Force-balance equation for a pinned lattice of Abrikosov vortices

1996 ◽  
Vol 54 (21) ◽  
pp. 15468-15470 ◽  
Author(s):  
Kwangyl Bark ◽  
Gabriele F. Giuliani
Keyword(s):  
Balance Equation ◽  
Force Balance ◽  
Force Balance Equation ◽  
Abrikosov Vortices

scholarly journals Force balance in current sheets in collisionless plasma

2021 ◽  
Vol 7 (2) ◽  
pp. 11-21
Author(s):  
Oleg Mingalev ◽  
Pavel Setsko ◽  
Mikhail Melnik ◽  
Igor Mingalev ◽  
Helmi Malova ◽  
...  
Keyword(s):  
Current Sheet ◽  
Balance Equation ◽  
Normal Component ◽  
Collisionless Plasma ◽  
Force Balance ◽  
One Dimensional ◽  
Current Sheets ◽  
First Time ◽  
The Magnetic Field ◽  
Force Balance Equation

In this paper, we derive a divergent form of the force balance equation for collisionless plasma in the quasineutrality approximation, in which the electric field and current density are excluded. For a stationary spatially one-dimensional current sheet with a constant normal component of the magnetic field and magnetized electrons, the general form of the force balance equation has been obtained for the first time in the form of a conservation law. An equation in this form is necessary for the correct formulation of boundary conditions when modeling asymmetric current sheets, as well as for the control of the stationarity of the numerical solution obtained in the model. Furthermore, the fulfillment of this equation is considered for two types of stationary configurations of a thin current sheet, which are obtained using a numerical model. The derived equation makes it possible to develop models of asymmetric current sheets, in particular current sheets on the magnetopause flanks in the magnetotail.

scholarly journals Experimental test of the radial force balance equation in the compact helical system

2001 ◽  
Vol 8 (1) ◽  
pp. 1-4 ◽  
Author(s):  
K. Ida ◽  
A. Fujisawa ◽  
H. Iguchi ◽  
Y. Yoshimura ◽  
T. Minami ◽  
...  
Keyword(s):  
Experimental Test ◽  
Balance Equation ◽  
Radial Force ◽  
Force Balance ◽  
Force Balance Equation

Impurity Resistivity under Thermalized Condition

1992 ◽  
Vol 06 (07) ◽  
pp. 1079-1098 ◽  
Author(s):  
C.S. Ting ◽  
L.Y. Chen
Keyword(s):  
Relaxation Time ◽  
Balance Equation ◽  
Center Of Mass ◽  
Charge Carriers ◽  
Force Balance ◽  
Electron Interaction ◽  
Time Approximation ◽  
Relaxation Time Approximation ◽  
Scattering Time ◽  
Force Balance Equation

The standard impurity resistivity based upon the force-balance equation is derived with use of the method of closed-time-path Green’s functions. In this the effects from both the noncommutability of the center of mass fluctuations at different times and the exact noncannonical commutation relations between the coordinates and momentum of relative electrons are considered. In the presence of a short momentum-conserving inelastic scattering time due to electron-electron interaction, fast thermalization among charge carriers can be achieved. Under this condition, the (thermalized) impurity resistivity will have different form than the standard impurity resistivity and it is practically given by the lowest order electron-impurity term in the force balance equation. We also demonstrate that this conclusion is consistent with results based upon the Boltzmann equation in a relaxation time approximation.

