John W. Bieber

Dominant two‐dimensional solar wind turbulence with implications for cosmic ray transport

Two new methods for distinguishing two-dimensional (2D) turbulence from slab turbulence are applied to Helios magnetometer data. Two-component models with varying slab and 2D ingredients are considered. Both methods indicate that solar wind magnetic turbulence possesses a dominant (∼85 % by energy) 2D component. The presence of such a large 2D component provides a natural solution to the long-standing problem of “too small” cosmic ray mean free paths derived from quasilinear scattering theory when using the slab model.

Nonlinear Collisionless Perpendicular Diffusion of Charged Particles

A nonlinear theory of the perpendicular diffusion of charged particles is presented, including the influence of parallel scattering and dynamical turbulence. The theory shows encouraging agreement with numerical simulations. Subject headings: diffusion — turbulence

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

Perpendicular Transport of Charged Particles in Composite Model Turbulence: Recovery of Diffusion

The computation of charged particle orbits in model turbulent magnetic fields is used to investigate the properties of particle transport in the directions perpendicular to the large-scale magnetic field. Recent results by Qin, Matthaeus, & Bieber demonstrate that parallel scattering suppresses perpendicular diffusion to a subdiffusive level when the turbulence lacks transverse structure. Here numerical computations are used to show that in turbulence in which there is substantial transverse structure, a second regime of diffusive transport can be established. In both the subdiffusion regime and this second diffusion regime, perpendicular transport is intrinsically nonlinear. The regime of second diffusion persists for long times and may therefore be of interest in astrophysical transport problems such as the scattering and solar modulation of cosmic rays.

Nonlinear parallel and perpendicular diffusion of charged cosmic rays in weak turbulence

The problem of particle transport perpendicular to a magnetic background field is well known in cosmic-ray astrophysics. Whereas it is widely accepted that quasi-linear theory (QLT) of particle transport does not provide the correct results for perpendicular diffusion, it was assumed for a long time that QLT is the correct theory for parallel diffusion. In the current paper we demonstrate that QLT is in general also incorrect for parallel particle transport if we consider composite turbulence geometry. Motivated through the recent success of the so-called nonlinear guiding center theory of perpendicular diffusion, we present a new theory for parallel and perpendicular diffusion of cosmic rays. This new theory is a nonlinear extension of QLT and provides us with a coupled system of nonlinear Fokker-Planck coefficients. By solving the resulting system of integral equations we obtain new results for the pitch-angle Fokker-Planck coefficient and the Fokker-Planck coefficient of perpendicular diffusion. By integrating over pitch angle we calculate the parallel and perpendicular mean free path. To our knowledge the new theory is the first that can deal with both parallel and perpendicular diffusion in agreement with simulations.

The radial and latitudinal dependence of the cosmic ray diffusion tensor in the heliosphere

The radial and latitudinal dependence of the cosmic ray diffusion tensor is investigated on the basis of a recently developed model of magnetohydrodynamic turbulence in the expanding solar wind [Zank et al., 1996a,b; Matthaeus et al., 1996]. In the ecliptic plane, decaying magnetohydrodynamic turbulence is assumed to be replenished in situ by turbulence generated through the interaction of streams (both shear and compressional effects) and by the creation of pickup ions. In the polar region, at least during solar minimum, stream interaction driven turbulence is neglected and only pickup ion driven turbulence is included. To model the perpendicular and drift elements of the cosmic ray diffusion tensor, we employ both a quasi-linear theory (QLT) and a newly developed nonperturbative theory (NPT) to describe the field line wandering which drives perpendicular transport. A resonant quasi-linear description is applied to the parallel component. For the QLT approach, we find that in the solar wind ecliptic plane (1) the radial diffusive length scale or mean free path (mfp) is very nearly constant until some 10 AU, after which it experiences some variation with increasing heliocentric distance; (2) the radial mfp is dominated at all radial distances by the component parallel to the mean magnetic field and the perpendicular component is completely unimportant; (3) the length scale associated with the drift component of the cosmic ray diffusion tensor is only comparable to the radial mfp beyond ∼ 10 AU; and (4) the rigidity P dependence of the radial mfp within 10 – 20 AU is weak and proportional to P1/3, but in the far outer heliosphere it is proportional to P2. For the QLT model in the polar region of the solar wind, we find that the radial cosmic ray mfp is much greater than the corresponding mfp in the ecliptic region, consistent with observed mfps for pickup ions reported by Gloeckler et al. [1995]. The polar models are, however, preliminary and assume vanishing cross-helicity. The polar radial mfp is dominated by the parallel component, and drift length scales are never comparable to the radial mfp in the high polar latitudes. By using instead a nonperturbative model for the perpendicular and drift components of the cosmic ray diffusion tensor, it was found that the mfps for these coefficients could be significantly larger than their QLT counterparts. The increased perpendicular mfp was found to be important in the radial mfp only beyond ∼ 20 AU, which remains dominated by the parallel diffusion within this distance. Within the ecliptic, the nonperturbative model yields a radial mfp for cosmic rays that is almost constant with heliocentric distance. Similar order of magnitude differences between the radial mfps in the ecliptic and polar regions of the solar wind are found with the nonperturbative models.

Solar cycle variation of the interplanetary magnetic field spiral

Interplanetary measurements spanning the time interval from 1965 through 1987 and a distance range from 0.7 to 15.9 AU are employed to test the Parker (1958) theory for the large-scale structure of the interplanetary magnetic field. Examination of data recorded by earth-orbiting spacecraft reveals that the interplanetary magnetic field spiral depends upon the phase of the solar cycle, such that the annual mean winding angle in the years surrounding solar maximum is about 10 deg larger than in the years surrounding solar minimum. The observed variation of the solar wind speed with the solar cycle is shown to account for much of the recorded variation in the winding angle. It is suggested that nonzero azimuthal field components arising from differential solar rotation may be convected into the corona to provide a steady source of azimuthal magnetic fields at the source point of the solar wind. A straightforward extension of the Parker theory shows how such seed fields would account for the observed discrepancy in the interplanetary spiral winding. 38 refs.

Analytic Forms of the Perpendicular Diffusion Coefficient in Magnetostatic Turbulence

Recently, a nonlinear theory for perpendicular diffusion of charged particles was presented. This theory is called the nonlinear guiding center theory and provides an integral equation for the perpendicular mean free path. In this paper we consider analytical solutions of this equation in the case of magnetostatic turbulence. The resulting formulas for the perpendicular mean free path are discussed. We also compare these new results with results of the quasi-linear theory for parallel diffusion and with observational results.

Cosmic-ray anisotropies and gradients in three dimensions

Neutron monitor data recorded at Thule, Greenland, and McMurdo, Antarctica, are used to determine the cosmic-ray north-south anisotropy over the period 1961-1988. This anisotropy shows an 11 yr sunspot cycle variation, but it does not exhibit a dependence upon the direction of the Suns magnetic dipole. The north-south anisotropy together with the two components of the diurnal anisotropy comprise a three-dimensional anisotropy, from which we extract detailed new information on the radial and latitudinal gradients of cosmic-ray density and the cosmic-ray scattering mean free path near Earth. We find that the bidirectional latitude gradient reverses sign with the solar magnetic polarity reversal, in accord with the predictions of drift theory, and its magnitude is generally larger during negative solar polarity than during positive polarity

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