In Chapter 1 we have presented some brief introduction to plasma physics, MHD theory, and the Caltech plasma jet experiment. A more detailed introduction regarding specific topics will be given individually in each chapter.
In Chapter 2 we will give a brief review of astrophysical jets and show the similarity between the plasma jet experiment and astrophysical jets in terms of electromagnetic con- figurations at the jet boundary and the global magnetic structure. We use an astrophysical magnetic tower model initially proposed by Lynden-Bell [74, 75] as the base model and present three-dimensional ideal MHD simulations of the plasma jet experiment. A localized magnetic energy and helicity injection is implemented in the simulation to mimic both the experimental and astrophysical situations. Detailed analysis to the simulation results and
comparison between the experiment and simulation give a comprehensive description of the jet collimation and acceleration processes. We study numerically the magnetic to kinetic energy conversion and obtain quantitative agreement between the simulation results and the experiment.
As shown in § 1.2.1, the plasma jet undergoes a global kink instability and then a secondary local Rayleigh-Taylor instability due to lateral acceleration of the kink instability.
This Rayleigh-Taylor instability is very interesting because it occurs on a cylindrical surface of an MHD-collimated plasma tube and the direction of gravity is not always perpendicular to the interface. We found that the conventional hydrodynamic and magnetic Rayleigh- Taylor theories, which only consider 2D planar interface, give incorrect results when applied to our case. In Chapter 3 we use linear stability analysis to develop an MHD theory of the Rayleigh-Taylor instability on the cylindrical surface of a plasma flux rope in the presence of a lateral external gravity. The Rayleigh-Taylor instability is found to couple to the classic current-driven instability, resulting in a new type of hybrid instability. The coupled instability, produced by combination of helical magnetic field, curvature of the cylindrical geometry, and lateral gravity, is fundamentally different from the classic magnetic Rayleigh-Taylor instability occurring at a two-dimensional planar interface. The theory gives instability wavelengths and growth rates that match with experiments having several different configurations. We also show that this hybrid instability theory can be applied to many situations in solar physics.
Chapter 3solves the Rayleigh-Taylor instability in the early phase when the linear sta- bility analysis is still valid. In the experiment, however, this instability quickly evolves to a nonlinear phase and eventually leads to the failure of MHD. The Rayleigh-Taylor instability compresses and pinches the plasma jet to a scale smaller than the ion skin depth and then triggers a fast magnetic reconnection. In Chapter4we present measurements of high-speed magnetic fluctuations at the time of the reconnection and show that these fluctuations contain broadband right-hand circularly polarized whistler waves associated with the fast reconnection. With the specially designed high-speed 3D magnetic probe (Chapter 5), we are able to resolve the circular polarization of the whistler waves spontaneously generated in the fast magnetic reconnection.
Chapter5presents the philosophies and detailed designs of the high-speed 3D magnetic probe (whistler probe) that gives the magnetic fluctuations measurements in Chapter 4.
The whistler probe consists of six shielded loop B-dot probes made of semi-rigid coaxial cables. We implement an RF ground current diverting technique that was first used by Perkins & Bellan (2011) [89]. The whistler probe has a 70 dB rejection to electrostatic interference, making it ideal for high-speed time-dependent magnetic field detection in an extremely noisy environment such as the Caltech plasma jet experiment.
Chapter6presents an earth-isolated optically coupled DC-5 MHz wideband high voltage probe powered by solar cells under ambient lab light. The HV probe uses a lab-made 60 pF high-voltage capacitor and a commercial 100 nF low-voltage capacitor to form a 1000 : 0.6 voltage divider. The divided low voltage is coupled into a LED driver that converts the voltage signal into an amplitude-modulated infrared signal. The AM light signal is conveyed through an optical fiber and then converted back to an electric signal at the data acquisition device. The transmitter is powered by a 30µF capacitor pre-charged by solar cells under lab ambient light. Therefore, the high voltage probe is electrically isolated from earth ground.
The HV probe is being used in the cross-flux-tube experiment and other experiments in the Caltech Bellan group.
Chapter 2
Three-Dimensional MHD
Numerical Simulation of Caltech Plasma Jet Experiment
Magnetic fields are believed to play an essential role in astrophysical jets with observa- tions suggesting the presence of helical magnetic fields. Here, we present three-dimensional (3D) ideal MHD simulations of the Caltech plasma jet experiment using a magnetic tower scenario as the baseline model. Magnetic fields consist of an initially localized dipole-like poloidal component and a toroidal component that is continuously being injected into the domain. This flux injection mimics the poloidal currents driven by the anode-cathode volt- age drop in the experiment. The injected toroidal field stretches the poloidal fields to large distances, while forming a collimated jet along with several other key features. Detailed comparisons between 3D MHD simulations and experimental measurements provide a com- prehensive description of the interplay among magnetic force, pressure, and flow effects. In particular, we delineate both the jet structure and the transition process that converts the injected magnetic energy to other forms. With suitably chosen parameters that are derived from experiments, the jet in the simulation agrees quantitatively with the experimental jet in terms of magnetic/kinetic/inertial energy, total poloidal current, voltage, jet radius, and jet propagation velocity. Specifically, the jet velocity in the simulation is proportional to the poloidal current divided by the square root of the jet density, in agreement with both the experiment and analytical theory. This work provides a new and quantitative method for relating experiments, numerical simulations, and astrophysical observation, and demon- strates the possibility of using terrestrial laboratory experiments to study astrophysical jets.
Primary part of this chapter was published by Xiang Zhai, Hui Li, Paul M. Bellan, and Shengtai Li, in Astrophysical Journal, Volume 791:40, 2014 [130]. This work is under the collaboration between Bellan group in Caltech and Li group in LANL.