. Li, Wei and Feng (2001), Li and Wei (2001) and Li and Wei (2000a) present a new method to numerically simulate complex asymmetric corona with multi-streamer structures on the basis of the coronagraph observation from SOHO/LASCO. In this method, the initial coronal magnetic field is separated into potential part and non-potential part. The potential part is first fitted by using the sum of magnetic multi-poles, whereas the no-potential part is approximated by the magnetic field induced by some properly fitted current densities. Then, the total field is numerically modified in terms of Maxwell's equations. Based on the initial magnetic fields obtained in such a way, various complex asymmetric coronal structures can be generated by solving MHD system. In order to verify this procedure, the 2-D coronal structures prior to the December 1996 CME and August 1999 CME events are computed. The numerical results are on whole in agreement with observations, and hence set proper backgrounds for further studying the propagation of CME in various coronal structures. Based on a 2-D MHD model and time-relaxation method, using projective characteristic boundary conditions on the inner and outer boundaries, the effects of the magnetic field intensity on the steady coronal structures are investigated by Li and Wei (2000b). The simulation results show that with the increasing dipolar magnetic field, the constraint of the magnetic field on the solar wind is strengthened, the degree of the openness of the closed magnetic field in lower latitude decreases, taking maximum near the point where Alfvenic Mach number is 1, and the velocity transition region is steepened. On the other hand, with the increasing heliospheric distance, the velocity transition region is also steepened. The result can be used to qualitatively explain the Ulysses observation in regions far from the Sun.

III. CORONAL MASS EJECTIONSIt is believed that coronal mass ejections (CME) and solar flares are main factors that can generate the geophysical effects near the earth. Thus, the study of CME and solar flares play a special role in space weather research. From the point of view of space weather, the progress of the study of solar coronal mass ejections (CME) is reviewed

^{ }by Wang (1999). The probable contribution of the coronal holes' peripheral structures to the coronal mass ejections is discussed by Luo (1999). The magnetic field of the active regions, interrelated CMEs, the burst events and solar proton events are analysed for five typical selected active regions by Zhang (1999). The correlation between CME and solar flare phenomena (H_{ }, X-ray and XUV radiation, geomagnetic storms and magnetic clouds, and radio radiations) is discussed by Cao (1999). The magnetic field environment of two eruptive filaments in AR 6891 and the solar-terrestrial physical effects after the eruptions are comparatively analyzed by Yang and Wang (1999). And it is found that the eruption of filaments close to large-scale unipolar regions may lead to violent coronal mass ejections (CME). Xia and Chen (1999) found that Type II and Type IV bursts may have very good correlation with CME. On the basis of the open and closed magnetic field and of the radio radiation theory, the relation between CMEs and associated radio bursts and solar flare are studied by Ji (1999).In order to simulate the propagation characteristics of disturbances in solar chromosphere, transition layer and corona, the propagation process of a disturbance produced by a local heating in vicinity of transition layer, by adopting a 2-D MHD model under a self-consistent non-thermal, non-uniform initial state is numerically discussed by Li and Wang (2000). The results indicate that the disturbance propagates to ambient plasma with a speed of local fast MHD wave and numerical results can fit in with that computed via local fast MHD wave, its characteristics could explain wave events observed by SOHO/EIT.

A boundary layer theory is used by Wang and Wang (2001) to study the influence of plasma pressure on the coupling behavior of double resistive tearing mode in a multiple current layer. Simple analytical expressions are obtained for the tearing instability parameter

_{ }under the first leading order, taking account of the effects of plasma pressure. The results show that the inclusion of plasma pressure does not change the physical properties of linearly coupled double tearing mode when the plasma_{ }. The plasma pressure influences qualitatively the nonlinear solution tendency of the double tearing mode. These effects however, are mainly exhibited on the non-coupling term, namely, on the result obtained from single tearing mode, not on the coupling term caused by the coupling of the two rational surface modes through the outer.

The propagation of magnetoacoustic waves in the solar atmosphere consisting of the photosphere, chromosphere and corona has been studied numerically (Zheng et al., 2001) by time-dependent multi-dimensional magnetohydrodynamic (MHD) simulation. Pressure disturbances are introduced at the bottom of the chromosphere and at the bottom of the corona, respectively. The computational results show that incurred fast and slow MHD waves propagate away from the source of the disturbances. The fast MHD wave propagates as an expansive wave in the radial direction, while the slow one steepens and it may evolve into a slow shock. The numerical results suggest that the extreme ultraviolet imaging telescope wave observed by SOHO and Moreton wave are a fast MHD wave propagating in the corona and in the chromosphere, respectively.

