scholarly journals Evolution of the plasma sheet electron pitch angle distribution by whistler-mode chorus waves in non-dipole magnetic fields

2012 ◽  
Vol 30 (4) ◽  
pp. 751-760 ◽  
Author(s):  
Q. Ma ◽  
B. Ni ◽  
X. Tao ◽  
R. M. Thorne
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Diffusion Equation ◽  
Plasma Sheet ◽  
Diffusion Coefficients ◽  
Electron Distribution ◽  
Dipole Field ◽  
Whistler Mode ◽  
Chorus Waves ◽  
Fokker Planck

Abstract. We present a detailed numerical study on the effects of a non-dipole magnetic field on the Earth's plasma sheet electron distribution and its implication for diffuse auroral precipitation. Use of the modified bounce-averaged Fokker-Planck equation developed in the companion paper by Ni et al. (2012) for 2-D non-dipole magnetic fields suggests that we can adopt a numerical scheme similar to that used for a dipole field, but should evaluate bounce-averaged diffusion coefficients and bounce period related terms in non-dipole magnetic fields. Focusing on nightside whistler-mode chorus waves at L = 6, and using various Dungey magnetic models, we calculate and compare of the bounce-averaged diffusion coefficients in each case. Using the Alternative Direction Implicit (ADI) scheme to numerically solve the 2-D Fokker-Planck diffusion equation, we demonstrate that chorus driven resonant scattering causes plasma sheet electrons to be scattered much faster into loss cone in a non-dipole field than a dipole. The electrons subject to such scattering extends to lower energies and higher equatorial pitch angles when the southward interplanetary magnetic field (IMF) increases in the Dungey magnetic model. Furthermore, we find that changes in the diffusion coefficients are the dominant factor responsible for variations in the modeled temporal evolution of plasma sheet electron distribution. Our study demonstrates that the effects of realistic ambient magnetic fields need to be incorporated into both the evaluation of resonant diffusion coefficients and the calculation of Fokker-Planck diffusion equation to understand quantitatively the evolution of plasma sheet electron distribution and the occurrence of diffuse aurora, in particular at L > 5 during geomagnetically disturbed periods when the ambient magnetic field considerably deviates from a magnetic dipole.

scholarly journals Bounce-averaged Fokker-Planck diffusion equation in non-dipolar magnetic fields with applications to the Dungey magnetosphere

2012 ◽  
Vol 30 (4) ◽  
pp. 733-750 ◽  
Author(s):  
B. Ni ◽  
R. M. Thorne ◽  
Q. Ma
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Diffusion Equation ◽  
Diffusion Coefficients ◽  
Diffusion Processes ◽  
Accurate Determination ◽  
Planck Equation ◽  
Loss Cone ◽  
Scattering Loss ◽  
Fokker Planck

Abstract. We perform a detailed derivation of the bounce-averaged relativistic Fokker-Planck diffusion equation applicable to arbitrary magnetic field at a constant Roederer L. The form of the bounce-averaged diffusion equation is found regardless of details of the mirror geometry, suggesting that the numerical schemes developed for solving the modified two-dimensional (2-D) Fokker-Planck equation in a magnetic dipole should be feasible for similar computation efforts on modeling wave-induced particle diffusion processes in any non-dipolar magnetic field. However, bounce period related terms and bounce-averaged diffusion coefficients are required to be computed in realistic magnetic fields. With the application to the Dungey magnetosphere that is controlled by the intensity of southward interplanetary magnetic field (IMF), we show that with enhanced southward IMF the normalized bounce period related term decreases accordingly, and bounce-averaged diffusion coefficients cover a broader range of electron energy and equatorial pitch angle with a tendency of increased magnitude and peaking at lower energies. The compression of the Dungey magnetosphere can generally produce scattering loss of plasma sheet electrons ~100 keV on a timescale shorter than that in a dipolar field, and induce momentum diffusion at high pitch angles closer to 90°. Correspondingly, the strong diffusion rate drops considerably as a product of changes in both the equatorial loss cone and the bounce period. The extent of differences in all the parameters introduced by the southward IMF intensification also becomes larger for a field line with higher equatorial crossing. With the derived general formulism of bounce-averaged diffusion equation for arbitrary 2-D magnetic field, our results confirm the need for the adoption of realistic magnetic fields to perform accurate determination of electron resonant scattering rates and precise multi-dimensional diffusion simulations of magnetospheric electron dynamics.

scholarly journals Resonant scattering of plasma sheet electrons leading to diffuse auroral precipitation: 2. Evaluation for whistler mode chorus waves

2011 ◽  
Vol 116 (A4) ◽  
pp. n/a-n/a ◽  
Author(s):  
Binbin Ni ◽  
Richard M. Thorne ◽  
Nigel P. Meredith ◽  
Richard B. Horne ◽  
Yuri Y. Shprits
Keyword(s):  
Plasma Sheet ◽  
Resonant Scattering ◽  
Whistler Mode ◽  
Chorus Waves

scholarly journals Townsend Discharges in Transverse Magnetic Fields

1983 ◽  
Vol 36 (6) ◽  
pp. 859 ◽  
Author(s):  
HA Blevin ◽  
MJ Brennan
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Magnetic Fields ◽  
Drift Velocity ◽  
Transverse Magnetic Field ◽  
Electron Concentration ◽  
Diffusion Coefficients ◽  
Concentration Distribution ◽  
Transverse Magnetic ◽  
Electron Drift

Expressions are derived for the electron concentration in Townsend discharges in the presence of a transverse magnetic field for both steady state and pulsed conditions. These results indicate that the two components of the electron drift velocity and the four diffusion coefficients required to describe the concentration distribution can be determined by observation of photons emitted from the discharge.

scholarly journals Pulsation of Rotating Magnetic Stars

1993 ◽  
Vol 139 ◽  
pp. 134-134
Author(s):  
H. Shibahashi ◽  
M. Takata
Keyword(s):  
Magnetic Field ◽  
Fine Structure ◽  
Magnetic Fields ◽  
Rotation Axis ◽  
Dipole Field ◽  
Dipole Mode ◽  
Magnetic Stars ◽  
Ap Stars ◽  
The Magnetic Field ◽  
Split Frequency

Recently, one of the rapidly oscillating Ap stars, HR 3831, has been found to have an equally split frequency septuplet, though its oscillation seems to be essentially an axisymmetric dipole mode with respect to the magnetic axis which is oblique to the rotation axis (Kurtz et al. 1992; Kurtz 1992). In order to explain this fine structure, we investigate oscillations of obliquely rotating magnetic stars by taking account of the perturbations due to the magnetic fields and the rotation. We suppose that the star is rigidly rotating and that the magnetic field is a dipole field and its axis is oblique to the rotation axis. We treat the effects of the rotation and of the magnetic field as perturbations. In doing so, we suppose that the rotation of the star is slow enough so that the effect of the rotation on oscillations is smaller than that of the magnetic field.

Cosmic Ray Particle Diffusion and the Fokker-Planck Equation

1974 ◽  
Vol 2 (5) ◽  
pp. 306-307
Author(s):  
I. H. Urch
Keyword(s):  
Magnetic Field ◽  
Diffusion Coefficients ◽  
Interplanetary Medium ◽  
Planck Equation ◽  
Cosmic Ray ◽  
Particle Diffusion ◽  
Fokker Planck Equation ◽  
The Mean ◽  
Number Of Authors ◽  
Fokker Planck

The Fokker-Planck equation has been used by a number of authors (Jokipii 1966, 1971; Hall and Sturrock 1967; Hasselmann and Wibberentz 1968; Roelof 1968) to deduce the diffusion coefficients of cosmic-ray particles in the interplanetary magnetic field. However, these calculations suggest that the diffusion of particles perpendicular to the mean magnetic field is implausibly large; so large that the validity of a Fokker-Planck approach as applied to the interplanetary medium must be doubted.

scholarly journals Magnetic field evolution in magnetars

2012 ◽  
Vol 8 (S291) ◽  
pp. 425-427
Author(s):  
Yasufumi Kojima
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Field Strength ◽  
Neutron Stars ◽  
Dipole Field ◽  
Polar Field ◽  
Nonlinear Coupling ◽  
Strong Magnetic Fields ◽  
Field Decay ◽  
The Magnetic Field

AbstractDynamics of magnetic field decay is numerically studied. For neutron stars with strong magnetic fields, the Hall drift timescale in their crust is very short, and therefore the evolution is significantly affected. The nonlinear coupling between poloidal and toroidal components of the magnetic field is studied. It is also found that the polar field at the surface is highly distorted during the Hall drift timescale. For example, polar dipole field-strength temporarily decreases not by dissipation but by advection. This fact suggests that the dipole field-strength is not sufficient to determine the border between pulsars and magnetars.

Cosmic ray transport in non-uniform magnetic fields: consequences of gradient and curvature drifts

2010 ◽  
Vol 76 (3-4) ◽  
pp. 317-327 ◽  
Author(s):  
R. SCHLICKEISER ◽  
F. JENKO
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Magnetic Fields ◽  
Transport Equation ◽  
Diffusion Coefficients ◽  
Cosmic Ray ◽  
Spatial Diffusion ◽  
Phase Space Density ◽  
Space Density ◽  
Drift Terms

AbstractLarge-scale spatial variations of the guide magnetic field of interplanetary and interstellar plasmas give rise to the mirror force −(p⊥2/2mγB)∇B). The parallel component of this mirror force causes adiabatic focusing of the cosmic ray guiding center whereas the perpendicular component of the mirror force gives rise to the gradient and curvature drifts of the cosmic ray guiding center. Adiabatic focusing and the gradient and curvature drift terms additionally enter the Fokker–Planck transport equation for the gyrotropic cosmic ray particle phase space density in partially turbulent non-uniform magnetic fields. For magnetohydrodynamic turbulence with dominating magnetic fluctuations, the diffusion approximation is justified, which results in a modification of the diffusion–convection transport equation for the isotropic part of the gyrotropic phase space density from the additional focusing and drift terms. For axisymmetric undamped slab Alfvenic turbulence we show that all perpendicular spatial diffusion coefficients are caused by the non-vanishing gradient and curvature drift terms. For a specific (symmetric in μ) choice of the pitch-angle Fokker–Planck coefficients we show that the ratio of the perpendicular to parallel spatial diffusion coefficients apart from a constant is determined by the spatial first derivatives of the non-constant cosmic ray Larmor radius in the non-uniform magnetic field.

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