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Modelling and observing Jovian electron propagation times in the inner heliosphere
Abstract
The propagation of Jovian electrons in interplanetary space was modelled by solving the relevant transport equation numerically through the use of stochastic differential equations. This approach allows us to calculate, for the first time, the propagation time of Jovian electrons from the Jovian magnetosphere to Earth. Using observed quiet-time increases of electron intensities at Earth, we also derive values for this quantity. Comparing the modelled and observed propagation times we can gauge the magnitude of the transport parameters sufficiently to place a limit on the 6 MeV Jovian electron flux reaching Earth. We also investigate how the modelled propagation time, and corresponding Jovian electron flux, varies with the well-known ∼13 month periodicity in the magnetic connectivity of Earth and Jupiter. The results show that the Jovian electron intensity varies by a factor of ∼10 during this cycle of magnetic connectivity.
... As this is done by a convolution with the source spectrum (see e .g. Strauss & Effenberger 2017, and references therein), an equivalent convolution is applied to the simulation times provided by the SDEs code. It has been demonstrated that the method of calculating residence times employed by, e.g., Florinski & Pogorelov (2009) and Strauss et al. (2013), cannot Vogt et al. (2018).The upper panel shows the source spectrum as fitted to the Pioneer 10 CPI and Ulysses COSPIN/KET data. The Voyager 1 TET data added in this plot appears to be in agreement as well. ...
... Typically, in previous works, ρ is constructed from the SDE solutions as the (normalised) distribution of the pseudoparticles' exit time (see e. g. Florinski & Pogorelov 2009;Strauss et al. 2013). For 6 MeV Jovian electrons, these distributions are shown in Fig. 6, as the red histogram, for the case of good (left) and bad (right) magnetic connection to the source. ...
... An observational estimate to compare with is discussed by Strauss et al. (2013). Investigating quiet-time increases (QTIs) (see e. g. ...
Context. Jovian electrons serve an important role in test-particle distribution in the inner heliosphere. They have been used extensively in the past to study the (diffusive) transport of cosmic rays in the inner heliosphere. With new limits on the Jovian source function, that is, the particle intensity just outside the Jovian magnetosphere, and a new set of in-situ observations at 1 AU for cases of both good and poor magnetic connection between the source and observer, we revisit some of these earlier simulations.
Aims. We aim to find the optimal numerical set-up that can be used to simulate the propagation of 6 MeV Jovian electrons in the inner heliosphere. Using such a setup, we further aim to study the residence (propagation) times of these particles for different levels of magnetic connection between Jupiter and an observer at Earth (1 AU).
Methods. Using an advanced Jovian electron propagation model based on the stochastic differential equation approach, we calculated the Jovian electron intensity for different model parameters. A comparison with observations leads to an optimal numerical setup, which was then used to calculate the so-called residence (propagation) times of these particles.
Results. Through a comparison with in-situ observations, we were able to derive transport parameters that are appropriate for the study of the propagation of 6 MeV Jovian electrons in the inner heliosphere. Moreover, using these values, we show that the method of calculating the residence time applied in the existing literature is not suited to being interpreted as the propagation time of physical particles. This is due to an incorrect weighting of the probability distribution. We applied a new method, where the results from each pseudo-particle are weighted by its resulting phase-space density (i.e. the number of physical particles that it represents). We thereby obtained more reliable estimates for the propagation time.
... In order to compare the validity and runtime performance of the CUDA code we implemented a CPU version of the same algorithm using OpenMP to exploit the multi-thread capabilities of CPUs. For the generation of pseudorandom numbers for the CPU version we made use of the implementation of [27]. For the CUDA XORWOW and the CPU implementation we injected 400000 particles and 393216 for the CUDA MTGP32 code. ...
... For the CUDA XORWOW and the CPU implementation we injected 400000 particles and 393216 for the CUDA MTGP32 code. Note that the results of Strauss et al. [27] are based on 1000 particles that hit the Jovian source for every injection point. Right: The orbit of Jupiter (orange, 5.2 AU), Earth (dashed green, 1 AU) and two Parker field lines for a good magnetic connection (red) and a bad connection (red). ...
... The CPU implementation is indicated by the orange dots. The green dots represent the data presented by Strauss et al. [27]. For the CUDA XORWOW and the CPU implementation we injected 400000 pseudoparticle at every injection point and 393216 (24 · 16384) pseudo-particle for the MTGP32 code. ...
The numerical solution of transport equations for energetic charged particles in space is generally very costly in terms of time. Besides the use of multi-core CPUs and computer clusters in order to decrease the computation times, high performance calculations on graphics processing units (GPUs) have become available during the last years. In this work we introduce and describe a GPU-accelerated implementation of Parker’s equation using Stochastic Differential Equations (SDEs) for the simulation of the transport of energetic charged particles with the CUDA toolkit, which is the focus of this work. We briefly discuss the set of SDEs arising from Parker’s transport equation and their application to boundary value problems such as that of the Jovian magnetosphere. We compare the runtimes of the GPU code with a CPU version of the same algorithm. Compared to the CPU implementation (using OpenMP and eight threads) we find a performance increase of about a factor of 10-60, depending on the assumed set of parameters. Furthermore, we benchmark our simulation using the results of an existing SDE implementation of Parker’s transport equation.
... For the work presented here, we use the model of Strauss et al. (2011), rewritten by Dunzlaff et al. (2015), to solve the Parker (1965) transport equation and simulate the intensities of Jovian electrons in the inner heliosphere. This model was also used previously to calculate Jovian electron propagation times (Strauss et al. 2013), a calculation later refined by Vogt et al. (2020). For this model we adopt a Parker (1958) heliospheric magnetic field with a nominal solar wind speed of 400 km s −1 . ...
In this paper we explore the idea of using multi-spacecraft observations of Jovian electrons to measure the 3D distribution of these particles in the inner heliosphere. We present simulations of Jovian electron intensities along selected spacecraft trajectories for 2021 and compare these, admittedly qualitatively, to these measurements. Using the data-model comparison we emphasize how such a study can be used to constrain the transport parameters in the inner heliosphere, and how this can lead to additional insight into energetic particle transport. Model results are also shown along the expected trajectories of selected spacecraft, including the off-ecliptic phase of the Solar Orbiter mission from 2025 onward. Lastly, we revisit the use of historical data and discuss upcoming missions that may contribute to Jovian electron measurements. Unified Astronomy Thesaurus concepts: Heliosphere (711); Interplanetary turbulence (830); Cosmic rays (329)
... Electron (negatrons including positrons) observations go back to the 1960's on balloons (Webber et al. 1973;Freir and Waddington 1965) and on spacecraft to the 1970's with the launch of the Orbiting Geophysical Observatories (OGO)-5 and International Sun Earth Explorer (ISEE)-3/International Cometary Explorer (ICE) close to Earth (Burger and Swanenburg 1973;Garcia-Munoz et al. 1986;Clem et al. 1996). Until the 1990's there had been no mission exploring GCR electron fluxes beyond the Earth orbit due to the limitation of the instrumentation and Jupiter's dominance as a source of electrons in the intermediate heliosphere out to at least 20 AU. Strauss et al. 2013a). However, Nndanganeni and , in an updated modelling of jovian electrons, showed that the contribution of GCR electrons below 100 MeV becomes increasingly dominant with radial distances beyond 30 AU. ...