The global large amplitude waves propagating across the solar disk observed by the SOHO/Extreme Ultraviolet Imaging Telescope (EIT) are investigated by Wu et al. (2001). These waves appear to be similar to those observed in

_{ }in the chromosphere and which are known as “Moreton waves: associated with large solar flares. Uchida (see Wu et al., 2001 and references therein) interpreted these Moreton waves as the propagation of a hydromagnetic disturbance in the corona with its wavefront intersecting the chromosphere to produce the Moreton wave as observed in movie sequences of_{ }images. To search for an understanding of the physical characteristics of the newly observed EIT waves, Wu et al. (2001) constructed a three-dimensional, time-dependent, numerical MHD model by using the fractional step method. Measured global magnetic fields, obtained from the Wilcox Solar Observatory (WSO) at Stanford University, are used as the initial magnetic field to investigate hydromagnetic wave propagation in a three-dimensional spherical geometry. Using magnetohydrodynamic wave theory together with simulation, the authors identify these observed EIT waves as fast mode MHD waves dominated by the acoustic mode called magnetosonic waves. Their main results are as follows: (1) Comparison of observed and simulated morphology projected on the disk and the distance-time curves on the disk; (2) Three-dimensional evolution of the disturbed magnetic field lines at various viewing angles; (3) Evolution of the plasma density profile at a specific location as a function of latitude;4.Computed Friedrich's diagrams to identify the MHD wave characteristics.Using 2D MHD simulations, Xiang et al. (2000a) have compared CMEs associated with the perturbations of momentum and temperature respectively. Both are similar in the spatial structure, the evolution of the leading shock, the formation and the role of dark cavity and the characteristics of newly erupted materials near the solar surface. But they are different in the propagation velocity, the strength and the progress of radial evolution of the leading shock, the magnetic field strength and the action of the dark cavity, and the density of the following plasmoid.

Conceptually speaking, coronal mass ejections (CMEs) are usually originated in large closed magnetic field regions, which are found in the coronal streamer belt near the solar surface. Zhang and Wang (2000) use a thermal driving force so strong that portions of the closed magnetic fields are carried away by the strong disturbance. A CME-shock system is obtained in the inner corona. The legs of loop-like CMEs are again obtained at the interface between the coronal open and closed fields. However, there is no counterpart in outer space. The shock is a combined one with an intermediate shock near the equator at its early stage. Ultimately, it becomes a pure fast shock. A plasmoid with higher density and bubble-like magnetic fields is formed behind the MHD shock wave. It propagates at high speed. The results show that the high-speed plasmoid does not propel the MHD shock in front of it; rather the plasmoid forms behind the MHD shock.

Using a simple model for the onset of solar eruptions, how an existing magnetic configuration containing a flux rope evolves in response to new emerging flux is investigated by Lin, Forbes and Isenberg (2001). Their results show that the emergence of new flux can cause a loss of ideal MHD equilibrium under certain circumstances, but the circumstances, which lead to eruption, are much richer and more complicated than one might expect given the simplicity of the model. The model results suggest that the actual circumstances leading to an eruption are sensitive not only to the polarity of the emerging region, but also to several other parameters, such as the strength, distance, and area of the emerging region. It has been suggested by various researchers that emergence of new flux with an orientation which allows reconnection with the pre-existing flux (a process sometimes referred to as tether cutting) will generally lead to destabilization of the coronal or prominence magnetic field. Although the results of this paper can replicate such behavior for certain restricted classes of boundary conditions, there is no simple, universal relation between the orientation of the emerging flux and the likelihood of an eruption.

Lin and Forbes (2000) investigated how magnetic reconnection affects the acceleration of coronal mass ejections and how the acceleration in turn affects the reconnection process. To model the CME process, the authors use a two-dimensional flux rope model, which drives the ejection by means of a catastrophic loss of mechanical equilibrium. The model provides a method for relating the motion of the ejected material to the reconnection rate in the current sheet created by the erupting field. In the complete absence of reconnection the tension force associated with the current sheet is always strong enough to prevent the flux rope from escaping from the sun. However, the results imply that even a fairly small reconnection rate is sufficient to allow the flux rope to escape. Specifically, for a coronal density model that decreases exponentially with height they find that average Alfvén Mach number for the inflow into the reconnection site can be as small as 0.005 and still be fast enough to give a plausible eruption. The best fit to observations is obtained by assuming an inflow rate on the order of

