Speculations about plasma free energy, 50 years later

Abstract

Plasma free energy is that part of the total energy that feeds the growth of turbulence. The most successful free energy formulation in plasma physics is the MHD Energy Principle – successful because, within magnetohydrodynamics (MHD), the free energy $\unicode[STIX]{x1D6FF}W$ is both exact and self-adjoint (or Hermitian). A corresponding result in Vlasov theory is the free energy of equilibria neighbouring stable Maxwellian states – again giving a free energy of Hermitian form for the linearized equations. Since quantum mechanics is inherently Hermitian, here I speculate that quantum free energy is the ultimate way to understand classical plasma dynamics.

A Quasi-static Hyper-resistive Model of Ultra-high-energy Cosmic-ray Acceleration by Magnetically Collimated Jets Created by Active Galactic Nuclei

“…In our model, the Central Column current is ultimately self-collimated by the magnetic pinch force, j × B, creating a magnetic tower (or "pinch"). As noted in the Abstract, we have shown in Fowler & Li (2016) -hereafter Paper III -that the existence of a self-collimated jet current automatically produces the electric fields that accelerate cosmic rays, as is further elaborated here in Section 3.…”

“…Magnetically-collimated jets produced in the laboratory employ plasma guns driven by a capacitor bank (Hooper, et al 2012;Zhai et al 2014;Fowler & Li 2016). Accretion disk jets are driven by disk rotation Ω, creating a dynamo similar to a Faraday disk but with self-excited growing magnetic flux (Balbus & Hawley 1998), given any pre-existing seed field near an evolving black hole (Appendix A.3).…”

“…First is a weaker precursor stage due to current-driven magnetohydrodynamic (MHD) kink instability known to accelerate ions in the laboratory (Rusbridge, et al 1997). This is followed by a powerful, purely kinetic stage based on a known ion cyclotron resonance instability that could be further explored in the laboratory, as discussed in Fowler & Li (2016).…”

A new simpler way to obtain high fusion power gain in tandem mirrors

“…(6) Sixth on our list would be application of PIC simulations to study turbulence in the End Plugs and Center Cell pedestal. In this regard, we note that the simple geometry of KSTM End Plugs may be a good candidate for a novel use of PIC simulation coding [57], in which semi-classical quantum PIC wavefunctions, explored by Dauger [58], could be employed to construct Hermitian eigenstates that could fully characterize sheath instability, AIC and other non-linear end-plug dynamics.…”