Mean free paths of energetic charged particles parallel and antiparallel to the interplanetary magnetic field

A new method to calculate the mean free paths of energetic particles propagating parallel and anti-parallel to the interplanetary magnetic field, based on quasi-linear theory and the complex spectral polarization analysis of the field, is developed and presented. Applications of the method using HEOS 2 (1 AU), Pioneer 10 (5 AU), Pioneer 11 (20 AU), ICE (Giacobini-Zinner's comet) data have been made, showing that: (a) The mean free paths parallel and anti-parallel to the field can be completely different in various regions of the interplanetary medium and different time periods. (b) Particles are preferentially scattered in one direction. (c) The parallel and anti-parallel mean free paths become equal at certain energy. Comparisons with the results from another computational method are made.     

Drift motion and perpendicular diffusion of energetic particles in interplanetary space based on spacecraft data

A realistic model of the interplanetary magnetic field (IMF) is constructed based on measurements taken by Pioneer 10 magnetometer at 5 AU. Energetic particle (0.1–100 MeV) propagation in this field is studied by a computer simulation of its motion in order to calculateK , the perpendicular diffusion coefficient, and V _D the average drift velocity of an ensemble of particles. Determinations ofK lie in the range 3×10¹⁹–8×10²⁰ cm² s^–1 for the energies considered and they show that perpendicular diffusion may be an important process at these heliodistances when compared with parallel diffusion results obtained by similar techniques, contrary to what was previously thought. Drift velocity calculations are very close to predictions of guiding centre theory (within 30%) suggesting that this theory can be applied in the IMF. This result shows that gradient and curvature drifts can be present even in a highly perturbed field and thus they can have some influence in cosmic ray modulation.     

Study of parallel diffusion of energetic particles in the interplanetary medium using spacecraft data at 1 and 5 AU

Energetic particle (1–100 MeV) pitch angle scattering in the Interplanetary Magnetic Field (IMF) is studied using spacecraft magnetometer data at 1 AU (IMP 7 and HEOS 2) and at 5 AU (Pioneer 10). Particle trajectories are followed by a computer simulation of their movement in a realistic model of the IMF. Determination of the pitch angle diffusion coefficient at 1 AU (D ) leads to a parallel mean free path which is roughly independent of particle energy, 0.03 AU. At the lowest energy our result is at least a factor of 3 larger than the predictions of quasi linear theory. Results at 5 AU lead to a radial mean free path which is between 2 to 6 times smaller than at 1 AU, probably indicating a greater importance for perpendicular diffusion at large heliodistances. In fact a roughly constant radial mean free path ( _r 0.01 AU) is obtained when the contribution of perpendicular diffusion at 5 AU is taken into account (Moussaset al., 1981).     

Numerical evaluation of statistical acceleration for energetic particles in the interplanetary medium at 2.5 and 5.0 AU

Numerical integration of particle trajectories is performed to evaluate the statistical acceleration coefficients D _TT for 1 to 100 MeV protons in a solar wind corotating interaction region (CIR) seen at 2.5 and 5.0 AU. Acceleration is followed in the solar wind reference frame and is due to random wave-particle interactions and to random drift motion in moderate scale field gradients. D _TT due to the first effect reaches a peak value of 4 × 10 ^–7 MeV² s^–1 post shock at 10 MeV at 2.5 AU consistent with estimates based both upon cyclotron resonance and transit time damping theory. D _TT from the second effect is less well established but is of the order of 10^–7 MeV² s^–1 at 10 MeV, 5 AU. A comparison is made between the time constant for statistical acceleration within this CIR and estimates for diffuse shock acceleration and adiabatic deceleration. All three time constants are of the same order, but deceleration is faster than shock acceleration which in turn is faster than statistical acceleration.     