_{ }. With this value the energy output matches the temporal behavior inferred for the long duration events often associated with CMEs.Hu and Liu (2000) presented a numerical study of large-radius coronal magnetic ropes, in which conserved quantities, such as the axial and annular magnetic fluxes and the magnetic helicity, were adopted to describe the physical properties of the ropes, and relationships were established between the geometrical parameters, including the height of the rope axis, the half-width of the rope, and the length of the vertical current sheet below the rope, and the conserved magnetic parameters mentioned above. Their results showed that the geometrical parameters increase monotonically and smoothly with increasing magnetic parameters, and no catastrophe occurs. In Hu and Liu (2000), the ambient magnetic field is a bipolar closed field, the magnetic flux rope emerges from the photosphere, and all the conserved quantities of the rope are controlled by a single emergence parameter, so that they can not be adjusted independently. Thus, their results failed to answer the question which of the three conserved quantities determines the equilibrium properties of the rope, and failed to establish a definite relation between the geometrical parameters and the magnetic helicity. In Hu, Jiang and Liu (2001), the authors continue to study this question by starting with a coronal flux rope in equilibrium embedded in the bipolar ambient magnetic field; at

_{ }, the axial and annular magnetic fluxes of the rope are abruptly changed, and then the system is let to evolve to a new equilibrium. The relation between the geometrical parameters and the magnetic helicity for the equilibrium is then established on this basis.

IV. MAGNETIC RECONNECTION PHENOMENAMagnetic reconnection phenomena are important in explaining many processes of solar physics and magnetospheric physics in observations, analyses and theories. Reconnection results in the rapid release of plasma energy stored in large-scale magnetic configuration, the formation of current sheet and magnetic cloud in solar corona. Therefore, it is an interesting topic in space physics.

In order to simulate the formation of coronal surges, the characteristics of magnetic reconnection caused by the resistive tearing instability in bipole-monopole magnetic field are studied numerically by Zheng, Su, Wang and Wu (2000) by using a two-dimensional, time-dependent, compressible magnetohydrodynamic model. The effect of pressure anisotropy on the magnetic reconnection of plasma is shown by Ma and Wang (2000) to suggest that mirror instability and tearing both affect the development of magnetic reconnection. Wei, Schwenn and Hu (1998) discover that magnetic reconnection phenomena exist in the interplanetary space basin on the analysis of magnetic field and plasma measurements in the period of 1975—1981 with 0.18 h average from Helios A and B. The observational examples for the possible occurrence of the turbulent magnetic reconnection in the solar wind are found by analysing Helios spacecraft's high-resolution data. Phenomena of turbulent magnetic reconnections in small scale solar wind are simulated by Wei, Hu, Schwenn and Feng (1999) with the code describing compressible 2-dimensional MHD flow by using an upwind-compact-difference scheme which has the third order accuracy. Numerical results prove that the turbulent magnetic reconnection process could occur in small scale interplanetary solar wind, which is a basic feature characterizing the magnetic reconnection in high-magnetic Reynolds number (

_{ }) solar wind. The configurations of the magnetic reconnection could evolve from a single X-line to a multiple X-line reconnection, exhibiting a complex picture of the formation, merging and evolution of magnetic islands, and finally the magnetic reconnection would evolve into a low-energy state. Its life-span of evolution is about one hour order of magnitude. The various magnetic and flow signatures are recorded in the numerical test for different evolution stages and along different crossing paths, which could in principle explain and confirm the observational samples from the Helios spacecraft. These results are helpful for revealing basic physical processes in the solar wind turbulence.Two types of dynamical reconnection processes are investigated by Wu, Wang and Zheng (2000) with two different spatial scale models: global and local scales. The global scale study invokes the anomalous resistivity reconnection process with spherical geometry and the local scale study invokes the tearing instability reconnection process with Cartesian geometry. Both cases are based on self-consistent, two dimensional planar MHD. The small-scale study consists of the evolution of a multi-polar complex region in a Cartesian coordinate system. The results show the formation of

_{ }surge and possible X-ray emission due to reconnection caused by plasma in-flow at the boundary. The global scale study describes a streamer and a flux-rope in a spherical coordinate system, and shows the formation of a tongue-shaped plasmoid due to field reconnection between the streamer and flux-rope.

The tearing mode instability and magnetic reconnection process in an anisotropic plasma are numerically studied by Ma and Wang (2001) by a two-dimensional three-component time-dependent compressible MHD simulation. It is found that the instability tends to become nonlinear saturated after a short period of linear growth. The growth rate will increase when the intensity of

pressure anisotropy

_{ }increases, while it will decrease with the decrease of the plasma_{ }and the augment in theycomponent by of magnetic field. In case of a large perpendicular anisotropy_{ }, when the magnetic island formed in the current sheet by magnetic reconnection becomes nonlinear saturation, there will be cavity structures formed near theXpoints. The cavities become larger gradually while the magnetic islands become smaller and vanish at last. In the plasma with a parallel anisotropy_{ }, the fire hose instability can only be excited in the central region of current sheet, and large magnetic island can not be formed in the current sheet.