We review recent observations and modeling developments on the subject of galactic cosmic rays through the heliosphere and in the Very Local Interstellar Medium, emphasizing knowledge that has accumulated over the past decade. We begin by highlighting key measurements of cosmic-ray spectra by Voyager, PAMELA, and AMS and discuss advances in global models of solar modulation. Next, we survey recent works related to large-scale, long-term spatial and temporal variations of cosmic rays in different regimes of the solar wind. Then we highlight new discoveries from beyond the heliopause and link these to the short-term evolution of transients caused by solar activity. Lastly, we visit new results that yield interesting insights from a broader astrophysical perspective.
... The present study aims to report on the radial and rigidity dependences of low-energy electron MFPs, as well as their values at Earth, by performing an extensive parameter study of the potential radial and rigidity dependencies required for parallel and perpendicular MFPs used in a Jovian electron transport code, as well as values for these quantities at Earth, so as to result in computed Jovian intensities in good agreement with observations at 1 au taken during periods of both good and poor magnetic connectivity. This approach takes advantage of the fact that Jovian electron transport would be predominantly governed by parallel diffusion during periods of good connectivity and perpendicular diffusion during periods of bad connectivity (see Strauss et al. 2013;Vogt et al. 2020). Although previous studies have been reported on Jovian electron MFPs in the past (e.g., Chenette et al. 1977;Zhang et al. 2007;Vogt et al. 2020Vogt et al. , 2022, this study is the first of its kind to do so in such a comprehensive manner, and therefore expands on the current understanding of the behavior of these MFPs, as well as the consensus range of values these quantities assume, providing an extended benchmark with which the predictions of various scattering theories can be compared. ...
Novel insights into the behavior of the diffusion coefficients of charged particles in the inner heliosphere are of great importance to any study of the transport of these particles and are especially relevant with regard to the transport of low-energy electrons. The present study undertakes an exhaustive investigation into the diffusion parameters needed to reproduce low-energy electron intensities as observed at Earth, using a state-of-the-art 3D cosmic ray transport code. To this end, the transport of Jovian electrons is considered, as Jupiter represents the predominant source of these particles in the inner heliosphere, and because a careful comparison of model results with observations taken during periods of good and poor magnetic connectivity between Earth and Jupiter allows for conclusions to be drawn as to both parallel and perpendicular diffusion coefficients. This study then compares these results with the predictions made by various scattering theories. Best-fit parameters for parallel and perpendicular mean free paths at 1 au fall reasonably well within the span of observational values reported by previous studies, but best-fit radial and rigidity dependences vary widely. However, a large number of diffusion parameters lead to reasonable to-good fits to observations, and it is argued that considerable caution must be exercised when comparing theoretical results for diffusion coefficients with diffusion parameters calculated from particle transport studies.
... Ferreira et al. (2001) and Potgieter and Ferreira (2002) could make predictions of the ratio of Jovian electrons to galactic electrons at 6 MeV and as a function of heliolatitude, especially along the Ulysses trajectory. They found that a significant fraction of these low-energy electrons observed at Earth, and out to ∼ 10 AU in the equatorial plane, is of Jovian origin (see also Strauss et al. 2013). This is in contrast to the inference made by Evenson and Clem (2011) that electron observations at Earth are dominated by the galactic component. ...
The propagation and modulation of electrons in the heliosphere play an important part in improving our understanding and assessment of the modulation processes. A full three-dimensional numerical model is used to study the modulation of galactic electrons, from Earth into the inner heliosheath, over an energy range from 10 MeV to 30 GeV. The modeling is compared with observations of 6–14 MeV electrons from Voyager 1 and observations at Earth from the PAMELA mission. Computed spectra are shown at different spatial positions. Based on comparison with Voyager 1 observations, a new local interstellar electron spectrum is calculated. We find that it consists of two power-laws: In terms of kinetic energy E, the results give E
−1.5 below ∼500 MeV and E
−3.15 at higher energies. Radial intensity profiles are computed also for 12 MeV electrons, including a Jovian source, and compared to the 6–14 MeV observations from Voyager 1. Since the Jovian and galactic electrons can be separated in the model, we calculate the intensity of galactic electrons below 100 MeV at Earth. The highest possible differential flux of galactic electrons at Earth with E=12 MeV is found to have a value of 2.5×10−1 electrons m−2 s−1 sr−1 MeV−1 which is significantly lower (a factor of 3) than the Jovian electron flux at Earth. The model can also reproduce the extraordinary increase of electrons by a factor of 60 at 12 MeV in the inner heliosheath. A lower limit for the local interstellar spectrum at 12 MeV is estimated to have a value of (90±10) electrons m−2 s−1 sr−1 MeV−1.
... This needs to be investigated further. They also disentangled the galactic and Jovian contributions to these electron observations, a process that improved understanding and the interpretation of Ulysses data (see also Strauss et al., 2013a). They found that Jovian electrons dominate the inner equatorial regions up to ∼ 10 -20 AU but it is unlikely that they can dominate the low-energy galactic electrons to heliolatitudes higher than ∼ 30°off the equatorial plane. ...
This is an overview of the solar modulation of cosmic rays in the
heliosphere. It is a broad topic with numerous intriguing aspects so that a
research framework has to be chosen to concentrate on. The review focuses on
the basic paradigms and departure points without presenting advanced
theoretical or observational details for which there exists a large number of
comprehensive reviews. Instead, emphasis is placed on numerical modeling which
has played an increasingly signi?cant role as computational resources have
become more abundant. A main theme is the progress that has been made over the
years. The emphasis is on the global features of CR modulation and on the
causes of the observed 11-year and 22-year cycles and charge-sign dependent
modulation. Illustrative examples of some of the theoretical and observational
milestones are presented, without attempting to review all details or every
contribution made in this ?eld of research. Controversial aspects are discussed
where appro- priate, with accompanying challenges and future prospects. The
year 2012 was the centennial celebration of the discovery of cosmic rays so
that several general reviews were dedicated to historical aspects so that such
developments are brie y presented only in a few cases.
