The thermal mean-field equilibrium of a translation-invariant, unbounded one-component guiding-centre plasma is studied by analytical techniques. A variational principle is constructed. It is shown that only radial symmetric, decreasing density profiles occur. Prescribing the total number of gyro centres N∊(0,∞), the energy E ∊(E0,∞) and the canonical angular momentum M ∊ (0, ∞] uniquely determines a profile. Metastable or unstable profiles do not exist. A simple algebraic relation betweenN, M, the guiding-centre temperature β-1and the characteristic Larmor frequency w is derived. This explains Williamson’s computer-based observations.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics