Transmission-line-circuit model of an 85-TW, 25-MA pulsed-power accelerator

Abstract

We have developed a physics-based transmission-line-circuit model of the Z pulsed-power accelerator. The 33-m-diameter Z machine generates a peak electrical power as high as 85 TW, and delivers as much as 25 MA to a physics load. The circuit model is used to design and analyze experiments conducted on Z. The model consists of 36 networks of transmission-line-circuit elements and resistors that represent each of Zs 36 modules. The model of each module includes a Marx generator, intermediate-energy-storage capacitor, laser-triggered gas switch, pulse-forming line, self-break water switches, and tri-plate transmission lines. The circuit model also includes elements that represent Zs water convolute, vacuum insulator stack, four parallel outer magnetically insulated vacuum transmission lines (MITLs), double-post-hole vacuum convolute, inner vacuum MITL, and physics load. Within the vacuum-transmission-line system the model conducts analytic calculations of current loss. To calculate the loss, the model simulates the following processes: (i) electron emission from MITL cathode surfaces wherever an electric-field threshold has been exceeded; (ii) electron loss in the MITLs before magnetic insulation has been established; (iii) flow of electrons emitted by the outer-MITL cathodes after insulation has been established; (iv) closure of MITL anode-cathode (AK) gaps due to expansion of cathode plasma; (v) energy loss to MITL conductors operated at high lineal current densities; (vi) heating of MITL-anode surfaces due to conduction current and deposition of electron kinetic energy; (vii) negative-space-charge-enhanced ion emission from MITL anode surfaces wherever an anode-surface-temperature threshold has been exceeded; and (viii) closure of MITL AK gaps due to expansion of anode plasma. The circuit model is expected to be most accurate when the fractional current loss is small. We have performed circuit simulations of 52 Z experiments conducted with a variety of accelerator configurations and load-impedance time histories. For these experiments, the apparent fractional current loss varies from 0% to 20%. Results of the circuit simulations agree with data acquired on 52 shots to within 2%.

Large time-varying inductance load for studying power flow on the Z machine

“…Present theories for current loss in the load region state that undesirable plasma generation results in some level of current shorting at or within the convolute radius. Possible plasma sources being considered include the aforementioned electron flow current, enhanced SCL ion emission, desorbed and ionized water/contaminants from the MITL surfaces, and/or vaporized metal due to heavy Joule heating [3,19,24]. Beyond the classical shorting that can occur due to these plasmas, in the next section we will present evidence for the presence of plasma invalidating the fundamental MHD assumptions used to model Z machine target dynamics.…”

“…The resulting current pulse thus has a very high dI=dt compared to most shock-ramp pulses. Figure 3 shows the PF current pulse produced by the Z circuit model [19] and the associated time-varying load inductance; a reference DMP shock-ramp pulse is included for comparison. The load inductance in the stripline geometry is driven by the divergence of the anode and cathode striplines as the load AK gap opens under magnetic pressure.…”

“…One potential theory for the loss mechanism comes from the flow current model outlined by Hutsel et al in Ref. [19]. The electron flow current traveling in a magnetically insulated layer above each cathode MITL is represented in the Z circuit model as…”

“…The flow current plays a roll in an additional loss mechanism that is not included in the Z circuit model utilized above, but is described in Ref. [19], namely the positive ion current. Ion generation is sourced under the assumption that the MITLs behave as an enhanced space charge limited (SCL) emission source, such that the ion current is given by…”

“…The new variables in Eq. (3) represent the accumulated electron charge (Q e ) and a nondimensional constant representing the average ion velocity in the AK gap (k) [19]. We now define the enhanced space charge limited current as…”