David Ruffolo

Effect of adiabatic deceleration on the focused transport of solar cosmic rays

In the framework of focused transport theory, adiabatic deceleration arises from adiabatic focusing in the solar wind frame and from differential solar wind convection. An explicit formula is given for the deceleration of individual particles as a function of the pitch angle. Deceleration and other first-order effects of the solar wind, including convection, are incorporated into a numerical code for simulating the transport of energetic particles along the interplanetary magnetic field. We use this code to model the transport of solar flare protons. We find that including deceleration can increase the decay rate of the near-Earth intensity by 75\% more than would be expected based on advection from higher momenta, due to an interplay with diffusive processes. Improved response functions are derived for the impulsive injection of particles near the Sun, and it is found that neglecting deceleration leads to incorrect estimates of the scattering mean free path based on the intensity decay alone, especially for lower-energy particles.

ENERGETIC PARTICLE OBSERVATIONS DURING THE 2000 JULY 14 SOLAR EVENT

Data from nine high-latitude neutron monitors are used to deduce the intensity-time and anisotropytime pro—les and pitch-angle distributions of energetic protons near Earth during the major solar event on 2000 July 14 (also known as the Bastille Day event). In addition, particle and magnetic —eld measurements from W ind, the Advanced Composition Explorer, and the Solar and Heliospheric Observatory (SOHO) are used in the analysis. The observations are —tted with good agreement between two independent numerical models of interplanetary transport. The rapid decrease of anisotropy from a high initial value cannot be explained by a simple model of interplanetary transport. Hence, we invoke a barrier or magnetic bottleneck consistent with an observed magnetic disturbance from an earlier coronal mass ejec

Spectral Properties and Length Scales of Two-dimensional Magnetic Field Models

Two-dimensional (2D) models of magnetic field fluctuations and turbulence are widely used in space, astrophysical, and laboratory contexts. Here we discuss some general properties of such models and their observable power spectra.Whilethefieldlinerandomwalkinaone-dimensional(slab)modelisdeterminedbythecorrelationscale,for 2Dmodels,itischaracterizedbyadifferentlengthscale,theultrascale.Wediscusspropertiesofcorrelationscalesand ultrascales for 2D models and present a technique for determining an ultrascale from observations at a single spacecraft, demonstrating its accuracy for synthetic data. We also categorize how the form of the low-wavenumber spectrum affects the correlation scales and ultrascales, thus controlling the diffusion of magnetic field lines and charged test particle motion. Subject headingg diffusion — magnetic fields — turbulence

SPACESHIP EARTH OBSERVATIONS OF THE EASTER 2001 SOLAR PARTICLE EVENT

The largest relativistic (~1 GeV) solar proton event of the current solar activity cycle occurred on Easter 2001 (April 15). This was the first such event to be observed by Spaceship Earth, an 11-station network of neutron monitors optimized for measuring the angular distribution of solar cosmic rays. We derive the particle density and anisotropy as functions of time and model these with numerical solutions of the Boltzmann equation. We conclude that transport in the interplanetary medium was diffusive in this event, with a radial mean free path of 0.17 AU. The high time resolution of the Spaceship Earth network and the fast particle speed permit accurate determination of particle injection timing at the solar source. We find that particle injection at the Sun began at 13:42 UT ±1 minute, about 14 minutes before the first arrival of particles at Earth, in close association with the onset of shock-related radio emissions and ~15 minutes after liftoff of a coronal mass ejection (CME). Our results are consistent with the hypothesis that solar particles were accelerated to GeV energies on Easter 2001 by a CME-driven shock wave.

Separation of Magnetic Field Lines in Two-Component Turbulence

The problem of the separation of random magnetic field lines in collisionless astrophysical plasmas is closely related to the problem of the magnetic field line random walk and is highly relevant to the transport of charged particles in turbulent plasmas. In order to generalize treatments based on quasi-linear theory, here we examine the separation of nearby magnetic field lines by employing a nonperturbative technique based on the Corrsin independence hypothesis. Specifically, we consider the case of two-component turbulence in which the magnetic field fluctuations are a mixture of one-dimensional (slab) and two-dimensional ingredients, as a concrete example of anisotropic turbulence that provides a useful description of turbulence in the solar wind. We find that random field trajectories can separate in general through three regimes of the behavior of the running diffusion coefficient: slow diffusive separation, an intermediate regime of superdiffusion, and fast diffusive separation at large distances. These features are associated with the gradual, exponential divergence of field lines within islands of two-dimensional turbulence, followed by diffusive separation at long distances. The types of behavior are determined not by the Kubo number but rather a related ratio that takes the turbulence anisotropy into account. These results are confirmed by computer simulations. We discuss implications for space observations of energetic charged particles, including ‘‘dropouts’’ of solar energetic particles.

