Charged state of a spherical plasma in vacuum

A model Vlasov-Poisson system is simulated close to the point of marginal stability, thus assuming only the wave-particle resonant interactions are responsible for saturation, and shown to obey the power-law scaling of a second-order phase transition. The set of critical exponents analogous to those of the Ising universality class is calculated and shown to obey the Widom and Rushbrooke scaling and Josephson's hyperscaling relations at the formal dimensionality d=5 below the critical point at nonzero order parameter. However, the two-point correlation function does not correspond to the propagator of Euclidean quantum field theory, which is the Gaussian model for the Ising universality class. Instead, it corresponds to the propagator for the fermionic vector field and to the upper critical dimensionality d(c)=2. This suggests criticality of collisionless Vlasov-Poisson systems corresponds to a universality class analogous to that of critical phenomena of a fermionic quantum field description.