Non-linear momentum diffusion of heliospheric cosmic rays

Besides parallel and perpendicular spatial diffusion, momentum diffusion can be seen as the third important process of cosmic ray transport. In this paper, the recently derived weakly non-linear theory is applied for a simple quasi-magnetostatic composite model to determine the momentum diffusion coefficient. It is demonstrated that non-linear effects are essential and cannot be neglected. Therefore, the weakly non-linear transport theory has to be preferred over the traditional quasi-linear approach. Within this improved theory, we find for the rigidity dependence of the momentum diffusion coefficient   A ∼ R ^1.4  for relativistic and   A ∼ R ^0.4  for non-relativistic cosmic rays.     

Modelling heliospheric current sheet drift in stochastic cosmic ray transport models

Drifts are one of the major cosmic ray modulation mechanisms in the heliosphere. Three types of drifts occur in the background heliospheric magnetic field, namely curvature, gradient and current sheet drifts. The last component occurs because of the switch in magnetic field polarity across the heliospheric current sheet and is the main topic of study. We discuss and implement a new approach to model drifts in a numerical modulation model. The model employs stochastic differential equations to solve the relevant transport equation in five (three spatial, energy and time) dimensions. What is of interest is the fact that the model can handle current sheet tilt angles up to the theoretical maximum of α=90° and still remain numerically stable. We use the additional insights gained from the numerical model to investigate the effectiveness of drifts along the current sheet by examining the relationship between the current sheet path length and the cosmic ray propagation time. It is found that diffusion can disrupt the drift process very effectively, leading to diffusive short circuiting of the current sheet by the cosmic rays.     

Effect of solar heliospheric parameters on different components of daily variation in cosmic rays

In the present work the data of three different neutron monitoring stations, Deep River, Tokyo and Inuvik located at different geomagnetic cutoff rigidities and altitudes has been harmonically analysed for the period 1980–1993, 1980–1990 and 1981–1993 respectively to investigate for a comparative study of diurnal, semi-diurnal and tri-diurnal anisotropies in cosmic ray (CR) intensity in connection with the change in IMF Bz component and solar wind velocity on 60 quietest days. It is observed that the amplitude of first harmonic is highly anti-correlated to the solar wind velocity during the period of high-speed solar wind stream (HSSWS) epoch on quiet days for three neutron monitor stations at different geomagnetic rigidity thresholds. During quiet days the amplitude of all the three harmonics significantly deviates on the onset of HSSWS epoch, whereas the direction of the anisotropy of all the three harmonics remains time invariant at three different cut off rigidity stations. The amplitude as well as the direction of anisotropy of all the three harmonics does not have time variation characteristics associated with Bz component of IMF on geo-magnetically most quiet days.     

Acceleration of anomalous cosmic rays at the heliospheric termination shock

Astronomy Letters - The acceleration of anomalous cosmic rays (ACRs) at the heliospheric termination shock and their influence on the shock structure and location are analyzed in terms of a...     

Influence of solar heliospheric parameters on cosmic rays anisotropy

In the present work the cosmic ray data of three different neutron monitoring stations, Deep River, Inuvik, and Tokyo, located at different geomagnetic cutoff rigidities and altitudes have been harmonically analyzed for the period 1980–95 for a comparative study of diurnal semi-diurnal and tri-diurnal anisotropies in cosmic ray intensity in connection with the change in interplanetary magnetic field Bz component and solar wind velocity on 60 quietest days. It is observed that the amplitudes of all the three harmonics increase during the period 1982–84 at all the stations during the high speed solar wind stream epoch and remain low during the declining phase of the stream. The amplitudes of the three harmonics have no obvious characteristics associated with the time variation of magnitude of the Bz component. The phases of all the three harmonics have no time variation characteristics associated with solar wind velocity and Bz. Published in Astrofizika, Vol. 49, No. 4, pp. 651–664 (August 2006).     

