skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Modified Coulomb Law in a Strongly Magnetized Vacuum

Abstract

We study the electric potential of a charge placed in a strong magnetic field B>>B{sub 0}{approx_equal}4.4x10{sup 13} G, as modified by the vacuum polarization. In such a field the electron Larmour radius is much less than its Compton length. At the Larmour distances a scaling law occurs, with the potential determined by a magnetic-field-independent function. The scaling regime implies short-range interaction, expressed by the Yukawa law. The electromagnetic interaction regains its long-range character at distances larger than the Compton length, the potential decreasing across B faster than along. Correction to the nonrelativistic ground-state energy of a hydrogenlike atom is found. In the limit B={infinity}, the modified potential becomes the Dirac {delta} function plus a regular background. With this potential the ground-state energy is finite - the best pronounced effect of the vacuum polarization.

Authors:
 [1];  [2]
  1. P.N. Lebedev Physics Institute, Moscow 117924 (Russian Federation)
  2. Center for Astrophysics, Weizmann Institute, Rehovot 76100 (Israel)
Publication Date:
OSTI Identifier:
20951320
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 18; Other Information: DOI: 10.1103/PhysRevLett.98.180403; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRECTIONS; DELTA FUNCTION; ELECTRIC POTENTIAL; ELECTROMAGNETIC INTERACTIONS; ELECTRONS; GROUND STATES; INTERACTION RANGE; LARMOR RADIUS; MAGNETIC FIELDS; POTENTIALS; SCALING LAWS; VACUUM POLARIZATION

Citation Formats

Shabad, Anatoly E., and Usov, Vladimir V. Modified Coulomb Law in a Strongly Magnetized Vacuum. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.180403.
Shabad, Anatoly E., & Usov, Vladimir V. Modified Coulomb Law in a Strongly Magnetized Vacuum. United States. doi:10.1103/PHYSREVLETT.98.180403.
Shabad, Anatoly E., and Usov, Vladimir V. Fri . "Modified Coulomb Law in a Strongly Magnetized Vacuum". United States. doi:10.1103/PHYSREVLETT.98.180403.
@article{osti_20951320,
title = {Modified Coulomb Law in a Strongly Magnetized Vacuum},
author = {Shabad, Anatoly E. and Usov, Vladimir V.},
abstractNote = {We study the electric potential of a charge placed in a strong magnetic field B>>B{sub 0}{approx_equal}4.4x10{sup 13} G, as modified by the vacuum polarization. In such a field the electron Larmour radius is much less than its Compton length. At the Larmour distances a scaling law occurs, with the potential determined by a magnetic-field-independent function. The scaling regime implies short-range interaction, expressed by the Yukawa law. The electromagnetic interaction regains its long-range character at distances larger than the Compton length, the potential decreasing across B faster than along. Correction to the nonrelativistic ground-state energy of a hydrogenlike atom is found. In the limit B={infinity}, the modified potential becomes the Dirac {delta} function plus a regular background. With this potential the ground-state energy is finite - the best pronounced effect of the vacuum polarization.},
doi = {10.1103/PHYSREVLETT.98.180403},
journal = {Physical Review Letters},
number = 18,
volume = 98,
place = {United States},
year = {Fri May 04 00:00:00 EDT 2007},
month = {Fri May 04 00:00:00 EDT 2007}
}
  • In a strongly magnetized plasma, where the electron cyclotron radius is less than the Debye length, the Rutherford scattering formula is expected to break down. In this paper, analytic expressions are developed for classical, small-angle scattering of electrons and ions in strong magnetic fields. Numerical evaluation of these expressions shows quantitatively how strong B fields can significantly inhibit electron deflections. The influence of the field on transport phenomena is then explored{emdash}in particular, a generalized Coulomb logarithm which includes the effects of a magnetic field is formulated and computed for a wide range of trajectory pitch angles. This generalized Coulomb logarithmmore » is used to illustrate how a strong field influences the effective electron-ion cross section, the electron velocity diffusion coefficient, and the (parallel) electrical and thermal resistivity in a variety of astrophysical and terrestrial plasmas. {copyright} {ital 1997 American Institute of Physics.}« less
  • The proper time method is used to examine the effect of polarization of the electron-positron vacuum on the nature of the interaction of a charged particle with the field of a nucleus and a magnetic field. It is shown that the interaction of an electron with a nucleus becomes anisotropic in the presence of a magnetic field. The dielectric constants of the vacuum and the effective charge of the Coulomb center are calculated.
  • We present Submillimeter Array 880 μ m dust polarization observations of six massive dense cores in the DR21 filament. The dust polarization shows complex magnetic field structures in the massive dense cores with sizes of 0.1 pc, in contrast to the ordered magnetic fields of the parsec-scale filament. The major axes of the massive dense cores appear to be aligned either parallel or perpendicular to the magnetic fields of the filament, indicating that the parsec-scale magnetic fields play an important role in the formation of the massive dense cores. However, the correlation between the major axes of the cores andmore » the magnetic fields of the cores is less significant, suggesting that during the core formation, the magnetic fields below 0.1 pc scales become less important than the magnetic fields above 0.1 pc scales in supporting a core against gravity. Our analysis of the angular dispersion functions of the observed polarization segments yields a plane-of-sky magnetic field strength of 0.4–1.7 mG for the massive dense cores. We estimate the kinematic, magnetic, and gravitational virial parameters of the filament and the cores. The virial parameters show that the gravitational energy in the filament dominates magnetic and kinematic energies, while the kinematic energy dominates in the cores. Our work suggests that although magnetic fields may play an important role in a collapsing filament, the kinematics arising from gravitational collapse must become more important than magnetic fields during the evolution from filaments to massive dense cores.« less
  • We derive a simple analytical expression for the two-body force in a subclass of modified Newtonian dynamics (MOND) theories and make testable predictions in the modification to the two-body orbital period, shape, precession rate, escape speed, etc. We demonstrate the applications of the modified Kepler's law in the timing of satellite orbits around the Milky Way, and checking the feasibility of MOND in the orbit of the large Magellanic cloud, the M31 galaxy, and the merging bullet clusters. MOND appears to be consistent with satellite orbits although with a tight margin. Our results on two-bodies are also generalized to restrictedmore » three-body, many-body problems, rings, and shells.« less