Particle orbits in field-reversed mirrors

Abstract

The particle orbits in field-reversed mirrors (FRM) are studied. It is found that the orbit can be expressed in terms of the first and third kind of elliptic integral for particles moving in the centre plane of the Hill vortex configuration. Requirements for absolute confinement are obtained, and four distinct classes of orbits are identified that are bounded by limits on the canonical angular momentum Pθ. The improvement in confinement over a simple mirror as well as natural divertor properties of the FRM are illustrated by these results.

Regular and stochastic orbits of ions in a highly prolate field-reversed configuration

“…8 Particle orbits in FRC and FRC-like geometries have been previously studied. The phasespace structure in the z = 0 subspace is investigated by Wang and Miley (WM) 9 . Throughout this paper we use a cylindrical coordinate system (r, z, φ), with r the radius of the device, and z the distance along the axis from the midplane at z = 0.…”

Regular and Stochastic Orbits of Ions in a Highly Prolate Field-reversed Configuration

“…9 The orbits are that of a particle in a 1-D effective potential V eff = V 0 υ(ρ, 0, π φ ) and are therefore integrable. Figure 1 shows four possible shapes of the scaled potential energy υ for representative values of π φ .…”

“…The phasespace structure in the z = 0 subspace is investigated by Wang and Miley (WM) 9 . Throughout this paper we use a cylindrical coordinate system (r, z, φ), with r the radius of the device, and z the distance along the axis from the midplane at z = 0.…”

Electron Acceleration in the Field-reversed Configuration (FRC) by Slowly Rotating Odd-parity Magnetic Fields

“…Electrons with 100 eV perform cyclotron orbits, unless they are very close to the O-point null line, in which case they may perform null-line-crossing betatron orbits. 13,14 In an FRC, electron cyclotron orbits drift in one toroidal direction, parallel to the FRC's current, thus reducing it, while betatron orbits move in the opposite direction, adding to the current. The sign of ω R is positive when the RMF o rotates in the direction of the electron betatron motion.…”

“…Because the FRC has a minimum-B geometry with B = 0 at the O point, r = r o and z = 0, an electron there is guided toroidally around the FRC in a near-circular orbit of radius r = r o , 3 with small axial and radial betatron modulations. 13,14 The RMF o produces an azimuthal electric field via the time derivative −(∂A φ,odd /∂t)/c of Eqn. (3), causing the electron to accelerate azimuthally.…”