Unified theory of the interplanetary magnetic field

A simple model is used to present a unified picture of the polarity pattern of the interplanetary magnetic field observed during the solar cycle. Emphasis in this paper is on the field near solar maximum. The heliographic latitude dependence of the dominant polarity of the interplanetary magnetic field is explained in terms of weak poloidal (dipolar) field sources in the sun's photosphere. Unlike the Babcock theory, the author hypothesizes that the dipolar field exists at equatorial latitudes (0–20°), too, (as well as in polar regions) and that the major source of the interplanetary magnetic field observed near the ecliptic plane is the dipolar field from equatorial latitudes. The polarity of the interplanetary field data taken in 1968 and in the first half of 1969 near solar maximum may possibly be explained in terms of a depression of the dipolar field boundary in space. The effect on the solar wind of the greater activity in the northern hemisphere of the sun that existed in 1968 and in the first half of 1969 is believed responsible for this hypothesized depression, especially near solar maximum, of the plane separating the + and - dipolar polarity below the solar equatorial plane in space. Predictions are made concerning the interplanetary field to be observed near the ecliptic plane in each portion of the next solar cycle.     

The generation of a large-scale Galactic magnetic field by electric currents of energetic particles

We consider the generation of a magnetic field in the Galaxy by the electric currents excited by cosmic-ray particles in the disk and halo. We assume that the sources of relativistic particles are distributed continuously and uniformly in the Galactic disk, their total power is equal to the observed value, and the particles themselves undergo anisotropic diffusion in a homogeneous medium. We take into account the differential rotation of the Galactic disk but disregard the turbulence gyrotropy (the α effect). The strength of the generated magnetic field in our model is shown to strongly depend on the symmetry of the relativistic proton and thermal electron diffusion tensors, as well as on the relations between the tensor components. In particular, if the diffusion is isotropic, then no magnetic field is generated. For the independent tensor components estimated from observed parameters of the Galactic medium and with a simultaneous allowance made for the turbulent field dissipation processes, the mechanism under consideration can provide an observable magnetic-field strength of the order of several microgauss. This mechanism does not require any seed magnetic field, which leads us to suggest that relativistic particles can give an appreciable and, possibly, determining contribution to the formation of the global Galactic magnetic field. However, a final answer can be obtained only from a nonlinear self-consistent treatment, in which the symmetry and magnitude of the particle diffusion tensor components should be determined together with the calculation of the magnetic field.     

Comparison of the mean photospheric magnetic field and the interplanetary magnetic field

The mean photospheric magnetic field of the sun seen as a star has been compared with the interplanetary magnetic field observed with spacecraft near the earth. Each change in polarity of the mean solar field is followed about 4 1/2 days later by a change in polarity of the interplanetary field (sector boundary). The scaling of the field magnitude from sun to near earth is within a factor of two of the theoretical value, indicating that large areas on the sun have the same predominant polarity as that of the interplanetary sector pattern. An independent determination of the zero level of the solar magnetograph has yielded a value of 0.1±0.05 G. An effect attributed to a delay of approximately one solar rotation between the appearance of a new photospheric magnetic feature and the resulting change in the interplanetary field is observed.     

Power spectra of the interplanetary magnetic field

Power spectra based on Pioneer 6 interplanetary magnetic field data in early 1966 exhibit a frequency dependence of f ^–2 in the range 2.8 × 10^–4 to 1.6 × 10^–2 cps for periods of both quiet and disturbed field conditions. Both the shape and power levels of these spectra are found to be due to the presence of directional discontinuities in the microstructure (< 0.01 AU) of the interplanetary magnetic field. Power spectra at lower frequencies, in the range of 2.3 × 10^–6 to 1.4 × 10^–4 cps, reflect the field macrostructure (> 0.1 AU) and exhibit a frequency dependence roughly between f ^–1 and f ^–3/2. The results are related to theories of galactic cosmic-ray modulation and are found to be consistent with recent observations of the modulation.     

The effect of interplanetary acceleration on the propagation of energetic solar particles in prompt events

Crank-Nicholson solutions are obtained to the time-dependent Fokker-Planck equation for propagation in the interplanetary medium following a point in time injection of energetic solar particles and including the acceleration terms $$\frac{\partial }{{\partial T}}\left( {D_{TT} \frac{{\partial U}}{{\partial T}}} \right) - \frac{\partial }{{\partial T}}\left( {\frac{{D_{TT} U}}{{2T}}} \right)$$ . The diffusion coefficient in kinetic energyD _TT is allowed to be either independent of radial distance,R(AU), or follow the lawD _TT=D₀T²R ₀ ² /(A²+R²) in either case with the 1 AU value ofD _TT at 10 MeV ranging between 10^?4 (MeV)² s^?1 and zero. The spatial diffusion mean free path at the Earth's orbit is fixed at λ_‖ AU at 10 MeV according to numerical estimates made by Moussas and Quenby. However, a variety ofR dependences are allowed. Reasonable agreement with experimental data out to 4 AU is obtained with the above values ofD _TT and the spatial diffusion coefficientK _r=K₀R^?2 forR«1 andK _r=K₀R^0.4 forR»1 AU. It is only in the decay phases of prompt events as seen at 2–4 AU that significant differences in the temporal behaviour of the events can be distinguished, depending on the value ofD _TT chosen within the above range. Experimental determination of the decay constant is difficult.     

The interplanetary magnetic field environment at Mercury's orbit

Mercury is exposed to the most dynamic heliospheric space environment of any planet in the solar system. The magnetosphere is particularly sensitive to variations in the interplanetary magnetic field (IMF), which control the intensity and geometry of the magnetospheric current systems that are the dominant source of uncertainty in determinations of the internal planetary magnetic field structure. The Magnetometer on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft has made extensive magnetic field observations in the inner heliosphere over the heliocentric distances of Mercury's orbit, between 0.31 and 0.47 AU. In this paper, Magnetometer data from MESSENGER, obtained at rates of 2 and 20 vector samples per second, are used together with previous observations in the inner heliosphere by Helios and at Earth by the Advanced Composition Explorer, to study the characteristics of IMF variability at Mercury's orbit. Although the average IMF geometry and magnitude depend on heliocentric distance as predicted by Parker, the variability is large, comparable to the total field magnitude. Using models for the external current systems we evaluate the impact of the variability on the field near the planet and find that the large IMF fluctuations should produce variations of the magnetospheric field of up to 30% of the dipole field at 200 km altitude, corresponding to the planned periapsis of MESSENGER's orbit at Mercury. The IMF fluctuations in the frequency range are consistent with turbulence, whereas evidence for dissipation was observed for . The transition between the turbulent and dissipative regimes is indicated by a break in the power spectrum, and the frequency of this break point is proportional to the IMF magnitude.     

Directional discontinuities in the interplanetary magnetic field

It is shown that the interplanetary magnetic field has different characteristics on different scales, and it is noted that a given physical theory may not be applicable or relevant on all scales. Four scales are defined in terms of time intervals on which the data may be viewed. Many discontinuities in the magnetic-field direction are seen on the mesoscale ( 4 days, 1 AU). The characteristics of such directional discontinuities which were observed by Pioneer 6 during the period December 16, 1965-January 4, 1966 are presented, with special emphasis on their distribution in time. Previously, it was suggested that such discontinuities are simply boundaries of spaghetti-like filaments extending from the sun to the earth. Here it is shown that on the mesoscale unique filaments with sharp boundaries containing well-ordered magnetic fields are not always seen although discontinuities are always present at 1 AU. Thus, the interplanetary medium appears to be discontinuous rather than filamentary. The filamentary model implies that discontinuities originate at the sun and are convected with the solar wind. The discontinuous model allows the additional possibility that the discontinuities form in the interplanetary medium far from the sun.     

Large-scale three-dimensional structure of the interplanetary magnetic field

Analysis of observations of the white-light corona performed aboard OSO-7 is evidence for the existence of coronal ribbon-structures, which may be observed on the limb as coronal streamers. It is shown that prolongation of these structures into interplanetary space forms a curved surface; intersection of this surface is accompanied by a change of polarity of the interplanetary magnetic field, which existed in May–July 1973; and its connection with several phenomena in the solar atmosphere, has been found.     

Search for long term variations of the interplanetary magnetic field

A statistical study is made of the long term variations of the interplanetary magnetic field parameters collected in the years 1964 to 1973 by 12 spacecraft (IMP's, Pioneers and HEOS). Although temporal fluctuations are observed on field components and magnitudes no clear solar cycle variation is found. The same conclusion holds for the statistical distributions and variances of these parameters. A search for possible heliographic latitude effects on the field also leads to a negative conclusion.     

Auroral boundary variations and the interplanetary magnetic field

This paper describes a DMSP data set of 150 auroral images during magnetically quiet times which have been analyzed in corrected geomagnetic local time and latitudinal coordinates and fit to offset circles. The fit parameters R (circle radius) and (X, Y) (center location) have been compared to the hourly interplanetary magnetic field (IMF) prior to the time of the satellite scan of the aurora. The results for variation of R with B_z, agree with previous works and generally show about a 1° increase of R with increase of southward B_z by 1 nT. The location of the circle center also has a clear statistical shift in the Southern Hemisphere with IMF B_y such that the southern polar cap moves towards dusk (dawn) with B_y > (B_y < 0).     