Radio mapping of the heliospheric current sheet

Synoptic plots of solar radio noise storms in the interval 1973 to 1984 are described. The dividing line between opposite noise storm polarities appears to be a good representation of the heliospheric current sheet out to displacements in latitude of ± 50° from the solar equator. This result is surprising, because noise storms are closely associated with closed magnetic field regions near sunspots. The possibility that noise storm polarity is determined by mode coupling high in the corona, where field lines are open, can be ruled out by the available evidence. This leads us to conclude that it is the clustering in longitude of active region complexes which determines the sector structure of the interplanetary magnetic field.     

Radio mapping of the heliospheric current sheet

Synoptic plots of solar radio noise storms in the interval 1973 to 1984 are described. The dividing line between opposite noise storm polarities appears to be a good representation of the heliospheric current sheet out to displacements in latitude of ～ ± 50° from the solar equator. This result is surprising, because noise storms are closely associated with closed magnetic field regions near sunspots. The possibility that noise storm polarity is determined by mode coupling high in the corona, where field lines are open, can be ruled out by the available evidence. This leads us to conclude that it is the clustering in longitude of active region complexes which determines the sector structure of the interplanetary magnetic field.     

Regularities of variation of the heliospheric current sheet orientation during the solar activity cycle

Evolution of spatial orientation of the heliospheric current sheet (HCS) has been studied in detail using synoptic maps of the HCS configuration over the period 1971–1989. Analysis involves all phases of the sunspot cycle except for two years of maximum solar activity. The helmet-like coronal streamers are confirmed to be structural elements of the HCS. The r.m.s. deviation of a real HCS configuration from a plane does not exceed about 10° during most of the sunspot cycle length. Hence, minimum-type corona should be observed every time the HCS is oriented parallel to the line-of-sight, independent of the cycle phase. Such occasions have been observed apart from the sunspot minimum epochs at the solar eclipses of 31 August, 1932 and 11 July, 1991.Regularities of variation of the two following parameters of the HCS orientation have been revealed: obliquity to the solar equator plane (heel or tilt) and longitudinal orientation (yawing). Behaviour of the above parameters is repeated in different cycles. However, heeling and yawing occur probably not synchronous but rather independent of one another.     

The three-dimensional geometry of the heliospheric current sheet

The three-dimensional geometry of the heliospheric current sheet seen from fixed points in interplanetary space is constructed for idealized (sinusoidal) magnetic neutral lines (equators) and for an observed magnetic equator on the basis of the “kinematic method” developed by Hakamada and Akasofu (1982). The cross-sections of the wavy current sheet at distances 1, 2 and 5 a.u. are also constructed for the idealized magnetic neutral lines.     

Earth's equatorial ionosphere and the heliospheric current sheet

Evidence is presented to show that during epochs of high sunspot activity, the duration of manifestation of equatorial spread-F (ESF) irregularities in the Earth's equatorial ionosphere undergoes a systematic modulation around the times of crossing of the heliospheric current sheet by the Earth. The modulation which is assessed as an indirect and geomagnetic activity-associated effect, is characterised by an enhancement in the duration of ESF conditions prior to the current sheet crossing and a reduction thereafter. It is suggested that the observed response of the equatorial ionosphere to the current sheet passage is primarily a manifestation of the geomagnetic activity related modifications in the equatorial east-west electric field in the post-sunset period.     

Intensity of galactic cosmic rays in the early sun epoch

The process of heliospheric modulation of intensity of galactic cosmic rays is investigated by solving the transport equation. The spatial-energetic distribution of cosmic rays in the present epoch and in the past is analyzed. It is demonstrated that the particle density and the energy density of cosmic rays in the Solar System in the distant past were much lower than the corresponding current values. The cosmic ray intensity modulation in the early heliosphere was especially strong in the case of low-energy particles.     

