Particle in cell and hybrid simulations of the Z double-post-hole convolute cathode plasma evolution and dynamics

The Z-accelerator at Sandia National Laboratories (SNL), is a high-current pulsed power machine used to drive a range of high energy density physics (HEDP) experiments [1]. To achieve peak currents of >20MA, in a rise time of ∼100ns, the current is split over four levels of transmission line, before being added in parallel in a double-post-hole convolute (DPHC) and delivered to the load through a single inner magnetically insulated transmission line (MITL). The electric field on the cathode electrode, >107Vm−1, drives the desorption and ionisation of neutral contaminants to form a plasma from which electrons are emitted into the anode-cathode (a-k) gap. The current addition path in the DPHC forms magnetic ’null’ regions, across which electrons are lost to the anode, shunting current from the inner MITL and load. In experiment, current losses of >10% have been measured within the convolute; this reduces the power delivered to the load, negatively impacting the load performance, as well as complicating the prediction of the Poynting flux used to drive detailed magneto-hydrodynamic (MHD) simulations [2, 3]. In this thesis we develop 3-dimensional (3D) Particle-in-Cell (PIC) and hybrid fluid-PIC computer models to simulate the plasma evolution in the DPHC and inner MITL. The expected experimental current loss at peak current was matched in simulations where Hydrogen plasma was injected from the cathode electrode at a rate of 0.0075mlns−1 (1ml=1015cm−2), with an initial temperature of 3eV. The simulated current loss was driven by plasma penetrating the downstream side of the anode posts, reducing the effective a-k gap spacing and enhancing electron losses to the anode. The current loss at early time (<10MA), was matched in simulations where space-charge-limited (SCL) electron emission was allowed directly from the cathode; to match the loss over the entire current pulse, a delay model is motivated. Here, plasma injection was delayed after the start of SCL emission, based on realistic plasma expansion velocities of ∼3cmμs−1. The PIC model, which was necessary to accurately simulate the kinetic behaviour of the lower density plasma and charged particle sheaths, was computationally intensive such that the spatial resolutions achieved in the 3D simulations were relatively poor. With the aim of reducing the computational overhead, allowing finer spatial resolutions to be accessed, we investigate the applicability of hyBritish Crown Copyright 2012/MOD iii brid techniques to simulating the cathode plasma in the convolute. Our PIC model was both implemented in the resistive MHD code, Gorgon, where part of the plasma was modelled in the single fluid approximation, and extended to include an inertial two-fluid description of the plasma. The hybrid models were applied to the DPHC simulations, the results from which are used to motivate a three component model; here, the densest part of the convolute plasma is modelled using the single fluid MHD approximation, transitioning to a fully kinetic PIC description of the lower density plasma and charged particle sheaths, linked by a two-fluid description. British Crown Copyright 2012/MOD iv c ©Crown Copyright 2012 “This documents consists of or is adapted from material that is the property of the Secretary of State for Defence of the United Kingdom of Great Britain and Northern Ireland. It is furnished in confidence and may not be further copied, used or disclosed, in whole or in part, without the prior written consent of D/IPR, MOD, Abbey Wood, Bristol, BS34 8JH, UK. ”