Magnetosphere-relevant wave research at Caltech involving or motivated by lab experiments

Laboratory experiments at Caltech use pulsed power methods to produce plasmas that replicate both solar corona loops and astrophysical jets. The solar loop and jet experiments use similar technology and diagnostics but differ in the symmetry of the boundary conditions. Both types of plasmas evolve through a reproducible sequence starting with MHD-driven flows and expansion, followed by MHD instabilities, and then coupling of the MHD instabilities to non-MHD phenomena instigating various non-MHD waves and also extreme electron energization. The MHD flows are driven either directly by $\mathbf{J} \times \mathbf{B}$ forces or else indirectly by $\mathbf{J} \times \mathbf{B}$ forces creating a pressure gradient that then drives flows. The instabilities are kink, sausage, or Rayleigh-Taylor and in some cases are Rayleigh-Taylor instigated by the effective gravity produced by a kink. Typically, the MHD instabilities cause a thinning of the current channel causing the current density to increase. The current density has to increase because the large inductance of the circuit causes the system to behave as a constant-current system. A technique [1] for measuring the $\mathbf{k}$-vector of waves for which displacement current can be ignored has been developed and used in the lab [2] and also for the MMS spacecraft [3]. The class of waves where displacement current can be ignored includes Alfven and whistler waves. The technique measured a whistler wave excited at a magnetic reconnection location and since $\mathbf{k}=\mathbf{k}(\omega)$ the whistler dispersion was identified by this dependence [2]. A separate model concerns the Doppler-shifted cyclotron resonance of relativistic electrons; namely the situation where $\omega-\mathrm{kv}_{\mathrm{par}}=\Omega_{\mathrm{c}} / \gamma$. By using relativistic transformations of both the fields and dynamics to the wave frame it is found that the energy an electron gains from ‘resonance’ tends to knock the electron out of resonance with the net result that the electron bounces in and out of resonance. This process has been shown [4] to map exactly to that of a pseudo-particle trapped in a pseudo-potential well where the pseudo-kinetic energy is given by the square of the acceleration as measured in the wave frame and the pseudo-potential is a function of $\mathrm{v}_{\text {par }}$. Curious features are that the shape of the pseudo-potential is governed by initial conditions and that maximum pitch angle scattering comes from electrons that do not start at exact resonance. For certain initial conditions the pseudo-potential shape has a two-valley structure which results in a very large pitch angle scattering. This can be the dominant contributor to pitch angle scattering [5] and results from the extent of the $\mathrm{V}_{\text {par }}$ oscillation (analog to position oscillation of a normal harmonic oscillator) being approximately double that of a one-valley structure.