Adiabatic deceleration of cosmic rays near their sources

Every plausible source of cosmic rays yields a high flux of cosmic rays near the source. The high flux leads to plasma effects that cause scattering of the cosmic rays, coupling to the interstellar gas and hence to adiabatic deceleration. The cosmic rays are released from the gas only when their pressure has fallen to the cosmic-ray pressure near the Sun multiplied by a factor between 10 and 100. I discuss a model aimed to minimize the deceleration before the cosmic rays are released. The volume which cosmic rays occupy before scattering is maximized by injection into a large but thin disk. Even then, deceleration is reduced only to a factor of two. Such deceleration should cause quasi-supernova remnants somewhat resembling the Cygnus loop but associated with much younger pulsars. Since both the required model and the predicted observations cause difficulties, the problem of adiabatic deceleration remains severe.Work supported by NSF grant GP-34742.     

Evolution and nature of north-south asymmetry in the heliospheric current sheet

The nature and evolution of north-south asymmetry in the heliospheric current sheet (HCS) has been investigated using solar and interplanetary magnetic field (IMF) observations for the past few solar cycles. The mean heliographic latitude of the HCS (averaged over the solar longitude) a ₀ is found to be non-zero during many solar rotations indicating that the large-scale solar magnetic field is more ordered in a system where the origin is shifted away from the centre of the Sun. We have shown that the asymmetry in HCS manifests in different forms depending on the transition heliographic latitude of the reversal of dominant polarity of the IMF ( _T) and the difference in the maximum latitudinal extension of the HCS in the two solar hemispheres (). The classification of the observed asymmetry during 1971–1985 and its effect on IMF observations near Earth has been studied. We have also inferred the sign of _T during 1947–1971 using inferred IMF polarity data. The observed sign reversals of _T suggest the importance of periodicities less than the solar cycle period to be associated with the evolution of asymmetry in HCS. Asymmetry in sunspot activity about the solar equator does not seem to relate consistently well with the asymmetry in HCS about the heliographic equator.     

North-south asymmetry in the heliospheric current sheet and the IMF sector structure

It is shown that in a heliomagnetic field the presence of a magnetic quadrupole in addition to a magnetic dipole introduces a north-south asymmetry in the heliospheric current sheet (HCS) about the heliographic equator. The dominant polarity of the interplanetary magnetic field (IMF) for the above type of current sheet reverses sign at a transition latitude _T, which lies in a heliohemisphere opposite to the one in which the HCS has more heliolatitudinal extension. The position of _T in the heliosphere and the north-south asymmetry introduced in the HCS change with the relative phase of the dipole and quadrupole components present in the solar magnetic field. The effect of the above type of asymmetric HCS in the IMF mean sector width is evaluated and the results are in agreement with the observations during the minima of solar cycle 21.     

Galactic cosmic ray distribution in the simplest model of termination shock near the heliospheric boundaries

The termination shock at the heliospheric boundary is simulated in terms of a two-layer turbulent medium for which the average radial component of solar wind velocity is nonzero inside the heliosphere and zero for external magnetic inhomogeneities. Galactic cosmic rays (GCRs) are scattered more strongly in the solar wind than in the interstellar medium. A boundary value problem for density is defined to describe GCR propagation in the given two-layer medium. The exact analytical solution of it is derived. The phase density and GCR fluxes in the whole range of the particle energies, as well as the degree of anisotropy of high-energy GCRs, are determined. The qualitative agreement of theoretical calculations and observed GCR distributions is obtained. In particular, in the region near the termination shock, an increase in the high-energy particle density and a decrease in the low-energy particle density are observed.     

Azimuthal structure of the solar wind velocity andK-corona brightness in the heliospheric current sheet

The solar wind velocity near Earth shows systematic structure in and around the heliospheric current sheet. The solar wind velocity measurements at IMF sector boundary crossings at 1 AU during 1972–1977 have been used to infer the azimuthal structure of the solar wind velocity in the current sheet. We found that the solar wind velocity in the in-ecliptic portion of the current sheet varies from longitude to longitude, where it originates from the corona. Also, the yearly average value of solar wind velocity in the HCS is found to vary with the phase of the solar cycle; with a maximum value around 1974. TheK-corona brightness on the source surface corresponding to the IMF sector boundary crossings during the period of study also shows a similar but opposite pattern of variation when the data are averaged over a long period. However, this relation is not observed when we considered them individually. So, we conclude that there exists a longitudinal variation of solar wind velocity in the heliospheric current sheet.     

