Drift Instability in the Presence of Nonuniform Radial Electric Fields

1971 ◽  
Vol 49 (12) ◽  
pp. 1630-1640 ◽  
Author(s):  
C. E. Capjack ◽  
T. E. Stringer
Keyword(s):  
Kinetic Equation ◽  
Electric Field ◽  
Electric Fields ◽  
Numerical Solutions ◽  
Radial Electric Field ◽  
Drift Instability

An equation describing the drift instability in a collisionless low-β plasma, in the presence of a nonuniform radial electric field is derived from guiding center equations for the ions and the drift kinetic equation for the electrons. Numerical solutions to this equation indicate that the influence of a nonuniform radial electric field on the drift instability may be determined from the manner in which this field modifies the macroscopic electron rotation profile.

scholarly journals Bootstrap current and parallel ion velocity in imperfectly optimized stellarators

2020 ◽  
Vol 86 (1) ◽  
Author(s):  
Peter J. Catto ◽  
Per Helander
Keyword(s):  
Magnetic Field ◽  
Kinetic Equation ◽  
Electric Field ◽  
Flow Velocity ◽  
Collision Frequency ◽  
Rotation Frequency ◽  
Radial Electric Field ◽  
Local Form ◽  
Bootstrap Current ◽  
Ion Velocity

A novel derivation of the parallel ion velocity, and the bootstrap and Pfirsch–Schlüter currents in an imperfectly optimized (that is, almost omnigenous) stellarator magnetic field, $\boldsymbol{B}$ , is presented that somewhat more generally recovers expressions completely consistent with previous analytic results. However, it is also shown that, when the conventional radially local form of the drift kinetic equation is employed, the flow velocity and the bootstrap current acquire a spurious contribution proportional to $\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708}$ , where $\unicode[STIX]{x1D714}$ denotes the $\boldsymbol{E}\times \boldsymbol{B}$ rotation frequency (due to the radial electric field $\boldsymbol{E}$ ) and $\unicode[STIX]{x1D708}$ the collision frequency. This contribution is particularly large in the $\sqrt{\unicode[STIX]{x1D708}}$ regime and at smaller collisionalities, where $\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708}\gtrsim 1$ , and is presumably present in most numerical calculations, but it disappears if a more accurate drift kinetic equation is used.

Derivation of radial electric fields using kinetic theory in tokamak

2013 ◽  
Vol 79 (5) ◽  
pp. 513-517
Author(s):  
K. NOORI ◽  
P. KHORSHID ◽  
M. AFSARI
Keyword(s):  
Kinetic Theory ◽  
Electric Field ◽  
Electric Fields ◽  
Driving Forces ◽  
Radial Electric Field ◽  
Radial Pressure ◽  
Momentum Balance ◽  
Balance Equations ◽  
Radial Pressure Gradient ◽  
Poloidal Rotation

AbstractIn the current study, radial electric field with fluid equations has been calculated. The calculation started with kinetic theory, Boltzmann and momentum balance equations were derived, the negligible terms compared with others were eliminated, and the radial electric field expression in steady state was derived. As mentioned in previous researches, this expression includes all types of particles such as electrons, ions, and neutrals. The consequence of this solution reveals that three major driving forces contribute in radial electric field: radial pressure gradient, poloidal rotation, and toroidal rotation; rotational terms mean Lorentz force. Therefore, radial electric field and plasma rotation are connected through the radial momentum balance.

OSCILLATORY SQUEEZE FLOW OF ELECTRORHEOLOGICAL FLUID WITH TRANSITIONAL ELECTRIC FIELD

2005 ◽  
Vol 19 (07n09) ◽  
pp. 1249-1255 ◽  
Author(s):  
JIE PENG ◽  
KE-QIN ZHU
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Phase Difference ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Electrorheological Fluid ◽  
Squeeze Flow ◽  
Field Frequency ◽  
Er Fluid ◽  
Oscillatory Squeeze Flow

The oscillatory squeeze flow of electrorheological (ER) fluid between two parallel discal electrode with transitional electric field is studied numerically in this paper. The ER fluid is modeled as Bingham-like fluid with the continuous modification model proposed by Papanastasiou. The numerical solutions based on the Navier-Stokes equations are presented by using the finite volume methods on the deforming grid. The force transmitted across the fluid under dc and ac electric fields are calculated. The effects of the electric field frequency and the phase difference between the ac electric field and mechanical oscillation are studied. The magnitude and the shape of the transmitted forces is shown to be not only a function of the applied voltage and the mechanical frequency but also the phase difference.