The mean magnetic field of the Sun: Method of observation and relation to the interplanetary magnetic field

The mean solar magnetic field as measured in integrated light has been observed since 1968. Since 1970 it has been observed both at Hale Observatories and at the Crimean Astrophysical Observatory. The observing procedures at both observatories and their implications for mean field measurements are discussed. A comparison of the two sets of daily observations shows that similar results are obtained at both observatories. A comparison of the mean field with the interplanetary magnetic polarity shows that the IMF sector structure has the same pattern as the mean field polarity.     

A Hall MHD model to study energetic charged particle events produced during fluctuations in the interplanetary magnetic field intensity

Energetic charged particles, which are often observed in solar active regions, may be also produced in interplanetary space due to the decoupling of ions and electrons in plasma. The Hall term in general Ohm's law is generally thought to be responsible for the decoupling of electrons and ions in plasma during magnetic reconnection. In this paper, a Hall MHD model is developed to study energetic charged particle events produced during fluctuations in the interplanetary magnetic field intensity. Two energetic charged particle events are used to test this model. It is concluded that the Hall effect does not only play the important role in the process of magnetic reconnection, but also in energetic charged particle events produced during fluctuations in the interplanetary magnetic field intensity.     

Spectral polarization analysis of the interplanetary magnetic field fluctuations

A new computational method and algorithm, based on complex Fourier analysis, is used to derive the spectral density of plane and circularly polarized fluctuation components of the interplanetary magnetic field. Applications of the method have been made using HEOS 2 (1 AU), Pioneer 10 (5 AU), Pioneer 11 (20 AU), and ICE (Giocabini-Zinner's comet) data sets. The results show the existence of circularly polarized MHD waves in all cases.     

A solar cycle variation of the interplanetary magnetic field

Measurements of the north-south (B _z component of the interplanetary field as compiled by King (1975) when organized into yearly histograms of the values of ¦B _z ¦ reveal the following. (1) The histograms decrease exponentially from a maximum occurrence frequency at the value ¦B _z ¦ = 0. (2) The slope of the exponential on a semi-log plot varies systematically roughly in phase with the sunspot number in such a way that the probability of large values of ¦B _z ¦ is much greater in the years near sunspot maximum than in the years near sunspot minimum. (3) There is a sparsely populated high-value tail, for which the data are too meager to discern any solar cycle variation. The high-value tail is perhaps associated with travelling interplanetary disturbances. (4) The solar cycle variations of B _z and the ordinary indicators of solar activity are roughly correlated. (5) The solar cycle variation of B _z is distinctly different than that of the solar wind speed and that of the geomagnetic Ap disturbance index.Now at the Aerospace Corporation, El Segundo, Calif. 90245, U.S.A.     

Dynamics of charged particles and perpendicular diffusion in turbulent magnetic field

A test particle code is employed to explore the dynamics of charged particles and perpendicular diffusion in turbulent magnetic field, where a three-dimensional (3D) isotropic turbulence model is used in this paper. The obtained perpendicular diffusion at different particle energies is compared with that of the nonlinear guiding center (NLGC) theory. It is found that the NLGC theory is consistent with test particle simulations when the particle energies are small. However, the difference between the NLGC theory and test particle simulations tends to increase when the particle energy is sufficiently large, and the threshold is related to the turbulence bend-over length. In the NLGC theory, the gyrocenter of a charged particle is assumed to follow the magnetic field line. Therefore, when the particle has sufficiently large energy, its gyroradius will be larger than the turbulence bend-over length. Then the particle can cross the magnetic field lines, and the difference between the test particle simulations and NLGC theory occurs.     

Motion and diffusion of energetic particles in the outer zone

The longitudinal changes in drift velocity and bounce period are obtained using two theorems on magnetic flux conservation. As a consequence radial diffusion due to pitch-angle scattering is derived. The use of the same analytical model enables the comparison of this process with radial diffusion due to compressions of the magnetosphere. The two processes are competitive for intermediate colatitudes.