Feng et al. (2000) used a special transformation to solve the magnetohydrodynamic equations and two classes of exact analytical time-dependent solutions of magnetic annihilation for incompressible magnetic fluid have been found. The solutions derived here possess scaling property with time as the scale factor. The current owns the soliton-like behavior in case of asymmetric inflow and the relevant evolutionary characteristics in the process of magnetic annihilation are also revealed.

The magnetic reconnection is an important physical process, which has been paid broad attention in solar physics and magnetospheric physics. From induction mechanism, the magnetic reconnections can be divided into two classes: the spontaneous and driven reconnections caused respectively by the resistive tearing mode instability and the plasma bulk moving towards the current sheet. Much work has been done on finding the interplanetary evidence of the closed structures formed by magnetic reconnection process in solar atmosphere, based on the inference from partial observations or numerical study of the coronal mass ejection (CME) by the symmetrically driven reconnection with incompressible MHD models. There is little work on the direct observation evidence and correlative numerical investigation. Meanwhile, the problem whether the magnetic reconnection process can occur in interplanetary space has not been answered yet. In a series of work, Wei, Hu and Feng (2001), Wei, Schwenn and Hu (2000) presented some observational evidence of magnetic reconnection in interplanetary space from Helios Spacecraft and numerical simulation results of the magnetic reconnections possibly occurring in interplanetary space. In order to confirm the observations, the possibility of magnetic reconnection in interplanetary space and to explain the occurrence of large scale magnetic reconnection phenomena under interplanetary conditions, this study include two parts: one devoted to the discussion of the possibility of the small scale turbulent reconnection in solar wind (Wei, Schwenn and Hu, 2000) and the other the asymmetrically driven magnetic reconnection produced by the plasma bulk moving towards interplanetary current sheet with the characteristic thickness

_{ }(Wei, Hu and Feng , 2001).

V. INTERPLANETARY TRANSIENT PHENOMENABy introducing the generalized Rankine-Hugoit jump conditions, new approaches for hydrodynamic and hydromagnetic interplanetary shock waves in solar wind are developed by Feng and Wei (1999a; 1999b). These multi-step or six step methods are helpful to the generation of a quick as well as operational forecasting diagnosis of space weather numerical prediction. New solution methods of shock dynamic in fluid mechanics and interplanetary physics are proposed by Feng and Wei (1999c) from the concept of viewing the discontinuity as shock manifold in the domain under consideration, which are especially original in its successful establishment of weak shock trajectory formula. Based on formerly existent numerical schemes for fluid mechanics and magnetohydrodynamics, a modified Lax-Friedrichs type difference scheme is proposed by Feng et al. (2002) for three-dimensional time-dependent ideal magnetohydrodynamics in spherical coordinates by taking account of the quality of difference schemes such as the convergence rate, stability, resolution

This second-order accurate scheme developed here has a high robustness of stability, and can capture the shock in about 2 grid meshes. Its simplicity also lies in that it does not need to split the associated Jacobian matrix and can avoid the calculation of the eigenvalues and eigenvectors. This scheme provides a potential to yield a quick numerical 3-D modeling of interplanetary shocks. Analytical solution approaches for nonlinear physical equations in magnetohydrodynamics are motivated by Feng et al. (2000) and Feng (2000)..Lu and Wei (1999) use a two-dimensional MHD model to numerically study the propagation of slow mode shocks propagating in open and closed fields, which shows that slow mode shocks in open magnetic field keep its basic properties with traveling through the interplanetary space. But in closed magnetic field they may turn into intermediate shocks while they propagate through helmet current sheet into the open magnetic field.

In Liu and Wei (2002), a statistical study of magnetic fluctuations near the front boundaries of magnetic clouds is approached with the method of minimum variance analysis, based on the data of Imp8 and Wind spacecraft. New discoveries are that: (1) Fluctuation anisotropy tends to increase across the front boundaries of magnetic clouds; (2) There exists a good correlation between the fluctuation anisotropy and the geomagnetic activity indices; (3) in some cases, although there is southward field component immediately after the front boundary, Kp index descends (or Dst index ascends) with a corresponding decrease of the fluctuation anisotropy; in other cases with no distinct southward field component, Kp index ascends (or Dst index descends) with a corresponding increase of the fluctuation anisotropy. Thus the authors suggest that the fluctuation anisotropy might be a useful indicator in diagnosing the magnetic activities of magnetic clouds.