Extension–torsion–inflation coupling in compressible electroelastomeric thin tubes

2019 ◽  
Vol 25 (3) ◽  
pp. 644-663 ◽  
Author(s):  
Shashank Saxena ◽  
Darius Diogo Barreto ◽  
Ajeet Kumar
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Variational Formulation ◽  
Radial Direction ◽  
Radial Electric Field ◽  
Algebraic Equations ◽  
Deformation Problem ◽  
Thin Tube ◽  
Poling Direction ◽  
Helical Anisotropy

We present an axisymmetric and axially homogeneous variational formulation to obtain coupled extension–torsion–inflation deformation in compressible electroelastomeric tubes in the presence of axial and radial electric fields. We show that such deformations occur under the following two conditions: (1) only the axial electric field is imposed, with the electric poling direction in the tube (if present) lying in the radial plane; and (2) only the radial electric field is imposed within the tube, with the electric poling direction (if present) also along the radial direction. The poling direction in condition (1) generates helical anisotropy in the tube. We then obtain the governing differential equations necessary to solve the above deformation problem for thick tubes. We further apply the thin tube limit to obtain simplified algebraic equations to solve the same deformation problem. The effect of applied electric field parameters on the extension–inflation coupling and induced internal pressure vs. imposed inflation behavior is finally presented through numerical solution of the above obtained algebraic equations. The study will be useful in designing soft electroelastic tubular actuators.

Numerical Study of EHD-Enhanced Forced Convection Using Two-Way Coupling

2003 ◽  
Vol 125 (4) ◽  
pp. 760-764 ◽  
Author(s):  
M. Huang ◽  
F. C. Lai
Keyword(s):  
Heat Transfer ◽  
Electric Field ◽  
Heat Transfer Enhancement ◽  
Forced Convection ◽  
Electric Fields ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Transfer Enhancement ◽  
Wide Range ◽  
The Difference

Numerical results are presented for heat transfer enhancement using electric field in forced convection in a horizontal channel. The main objective of the present study is to verify the assumption that is commonly used in the numerical study of this kind of problem, which assumes that the electric field can modify the flow field but not vice versa (i.e., the so-called one-way coupling). To this end, numerical solutions are obtained for a wide range of governing parameters (V0=10, 12.5, 15 and 17.5 kV as well as ui=0.0759 to 1.2144 m/s) using both one-way and two-way couplings. The results obtained, in terms of the flow, temperature, and electric fields as well as the heat transfer enhancement, are thoroughly examined. Since the difference in the results obtained by two approaches is insignificant, it is concluded that the assumption of one-way coupling is valid for the problem considered.

Collisional drift instability in a variable radial electric field

1986 ◽  
Vol 28 (9B) ◽  
pp. 1461-1482 ◽  
Author(s):  
E M Marshall ◽  
R F Ellis ◽  
J E Walsh
Keyword(s):  
Electric Field ◽  
Radial Electric Field ◽  
Drift Instability

Modification of electrostatic fluctuations by externally imposed radial electric fields

2000 ◽  
Vol 64 (3) ◽  
pp. 227-233
Author(s):  
C. RICCARDI ◽  
C. BEVILACQUA ◽  
G. CHIODINI ◽  
E. SINDONI ◽  
M. FONTANESI
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Radial Electric Field ◽  
Plasma Parameters ◽  
Electrostatic Fluctuations

This paper concerns experiments on the turbulence of a toroidal magnetoplasma in the presence of a radial electric field. The possibility of reduction of turbulence through the application of an external biasing potential has been evaluated by measuring the electrostatic fluctuations and main plasma parameters.