Aims. We investigate the energy dependence of Jovian electron residence times, which allows for a deeper understanding of adiabatic energy changes that occur during charged particle transport, as well as of their significance for simulation approaches. Thereby we seek to further validate an improved approach to estimate residence times numerically by investigating the implications on previous analytical approaches and possible effects detectable by spacecraft data.
Methods. Utilising a propagation model based on a stochastic differential equation (SDE) solver written in CUDA, residence times for Jovian electrons were calculated over the whole energy range dominated by the Jovian electron source spectrum. We analysed the interdependences both with the magnetic connection between the observer and the source as well as between the distribution of the exit (simulation) times and the resulting residence times.
Results. We point out a linear relation between the residence time for different kinetic energies and the longitudinal shift of the 13 month periodicity typically observed for Jovian electrons and discuss the applicability of these findings to data. Furthermore, we utilise our finding that the simulated residence times are approximately linearly related to the energy loss for Jovian and Galactic electrons, and we develop an improved analytical estimation in agreement with the numerical residence time and the longitudinal shift observed by measurements.
This work studies the influence of the structure of inner heliospheric magnetic field on the propagation of Jovian electrons from Jupiter to the Earth orbit. Beginning from 1974, 13-month variations of relativistic Jovian electron fluxes were recorded by spacecraft near the Earth. 22 synodic cycles are analysed. The best connection in each cycle was found within a narrow longitudinal interval with an angular divergence of the planets 230 ± 20°, when the Parker field line connecting the two planets is formed at solar wind speed 450 ± 50 km s−1. Such invariability for more than 45 yr could not be accidental. We attribute the observed phenomenon to the long-term presence of recurrent stationary structures in the solar wind generated near the Sun. This assumption is confirmed by comparing the time profiles of the solar wind speed measured over all solar rotations in the solar activity minima in 1975 and 2007–2008.
Context. Since the Pioneer 10 flyby of Jupiter it has become well known that electrons of Jovian origin dominate the lower MeV range of charged energetic particles in the inner heliosphere.
Aims. Because the Jovian source can be treated as point-like in numerical models, many attempts to investigate charged particle transport in the inner heliosphere have utilized Jovian electrons as test particles. The reliability of the derived parameters for convective and diffusive transport processes are therefore highly dependent on an accurate estimation of the Jovian source spectrum. In this study we aim to provide such an estimation.
Methods. In this study we have proposed a new electron source spectrum, specified at the boundary of the Jovian magnetosphere, fitted to flyby measurements by Pioneer 10 and Ulysses , with a spectral shape also in agreement with measurements at Earth’s orbit by Ulysses , Voyager 1, ISEE and SOHO.
Results. The proposed spectrum is consistent with all previous theoretical suggestions, but deviates considerably in the lower MeV range which was inaccessible to those studies.
In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via "toy models". Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.
The transport of energetic particles such as cosmic rays is governed by the properties of the plasma being traversed. While these properties are rather poorly known for galactic and interstellar plasmas due to the lack of in situ measurements, the heliospheric plasma environment has been probed by spacecraft for decades and provides a unique opportunity for testing transport theories. Of particular interest for the three-dimensional (3D) heliospheric transport of energetic particles are structures such as corotating interaction regions, which, due to strongly enhanced magnetic field strengths, turbulence, and associated shocks, can act as diffusion barriers on the one hand, but also as accelerators of low energy CRs on the other hand as well. In a two-fold series of papers, we investigate these effects by modeling inner-heliospheric solar wind conditions with a numerical magnetohydrodynamic (MHD) setup (this paper), which will serve as an input to a transport code employing a stochastic differential equation approach (second paper). In this first paper, we present results from 3D MHD simulations with our code CRONOS: for validation purposes we use analytic boundary conditions and compare with similar work by Pizzo. For a more realistic modeling of solar wind conditions, boundary conditions derived from synoptic magnetograms via the Wang-Sheeley-Arge (WSA) model are utilized, where the potential field modeling is performed with a finite-difference approach in contrast to the traditional spherical harmonics expansion often utilized in the WSA model. Our results are validated by comparing with multi-spacecraft data for ecliptical (STEREO-A/B) and out-of-ecliptic (Ulysses) regions.
A heliopause spectrum at 122 AU from the Sun is presented for galactic electrons over an energy range from 1 MeV to 50 GeV that can be considered the lowest possible local interstellar spectrum (LIS). The focus of this work is on the spectral shape of the LIS below ∼1.0 GeV. The study is done by using a comprehensive numerical model for solar modulation in comparison with Voyager 1 observations at ∼112 AU from the Sun and PAMELA data at Earth. Below ∼1.0 GeV, this LIS exhibits a power law with E−(1.55 ± 0.05), where E is the kinetic energy of these electrons. However, reproducing the PAMELA electron spectrum averaged for 2009, requires a LIS with a different power law of the form E−(3.15 ± 0.05) above ∼5 GeV. Combining the two power laws with a smooth transition from low to high energies yields a LIS over the full energy range that is relevant and applicable to the modulation of cosmic ray electrons in the heliosphere. The break occurs between ∼800 MeV and ∼2 GeV as a characteristic feature of this LIS. The power-law form below ∼1 GeV produces a challenge to the origin of these low energy galactic electrons. On the other hand, the results of this study can be used as a gauge for astrophysical modeling of the local interstellar spectrum for electrons.
We present calculations of the propagation times and energy losses of
cosmic rays as they are transported through the heliosphere. By
calculating these quantities for a spatially 1D scenario, we benchmark
our numerical model, which uses stochastic differential equations to
solve the relevant transport equation, with known analytical solutions.
The comparison is successful and serves as a vindication of the modeling
approach. A spatially 3D version of the modulation model is subsequently
used to calculate the propagation times and energy losses of galactic
electrons and protons in different drift cycles. We find that the
propagation times of electrons are longer than those of the protons at
the same energy. Furthermore, the propagation times are longer in the
drift cycle when the particles reach the Earth by drifting inward along
the heliospheric current sheet. The calculated energy losses follow this
same general trend. The energy losses suffered by the electrons are
comparable to those of the protons, which is in contrast to the
generally held perception that electrons experience little energy losses
during their propagation through the heliosphere.
