Flux stationnaires et supersoniques de protons, paralleles au champ magnétique

1974 ◽  
Vol 52 (23) ◽  
pp. 2402-2421 ◽  
Author(s):  
M. Fridman
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Heat Flux ◽  
Transport Equations ◽  
Total Loss ◽  
Gyration Radius ◽  
Maximum Order ◽  
Champ Magnétique ◽  
The Magnetic Field

Using the gyration radius as the parameter to expand the differential equation for the moments, the transport equations for highly supersonic flux, which is parallel to the magnetic field, are obtained. The maximum order one can hope to obtain for the invariants is discussed together with the relation between the function of distribution f1 proposed by Whang and that which must result at 1 AU if f1 or a bimaxwellian function are used at the origin. Using f01 at the base (~ 55 Rs) it can be estimated that the total loss of heat flux under 1 AU is of the order of 70% on condition that the values obtained after f1 are utilized.

CGL Invariants and the Moments of the Boltzmann–Vlasov Equation

1974 ◽  
Vol 52 (14) ◽  
pp. 1345-1357 ◽  
Author(s):  
M. Fridman
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Solar Wind ◽  
Vlasov Equation ◽  
Gyration Radius ◽  
Solar Wind Parameters ◽  
Essential Problem ◽  
The Magnetic Field ◽  
Transport Laws ◽  
Good Agreement

The transport laws of the noncollisional systems must be obtained from the Boltzmann–Vlasov equation. The most simple cases are the CGL invariants along the magnetic field. The essential problem is to determine the criteria necessary to close the moments system. The lower order in the gyration radius expansion gives the perpendicular contribution to the heat flux. After expansion with the supersonic conditions, the parallel contribution is obtained, and also the second term of the expansions in which the first term is the "invariant." The numerical value of the heat flux can be considered in good agreement with the solar wind parameters, and the corrections to the invariants are found to agree with previous results (kinetical and 20-moments Grad approximation).

scholarly journals Comparison of the measured and modelled electron densities and temperatures in the ionosphere and plasmasphere during 20-30 January, 1993

2000 ◽  
Vol 18 (10) ◽  
pp. 1257-1262 ◽  
Author(s):  
A. V. Pavlov ◽  
T. Abe ◽  
K.-I. Oyama
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Electron Temperature ◽  
Field Line ◽  
Electron Density ◽  
Magnetic Field Line ◽  
New Approach ◽  
Additional Heating ◽  
Vibrational Levels ◽  
The Magnetic Field

Abstract. We present a comparison of the electron density and temperature behaviour in the ionosphere and plasmasphere measured by the Millstone Hill incoherent-scatter radar and the instruments on board of the EXOS-D satellite with numerical model calculations from a time-dependent mathematical model of the Earth's ionosphere and plasmasphere during the geomagnetically quiet and storm period on 20–30 January, 1993. We have evaluated the value of the additional heating rate that should be added to the normal photoelectron heating in the electron energy equation in the daytime plasmasphere region above 5000 km along the magnetic field line to explain the high electron temperature measured by the instruments on board of the EXOS-D satellite within the Millstone Hill magnetic field flux tube in the Northern Hemisphere. The additional heating brings the measured and modelled electron temperatures into agreement in the plasmasphere and into very large disagreement in the ionosphere if the classical electron heat flux along magnetic field line is used in the model. A new approach, based on a new effective electron thermal conductivity coefficient along the magnetic field line, is presented to model the electron temperature in the ionosphere and plasmasphere. This new approach leads to a heat flux which is less than that given by the classical Spitzer-Harm theory. The evaluated additional heating of electrons in the plasmasphere and the decrease of the thermal conductivity in the topside ionosphere and the greater part of the plasmasphere found for the first time here allow the model to accurately reproduce the electron temperatures observed by the instruments on board the EXOS-D satellite in the plasmasphere and the Millstone Hill incoherent-scatter radar in the ionosphere. The effects of the daytime additional plasmaspheric heating of electrons on the electron temperature and density are small at the F-region altitudes if the modified electron heat flux is used. The deviations from the Boltzmann distribution for the first five vibrational levels of N2(v) and O2(v) were calculated. The present study suggests that these deviations are not significant at the first vibrational levels of N2 and O2 and the second level of O2, and the calculated distributions of N2(v) and O2(v) are highly non-Boltzmann at vibrational levels v > 2. The resulting effect of N2(v > 0) and O2(v > 0) on NmF2 is the decrease of the calculated daytime NmF2 up to a factor of 1.5. The modelled electron temperature is very sensitive to the electron density, and this decrease in electron density results in the increase of the calculated daytime electron temperature up to about 580 K at the F2 peak altitude giving closer agreement between the measured and modelled electron temperatures. Both the daytime and night-time densities are not reproduced by the model without N2(v > 0) and O2(v > 0), and inclusion of vibrationally excited N2 and O2 brings the model and data into better agreement.Key words: Ionosphere (ionospheric disturbances; ionosphere-magnetosphere interactions; plasma temperature and density)  

Viscomagnetic Heat Flux Experiments as a Test of Gas Kinetic Theory in the Burnett Regime

