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Hamiltonian of a homogeneous two-component plasma
KTH, Superseded Departments, Mechanics.
KTH, Superseded Departments, Mechanics.
2004 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 69, no 3Article in journal (Refereed) Published
Abstract [en]

The Hamiltonian of one- and two-component plasmas is calculated in the negligible radiation Darwin approximation. Since the Hamiltonian is the phase space energy of the system its form indicates, according to statistical mechanics, the nature of the thermal equilibrium that plasmas strive to attain. The main issue is the length scale of the magnetic interaction energy. In the past a screening length lambda=1/rootr(e)n, with n number density and r(e) classical electron radius, has been derived. We address the question whether the corresponding longer screening range obtained from the classical proton radius is physically relevant and the answer is affirmative. Starting from the Darwin Lagrangian it is nontrivial to find the Darwin Hamiltonian of a macroscopic system. For a homogeneous system we resolve the difficulty by temporarily approximating the particle number density by a smooth constant density. This leads to Yukawa-type screened vector potential. The nontrivial problem of finding the corresponding, divergence free, Coulomb gauge version is solved.

Place, publisher, year, edition, pages
2004. Vol. 69, no 3
Keyword [en]
weakly relativistic plasma, one-component plasma, phase-space energy, darwin interactions, charged-particles, magnetic-interactions, radiation, simulation, model, lagrangians
National Category
Applied Mechanics
URN: urn:nbn:se:kth:diva-23315DOI: 10.1103/PhysRevE.69.036404ISI: 000220729400069ScopusID: 2-s2.0-42749098044OAI: diva2:342013
QC 20100525 QC 20111027Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2011-10-27Bibliographically approved

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Essén, HannoNordmark, Arne B.
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