We present a newly developed numerical modulation model to study the transport of galactic and Jovian electrons in the heliosphere. The model employs stochastic differential equations (SDEs) to solve the corresponding transport equation in five dimensions (time, energy, and three spatial dimensions) which is difficult to accomplish with the numerical schemes used in finite difference models. Modeled energy spectra for galactic electrons are compared for the two drift cycles to observations at Earth. Energy spectra and radial intensity profiles of galactic and Jovian electrons are compared successfully to results from previous studies. In line with general drift considerations, it is found that most 100 MeV electrons observed at Earth enter the heliosphere near the equatorial regions in the A > 0 cycle, while they enter mainly over the polar regions in the A < 0 cycle. Our results indicate that 100 MeV electrons observed at Earth originate at the heliopause with ~600 MeV undergoing adiabatic cooling during their transport to Earth. The mean propagation time of these particles varies between ~180 and 300 days, depending on the drift cycle. For 10 MeV Jovian electrons observed at Earth, a mean propagation time of ~40 days is obtained. During this time, the azimuthal position of the Jovian magnetosphere varies by ~1°. At a 50 AU observational point, the mean propagation time of these electrons increases to ~370 days with an azimuthal position change of Jupiter of ~20°. The SDE approach is very effective in calculating these propagation times.
Pioneer 10 observations of electrons in the energy range from 1.75 to 25 MeV over the heliocentric radial distance 1.0-21.5 AU are presented. The minimum intensity levels of 1-25 MeV electrons about 4.5 AU upwind of Jupiter and about 16.5 AU downwind of Jupiter's orbit are of Jovian origin. The expected galactic electron flux at 1 AU is found to be a factor of 50 or more below the observed quiet-time 12 MeV electron flux, and the evidence confirms the hypothesis advanced by Teegarden et al. (1974) that Jupiter is the source of the approximately 1-25 MeV quiet-time electrons near 1 AU. No evidence was found to support the hypotheses that electrons of either solar or galactic origin contribute significantly to the quiet-time flux inside of 22 AU at low heliographic latitudes.
The predictions of a conventional, spherically symmetric model of solar modulation have been compared with the measured spectra of positively and negatively charged galactic cosmic-ray particles at 1 AU throughout the 1965-1976 solar cycle and through the enhanced modulation of 1979. For the proton/helium, proton/electron, and helium/electron flux ratios, there is remarkably good agreement between theory and experiment, except for small differences in 1965 and 1969. Possible systematic experimental errors are discussed, and it is concluded that: (1) the 11 year modulation process is largely independent of the sign of the particle charge; and (2) the assumption of steady state is a fairly good approximation for long term modulation.
The 2009 flight of the balloon borne instrument LEE returned a truly exciting result. Although the payload only reached about 141,000 feet, significantly less than the record flight to 161,000 feet in 2002, the extremely low modulation level allowed a complete electron spectrum from 20 MeV to 5 GeV to be observed for the very first time. The nearly power law behavior of the spectrum below 100 MeV now stands out as clearly distinct from the Jovian spectrum. The possibility that these electrons come from Jupiter via simple diffusion in the interplanetary magnetic field is essentially eliminated. Direct measurements of the electron spectrum in the outer heliosphere from the Voyager spacecraft are also now available. Surprisingly the electron fluxes at 1 AU are intermediate between the levels observed at two locations in the outer heliosphere. We discuss possible interpretations of these observations.
Much work has been done on Corotating Interaction Regions (CIRs), see e.g. \citet{balo99}. Apart from the actual impact of CIRs on the solar wind plasma environment, the influence of CIRs on energetic particle populations has been of special interest. In this paper we study the influence of a CIR on the propagation of Jovian electrons to a spacecraft located at 1 AU. Recent modelling in this field has been concentrated on the local influence of CIRs on the electron flux at distances greater than 1 AU. This is due to the fact that modelling on larger spatial scales thus reaching closer to the Sun requires a 3D numerical model which also includes an energy and time dependence of the intensities. With our recently developed numerical model we were able to fulfil these requirements. We show the results of the calculated influence of CIRs on the Jovian and Galactic electron intensity at 1 AU, compared to data taken by the IMP 8 spacecraft, and discuss the implications for the CIR effects on the transport of energetic electrons.
Previously, the latitudinal transport of ~7 MeV electrons was studied by comparing the results of a newly developed three-dimensional model, based on the numerical solution of Parker's transport equation including the Jovian source, with Ulysses observations. Here, the radial transport of ~16 MeV electrons is studied by comparing the model results with the ~16 MeV electron intensities observed by Pioneer 10 up to ~70 AU. Electron modulation responds directly to the energy dependence of the diffusion coefficients below ~500 MeV, in contrast to protons, which experience large adiabatic energy losses below this energy, and in addition, low-energy electrons do not experience significant drifts. The modulation of low-energy electrons is therefore a handy tool to find a diffusion tensor suitable to the heliospheric modulation of electrons. It is illustrated that the computed electron intensities are sensitive to the radial dependence of the diffusion coefficients in the inner heliosphere and that compatibility between the model and observations gives an indication as to the radial dependence of the diffusion coefficients. The effects of different perpendicular diffusion coefficients in the radial direction are also shown, and an upper limit for the value of this coefficient is proposed. Finally, the relative contributions of the Jovian and galactic electrons to the total electron intensity are shown along the Pioneer 10 trajectory, illustrating that the Jovian electrons dominate the total electron intensity at these low energies in the inner equatorial regions only up to ~9 AU. From 15 AU outward, the Jovian contribution becomes less than 20%, decreasing rapidly as a function of increasing distance.
The heliospheric modulation of galactic and Jovian electrons is studied using a fully three-dimensional, steady state model based on Parker's transport equation including the Jovian source. The modulation of low-energy electrons is a handy tool to establish and to construct a suitable diffusion tensor to assure compatibility between model computations and observations from the Ulysses spacecraft. This is because electron modulation responds directly to the energy dependence of the diffusion coefficients below ~500 MeV in contrast to protons which experience large adiabatic energy losses below this energy. The model is used to study the latitudinal transport of both Jovian and 4-20 MeV galactic electrons by illustrating how the electron intensities are affected at different latitudes when enhancing perpendicular diffusion in the polar direction. In particular, the electron intensity-time profile along the Ulysses trajectory is calculated for various assumptions for perpendicular diffusion in the polar direction and compared to the 3-10 MeV electron flux observed by Ulysses from launch up to the end of the first out of the ecliptic orbit. Comparison of the model computations and the observations give an indication as to the magnitude of this diffusion coefficient. The relative contributions of the Jovian and galactic electrons to the total electron intensity is shown along the Ulysses trajectory.
The latitudinal gradient of cosmic ray protons observed by Ulysses during September 1994 to July 1995 is small, and it increases as function of rigidity up to ∼ 2 GV and then decreases. Although previous drift models could reproduce the observed small positive gradient for an A > 0 solar polarity cycle, they produced a maximum at a rigidity well below 1 GV, in contrast to the observations. After exploring various options, it turns out that changing the rigidity dependence of the perpendicular diffusion coefficient (DC) in the polar direction so that it differs from that of the parallel DC is the most effective way to obtain good agreement with data. Specifically, we find that this DC must have a flatter rigidity dependence than the parallel DC in order to reproduce the observed rigidity dependence of the latitudinal gradient of protons during an A > 0 solar polarity cycle. We argue that the present study, combined with studies by other authors, suggests that the perpendicular mean-free path of particles with rigidity R ≳ 0.1 GV has at least two distinct components. One is independent of particle rigidity, and one is proportional to the square of the particle rigidity at low rigidity and flattens to become almost independent of it at higher rigidity. We also show an example of the rigidity dependence of this gradient that Ulysses might observe during an A < 0 cycle. We point out that the gradient is then more sensitive to modulation parameters than during an A > 0 cycle and could impose stricter constraints on the diffusion tensor.
