Cosmic Rays In Interplanetary Space Research Articles

The single mechanism of solar and galactic cosmic rays acceleration arising during the flare process

Solar flares take place in the solar corona due to release of magnetic energy accumulated in the magnetic field of current sheet during instability of the current sheet.Solar cosmic rays are accelerated in the inductive electric field of the current sheet. The magnetic field of the solar wind forms the shape of an Archimedes spiral and affects the propagation of solar cosmic rays in interplanetary space. The modern detection of giant flares on the class G star dwarfs with the energy significantly exceeding the energy of the solar flares indicates the possibility of proton acceleration beyond the boundary of the solar system to energies significantly greater than the energy of solar cosmic rays. The recent experimental data shows that the energy of the stellar flares can exceed energy of 1036 erg. It is by 3-4 orders greater than the energy of a large solar flare, and, apparently, the energy of the protons accelerated in these stellar flares can significantly exceed the energy of the particles registered from flares on the Sun. Thus, the flare can be a universal astronomical process responsible for proton acceleration on the Sun and on the stars.

Particle Acceleration and Alfv’en Wave Generation at the April 4, 2001 Interplanetary Shock

Based on the theory of diffusive shock acceleration of charged particles, we investigate the formation of proton spectra and the generation of an Alfv’en turbulence spectrum by accelerated (storm) particles at the interplanetary shock front in the event occurred at 14:22 UT on April 4, 2001. We formulate a scenario whereby a satisfactory theoretical description of the observed proton and Alfv’en wave spectra obtained from measurements becomes possible: the propagation of solar cosmic rays in interplanetary space before the interplanetary shock arrival at the Earth’s orbit creates an enhanced level of Alfv’en turbulence in the solar wind, which reduces the diffusion coefficient of particles and increases the efficiency of their acceleration.

Description of Solar Cosmic Ray Propagation in the Interplanetary Medium on the Basis of the Kinetic Equation

The propagation of solar cosmic rays in interplanetary space is considered based on the kinetic equation. The expression for cosmic ray density under instantaneous particle injection by a point-like source is obtained. The set of a differential equation system for harmonics of cosmic ray distribution function is obtained starting from the kinetic equation. The cosmic ray transport equation, taking into account the presence of the second harmonic of particle angular distribution, is derived and the solution of this equation is obtained.

The theory of particle diffusion in a strong random magnetic field with an allowance for higher multipole moments of the distribution function

The kinetic equation including a small-scale collisional integral for the particles propagating in a strong random and regular magnetic field [29] is solved by expanding the distribution function into series in spherical harmonics of the particle momentum angles. Using methods of the quantum theory of the angular moment [41], the equations for higher multipole moments of the distribution function in the space of momentum angles are derived and solved in the stationary case for the galactic cosmic rays in interplanetary space. The observed amplitudes and phases of the diurnal variation harmonics can be explained using the results of measurements of the interplanetary magnetic field performed on board the Ulysses spacecraft [12–14] and other satellites [45, 46] with an allowance for redistribution of the interplanetary and interstellar magnetic field lines. The spatial structure of the convection and diffusion fluxes of the galactic cosmic rays is refined. Formulas taking into account a change in the Earth’s axis tilt relative to the direction toward the Sun are derived, which allow the annual changes in contributions to the diurnal variation harmonics to be determined. The equation of diffusion taking into account the 2nd harmonic is obtained, and the contribution of this effect to the relative particle density in the cosmic rays in a spherically symmetric case is analyzed.

A New Model for Solar-Terrestrial Propagation of Solar Cosmic Rays

A new solar-terrestrial propagation model is presented for solar cosmic rays, which includes a coronal distribution source of flare particles and the propagation equation for solar cosmic rays in interplanetary space. Based on observations of sunspot group characteristics of a solar cosmic ray flare, two-step coronal transport processes and transport equations are proposed for solar flare particles, which result from the annihilations of sunspots in a sunspot group with magnetic multi-polarities. A coronal distribution of flare particles is obtained, which is consistent with the observational properties relative to coronal transport. During the first step process, which is of about the same duration as the flare impulsive phase, the flaring region is filled nearly uniformly with accelerated particles, it leads to the formation of the fast propagation region (FPR). During the second step process, which follows the impulsive phase, accelerated particles gradully diffuse through ambient corona about the FPR, which are called the slower propagation process, and escape towards interplanetary space. The interplanetary propagation of solar cosmic rays is described by the equation for solar cosmic-ray propagation in an infinite, homogeneous and orthotropic medium. The intensity-time profiles given by numerical calculation of the proposed model are compared with the observations for the event on 24 September 1997 from SOHO. The predicted results give a good fit to the data.