Based on the analysis of the boundaries of 70 magnetic clouds from 1967 to 1998, with relatively complete spacecraft observations available, Wei et al. (2002) suggested that the magnetic cloud boundaries be boundary layers formed through the interaction between the magnetic clouds and the ambient medium. Most of the outer boundaries of the layers, with relatively high proton temperature, density and plasma β, are magnetic reconnection boundaries, while the inner boundaries, with low proton temperature, proton density and plasma β, separate the main body of magnetic clouds, which has not been affected by the interaction, from the boundary layers. The average time scale of the front boundary layer is 1.7 hours and 3.1 hours for the tail boundary layer. It is also found that the magnetic probability distribution function undergoes significant changes across the boundary layers. This new definition, supported by the preliminary numerical simulation in principle, could qualitatively explain the observations of interplanetary magnetic clouds, and could help resolve the controversy in identifying the boundaries of magnetic clouds. Our concept of the boundary layer may provide some understanding of what underlies the observations, and a fresh train of thought in the interplanetary dynamics research.

Ye et al. (2001), Ye, Wei and Feng (2000) employed non-free parameter scheme for three-dimensional time-dependent hydrodynamic model to compute the background fluid field and disturbance propagation associated with the coronal mass ejection occurring in May 1998. In this model, a density distribution similar to that of radial magnetic field on solar source surface determined from the HAO K-corona meter polarization brightness data is used as the inner boundary density distribution. The propagation of disturbance shows a sharp discontinuity without spurious oscillation and dispersion. Also, the numerical test shows that the scheme keeps a stable iteration without any artificial diffusion being added. On the other hand, the source code programmed with this hydrodynamic model can be used to model the specific coronal mass ejection when the magnetic field is not decisive in the solar wind flow.

Three-dimensional coronal structure of Carrington rotation 1935 at May 1998 is obtained by Ye et al. (2001a) by using a three-dimensional numerical model of ideal MHD equations with MacCormack II scheme. The initial magnetic field is constructed from photospheric observation at 1935 Carrington rotation by Legendre expansion. The numerical results show that: (1) the source surface magnetic field is nearly radial with non-radial component no more than

_{ }near the neutral line; (2) the radial magnetic field has no drastic variation except near the neutral line. The 3-D numerical coronal structure agrees qualitatively with Ulysses observation.Ye et al. (2001b) employed a 2-D MHD model with spherical coordinates

_{ }on the plane of sky is employed to simulate white light coronagraph figure observed SOHO mission at May 2, 1998. Numerical white light figure of the final self-consistent steady state, calculated with initial magnetic field constructed from a magnetic hexapole and several dipoles and with projected characteristic inner boundary condition, agrees basically with the observed coronal structure.In Feng, Wu et al. (2002), according to the characteristics of numerically modeling solar wind, a new numerical scheme of TVD type for magnetohydrodynamic equations in spherical coordinates is proposed by taking into account of the quality such as convergence, stability, resolution. This new MHD model is established by solving the fluid equations of MHD system with a modified Lax-Friedrichs scheme and the magnetic induction equations with MacCormack II scheme for the purpose of developing a combined scheme of quick convergence as well as of TVD property. To verify the validation of the scheme, the propagation of one-dimensional MHD fast and slow shock problem is discussed with the numerical results conforming to the existing results obtained by the piece-wise parabolic method. Under typical physical parameters on the solar surface, using a dipole as initiation, the steady state numerical results for the solar wind flow are reached by time-relaxation approach. This shows that this numerical model has potential application in modeling solar wind of complex magnetic field and realistic solar-interplanetary storms.

By a two-dimensional triggering model with concentrically circular closed magnetic field line structure, numerical research is made by Ye et al. (2002) for the asymmetric propagation feature of coronal mass ejection (CME) under two cases emerging at the solar northern latitudes 10º and 45º respectively. The numerical results can qualitatively explain some features of CME event observed by the spacecraft SOHO and show that: (1) under these two cases, the triggering model can initiate CME with an asymmetric close magnetic field structure; (2) closed magnetic structure of CME event will keep deflecting to the current sheet when it propagates away from the sun and this deflecting effect mostly happens within tens of solar radii before CME travels finally along the current sheet; (3) the triggering model with emerging sources at different locations can introduce CME events with different magnetic shapes. This shape happens to be circular and crescent when the triggering model emerges at the northern latitudes 10º and 45º, respectively.