Consistent derivation of impurity resistivity from the force-balance equation

1990 ◽  
Vol 42 (2) ◽  
pp. 1129-1141 ◽  
Author(s):  
L. Y. Chen ◽  
C. S. Ting ◽  
N. J. M. Horing
Keyword(s):  
Balance Equation ◽  
Force Balance ◽  
Force Balance Equation

scholarly journals Force balance in current sheets in collisionless plasma

2021 ◽  
Vol 7 (2) ◽  
pp. 12-23
Author(s):  
Oleg Mingalev ◽  
Pavel Setsko ◽  
Mikhail Melnik ◽  
Igor Mingalev ◽  
Helmi Malova ◽  
...  
Keyword(s):  
Current Sheet ◽  
Balance Equation ◽  
Normal Component ◽  
Collisionless Plasma ◽  
Force Balance ◽  
One Dimensional ◽  
Current Sheets ◽  
First Time ◽  
The Magnetic Field ◽  
Force Balance Equation

In this paper, we derive a divergent form of the force balance equation for collisionless plasma in the quasineutrality approximation, in which the electric field and current density are excluded. For a stationary spatially one-dimensional current sheet with a constant normal component of the magnetic field and magnetized electrons, the general form of the force balance equation has been obtained for the first time in the form of a conservation law. An equation in this form is necessary for the correct formulation of boundary conditions when modeling asymmetric current sheets, as well as for the control of the stationarity of the numerical solution obtained in the model. Furthermore, the fulfillment of this equation is considered for two types of stationary configurations of a thin current sheet, which are obtained using a numerical model. The derived equation makes it possible to develop models of asymmetric current sheets, in particular current sheets on the magnetopause flanks in the magnetotail.

scholarly journals NONISOTHERMAL NEWTONIAN FILM BLOWING

2005 ◽  
Vol 10 (3) ◽  
pp. 305-318
Author(s):  
I. M. R. Pinheiro
Keyword(s):  
Balance Equation ◽  
Force Balance ◽  
The Other ◽  
Balance Equations ◽  
Film Blowing ◽  
Actual System ◽  
Future Work ◽  
Far Future ◽  
Force Balance Equation

In this paper, we refine Han and Park results for nonisothermal film blowing: we propose a correction in their temperature and force balance equations, and prove that with this change the actual system should be split into three other systems, and use a different scaling supposedly more suitable to find the solution of the equations. Besides all that, we also provide an analysis on how our nonisothermal model could improve modeling of the film blowing process. It is worth mentioning that, even though we have corrected (mathematically) the force balance equation by Han and Park, we only make use of the first version of the split model in our simulations to match the other simulations done with the model so far. Future work will include further refinements on the simulations. Šiame straipsnyje tobulinami Hano ir Parko rezultatai apie neizotermini filmo juostos pūtima. Autoriai patikslina temperatūros ir jegu balanso lygtis ir irodo, kad tai išskaido lygčiu sistema i tris sistemas. Tai igalina rasti uždavinio sprendini. Taip pat pateikta analize kaip šis modelis, gali patobulinti pūtimo procesa. Kadangi naudojamas pataisytas Hano ir Parko modelis, todel modeliuojant gauti rezultatai ne visuomet sutampa su kitu eksperimentu rezultatais. Ateityje numatoma tobulinti šiuos eksperimentus.

scholarly journals Study of up–down poloidal density asymmetry of high- impurities with the new impurity version of XGCa

2019 ◽  
Vol 85 (5) ◽  
Author(s):  
J. Dominski ◽  
C. S. Chang ◽  
R. Hager ◽  
P. Helander ◽  
S. Ku ◽  
...  
Keyword(s):  
Distribution Function ◽  
Friction Force ◽  
Balance Equation ◽  
Numerical Data ◽  
Force Balance ◽  
Viscous Force ◽  
Plasma Transport ◽  
Particle In Cell ◽  
Impurity Ions ◽  
Force Balance Equation

Addition of multispecies impurity ions to the total-f gyrokinetic particle-in-cell code XGCa is reported, including a cross-verification of neoclassical physics against the NEO code. This new version of the neoclassical gyrokinetic code XGCa is used to benchmark and confirm the previous reduced-equation-based prediction that high- $Z$ impurity particles in the Pfirsch–Schlüter regime can exhibit a significant level of up–down poloidal asymmetry, through the large parallel friction force, and thus influence the radial plasma transport significantly. The study is performed in a plasma with weak toroidal rotation. In comparison, when the impurity particles are in the plateau regime, the up–down poloidal asymmetry becomes weak, with the parallel friction force becoming weaker than the parallel viscous force. It is also found that the linearization of the perturbed distribution function, based on the small poloidal asymmetry assumption, can become invalid. Using the numerical data from XGCa, each term in the parallel fluid force-balance equation have been analysed to find that both the main ions and the electrons respond to the poloidal potential variation adiabatically when the high- $Z$ tungsten possesses large poloidal variation.