Propagation model of high-energy solar cosmic rays in interplanetary space and Green function

Based on main observational characteristics of solar flare particle transport in the coronal, a mathematical description of coronal transport is proposed. A model is presented for solar cosmic-ray propagation in solar-terrestrial space of infinite, homogeneous orthotropic medium. A Green function to the propagation equation with source is found. The integral solution to the propagation equation with the source, as well as the analytical solution to the equation for a pulse point source, is obtained by using the Green function in the medium.

Propagation effects in the hydrogen-to-helium ratio in the solar cosmic rays

Taking as basis my dimensional solution of the propagation equation of solar cosmic rays in interplanetary space and using the equivalent diffusion coefficient found from observed data on solar protons, I discuss the effects of propagation on the hydrogen-to-hellum ratio Including its variation with the speed of the solar wind and with location in space. After eliminating the variations with solar distance and energy from the HEOS and PIONEER data collected by Perron et al., this ratio will be seen to increase with the magnetic longitude of the parent flare. The Initial value of the hydrogen-to-helium ratio at the Sun's surface, obtained after applying the corrections for propagation, is close to the value in the solar wind.

Transport coefficients of low‐energy cosmic rays in interplanetary space

The propagation of energetic particles along and across the interplanetary magnetic field is governed by the large‐scale field geometry and by scattering in small‐scale turbulent fields. Values of the scattering mean free path parallel to the field, λ∥(R), are reviewed in prompt solar bursts and nonimpulsive (corotating) events. Analysis of intensity and anisotropy profiles in combination is a powerful tool for elucidating λ∥(R). A consensus is found: at 1 AU, λ∥ = 0.08–0.3 AU over a wide range of rigidity, R = 5 × 10−4 to 5 GV. Efforts to explain the discrepancy between empirical values of λ∥ and scattering theory are discussed. Quantitative measures of λ∥ in rare scatter‐free events, where λ∥ ≳ 1 AU, are discussed because they can provide important details of the scattering process and the magnetic power spectra. Cross‐field diffusion due to random walk of field lines is revisited. Recent values deduced from magnetic power spectra in interplanetary space, magnetic diffusion at the sun, Jovian electron propagation, and cosmic ray events are evaluated. Again, a consensus is sought, and a reasonable mean is K⊥r/β = 1021 cm² s−1. Previous arguments against a significant K⊥r are reassessed, including the problem of the persistence of intensity fluctuations in cosmic ray events. Combining the consensus for K⊥r/β with that for λ∥ gives K⊥r/K∥ < 0.1 at 1 AU, and thus neglect of K⊥r in the modeling of solar cosmic ray events appears justified (although account needs to be taken of coronal propagation). The outlook for the future includes better empirical values of λ∥ down to Ep ∼ 10 keV and Ee ∼ 1 keV, comparison with scattering theories at these energies, and comparison between empirical and theoretical λ∥ in other regions such as the magnetosheath and upstream solar wind.

Separation of the steady-state cosmic ray equation of transport: A generalization

The one-dimensional, steady-state equation of transport for cosmic rays including convection, diffusion and adiabatic deceleration is separated for a spatial diffusion coefficient with an arbitrary momentum dependence and for an arbitrary spatial dependence of the convection velocityV, and applies for planar, cylindrical and spherical geometries. As an application, the previously obtained spherically symmetric steady-state Green's functions, describing the propagation of cosmic rays in interplanetary space, are generalized to the case where the convection velocity is a function of position.

The interplanetary transport of solar cosmic rays

Numerical solutions are presented for the propagation of solar cosmic rays in interplanetary space, including the effects of pitch-angle scattering and adiabatic focusing. The intensity-time profiles can be well fitted by a simple radial spatial diffusion equation with scattering mean-free path lambda(fit). The radial mean-free path so obtained is significantly larger than the true scattering mean-free path for low-rigidity particles due to both adiabatic focusing and the inapplicability of the diffusive approximation early in the event. The well-known discrepancy between lambda(fit) and the theoretical predictions may be resolved by these calculations.