The results of a moderate drift model with anisotropic perpendicular diffusion for the heliospheric modulation of galactic cosmic rays were compared with electron spectra observed by the Kiel Electron Telescope on board the Ulysses spacecraft for four distinctive periods, 1992, 1995, 1996, and 1997, respectively, for relative large solar activity when Ulysses was at high heliolatitude; mid-latitudes and at low-latitudes with solar minimum modulation conditions. It was found that the model fit all the electron spectra well, except that for 1992, indicating that significant changes occurred between 1992 and 1995 in modulation conditions which must be presented in the model by a large time dependence, and/or a significant variation in the rigidity dependence of the diffusion coefficients. The latter is an aspect that has not been considered seriously in modelling before.
With several new incentives, revisiting electron modulation using a
comprehensive numerical model is appropriate. First, one has better
confidence in the galactic electron spectrum at energies <=300 MeV,
second, several good independent observations of modulated electron
spectra at 1 AU at solar minimum and along the Ulysses trajectory have
been made, and third, progress has been made about theoretical
predictions for mean free paths in the heliosphere. In this work, as a
first approach, an assessment of the various new predictions for
electron parallel mean free paths at 1 AU, especially their rigidity
dependencies, is made by looking at the effects of these predictions on
heliospheric modulation of galactic electron at energies below -300 MeV.
Electron modulation is most suitable at these energies because adiabatic
energy changes are still negligible and drift effects become less
important. Several spectra are shown together with the radial dependence
in the equatorial plane of the electron fluxes associated with each
approach that was used. It was found that a damping turbulence model
with composite slab, two-dimensional geometry gave parallel mean free
paths that resulted in reasonable electron modulation at these energies.
However, several other important modulating parameters have to be
considered of which diffusion perpendicular to the averaged magnetic
field is arguably the most important.
We present experimental and theoretical evidence suggesting that the
mean free path of cosmic-ray electrons and protons may be fundamentally
different at low to intermediate (less than 50 MV) rigidities. The
experimental evidence is from Helios observations of solar energetic
particles, which show that the mean free path of 1.4 MV electrons is
often similar to that of 187 MV protons, even though proton mean free
paths continue to decrease comparatively rapidly with decreasing rigidty
down to the lowest channels (about 100 MV) observed. The theoretical
evidence is from computations of particle scattering in dynamical
magnetic turbulence, which predict that electrons will have a larger
mean free path than protons of the same rigidity. In the light of these
new results, 'consensus' ideas about cosmic-ray mean free paths may
require drastic revision.
Observations of 5 - 30 MeV Jovian electrons from 1978 to 1984 have been
made at 1 AU by the University of Chicago electron spectrometer onboard
the ISEE 3 spacecraft. The six consecutive 13 month Jovian synodic
periods covered by these observations span the interval of maximum solar
activity. The 13 month variation in the Jovian electron intensity
measured by ISEE 3 continues to be well described by the
convection-diffusion model used by Conlon and Chenette to understand
propagation of Jovian electrons observed by IMP 8 during a time of lower
solar activity. Short-term intensity variations are attributed to
short-term changes in the degree of magnetic connection between the
spacecraft and Jupiter. The energy spectrum of Jovian electrons is
discussed in detail and the effect of adiabatic deceleration on the
shape of the spectrum is studied.
The rigidity dependence of solar particle scattering mean free paths in the range from 0.1 to a few GV is a key parameter to distinguish between different models for the nature of wave-particle interactions and of interplanetary magnetic turbulence. Here we present an analysis of electron and ion data, covering a large portion of the above range, obtained from modeling intensity and anisotropy profiles of a series of solar particle events in 1982 August that show exceptionally large but finite mean free paths. Combined with particle measurements from previously analyzed events that exhibit mean free paths in the range of 0.02 to 0.5 AU, we find that a uniform shape of the functional form of the rigidity dependence, which varies only in absolute height for different events, can explain all observations. These results place severe constraints on any propagation theory and rule out a number of recently suggested models to improve the standard quasilinear theory of particle scattering. Our findings may indicate that the component of the turbulence the particles interact with does not vary much with respect to its decomposition into different modes and their respective spectral and angular wavenumber dependencies, and basically the total power of this component is responsible for the level of the mean free paths.
We present a new analysis of the transport of cosmic rays in a turbulent magnetic field that varies in all three spatial dimensions. The analysis utilizes a numerical simulation that integrates the trajectories of an ensemble of test particles from which we obtain diffusion coefficients based on the particle motions. We find that the diffusion coefficient parallel to the mean magnetic field is consistent with values deduced from quasi-linear theory, in agreement with earlier work. The more interesting and less understood transport perpendicular to the average magnetic field is found to be enhanced (above the classical scattering result) by the random walk, or braiding, of the magnetic field. The value of κ⊥ obtained is generally larger than the classical scattering value but smaller than the quasi-linear value. The computed values of κ⊥/κ∥, for a representation of the interplanetary magnetic field, are 0.02-0.04; these values are of the same general magnitude as those assumed in recent numerical simulations of cosmic-ray modulation and transport in the heliosphere, and give reasonable agreement with spacecraft observations of cosmic rays. Some consequences of these results for the interpretation of heliospheric observations are discussed.
The 1974 mini-cycle is a medium term cosmic ray modulation event with about one year duration. It occurred in an A>0 epoch of solar magnetic polarity during conditions of low activity, but with an increase in the latitudinal extent of the
heliospheric current sheet (tilt angle α) and the magnitude B of the heliospheric magnetic field. This cosmic ray decrease can be used to test the hypothesis that such large scale decreases
(mini cycles) may be caused primarily by a combination of changes in α and B. For this purpose a fully time-dependent 2D model of solar modulation is used, which includes the effects of global and current
sheet drifts, and anisotropic perpendicular diffusion. Such models have been used successfully to describe the proton energy
spectrum as well as the radial and latitudinal gradients near 1 AU. Comparison of the model solutions with the observed decrease
for 1.8 GV protons allows us to study the combined influence of variable drift and diffusion effects throughout the event.