Xiang et al. (2002) introduced the method to analyze planar MHD shocks to determine local parameters of interplanetary simulated MHD shocks. The method was based on the hypothesis that interplanetary MHD shocks are locally planar with no thickness when analyzing their local properties and the fact that the variations of the physical quantities can be neglected in the area where no shock perturbs within a few hours. Their method includes defining the location of the shock, selecting the state parameters on the upper and lower reaches of the shock, computing the shock's local parameters, and classifying the shock according to its upstream and downstream Alfvén Mach numbers. The formation and evolution of the leading shock and the formation and role of the cavity in CME events are investigated by Xiang et al. (2000b) using MHD simulation. Jiang, Wang and Xiong (2000) employed a two-dimensional MHD model to numerically study the May 5, 1980 CME event. By adding suitable perturbation of velocity and magnetic field, the numerical result is qualitatively consistent with observation.

In Shi, Wei and Feng (2001a), based on a three-dimensional MHD model, a relatively real interplanetary solar wind background during January 1997 event is obtained by using a set of initial and boundary conditions derived from some observations near the real space environment. Results show that the magnetic field at the source surface is equatorially asymmetric and is obviously tilted and warped. In addition, the plasma variables are asymmetric in relation to the event location. The numerical experiment for the different schemes of

_{ }shows that under an obviously tilted current sheet,_{ }can not be assumed to be zero. Based on these background results, the propagation process of disturbance is obtained. The numerical result is also compared with the WIND observations.Ulysses has been the first spacecraft to explore the high latitudinal regions of the heliosphere till now. During its first rapid pole-to-pole transit from September 1994 to June 1995, Ulysses observed a fast speed flow with magnitude reaching 700-800 km/s at high latitudinal region except

_{ }20º area near the elliptic plane where the velocity is 300-400 km/s. The observations also showed a sudden jump of the velocity across the two regions. In Shi, Wei and Feng (2001b), based on the characteristic and representative observations of the solar magnetic field and K-coronal polarized brightness, the large-scale solar wind structure mentioned above is reproduced by using a 3-D MHD model. The numerical results are basically consistent with those of Ulysses observations. The results also show that the distributions of the magnetic field and plasma number density on the solar surface play an important role in governing this structure. Furthermore, the 3-D MHD model used here has a robust ability to simulate this kind of large-scale structure. Based on observations from some satellites, observatories and the obtained definitely realistic solar wind ambient, the propagation and evolution of the January 1997 interplanetary CME are numerically studied using a 3-D MHD model (Shi, Wei and Feng, 2001c; Shi, Wei and Feng, 2000). The numerical results show that the parameters obtained near the earth are in agreement with observations of WIND satellite, especially the temporal_{ }behavior at 1AU.It is well-known that the interplanetary medium is characterized by a heliospheric current sheet (HCS), a heliospheric plasma sheet (HPS) in which the HCS is embedded, a slow solar wind astride the HCS and HPS, and a fast wind at high latitudes. In Hu and Jia (2001), in terms of perdendicular shock approximation, a simplified one-dimensional analysis is presented on the interaction between interplanetary shocks and the HCS, HPS, and slow solar wind. It is shown that the HCS alone is transparent for the shock and the transmission and thus does not affect the shock propagation at all, whereas the HPS is too thin to produce any appreciable effect on the shock transmission. On the other hand, the slow wind astride the HCS and HPS does exert a significant influence on the shock, which is weakened in strength after its transmission, and the shock speed is significantly reduced both during and after the transmission. The authors concluded that it is not the HCS and HPS but the slow wind associated with them that affects the interplanetary shock propagation. Meanwhile, both HCS and HPS are distorted in shape and internal structure under the action of shocks although the interaction of the HCS and HPS on interplanetary shocks is negligible.

Using two-dimensional and two-component MHD model in the equatorial plane, the influence of the interplanetary current sheet on the distribution of the density ratio, the gas-pressure ratio, the kinetic pressure jump, and the ratio of magnetic field strength along the shock front near 1 AU is investigated by Jia et al. (2001) and Yang et al. (2000). It is shown that the influence is significant only for the shocks with the disturbance source close to the current sheet. Moreover, this influence is stronger for shocks generated by disturbance sources on the eastern side of the current sheet. When the disturbance source is located at the eastern (western) side of the current sheet, the peak of the kinetic parameters of the shock deviates eastward (westward) relative to the source center normal, and the western deflection of the peak of the magnetic field strength ratio is weakened (strengthened). The influence of the current sheet is closely related to its effect on the defection of the fastest propagation direction of the shock. On the other hand, the omnipresent western deflection of the peak of the magnetic field strength ratio stems from the spiral structure of interplanetary magnetic field.