1978 ◽  
Vol 33 (7) ◽  
pp. 749-760 ◽  
Author(s):  
G. E. J. Eggermont ◽  
P. W. Hermans ◽  
L. J. F. Hermans ◽  
H. F. P. Knaap ◽  
J. J. M. Beenakker
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Heat Flux ◽  
External Magnetic Field ◽  
Room Temperature ◽  
Flow Direction ◽  
Rectangular Channel ◽  
Gas Kinetic Theory ◽  
The Magnetic Field ◽  
Good Agreement

In a rarefied polyatomic gas streaming through a rectangular channel, an external magnetic field produces a heat flux perpendicular to the flow direction. Experiments on this “viscom agnetic heat flux” have been performed for CO, N2, CH4 and HD at room temperature, with different orientations of the magnetic field. Such measurements enable one to separate the boundary layer contribution from the purely bulk contribution by means of the theory recently developed by Vestner. Very good agreement is found between the experimentally determined bulk contribution and the theoretical Burnett value for CO, N2 and CH4 , yet the behavior of HD is found to be anomalous.

Etude Numérique de la Section Efficace de Diffusion d'un Faisceau Laser par un Plasma en Champ Magnétique. Application à la Détermination Expérimentale de la Direction du Champ Magnétique de Confinement

1973 ◽  
Vol 51 (3) ◽  
pp. 266-276 ◽  
Author(s):  
R. L. Meyer ◽  
G. Leclert ◽  
M. Felden
Keyword(s):  
Magnetic Field ◽  
Cross Section ◽  
Field Intensity ◽  
Magnetic Field Intensity ◽  
Scattered Wave ◽  
Magnetic Field Direction ◽  
Section Efficace ◽  
Experimental Conditions ◽  
Champ Magnétique ◽  
The Magnetic Field

We study the influence of the magnetic field intensity and direction with respect to the wave vector on the scattering cross-section resonances. We deduce the best experimental conditions for studying these resonances. It is shown that the spectrum modulation of the scattered wave can be used to measure, in some configurations, the confining magnetic field direction.

Theory of Lubrication With Ferrofluids: Application to Short Bearings

1982 ◽  
Vol 104 (4) ◽  
pp. 510-515 ◽  
Author(s):  
Nicolae Tipei
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Reynolds Equation ◽  
Viscous Fluids ◽  
Pressure Differential ◽  
Numerical Example ◽  
Bearing Stiffness ◽  
Pyromagnetic Coefficient ◽  
The Magnetic Field

The momentum equations are written for viscous fluids exhibiting magnetic stresses. The velocity profiles are deduced; then from continuity, a pressure differential equation, equivalent to Reynolds equation is obtained. This equation is discussed with emphasis on the case when magnetic stresses derive from a potential, also when the pyromagnetic coefficient vanishes. The boundary conditions for lubrication problems are then formulated. In particular, short bearings with ferromagnetic lubricants are considered. A numerical example yields the pressure diagrams at low and moderate eccentricity ratios and for different speeds. In conclusion, it is shown that ferromagnetic lubricants may improve substantially the performance of bearings operating under low loads and/or at low speeds. However, a correct variation of the magnetic field, toward the center of the lubricated area, is required. Under such conditions, the extent of the active area of the film is increased and bearing stiffness and stability are improved.

On the method of matched asymptotic expansions

1969 ◽  
Vol 65 (1) ◽  
pp. 263-284 ◽  
Author(s):  
L. E. Fraenkel
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Formal Method ◽  
Reynolds Numbers ◽  
Linear Ordinary Differential Equation ◽  
Steady Current ◽  
Formal Procedure ◽  
Small Reynolds Numbers ◽  
The Magnetic Field

AbstractThe formal method of matched expansions is applied to two further examples. The first concerns the magnetic field induced by a steady current in a thin toroidal wire. The second, which involves a non-linear ordinary differential equation of the fourth order, has been chosen to resemble the problem of flow past a circular cylinder at small Reynolds numbers. The results of the formal procedure are proved in each case to be expansions of the exact solution.

scholarly journals Investigating the n=1 and n=2 error fields in W7-X using the newly accelerated FIELDLINES code

2021 ◽  
Author(s):  
Dion Engels ◽  
Samuel A Lazerson ◽  
Victor Bykov ◽  
Josefine H E Proll
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Collision Model ◽  
Fusion Device ◽  
Load Asymmetry ◽  
Wall Collision ◽  
Error Field ◽  
Line Diffusion ◽  
And Control ◽  
The Magnetic Field

Abstract No fusion device can be created without any uncertainty; there is always a slight deviation from the geometric specification. These deviations can add up create a deviation of the magnetic field. This deviation is known as the (magnetic) error field. Correcting these error fields is desired as they cause asymmetries in the divertor loads and can thus cause damage to the device if they grow too large. These error fields can be defined by their toroidal (n) and poloidal number (m). The correction of the n = 1 and n = 2 fields in Wendelstein 7-X (W7-X) is investigated in this work. This investigation focuses on field line diffusion to the divertor, a proxy for divertor heat flux. Such work leverages the 25x speedup obtained through the implementation of a new particle-wall collision model. The n = 1 and n = 2 error fields of the as-built coils model of W7-X are corrected by scanning phase and amplitude of the trim and control coils. Reductions in the divertor load asymmetry by factors of four are demonstrated using error field correction. It is found that the as-built coils model has a significantly lower m⁄n = 1⁄1 error field than found in experiments.

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