The passage of cosmic ray particles and energetic solar particles through interplanetary space is illustrated with a number of idealized examples. The formal examples are worked out from the condition that energetic particles in interplanetary space random walk in the irregularities in the large-scale interplanetary magnetic field. The irregularities move with approximately the velocity of the solar wind. The classical probability distribution is describable by a Fokker-Planck equation. A general expression for the particle diffusion coefficient kij is worked out, including both scattering in magnetic irregularities and systematic pressure drifts. Magnetometer data from Explorer XVIII is presented to show the close average adherence of the quiet-day interplanetary magnetic field to the theoretical spiral angle, and to show the tendency for particles to move more freely along the field than across, k∥ >k⊥. The observed fields show that the diffusion coefficient is of the order of 1021–1022 cm2/sec, as had been estimated from earlier cosmic ray studies. A middle value of 3 × 1021 cm2/sec suggests a cosmic ray density gradient of about 10 per cent per a.u. across the orbit of Earth. Direct observations of the interplanetary magnetic field afford the possibility for quantitative estimate of Kij as a function of particle energy.The first example to be considered is isotropic diffusion in a spherical region r < R with uniform radial wind velocity v for the purpose of illustrating the general nature and duration of the passage of a cosmic ray particle through the solar system. It is shown that the cosmic ray density reduction is of the order of exp (−vR/k), and, hence, that during the years of solar activity vR/k is not less than about 1 for protons of one BeV or so. It follows from this that the galactic cosmic ray particles will generally have spent several days in the solar system by the time they are observed. During this time they are in the expanding magnetic fields carried in the solar wind and are adiabatically decelerated, losing 15 per cent or more of their energy by the time they are observed. The energy distribution is shown for particles starting all with the same energy T0 from interstellar space. The incoming probability wave of a single particle is computed as a function of time, showing how the particle is swept back by the wind.The converse problem of energetic solar particles is illustrated. The solar particles may typically lose half their initial energy before escaping into interstellar space. The outward motion of the wind displaces their probability distribution outward so that ultimately the maximum solar particle intensity may lie beyond the orbit of Earth. The outward motion of the wind steepens the decline of the solar particle intensity.The steady-state cosmic ray intensity is calculated throughout the spherical region r < R supposing a uniform cosmic ray density N0 to obtain in interstellar space. The calculation is carried out for isotropic Kij, which would obtain if the magnetic irregularities were of large amplitude and of a scale not exceeding the radius of gyration of the cosmic ray particles, and for anisotropic kij with k∥ ⪢ k⊥, which obtains when the field is relatively smooth. (The observations at sunspot minimum suggest k∥ ⪢ k⊥ at the orbit of Earth.) The particles diffuse only along the spiral lines of force when k∥ ⪢ k⊥, so their path in and out of the solar system is much longer than when Kij is isotropic. The result is a much greater reduction of the cosmic ray intensity for a given vR/|Kij|.There is no direct observational information on Kij beyond the orbit of Earth, where the intensity reduction takes place. Indirect information is available, however. There is the fact that the intensity of energetic solar particles at Earth often decays as t−g with g = 1·5–2·0. It is shown that in order for this to follow, it is necessary that |Kij| ∞ rs with s = 0·0–0·5 if kij is isotropic, and s = 2·0–2·5 if k∥ ⪢ k⊥. That is to say, if Kij should continue to be as anisotropic beyond Earth as it is observed to be near Earth, then the diffusion must increase rapidly with distance from the Sun. These qualitative features should be easily detectable with particle, field, and plasma observations beyond the orbit of Earth.РефератДaeтcя пoяcHeHиe, coпpoBoздaeмoe pядoм идeaлизиpoBa HHыч пpимepoB, пpoчoдa чacтиц кocмичecкич лyчeй чepeз мeзплaHeтHoe пpocтpaHcтBo. ФopмaльHыe пpимepы paзpaбoтaHы Ha пpeдпoлoзeHии, чтo эHepгeтичe cкиe чacтицы B мeзплaHeтHoм пpocтpaHcтBe блyздaют B HeoдHopoдHocтя ч B пpocтpaHHoм мeзплaHeтHoм мaгHитHoм пoлe. HeoдHopoдHocти пpoдBигaютcя co cкopo cтью пpиблизитeльHoй coлHeчHoмy Beтpy. BepoятHoe клaccичecкoe pacпpeдeлe Hиe мoзeт быть пoдBeдeHo пoд ypaBHeHиe Фoккep-ПлaHкa. paзpaбoтa Ho BыpaзeHиe oбщeгo чapaктepa для кoзффициeHтa Kij. pacceяHия чacтиц, Bкл ючaющee кaк pacceяHиe B мaгHитHыч HeoдHopoдHocтяч, тaк и дpeйфы cиcтeмaтичec кoгo дaBлeHия. Дaютcя мaгHитoмeтpoBыe дaHHыe, пoлyчeHHыe иccлeдoBaтeлeм Чy Ш, чтoбы пoкaзaть Hacкoлькo тecHo—B cpeдHeм—мeзплaHeтHoe мaгHитHoe пo лe, B cпoкoйHый дeиь, coглacyeтcя c тeopeтичecким cпиpaльHым yглoм, a тaкзe yкaзaть Ha тo, чтo чacтицы пpиBычHo пepeдBигaютcя cBoбoдHee Bдoль пoля, Heзeли пoпepeк Heгo, K∥,K⊥. Haблюдaeмыe пoля oбHapyзиBaют, чтo кoэффици eHт pacceяHия пpиHaдлeзит пopядкy B 1021–1022 CM2 ceк, cooтBeтcтByющeмy пpeзHим кaл ькyляцим B изyчeHии кocмичecкич лyчeй. cpeдHee зHaчeHиe B 3 × 1021 CM2 ceк, зacтaBляeт пpeдпoлaгaть, чтo гpaдиeHт плoтHocти кocмичecкич лyч eй пpибл. 