An interplanetary magnetic cloud (IMC) is an important solar-terrestrial connection event. It is an ideal object for the study of solar-terrestrial relations and space weather because the earth's space environment can be affected considerably during an IMC passage. An IMC was observed to pass the earth during October 18-20, 1995. Wind recorded its interplanetary characteristics at ~175

_{ }upstream of the earth's bow shock, and ~45 minutes later, Geotail, being near the nominal location of the dawn bow shock model, detected IMC-related multiple bow shock crossings. Using simultaneous measurements from Wind and Geotail, Wu, Chao and Lepping (2000) analyzed, with a semi-empirical bow shock model with two parameters, the bow shock motion caused by the interaction of the IMC with the magnetosphere during the passage. The bow shock motion predicted by the model, and hence the predicted Geotail bow shock crossings is compared with Geotail observations of the actual crossings. The results show that the observed multiple bow shock crossings, due to temporal variations of the upstream solar wind, can be well explained by the model-predicted bow shock motion.Burlaga, Richardson and Wang (2002) discussed the multiscale, statistical state of the speed observed near 60 AU from mid-1999 to mid-2000 by Voyager 2 (V2), and showed that a multifluid MHD model can explain the basic features of these observations. The probability distribution functions (PDFs) of the running speed differences (dVn) on scales from 1 day to 256 days provide a relatively complete description of some important properties of the large-scale speed fluctuations. On a scale of 1 or 2 days the PDFs of the positive and negative speed differences observed by V2 are approximately exponential, which is related to jump-ramp structures but might include a contribution from intermittent turbulence. On scales greater than 26 days (the solar rotation period) the PDFs of the speed differences are approximately Gaussian, i.e., quadratic on a semilog scale. On a scale of the order of several days, on which one sees jump-ramp structures in the speed profile, the PDF of the speed differences is cubic on a semilog scale. The standard deviation of dVn increases with increasing scale. The skewness and kurtosis of dVn are relatively large at small scales and decrease to Gaussian values at scales ≥16 days. The PDFs of speed differences and their lower moments versus scale near 60 AU were also derived from a speed profile predicted by the deterministic, spherically symmetric, multifluid, MHD model of Chi Wang, using ACE observations at 1 AU as the inner boundary conditions. Although the projected speed profile is not the same as the observed speed profile because ACE and Voyager are not radially aligned throughout the 1-year interval, the statistical properties of the observed profiles are essentially the same as the projected speed profiles. Significant evolution of the multiscale statistical properties of the solar wind speed fluctuations occurs between 1 and 60 AU; this evolution can be explained by a deterministic model.

The Bastille Day (14 July) 2000 CME is a fast, halo coronal mass ejection event headed earthward. The ejection reached Earth on 15 July 2000 and produced a very significant magnetic storm and widespread aurora. At 1 AU the Wind spacecraft recorded a strong forward shock with a speed jump from ～600 to over 1000 km s

^{-1}. About 6 months later, this CME-driven shock arrived at Voyager2(～63 AU) on 12 January 2001 with a speed jump of ～60 km s^{-1}. In order to study the shock propagation of this CME in the outer heliosphere, Wang, Richardson and Burlaga (2001) employed a 2.5-D MHD numerical model, which takes the interaction of solar wind protons and interstellar neutrals into account, to investigate the shock propagation in detail and compare the model predictions with the Voyager2observations. The Bastille Day CME shock undergoes a dramatic change in character from the inner to outer heliosphere. Its strength and propagation speed decay significantly with distance. The model results at the location of Voyager2 are in good agreement with in-situ observations. Wang, Richardson and Paularena (2001) used numerical models, which include the mutual influence of the interstellar and solar wind plasma and the interstellar neutral hydrogen to study the propagation of the strong CME shock to the locations of Voyager 1 and 2, the termination shock, and the heliopause. They predicted that Voyager 2 will see a relatively strong forward shock with a speed jump of ～65 km s^{-1}and a compression ratio of～1.9 in January 2001. Voyager 1 will see a similar shock in March 2001 with a speed jump of～60 km s^{-1}and a compression ratio of ～1.8. This strong shock will continue its journey through the heliosphere and is expected to arrive at the termination shock and heliopause in March and December 2001, respectively. The impingement of this strong interplanetary disturbance on the denser plasma past the heliopause could trigger the next 2-3 kHz heliospheric radio emission event, which would then occur at the end of 2001.Between days 175 and 180 (June 24 through 29) of 1999, the PLS instrument on Voyager 2 observed alpha particle enhancements with fractional percentages of alpha to proton number densities exceeding 10%. Ulysses (located at 5.3 AU) observed at least two candidate source features for these enhancements. To identify the correct source structure, a 1D MHD model was used by Paularena, Wang et al. (2001) to propagate the Ulysses plasma data to the Voyager radial position (58.2 AU). An ICME-related alpha enhancement observed by Ulysses beginning on day 331 (November 27), 1998 appears to be the correct feature. While a speed jump and cosmic ray decreases were observed by Ulysses in conjunction with this alpha enhancement, the timing of these features differed markedly at Voyager 2. The speed jump arrival-time difference is due to the faster propagation of the shock relative to the rest of the ejecta. It is unclear what mechanism is responsible for the delay in the cosmic ray decrease. Nevertheless, we have demonstrated that alpha enhancement signatures of ICMEs can be used to track these features to heliospheric distances > 50 AU.

