Can an isotropic plasma pressure distribution be in force balance with the T96 model field?

2003 ◽  
Vol 108 (A11) ◽  
Author(s):  
Sorin Zaharia
Keyword(s):  
Pressure Distribution ◽  
Plasma Pressure ◽  
Force Balance ◽  
Isotropic Plasma ◽  
Model Field

scholarly journals 3-D force-balanced magnetospheric configurations

2004 ◽  
Vol 22 (1) ◽  
pp. 251-265 ◽  
Author(s):  
S. Zaharia ◽  
C. Z. Cheng ◽  
K. Maezawa
Keyword(s):  
Magnetic Field ◽  
Pressure Distribution ◽  
Equatorial Plane ◽  
Pressure Profile ◽  
Plasma Pressure ◽  
Equatorial Region ◽  
Force Balance ◽  
Quiet Time ◽  
Magnetospheric Configuration And Dynamics ◽  
Field Lines

Abstract. The knowledge of plasma pressure is essential for many physics applications in the magnetosphere, such as computing magnetospheric currents and deriving mag-netosphere-ionosphere coupling. A thorough knowledge of the 3-D pressure distribution has, however, eluded the community, as most in situ pressure observations are either in the ionosphere or the equatorial region of the magnetosphere. With the assumption of pressure isotropy there have been attempts to obtain the pressure at different locations,by either (a) mapping observed data (e.g. in the ionosphere) along the field lines of an empirical magnetospheric field model, or (b) computing a pressure profile in the equatorial plane (in 2-D) or along the Sun-Earth axis (in 1-D) that is in force balance with the magnetic stresses of an empirical model. However, the pressure distributions obtained through these methods are not in force balance with the empirical magnetic field at all locations. In order to find a global 3-D plasma pressure distribution in force balance with the magnetospheric magnetic field, we have developed the MAG-3-D code that solves the 3-D force balance equation computationally. Our calculation is performed in a flux coordinate system in which the magnetic field is expressed in terms of Euler potentials as . The pressure distribution, , is prescribed in the equatorial plane and is based on satellite measurements. In addition, computational boundary conditions for ψ surfaces are imposed using empirical field models. Our results provide 3-D distributions of magnetic field, plasma pressure, as well as parallel and transverse currents for both quiet-time and disturbed magnetospheric conditions. Key words. Magnetospheric physics (magnetospheric configuration and dynamics; magnetotail; plasma sheet)

Plasma pressure and anisotropy inferred from the Tsyganenkomagnetic field model

1994 ◽  
Vol 12 (4) ◽  
pp. 286-295 ◽  
Author(s):  
F. Cao ◽  
L. C. Lee
Keyword(s):  
Magnetic Field ◽  
Field Model ◽  
Anisotropy Parameter ◽  
Numerical Procedure ◽  
Static Condition ◽  
Plasma Pressure ◽  
Field Configuration ◽  
Force Balance ◽  
Pressure Anisotropy ◽  
Empirical Field

Abstract. A numerical procedure has been developed to deduce the plasma pressure and anisotropy from the Tsyganenko magnetic field model. The Tsyganenko empirical field model, which is based on vast satellite field data, provides a realistic description of magnetic field configuration in the magnetosphere. When the force balance under the static condition is assumed, the electromagnetic J×B force from the Tsyganenko field model can be used to infer the plasma pressure and anisotropy distributions consistent with the field model. It is found that the J×B force obtained from the Tsyganenko field model is not curl-free. The curl-free part of the J×B force in an empirical field model can be balanced by the gradient of the isotropic pressure, while the nonzero curl of the J×B force can only be associated with the pressure anisotropy. The plasma pressure and anisotropy in the near-Earth plasma sheet are numerically calculated to obtain a static equilibrium consistent with the Tsyganenko field model both in the noon-midnight meridian and in the equatorial plane. The plasma pressure distribution deduced from the Tsyganenko 1989 field model is highly anisotropic and shows this feature early in the substorm growth phase. The pressure anisotropy parameter αP, defined as αP=1-P\\VertP⊥, is typically ~0.3 at x ≈ -4.5RE and gradually decreases to a small negative value with an increasing tailward distance. The pressure anisotropy from the Tsyganenko 1989 model accounts for 50% of the cross-tail current at maximum and only in a highly localized region near x\\sim-10RE. In comparison, the plasma pressure anisotropy inferred from the Tsyganenko 1987 model is much smaller. We also find that the boundary conditions have significant effects on the plasma pressure distributions and have to be considered carefully.

Inverse approach for estimating pressure and viscosity in the elastohydrodynamic lubrication of circular contacts

2003 ◽  
Vol 217 (4) ◽  
pp. 277-288 ◽  
Author(s):  
Rong-Tsong Lee ◽  
Hsiao-Ming Chu ◽  
Yuang-Cherng Chiou
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Measurement Errors ◽  
Reynolds Equation ◽  
Least Squares Method ◽  
Viscosity Index ◽  
Elastohydrodynamic Lubrication ◽  
Force Balance ◽  
Measuring Point ◽  
Inverse Approach

The film thickness under steady state conditions can be measured by using an optical interferometer. An inverse approach is proposed for estimating the pressure distribution on the basis of film thickness measurement in elastohydrodynamic lubrication (EHL) circular contacts. This approach is constructed from the approximated model of elastic deformation and force balance equations. To obtain an accurate pressure, it is necessary to divide the domain into a few regions on account of the singularity at the pressure spike. The principle of measuring point selection is proposed, and the problem of pressure fluctuation is overcome. On the basis of the smoothed pressure distribution, the apparent viscosity of the film can be obtained from the Reynolds equation. The least-squares method is used to compute the optimum value of the pressure-viscosity index. Results show that the best region for estimating the pressure-viscosity index is along the x axis because the Poiseuille term becomes zero in the Reynolds equation on account of the symmetry. In this region, the estimated pressure-viscosity index shows very good agreement with the exact value when measurement errors are neglected. When measurement errors are taken into account, the close agreement shows the potential of the proposed approach in estimating accurate values of the pressure-viscosity index. Generally, the error in estimating the pressure-viscosity index increases with increasing standard deviation of the measurement error, load, speed, material parameter and absolute error of the measured film thickness. The inverse approach can also be used to estimate the pressure distribution on a film thickness map obtained from an optical EHL tester. Moreover, the agreement between the actual and the estimated values of z is quite good.

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