

Article
Magnetohydrodynamic selfconsistent exact helical solutions
Authors: 
Essén, H. 
Document Type: 
Article 
Pubstate: 
Published 
Journal: 
J. Phys. A: Math. Gen 
Volume: 
37
98319840 
Year: 
2004 
AbstractWe 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 is also assumed. We show that suitably determined axially symmetric helical current densities within a straight infinite cylinder are exact selfconsistent solutions of magnetohydrodynamics. Selfconsistent 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 $v_z(\rho)$ and the azimuthal $v_(\rho)$ 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 selfconsistently 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.