Lubrication theory for electro-osmotic flow in a non-uniform electrolyte

2007 ◽  
Vol 576 ◽  
pp. 139-172 ◽  
Author(s):  
T. L. SOUNART ◽  
J. C. BAYGENTS
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Lubrication Theory ◽  
Debye Screening Length ◽  
Sample Stacking ◽  
Osmotic Flow ◽  
Analytic Expressions ◽  
Electro Osmotic Flow

A lubrication theory has been developed for the electro-osmotic flow of non-uniform buffers in narrow rectilinear channels. The analysis applies to systems in which the transverse dimensions of the channel are large compared with the Debye screening length of the electrolyte. In contrast with related theories of electrokinetic lubrication, here the streamwise variations of the velocity field stem from, and are nonlinearly coupled to, spatiotemporal variations in the electrolyte composition. Spatially non-uniform buffers are commonly employed in electrophoretic separation and transport schemes, including iso-electric focusing (IEF), isotachophoresis (ITP), field-amplified sample stacking (FASS), and high-ionic-strength electro-osmotic pumping. The fluid dynamics of these systems is controlled by a complex nonlinear coupling to the ion transport, driven by an applied electric field. Electrical conductivity gradients, attendent to the buffer non-uniformities, result in a variable electro-osmotic slip velocity and, in electric fields approaching 1 kV cm−1, Maxwell stresses drive the electrohydrodynamic circulation. Explicit semi-analytic expressions are derived for the fluid velocity, stream function, and electric field. The resulting approximations are found to be in good agreement with full numerical solutions for a prototype buffer, over a range of conditions typical of microfluidic systems. The approximations greatly simplify the computational analysis, reduce computation times by a factor 4–5, and, for the first time, provide general insight on the dominant fluid physics of two-dimensional electrically driven transport.

scholarly journals Analysis of the interaction of an electron with radial electric fields in the presence of a disclination

2019 ◽  
Vol 16 (11) ◽  
pp. 1950172
Author(s):  
Knut Bakke ◽  
Claudio Furtado
Keyword(s):  
Electric Field ◽  
Elastic Medium ◽  
Electric Fields ◽  
Bound States ◽  
Topological Defect ◽  
Radial Electric Field ◽  
Centrifugal Term ◽  
Radial Equation ◽  
Linear Distribution ◽  
Electric Charge Distribution

We consider an elastic medium with a disclination and investigate the topological effects on the interaction of a spinless electron with radial electric fields through the WKB (Wentzel, Kramers, Brillouin) approximation. We show how the centrifugal term of the radial equation must be modified due to the influence of the topological defect in order that the WKB approximation can be valid. Then, we search for bound states solutions from the interaction of a spinless electron with the electric field produced by this linear distribution of electric charges. In addition, we search for bound states solutions from the interaction of a spinless electron with radial electric field produced by uniform electric charge distribution inside a long non-conductor cylinder.

Numerical Study of EHD-Enhanced Forced Convection Using Two-Way Coupling

2001 ◽  
Author(s):  
M. Huang ◽  
F. C. Lai
Keyword(s):  
Heat Transfer ◽  
Electric Field ◽  
Heat Transfer Enhancement ◽  
Forced Convection ◽  
Electric Fields ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Transfer Enhancement ◽  
Wide Range ◽  
The One

Abstract In this paper, numerical results are presented for heat transfer enhancement using electric field in forced convection in a horizontal channel. The electric field is generated by charging a wire electrode located at the center of the channel with direct current at a high voltage. The main objective of the present study is to verify the assumption that is commonly used in the numerical study of this kind of problems, which assumes the electric field can modify the flow field but not vice versa (i.e., the so-called one-way coupling). To this end, numerical solutions have been obtained for a wide range of governing parameters (Vo = 10, 12.5, 15 and 17.5 kV as well as ui = 0.0759 to 1.2144 m/s) using both one-way and two-way couplings. Using the two-way coupling approach, the possible modification of the electric field by the primary flow, which was previously neglected, is accounted for. The results obtained using these two approaches, in terms of the flow, temperature, and electric fields as well as the heat transfer enhancement, are thoroughly examined. In addition, their influence over the flow stability is investigated. Finally, the conclusion about the validity of the one-way coupling is reached at the end of the study.

Sign in / Sign up

Export Citation Format

Share Document