Wang, Ye et al. (2002) identified 132 Earth-directed coronal mass ejections (CMEs) based on the observations of the Large Angle Spectroscopic Coronagraph (LASCO) and Extreme Ultraviolet Imaging Telescope (EIT) on board of Solar and Heliospheric Observatory (SOHO) from March 1997 to December 2000 and carried out a statistical study on their geoeffectiveness. The following results are obtained: (1) only 45% of the total 132 Earth-directed halo CMEs caused geomagnetic storms with Kp≥5; (2) the initial sites of these geoeffective halo CMEs are rather symmetrically distributed in the heliographic latitude of the visible solar disc, while asymmetrical in longitude with the majority located in the west side of the central meridian; (3) the frontside halo CMEs accompanied with solar flares (identified from GOES-8 satellite observations) seem to be more geoeffective; (4) only a weak correlation between the CMEs projected speed and the transit time is revealed. However, for the severe geomagnetic storms (with Kp≥7), a significant correlation at the confidence level of 99% is found by Wang, Ye et al. (2002).

A so-called “ISF” prediction method for geomagnetic disturbances caused by solar wind storm blowing to the earth is suggested by Wei et al. (2002). The method is based on a combined approach of solar activity, interplanetary scintillation (IPS) and geomagnetic disturbance observations in 1966—1982, dynamics of disturbance propagation and fuzzy mathematics. Prediction test has been made for 24 larger geomagnetic disturbance events that produced space disasters during the period of 1980—1998, in which the three dimensional propagation characteristics, the search of the best close degree of each radio source and the influence of the south-north components of interplanetary magnetic fields have also been considered. The main results are: (1) for onset time of the geomagnetic disturbance, events with the relative error

_{ }≤10% between the observation_{ }and the prediction_{ }, account for 45.8% of all events, ≤30% for 78.3% and ＞30% for only 21.7%;2.as for the magnetic disturbancemagnitude, events with the relative error

_{ }≤10% between the observation_{ }and the prediction_{ }, account for 41.6% of all events, ≤30% for 79% and ≤45% for 100%. For example, the prediction test of April-May event in 1998 indicates that_{ },_{ }. The result shows that the prediction method suggested in this paper has encouraging prospects in improving geomagnetic disturbance prediction in space weather events.Lu and Zank (2001) suggested a new approach to the time-dependent anisotropic propagation of interstellar pickup ions in the interplanetary medium. The model includes the effects of adiabatic focusing in a radial magnetic field, adiabatic deceleration, anisotropic pitch angle scattering, convection in the solar wind, and the continual injection of newly ionized particles. It is assumed that pickup ions experience difficulty in scattering through 90º. A two-timescale scattering operator is introduced together with a generalized hemispherical model for the transport of pickup ions. The approach described here significantly extends the previous studies in that the pitch angle dependence of the pickup ions is mot assumed to be of the form

_{ }(H(μ) is the Heaviside step function) from the outset. Wang and Richardson (2001) used a three-fluid approach to study the energy partition between solar wind protons and pickup ions in the distant heliosphere. For simplicity, they introduced a parameter, the energy partition ratioe, to represent the division of the total energy provided by the pickup process between the solar wind protons and pickup ions. We find that only a small percentage of this total thermal energy is needed to heat the solar wind proton to produce the observed temperature profile. As expected, the higher the interstellar neutral hydrogen density, the smaller the percentage. The energy partition ratio has little effect on the slowdown of the solar wind and the pickup ion density distribution in the outer heliosphere, which is primarily controlled by the interstellar neutral hydrogen density.

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* This work was jointly supported by the National Natural Science Foundation of China (Grant No. 49925412 and Grant No. 49990450)