10% Ha a.e. пoпepeк opбиты зeмли.HeпocpeдcтBeHHыe HaблюдeHия мeзплaHeтHoгo qmaгHитHoг o пoля пpeдocтaBляют BoзмoзHocть кoличecтBeHHoгo BычиcлeHия Kij, B кaчecт Be фyHкции эHepгии чacтиц. ПepBым пpимepoм, пoдлeзaщим paccмoтpeHию, яBляeтcя из oтpoпHoe pacceяHиe B cфepичecкoй oблacти r < R c paBHoмepHoй paдиaльHoй c кopocтью Beтpa v, и oH дaeтcя B дeляч иллюcтpaции oбщeгo чapaктepa пpoдoлзи тeльHocти пpoчoдa чacтицы кocмичecкoгo лyчa чepeз coлHeчHyю cиcтeмy. yк aзыBaeтcя, чтo плoтHocть кocмичecкич лyчeй coкpaщaeтcя B пopядкe eчp (−vR/K) и ч тo cлeдoBaтeльHo B гoды coлHeчHoй aктиBHocти vR>/K He мeHee чeм пpибл. 1 д ля пpoтoHoB oдHoгo Be V, или oкoлo этoгo. Из этoгo cлeдyeт, чтo гaлaктичecкиe чa cтицы кocмичecкич лyчeй, кo BpeмeHи HaблюдeHия ич, yзe oбычHo пpoBeли Hecкoлькo дHeй B coлHeчHoй cиcтeмe. B тeчeHиe этoгo пepиoдa oHи Haчoдятcя B pacши pяющичcя мaгHитHыч пoляч, Hecoмыe coлHeчHым Beтpoм, c aдиaбaтичecки зaмeд лeHHoй cкopocтью, yтpaчиBaя 15 или бoлee пpoцeHтoB cBoeй эHepгии к тoмy Bp eмeHи, чтo oHи пoдBepгaютcя HaблyдeHиям. pacпpeдeлeHиe эHepгии yкaзaHo длH чacти ц c oдиHaкoBoй иcчoдHoй зHepгиeй T0 oт мeззBeздHoгo пpocтpaHcтBa. H acтyпaющaя BepoятHaя BoлHa eдиHoй чacтицы иcчиcляeтcя B кaчecтBe фyHкции B peмeHи, yкaзыBaя кaк чacтицa oтHocитcя Beтpoм.Дaeтcя иллюcтpaция oбpaтHoй пpoблeмы эHHpгeтичecкич coлHeчHыч чacтиц. coлHeчHыe чacтицы мoгyт чapaктepHым oбpaзoм yтepять 50% cBoeй пepBoHaчaльHoй эHepгии дo тoгo, кaк ycкoльзHyть B мeззBeздHoe пpocтpa HcтBo. ДBизeHиe Beтpa, HaпpaBлeHHoe Hapyзy, пepeмeщaeт ич BepoятHoe pa cпpeдeлeHиe Hapyзy тaким oбpaзoм, чтo B кoHeчHoм cчeтe мaкcимaльHaя иHтeH cиBиocть coлHeчHoй чacтицы мoзeт Haчoдитьcя зa пpeдeлaми opбиты зeмли. Ha пpaBлeHHoe Hapyзy дBизeHиe Beтpa ycкopяeт пoHизeHиe иHтeHcиBHocти coлH eчHoй чacтицы. ycтoйчиBoe cocтoяHиe иHтeHcиBHocти кocмичecкич лyчe й Bычиcляeтcя пo Bceй cфepичecкoй oблacти r < R пpи ycлopии paBHoмepHocти плoтHocти No кocмичecкич лyчeй, пoлyчaeмoй B мeззBeздHoм пpocтpaHcтBe. pacчeт пpoизBoдитcя для изoтpoпHoгo Kij и oH пoлyчaeтcя пpи ycлoBии, чтo мaгHи тHыe HeoдHopoдHocти бoльшoй aмплитyды и мacштaбoм HeпpeBышaющим paдиyc B paщeHия чacтиц кocмичecкич лyчeй, a тaкзe для aHизoтpoпHoгo Kij, пpи K∥ ⪢ K⊥, пoлyчaeмoгo, кoгдa пoлe oтHocитeльHo cпoкoиHo. (HaблюдeHия пpи миHи мyмe coлиeчHыч пятeH зacтaBлHют пpeдпoлaгaть, чтo K∥ ⪢ K⊥ Haчoдитcя y o pбиты зeмли.) чacтицы pacceиBayтcя лишь Bдoль cпиpaльHыч лиHий cилы, кoгдa K∥ ⪢ K⊥ и тaким oбpaзoм ич пyть B и из coлHeчHoй cиcтeмы гopaздo длиHee, чeм B т oм cлyчae, кoгдa Kij изoтpoпHo. B paзyльтaтe, иHтeHcиBHocть кocмичecкич лy чeй пoHизaeтcя гopaздo бoльшe для дaHHoгo vR/kij.oтHocитeльHo Kij He имeeтcя HeпocpeдcтBeHHoй oбcepB aциoHHoй иHфopмaции зa пpeдeлoм opбиты зeмли, гдe пpoиcчoдит пoHизeHиe иHтeH cиBHocти. oдHaкo, B pacпopязeHии имeeтcя кocBeHHaя иHфopмaция, кaк тoт фa кт, чтo иHтeHcиBHocть эHepгeтичecкич coлHeчHыч чacтиц Hepeдкo зaтyчaeт, кa к t−g, пpи g = 1,5 – 2,0. yкaзыBaeтcя, чтo для тoгo, чтoбы зтo cлyчилocь, Heoбчoд имo, чтoбы |Kij| αrs пpи S = 0,0 – 0,5, ecли Kij изoтpoпHo, пpoдoлзaлo быть тaк зe aHи зoтpoпHo зa пpeдeлoм зeмли, кaк oHo Haблюдaлocь Bблизи зeмли, и тoг дa pacceяHиe дoлзHo быcтpo yBeличиBaтьcя c paccтoяHиeм oт coлHцa. Эти кoли чecтBeHHыe чapaктepиcтики мoгyт быть лeгкo oбHapyзeHы пpи HaблюдeHияч чacтиц, пo лeй и плaзмы зa пpeдeлoм opбиты зeмли.
Intensities of ∼1–10 MeV relativistic electrons in several energy channels of the high-energy telescope (HET) on Ulysses increase dramatically during its flybys of Jupiter in 1992 and 2004. Perpendicular diffusion coefficients of these particles are derived by fitting the spatial profile of Jovian electron intensity to a diffusion-convection model of particle transport. It is found that the latitudinal diffusion coefficient during the 2004 Jupiter flyby has to be enhanced from its value during the 1992 Jupiter flyby and it is also enhanced relative to the radial perpendicular diffusion. Such an enhancement of latitudinal particle transport was implied previously through the observations of Jovian electrons, cosmic rays and solar energetic particles at high heliographic latitudes, and now this requirement extends further to low latitude region of the heliosphere. Energy dependence of the perpendicular diffusion coefficient is obtained quite precisely through the variation in the slope of energy spectrum of Jovian electrons. The perpendicular diffusion coefficient increases with energy, which can put a tight constraint on models of the particle transport coefficient. The newest nonlinear guiding center (NLGC) theory of perpendicular diffusion is consistent with this observation, but only when it is combined with a parallel diffusion coefficient from the quasilinear theory in a slab magnetic turbulence without dynamic damping.