Interplanetary transport of decay protons from solar flare neutrons

We have developed models for the propagation of protons produced by the decay of solar flare neutrons. These models are applied to the observation of such protons on 1982 June 3 and 1984 April 25. Since the decay protons are produced with the same direction and velocity as the parent neutrons, these events provide a unique opportunity to measure the spectrum of emitted neutrons and to study the pitch-angle scattering of energetic protons as it transforms a monodirectional beam into an isotropic distribution

On the Estimation of Solar Energetic Particle Injection Timing from Onset Times near Earth

We examine the accuracy of a common technique for estimating the start time of solar energetic particle injection based on a linear fit to the observed onset time versus 1/(particle velocity). This is based on a concept that the first arriving particles move directly along the magnetic field with no scattering. We check this by performing numerical simulations of the transport of solar protons between 2 and 2000 MeV from the Sun to the Earth, for several assumptions regarding interplanetary scattering and the duration of particle injection, and by analyzing the results using the inverse velocity fit. We find that, in most cases, the onset times align close to a straight line as a function of inverse velocity. Despite this, the estimated injection time can be in error by several minutes. Also, the estimated path length can deviate greatly from the actual path length along the interplanetary magnetic field. The major difference between the estimated and actual path lengths implies that the first arriving particles cannot be viewed as moving directly along the interplanetary magnetic field.

Loss Cone Precursors to Forbush Decreases and Advance Warning of Space Weather Effects

Ground-based observations of cosmic rays by neutron monitors and muon detectors have found precursor anisotropies before the arrival of an interplanetary shock and subsequent Forbush decrease, possibly providing advance warning of space weather effects on shock impact at the Earths magnetosphere. Surprisingly, muon detectors observe precursors with a greater lead time than neutron monitors. Here, we explain both loss cone and shock reflection precursors in a common mathematical framework and perform time-dependent numerical simulations of cosmic-ray transport near an oblique, planar shock. We examine parameters of loss cone precursors as a function of the shock-magnetic field angle and q, the spectral index of magnetic turbulence. More energetic particles correspond to a lower value of q and a higher value of λ, the interplanetary scattering mean free path. We conclude that loss cones should typically be detectable 4 hr prior to shock arrival at neutron monitor energies (~10 GeV) and 15 hr prior to shock arrival at muon detector energies (~30 GeV). In addition, the angular width of the loss cone provides a potential method of forecasting the shock-field angle, as the predicted width is substantially larger for quasi-parallel shocks than for quasi-perpendicular shocks, leading to a better indication of the shock arrival time.

Relativistic Solar Protons on 1989 October 22: Injection and Transport along Both Legs of a Closed Interplanetary Magnetic Loop

Worldwide neutron monitor observations of relativistic solar protons on 1989 October 22 have proven puzzling, with an initial spike at some stations followed by a second peak, which is difficult to understand in terms of transport along a standard Archimedean spiral magnetic field or a second injection near the Sun. Here we analyze data from polar monitors, which measure the directional distribution of solar energetic particles (mainly protons) at rigidities of � 1‐3 GV. This event has the unusual properties that the particle density dips after the initial spike, followed by a hump with bidirectional flows and then a very slow decay. The spectral index, determined using bare neutron counters, varies dramatically, with energy dispersion features. The density and anisotropy data are simultaneously fit by simulating the particle transport for various magnetic field configurations and determining the best-fit injection functionneartheSun.ThedataarenotwellfitforanArchimedeanspiralfield,amagneticbottleneckbeyondEarth,or particle injection along one leg of a closed magnetic loop. A model with simultaneous injection along both legs of a closed loop provides a better explanation: particles moving along the near leg make up the spike, those coming from thefarlegmakeupthehump,bothlegscontributetothebidirectional streaming,andtrappingintheloopaccountsfor the slow decay of the particle density. Refined fits indicate a very low spectral index of turbulence, q < 1, a parallel mean free path of 1.2‐2.0 AU, a loop length of 4:7 � 0:3 AU, and escape of relativistic protons from the loop on a timescale of 3 hr. The weak scattering is consistent with reports of weak fluctuations in magnetic loops, while the low q-value may indicate a smaller correlation length as well.

Random Walk of Magnetic Field Lines in Nonaxisymmetric Turbulence

The random walk of turbulent magnetic field lines strongly affects transport of energetic particles in astrophysical plasmas, but is not well understood for general configurations that lack rotational symmetry. Here we derive nonperturbative field-line diffusion coefficients for magnetic fluctuations that are nonaxisymmetric with respect to the mean magnetic field. We consider a superposition of slab plus two-dimensional fluctuations, a model that has proven useful in heliospheric studies. Two independent parameters are introduced to allow polarization of the slab component and stretching of the two-dimensional component. With the assumptions of homogeneity, the diffusion approximation, and Corrsins independence hypothesis, we derive two coupled biquadratic equations for the diffusion coefficients. The results and underlying assumptions are confirmed by numerical simulations. Special cases of interest include the counterintuitive results that enhanced fluctuations in one direction lead to decreased diffusion in the other direction, and that extreme nonaxisymmetry leads to diffusion coefficients proportional to the rms two-dimensional fluctuation.