Criterion for bulk behavior of a Yukawa disk
Abstract
A Yukawa disk is a twodimensional system of n particles interacting through a Yukawa potential (i.e., a screened Coulomb or Debye potential) with Debye length {lambda} and confined in an isotropic parabolic well where the singleparticle oscillation frequency is {omega}{sub 0}. One example of a Yukawa disk is a twodimensional complex (dusty) plasma. The emergence of bulk (macroscopic) behavior in a strongly coupled Yukawa disk is studied by considering the dependence of the normalized, squared breathing frequency {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2} (i.e., the bulk modulus) on n, {lambda}, the disk radius R{sub 0}, and the nearestneighbor distance a. An analytical expression for {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2} is derived for the bulk limit, R{sub 0}>>{lambda}, with a/{lambda} finite. In the plasma regime a < or approx. {lambda}, so that each particle interacts with many other particles, {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2}{approx_equal}4 independent of a/{lambda}. In the nearestneighbor regime a > or approx. {lambda}, shortrange interactions dominate and {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2}{approx}a/{lambda}. Computational solutions of the model for n=1003200 particles approach the theoretical bulk limit as n increases. Solutions with n=3200 and a/{lambda} between 0.25 and 0.5 are found to give the best approximation to an unbounded plasma.
 Authors:
 Department of Physics and Astronomy, Ohio Northern University, Ada, Ohio 45810 (United States)
 Publication Date:
 OSTI Identifier:
 20974867
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 3; Other Information: DOI: 10.1063/1.2713722; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPROXIMATIONS; DEBYE LENGTH; INTERACTION RANGE; OSCILLATIONS; PLASMA; PLASMA WAVES; TWODIMENSIONAL CALCULATIONS; YUKAWA POTENTIAL
Citation Formats
Sheridan, T. E. Criterion for bulk behavior of a Yukawa disk. United States: N. p., 2007.
Web. doi:10.1063/1.2713722.
Sheridan, T. E. Criterion for bulk behavior of a Yukawa disk. United States. doi:10.1063/1.2713722.
Sheridan, T. E. Thu .
"Criterion for bulk behavior of a Yukawa disk". United States.
doi:10.1063/1.2713722.
@article{osti_20974867,
title = {Criterion for bulk behavior of a Yukawa disk},
author = {Sheridan, T. E.},
abstractNote = {A Yukawa disk is a twodimensional system of n particles interacting through a Yukawa potential (i.e., a screened Coulomb or Debye potential) with Debye length {lambda} and confined in an isotropic parabolic well where the singleparticle oscillation frequency is {omega}{sub 0}. One example of a Yukawa disk is a twodimensional complex (dusty) plasma. The emergence of bulk (macroscopic) behavior in a strongly coupled Yukawa disk is studied by considering the dependence of the normalized, squared breathing frequency {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2} (i.e., the bulk modulus) on n, {lambda}, the disk radius R{sub 0}, and the nearestneighbor distance a. An analytical expression for {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2} is derived for the bulk limit, R{sub 0}>>{lambda}, with a/{lambda} finite. In the plasma regime a < or approx. {lambda}, so that each particle interacts with many other particles, {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2}{approx_equal}4 independent of a/{lambda}. In the nearestneighbor regime a > or approx. {lambda}, shortrange interactions dominate and {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2}{approx}a/{lambda}. Computational solutions of the model for n=1003200 particles approach the theoretical bulk limit as n increases. Solutions with n=3200 and a/{lambda} between 0.25 and 0.5 are found to give the best approximation to an unbounded plasma.},
doi = {10.1063/1.2713722},
journal = {Physics of Plasmas},
number = 3,
volume = 14,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}

The standard Q criterion (with Q > 1) describes the stability against local, axisymmetric perturbations in a disk supported by rotation and random motion. Most astrophysical disks, however, are under the influence of an external gravitational potential, which can significantly affect their stability. A typical example is a galactic disk embedded in a dark matter halo. Here, we do a linear perturbation analysis for a disk in an external potential and obtain a generalized dispersion relation and the effective stability criterion. An external potential, such as that due to the dark matter halo concentric with the disk, contributes to themore »


Effect of the gravitational interaction on the behavior of the effective Yukawa and scalar coupling constants
A unified theory with the gauge group SU(2) and conformally connected to quantized Weyl gravity is studied. The oneloop counterterms are calculated and the contribution of the gravitational interaction to the renormgroup equations for the effective matter charges is obtained. It is shown that the gravitational interaction enhances the asymptotically free behavior of the general solution for the Yukawa coupling constant. The gravitational contribution to the general solution for the scalar coupling constant does not ensure asymptotic freedom. A particular solution of the renormgroup equations is found which leads to asymptotic freedom in all the coupling constants. Here the constantmore » 
The Yukawa behavior of strong gravity
The asymptotic Yukawa behavior of strong gravity is discussed on the classical basis of the scalartensor theory in the version of Callen et. al. (Ann. of Phys., 59: 42(1970)). 
Asymptotic behavior of the effective Yukawa coupling constants in quantum R sup 2 gravity with matter
We study the asymptotic behavior of the effective Yukawa coupling constants in the unified theory including quantum {ital R}{sup 2} gravity and the fieldtheory gauge model. The renormalization group equations for the effective gauge, gravitational, Yukawa, and scalar coupling constants have the same stable fixed points that arise if the Yukawa coupling is set directly equal to zero.