Gyro center invariant and associated diamagnetic current

Journal Article · Thu Dec 15 04:00:00 EST 2005 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.2139503· OSTI ID:20782388

Aaagren, O; Moiseenko, V; Johansson, C; Savenko, N ^[1]

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1. Uppsala University, Angstroem Laboratory, Division of Electricity and Lightning Research, Box 534, SE-751 21 Uppsala (Sweden)

The gyro center radial Clebsch coordinate r{sub 0} is an exact invariant in confining fields where the gyro center is restricted to move on a magnetic flux surface, and r{sub 0} could also be expected to be a useful approximating invariant in other confining magnetic fields. A radial drift invariant I{sub r} generalizes the invariance of r{sub 0} if there are oscillatory gyro center radial displacements off the magnetic surface. Expressions for r{sub 0}(x,v) and I{sub r}(x,v) are obtained for gyrating particles in the drift ordering. An exact energy integral is proven to exist for the first-order drift motion of the gyro center. The gyro center parallel motion is periodic with respect to a certain curve parameter {tau}{sub parallel} (the 'proper time' for the parallel motion) that deviates slightly, due to the slow perpendicular drift, from the ordinary time. A modification of the parallel invariant J{sub parallel} is derived which leads to an exact (not only adiabatic) invariant to first order. By using r{sub 0} in solutions of the Vlasov equation, it is demonstrated that the approximating gyro center invariant r{sub 0} determines the perpendicular plasma diamagnetic current. It is also shown that a fourth stationary motional invariant is required to calculate the parallel plasma current. Several systems with four time independent invariants are identified, and the general solution for straight cylindrical Vlasov equilibria with adiabatic particle motion is determined. A set ({epsilon},{mu},I{sub parallel},I{sub r}) of four invariants is proposed for adiabatic equilibria in general geometry, including systems where single valued flux surfaces may not exist.

• OSTI ID: 20782388
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 12 Vol. 12; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
BOLTZMANN-VLASOV EQUATION
CHARGED-PARTICLE TRANSPORT
COORDINATES
CYLINDRICAL CONFIGURATION
ELECTRIC CURRENTS
GEOMETRY
MAGNETIC FIELDS
MAGNETIC FLUX
MAGNETIC SURFACES
MATHEMATICAL SOLUTIONS
PERIODICITY
PLASMA
PLASMA CONFINEMENT
PLASMA DIAMAGNETISM
PLASMA WAVES
SURFACES