The effects of fluctuations and noise on the neutron monitor diurnal anisotropy, 2. Non-field-aligned diffusion

The effects of non-field-aligned diffusion (i. e., terms in the diffusion tensor proportional to the antisymmetric coefficient κA) on the observed day-to-day deviation of the diffusive diurnal anisotropy from the daily average magnetic field direction are considered. Using reasonable parameters for the diffusion of cosmic rays in interplanetary space, I show that these terms give a natural explanation for the angular difference between the anisotropy and field directions during normal quiet interplanetary epochs.

Simulation of solar flare particle interaction with interplanetary shock waves

In order to study the propagation of solar cosmic rays in interplanetary space a computer program has been developed using a Monte-Carlo technique, which traces the histories of particles released impulsively at the Sun. The particle propagation model considers the adiabatic deceleration during the convective and diffusive transport of the particles, and the model of the interplanetary medium incorporates a radially expanding blast wave which exerts a sweeping action on the particles and accelerates them through the first-order Fermi process. It is shown that energetic storm particle events cannot be simulated by assuming a pure sweeping action of the interplanetary blast wave, but that energization of the particles while reflected at the shock can explain many observed features of such events.

Propagation of solar-flare cosmic rays along corotating interplanetary flux-tubes

The propagation of solar-flare cosmic rays along a corotating spiral mean interplanetary magnetic flux-tube is investigated under a variety of initial, inner and outer boundary conditions, by solving the transport equations numerically. The inner boundary condition is shown to have negligible effects on the redistribution of the cosmic rays in interplanetary space, apart from a proportionality constant. The diffusion coefficients have been classified into type I and type II: for type I the peakalong-spiral stays at a finite heliocentric distance, while for type II it travels to infinity. The time dependence of the anisotropy vector is characteristically different in each type and in the case of type I is a function of the observation point. The general propagation characteristics with a free-escape outer boundary are like those of type I. It is shown that closely exponential decay can be produced without a free-escape boundary. The concept of an ‘equilibrium shape’ at late time is introduced. With a source that decays slowly, a maximum and minimum pair appears in the spatial distribution; the maximum subsequently propagates outward and the minimum inward. The impulsive models given do not reproduce satisfactorily all the observed characteristics of solar burst events and a solar source extended in time appears to be indicated.

Spatial dependence of the pitch-angle and associated spatial diffusion coefficients for cosmic rays in interplanetary space

The spatial dependence of the pitch-angle and associated spatial diffusion coefficients for cosmic ray particles in interplanetary space is calculated in the WKB approximation. The model considers only Alfven waves of solar origin to be responsible for scattering of moderate energy particles. After developing the general theory results are presented for the asymptotic case corresponding to radial distancesr greater than about 1 to 2 AU. The radial diffusion coefficientиr increases with energyE likeиr∼Eυ, wherev≈2/3. The radial mean free path turns out to increase proportional tor3 at medium and low heliographic latitudes. This behaviour is consistent with a very small radial cosmic ray gradient and the existence of a ‘free boundary’ for particle diffusion. At equal radial distances the high latitude mean free path is not only much smaller than the one calculated at the lower latitudes but in addition increases only weakly with distance. Some conceivable dynamical implications for the outer solar system are indicated.

Energy losses of solar cosmic rays in interplanetary space

A simple model of solar cosmic ray propagation which includes diffusion, convection, and energy loss by adiabatic deceleration is studied. A Monte Carlo technique is employed to investigate the variation of mean particle energy in the interplanetary medium after the impulsive release of mono-energetic particles at the Sun. At 1 AU typical energy losses are 43% at 20 h and 64% at 60 h after particle release for a diffusion coefficient κ(r)=κ 0rβ with β=+1/2 and κ0=1.33 × 1021 cm2 s−1. When κ 0 in this model is reduced by a factor of 4, the energy loss is greater by a factor of 2 at 60 h after particle release. When β is increased, the energy losses are greater. Using the model parameters above, an increase in solar wind speed from 300 to 600 km s−-1 gives rise to energy losses that are greater again by factor of 2 at a time of 60 h. Results are compared with an observation by Murray et al. (1971) of a ‘knee’ in the energy spectrum of solar protons. It is not considered likely that the change in the energy of the knee with time requires, in addition to adiabatic deceleration, another energy change process which acts to increase the energy of particles.