With a detector on board the OGO-5 satellite, the flux and energy spectrum of electrons in the 10-200-MeV range has been continuously measured from 1968 to 1971. Sudden increases in intensity by factors of up to 300% have been observed during solar quiet times. It is shown that these increases are nearly independent of energy up to about 25 MeV and disappear rapidly above that energy. The frequency of the increases peaks every 13 months at a time following the crossing by earth of the interplanetary magnetic-field line which passes the vicinity of the planet Jupiter. Most of the increases occur in a period of 3 to 5 months following this crossing and often appear to be 27 days apart. A Jovian origin for these electrons and their mode of transport to the inner solar system are discussed.
Observation of low-energy (0.2- to 8-MeV) electron increases observed in interplanetary space on Pioneer 10 as it approached within 1 AU of Jupiter. These discrete bursts or increases were typically several hundred times the normal quiet-time electron flux and became much more frequent with decreasing distance to Jupiter, the result being the quasi-continuous presence of large fluxes of these electrons in interplanetary space. In view of the likely origin of these electrons at Jupiter and the similarity of these increases to quiet-time electron increases previously observed at earth, the temporal presence of the quiet-time increases has been reexamined. It is found that these increases have a 13-month periodicity, indicating a Jovian origin for the events near the earth as well. It is noted that the integrated flux from quiet-time increase electrons at 1 AU is comparable to the integrated ambient electron flux itself.
An analysis of the Jovian electron flux increases observed by the earth-orbiting satellite Imp 8 throughout five 13 month Jovian synodic years during the period from launch of the satellite in 1973 to 1979 is presented. The analysis defines the characteristics of Jovian propagation to earth. Corotating interaction regions (CIR) that form at the leading edges of fast solar wind streams continue to modulate the propagation of MeV electrons from Jupiter to the orbit of the earth to produce approximately 27 day recurrent variations in the Jovian electron density. The new and significant result of this study is that these time-intensity profiles are more accurately described not by assumption that Jupiter is a constant source of electrons, but rather by assuming that electron emission is initiated with each passage of CIR by Jupiter with the emission continuing for only several days.
Residual cosmic-ray modulation at or near the solar minima of 1965 and 1972-75 is compared on the basis of ground-based and satellite observations of nonrelativistic proton and helium components as well as variations in the relativistic component. It is found that the nonrelativistic fluxes lagged behind the high-energy fluxes to form a hysteresis loop over the period from 1965 to 1973, that the 1975 proton fluxes were about 85% higher than the 1972 level and about 35% higher than the 1965 level, and that the 1975 helium fluxes were about 60% higher than in 1965. Some unique recovery events are discussed, and a time-lag effect dependent on magnetic rigidity is examined which was associated with dynamic changes in the heliosphere. A qualitative explanation is offered for the hysteresis effect.
Simultaneous sets of interplanetary and planetary data obtained by Pioneer 10 and Pioneer 11 are compared with a view toward identifying major changes in the solar wind and their possible influence on the Jovian magnetosphere. The results are discussed relative to variations in magnetopause location, pressure balance at the magnetopause, acceleration of energetic trapped radiation, plasma density from the response time of the Jovian magnetosphere, and time constants of magnetospheric circuit models. A major finding is that three out of four cases in which the Pioneers reentered the magnetosheath are the result of time variations associated with changing interplanetary conditions. The compressibility of the Jovian magnetosphere is enhanced because the field inside the magnetopause is not the planetary field but is primarily caused by currents inside the magnetosphere, presumably the equatorial current sheet.
Low energy electron flux as interplanetary radiation primary component, considering data from IMP-1 observations
Detailed examination of the intensity variations of 3- to 12-MeV interplanetary electrons. The data are from the Goddard cosmic-ray experiment on the Imp satellites and cover the period from just before the last solar minimum through the onset of the present solar maximum (i.e., from December 1963 through August 1969). A morphology for the intensity changes is tentatively proposed that includes solar-flare-associated events, solar co-rotating increases, Forbush decreases, quiet-time increases, and the long-term 11-year variation. It is contended that the electron components observed both during quiescent times and during quiet-time increases are galactic in origin. The quiet-time increases represent a completely new phenomenon that appears to be unique to the low-energy electron population. During a quiet-time increase the electron intensity is enhanced by a factor of 3 to 5 over a period of days, and, in general, these periods anticorrelate with low-energy solar particle events. Qualitatively, their amplitude diminishes with increasing solar activity.
Results are reported for a detailed analysis of Pioneer 10 data on energetic particle species in the magnetodisk region of Jupiter's magnetosphere. It is shown that the observed counting rates in the magnetodisk (beyond 20 Jupiter radii) were caused primarily by electrons with energies exceeding 0.06 MeV. Absolute omnidirectional electron intensities in the magnetodisk are presented for five integral energy ranges, and a model electron differential energy spectrum is found to fit the intensities throughout most of the encounter trajectory. It is suggested that the observed spectral shape results from losses of high-energy electrons by pitch-angle scattering. Observed equatorial energy spectra are used to compute distribution functions for several values of the first adiabatic invariant, mu. The radial profiles of the functions are found to have maxima at about 50 Jupiter radii inbound as well as at about 90 radii outbound and to diminish strongly for lesser radii. The large decreases in density are shown to require strong losses, and resonant electron whistler-mode pitch-angle scattering is suggested as a loss mechanism.
The influence of CIRs on the energetic electron flux at 1 AU Quiet-time increases of low-energy electrons – the Jovian origin
- R Kissmann
- H Fichtner
- S E S Ferreira
- J Heureux
- P Meyer
Kissmann, R., Fichtner, H., Ferreira, S.E.S. The influence of CIRs on the energetic electron flux at 1 AU. Astron. Astrophys. 419, 357–363, 2004. L'Heureux, J., Meyer, P. Quiet-time increases of low-energy electrons – the Jovian origin. Astrophys. J. 209, 955–960, 1976.
Modulation of Jovian and galactic electrons in the heliosphere 1: Latitudinal transport of a few MeV electrons New aspects of cosmic-ray modulation in 1974–1975 near solar minimum The transport of cosmic rays across a turbulent magnetic field
- S E S Ferreira
- M S Potgieter
- R A Burger
- B Heber
- H Fichtner
- M Garcia-Munoz
- G M Mason
- J A Simpson
Ferreira, S.E.S., Potgieter, M.S., Burger, R.A., Heber, B., Fichtner, H. Modulation of Jovian and galactic electrons in the heliosphere 1: Latitudinal transport of a few MeV electrons. J. Geophys. Res. 106 (A11), 24979–24988, 2001b. Garcia-Munoz, M., Mason, G.M., Simpson, J.A. New aspects of cosmic-ray modulation in 1974–1975 near solar minimum. Astrophys. J. 213, 263–268, 1977. Giacalone, J., Jokipii, J.R. The transport of cosmic rays across a turbulent magnetic field. Astrophys. J. 520, 204–214, 1999.