WKB approach to the problem of MHD shock propagation through the heliospheric current sheet

The interplanetary shock wave front shape and intensity are calculated numerically by means of the WKB-approach, with nonlinear effects taken into account. The solar flare is modelled as an isotropic point explosion at the solar wind base. The heliospheric current sheet (HCS) is represented by a radially diverging stream with a higher plasma concentration and a lower wind speed. Fast magnetosonic shock wave propagation along the HCS is connected with the effect of regular accumulation of the wave energy in the vicinity of the HCS. In this place the wave intensity is increased, and the corresponding front fragments go ahead to form a shock-wave forerunner as a pimple. The primple, in turn, is located inside a quite a large, but less-contrast, dimple in the wave surface. This dimple approximately coincides with the HCS stream contours. If the flare is outside the HCS boundaries, the picture discussed above is conserved, but asymmetry effects arise. Thus the interplanetary shock is stronger when the Earth's observer and the flare are on the same side of the HCS and is weaker in the opposite case.     

A mechanism for the formation of plasmoids and kink waves in the heliospheric current sheet

Satellite observations of the heliospheric current sheet indicate that the plasma flow velocity is low at the center of the current sheet and high on the two sides of current sheet. In this paper, we investigate the growth rates and eigenmodes of the sausage, kind, and tearing instabilities in the heliospheric current sheet with the observed sheared flow. These instabilities may lead to the formation of the plasmoids and kink waves in the solar wind. The results show that both the sausage and kink modes can be excited in the heliospheric current sheet with a growth time 0.05–5 day. Therefore, these modes can grow during the transit of the solar wind from the Sun to the Earth. The sausage mode grows faster than the kink mode for < 1.5, while the streaming kink instability has a higher growth rate for > 1.5. Here is the ratio between the plasma and magnetic pressures away from the current layer. If a finite resistivity is considered, the streaming sausage mode evolves into the streaming tearing mode with the formation of magnetic islands. We suggest that some of the magnetic clouds and plasmoids observed in the solar wind may be associated with the streaming sausage instability. Furthermore, it is found that a large-scale kink wave may develop in the region with a radial distance greater than 0.5–1.5 AU.Also at Department of Earth and Space Science, University of Science and Technology of China, Hefei Anhui 230029, China.     

On the stationary configuration of the heliospheric sheet

The expansion of solar coronal plasma is considered for the model described in Koutchmy et al. (1999). In addition to a spherical solar surface, the initial configuration represents a heliospheric sheet of dense plasma in the dipole equatorial plane. The heliospheric-sheet current decreases with distance as 1/r ², with its sign being opposite to the sign of the initial-dipole current. The latter follows from the fact that the plasma sheet is denser than the surrounding corona and that the equilibrium condition for the sheet in the gravitational and magnetic fields is satisfied. The field lines of this configuration are nearly straight. We have obtained a general solution of the steady-state MHD equations, which depends not only on distance r but also on latitude θ. Applicability of the solution to interpreting observational data, in particular, those obtained from the Ulysses spacecraft, is discussed.     

Interplanetary disturbances produced by a simulated solar flare and equatorially-fluctuating heliospheric current sheet

A recently developed nonplanar, time-dependent magnetohydrodynamic (MHD) model (Wuet al., 1983) was used to study the interplanetary disturbances produced by a compound event in the heliosphere. That is, a steady-state interplanetary medium is first disturbed by a simulated equatorially-fluctuating current sheet. After a few days (100 hr), the disturbed interplanetary medium is again perturbed by a solar-flare-generated shock wave. Attention is directed toward the differences that are caused by the presence of the equatorially-fluctuating (warped) current sheet.