Energy changes of cosmic rays in interplanetary space

The observation reported by Murray et al. (1971), in which a feature or ?kink' in the kinetic-energy spectrum of solar cosmic rays from a solar burst was seen to decrease with time, is examined. By means of calculations based on a model for cosmic ray bursts, it is demonstrated that the observed rate cannot be interpreted immediately as the rate of loss of energy, and factors are indicated which must be considered in the interpretation of the data.

Convection-dominated transport of solar cosmic rays

The Fokker-Planck equation for the transport of solar cosmic rays in interplanetary space, including the convection and energy-change terms as well as an absorbing boundary at finite distance from the sun, is solved for the exponential decay phase of solar particle events. The solution is applied to the case of low-energy (≈10 Mev) particles for which convection is important. Convective effects, particularly the relative constancy and energy-independency of the exponential decay time, previously noted in connection with the equilibrium anisotropy, appear explicitly in this solution.

Anisotropies of galactic cosmic rays in the solar system

At least four processes appear capable of contributing to the creation of an anisotropy of galactic cosmic rays in interplanetary space. All need not necessarily be active on a particular day to the same extent. The processes are (1) azimuthal streaming, (2) streaming due to non-uniform diffusion in a longitudinal sector structure, (3) the scattering at irregularities along the interplanetary magnetic field, and (4) latitudinal gradients in a relatively smooth magnetic field. The characteristics of the daily variation which must be expected from each process are quantitatively evaluated. Observational evidence derived from measurements of the daily variation from a network of super neutron monitors is used to derive, with precision, the spectrum of variation, the amplitude and the principal direction of maximum and minimum intensity in interplanetary space, on each day during 1964–65. The experimental results are compared with predictions to derive conclusions as to the process which operates on individual days. It is demonstrated that the diurnal and the semi-diurnal components of the anisotropy have characteristically different energy spectra of variation. The predominant process responsible for the diurnal component is the azimuthal streaming while the semidiurnal component appears to be due to scattering at magnetic field irregularities and latitudinal gradients. The manner in which the results can be used to derive the threshold energy below which isotropic diffusion seems to occur on individual days in the inner solar system is demonstrated. The results of the study strongly support the postulate of a gradient of galactic cosmic rays in the solar system perpendicular to the ecliptic.

Eleven-year modulation of galactic cosmic rays in interplanetary space

Almost the whole increase in the cosmic-ray intensity in the stratosphere during the period of decreasing solar activity (1960–64) was composed of a number of individual events occurring at intervals of 6–12 months. This phenomenon is almost entirely due to the corresponding decrease of solar activity (according to the sunspot number).Several interesting cases were found when solar-activity decreases to a new stationary level took place rapidly (within several days). After such events the cosmic-ray intensity gradually increased to reach a stationary level over a period of about two months. The time, tst, during which the cosmic-ray intensity in interplanetary space (after the above-mentioned events on the sun) approaches a stationary value is about 40, 60, and 80 days according to observations in 1961, 1963, and 1964 respectively.Some results have been obtained on the large-scale magnetic "clouds" which modulate the galactic cosmic rays in interplanetary space: (a) The velocity of propagation of these magnetic clouds is [Formula: see text]. According to the data on u and tst the radius of the sphere around the sun, r, within which the cosmic rays are modulated depends little on solar activity and is equal to 10–15 AU. (b) The density of magnetic clouds in space is either independent of the distance to the sun or decreases less rapidly than the inverse square law suggested by conservation of clouds.[Formula: see text]

Anisotropy of transient variations of cosmic-ray intensity

The angular distribution of the anisotropy of cosmic rays in interplanetary space is generally assumed to follow a cosine function. In the case of the daily variation, the source direction lies essentially in the equatorial plane. In the present calculation, the following three points were taken into account: (1) the latitude of the principal direction, (2) the angular distribution functions, and (3) the increases in flux of cosmic-ray particles. The response functions, the asymptotic directions, and the variation spectra are also involved in the calculation. Because of the rotation of the earth with respect to the source direction, which is fixed at the 12-h meridian, the daily variations are obtained. The variations include higher harmonics if the angular distribution is other than a simple cosine function.Comparing the calculated curves with observed data, the anisotropy in the space outside the geomagnetic field can be estimated with parameters such as the source direction in latitude and longitude, the half-width of the angular distribution, and the amplitude and exponent of the variation spectrum, which are all time-dependent. An increase which occurred on 24 March 1966 was analyzed.