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Magnetohydrodynamic self-consistent exact helical solutions
KTH, Superseded Departments, Mechanics.
2004 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, Vol. 37, no 41, 9831-9840 p.Article in journal (Refereed) Published
Abstract [en]

We consider the idealized case of a one-component plasma with aligned fluid velocity and current density. Constant density and pressure as well as zero external magnetic field are also assumed. We show that suitably determined axially symmetric helical current densities within a straight infinite cylinder are exact self-consistent solutions of magnetohydrodynamics. Self-consistent here means that the magnetic field is the field produced by the current density itself. The equation of motion gives a nonlinear differential equation that relates the axial upsilon(z)(rho) and the azimuthal upsilonphi(rho) velocities as functions of radial distance rho. Prescribing one of these gives a specific solution for the other. The solutions can be understood as a set of helix-shaped charged particle trajectories that spiral self-consistently through the magnetic field that they themselves give rise to. Four different specific exact solutions are given: (i) a single particle outside a rectilinear line current, (ii) current on a thin cylinder, (iii) current density with constant angular velocity and (iv) current density with constant axial velocity, both within a cylinder of finite radius.

Place, publisher, year, edition, pages
2004. Vol. 37, no 41, 9831-9840 p.
Keyword [en]
phase-space energy, magnetic-field, plasmas, instability, particle
National Category
Physical Sciences
URN: urn:nbn:se:kth:diva-23849DOI: 10.1088/0305-4470/37/41/014ISI: 000224808500015ScopusID: 2-s2.0-7544246329OAI: diva2:342548
QC 20100525 QC 20110914Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2011-09-14Bibliographically approved

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