Adiabatic resistivity from the force balance equation

1990 ◽  
Vol 73 (6) ◽  
pp. 437-440 ◽  
Author(s):  
L.Y. Chen ◽  
C.S. Ting ◽  
N.J.M. Horing
Keyword(s):  
Balance Equation ◽  
Force Balance ◽  
Force Balance Equation

Steady MHD flows with an ignorable co-ordinate and the potential transonic flow equation

1994 ◽  
Vol 52 (1) ◽  
pp. 141-188 ◽  
Author(s):  
G. M. Webb ◽  
M. Brio ◽  
G. P. Zank
Keyword(s):  
Fluid Dynamics ◽  
Balance Equation ◽  
Transonic Flow ◽  
Field Potential ◽  
Flow Equation ◽  
Force Balance ◽  
Mhd Flows ◽  
Field Force ◽  
Shafranov Equation ◽  
Force Balance Equation

The paper explores the interrelationship between the generalized Grad-Shafranov equation, or trans-field force balance equation, for steady MHD flows with an ingnorable co-ordinate, and work by Imai on field-aligned MHD flows. The development of Imai, assumes at the outset that the fluid velocity V is parallel to the magnetic field B, and exploits an analogy with steady compressible irrotational flow in ordinary fluid dynamics. In Imai's analysis the magnetic induction B is written in the form B = σb, where , and MA is the appropriate Alfvén Mach number. Gauss' law Δ. B = Δ. (σb) = 0 then plays a role analogous to the mass continuity equation in ordinary fluid dynamics, where σ corresponds to the density of the pseudo-fluid. Imai's analysis leads to a transonic equation for the field potential φ defined by b = Δφ. For a restricted class of flows the trans-field force balance equation formulation also leads to the transonic potential flow equation, but the assumption of an ignorable co-ordinate allows for the possibility of non-field-aligned flows with non-zero electric field potential ΦE The characteristics of the generalized Grad—Shafranov equation are related to the Mach cone and the group velocity surface for linear magnetosonic waves. The corresponding forms of the characteristics for the potential transonic flow equation in the (x, y) plane and in the (bx, by) hodograph plane are discussed. Sample solutions of the potential transonic flow equation for radial, helical and spiral flows are obtained by means of the hodograph transformation, and are used to illustrate the differences between hyperbolic and elliptic flows. The potential transonic flow equation is obtained for the case of an ignorable co-ordinate z of a rectangular Cartesian co-ordinate system (x, y, z), and also for the case of flows with an ignorable co-ordinate of a spherical polar co-ordinate system (r, θ, ω). Astrophysical applications are briefly discussed.

The Spread-Mathematical Model of Special-Shaped Steel Wire during the Rolling

2011 ◽  
Vol 340 ◽  
pp. 56-63
Author(s):  
Bo Jian Wang ◽  
Wei Ke Sun ◽  
Yong Jie Wang
Keyword(s):  
Mathematical Model ◽  
Balance Equation ◽  
Steel Wire ◽  
Rolling Process ◽  
Force Balance ◽  
Stress Increment ◽  
Rolling Deformation ◽  
The Mathematical Model ◽  
Theoretical Results ◽  
Force Balance Equation

This article studied the rolling process of metal card wire, and established the spread formula of flat wire to special-shaped steel wire by rolling. The metal stress-increment in rolling deformation zone for the special-shaped steel wire was solved by the force-balance equation, and the mathematical model of rolling-piece spread was established according to the displacement increment function solved. By means of experiments to verify the mathematical model, the results show: the theoretical results of different materials through the model to calculate is closer the actual value after rolled , the error is less than 5%.

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