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DOE OSTI2023

Seismic Monitoring at the Farnsworth CO2-EOR Field Using Time-Lapse Elastic-Waveform Inversion of 3D-3C VSP Data

During the Development Phase of the U.S. Southwest Regional Partnership on Carbon Sequestration, supercritical CO2 was continuously injected into the deep oil-bearing Morrow B formation of the Farnsworth Unit in Texas for Enhanced Oil Recovery (EOR). The project injected approximately 94 kilotons of CO2 to study geologic carbon storage during CO2-EOR. A three-dimensional (3D) surface seismic dataset was acquired in 2013 to characterize the subsurface structures of the Farnsworth site. Following this data acquisition, the baseline and three time-lapse three-dimensional three-component (3D-3C) vertical seismic profiling (VSP) data were acquired at a narrower surface area surrounding the CO2 injection and oil/gas production wells between 2014 and 2017 for monitoring CO2 injection and migration. With these VSP datasets, we inverted for subsurface velocity models to quantitatively monitor the CO2 plume within the Morrow B formation. We first built 1D initial P-wave (Vp) and S-wave (Vs) velocity models by upscaling the sonic logs. We improved the deep region of the Vp and Vs models by incorporating the deep part of a migration velocity model derived from the 3D surface seismic data. We improved the shallow region of 3D Vp and Vs models using 3D traveltime tomography of first arrivals of VSP downgoing waves. We further improved the 3D baseline velocity models using elastic-waveform inversion (EWI) of the 3D baseline VSP upgoing data. Our advanced EWI method employs alternative tomographic and conventional gradients and total-variation-based regularization to ensure the high-fidelity updates of the 3D baseline Vp and Vs models. We then sequentially applied our 3D EWI method to the three time-lapse datasets to invert for spatiotemporal changes of Vp and Vs in the reservoir. Our inversion results reveal the volumetric changes of the time-lapse Vp and Vs models and show the evolution of the CO2 plume from the CO2 injection well to the oil/gas production wells.

42 ENGINEERING↗

DOE OSTI2024

Investigating the potential of a higher reactivity fuel to achieve faster heat-up of aftertreatment systems

Shortening the aftertreatment system heat-up period will be crucial to meet upcoming emissions regulations, which mandate significant reductions in tail-pipe emissions for on-road heavy-duty vehicles. This work studies the impact of increasing fuel reactivity on the combustion of post injections during the expansion stroke. The work demonstrates an operating strategy using a blend of di-butyl ether (a potential low-carbon biofuel component) and #2 diesel that achieves higher exhaust enthalpy, while maintaining similar engine-out emissions (NOx and combustion efficiency) in comparison to the baseline #2 diesel fuel (cetane number 41). On average, a 12% increase in exhaust enthalpy was observed for the blend (cetane number 60) relative to the baseline fuel. The ability to operate the higher reactivity fuel at a more retarded post-injection timing, where combustion with #2 diesel was found to be more unstable, and less complete was key to achieving higher exhaust enthalpy. However, a small fuel penalty (3%–5%) was also associated with the higher reactivity fuel with this operating strategy. The formation of fuel lean regions, due to the long ignition delays at late injection conditions, was predicted to be the leading contributor to the increased emissions of products of partial combustion. Here, chemical kinetic simulations using surrogates for the fuels used in the experiments, demonstrated the ability of a higher cetane fuel to outperform the baseline fuel under fuel lean conditions with equivalence ratios less than 0.7.

09 BIOMASS FUELS↗

DOE OSTI2022

Implication of stratospheric aerosol geoengineering on compound precipitation and temperature extremes in Africa

Three Coupled Model Intercomparison Project 5 (CMIP5) models that simulated the G4 experiment of the Geoengineering Model Intercomparison Project (GeoMIP) were used to investigate the impact of stratospheric aerosol injection (SAI) on combined temperature and precipitation extremes in Africa that can have greater negative impacts on human and the environment than individual rainfall or temperature extremes. The examined compound extremes included the dry (R warm|dry and R cold|dry ) and wet (R warm|wet and R cold|wet ) modes assessed during the injection (SAI, 2050-2069) and post-injection (postSAI, 2070-2089) periods compared with the historical period (1986-2005). We found a significant projected change in the occurrence of both wet and dry modes during SAI and postSAI related to the historical period. The magnitude and sign of this change depend on the season and the geographical location. During the SAI and postSAI, the wet (R warm|wet and R cold|wet ) modes are projected to be significantly lower while the dry modes are noted to increase in a large part of African continent depending on the season and the geographical location and may consequently leads to an increase of the droughts prone areas. Furthermore, the termination effect is noted to re duce the occurrence of dry modes, which may reduce the potential negative effects of the injection after halting. As the effect may vary from one region to another and according to the season, it suggested assessing the key sector impacts of SAI. Thus, this change in dry modes due to SAI could affect all activities which depend on water resources such as water supply, agriculture and food production, energy demand, and production with adverse effects on health, security, and sustainable development, but this needs to be assessed and quantified at regional scales.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

First-Principles Approach for Assessing Cold Electron Injection Efficiency of Dye-Sensitized Solar Cell: Elucidation of Mechanism of Charge Injection and Recombination

The adequacy of the inclusion of spacer units in the metal-free D-π–A organic dyes pertaining to the augmentation of dye-sensitized solar cell (DSSC) efficiency has been examined through the excited-state simulations of the charge injection and recombination processes at the dye–semiconductor interface. Within the framework of the time-dependent density functional theory, the proposed computational studies focus on the precise evaluation of pivotal factors controlling the rates of photoinduced charge-transfer and energy-transfer processes, including electronic coupling, reorganization energy, and threshold energy barrier in the semiclassical Marcus formalism. The estimation of the fluorescent state appears to be the crucial step while explaining the ultrafast electron injection process and the charge recombination at the Marcus inverted region, as revealed by the obtained results. The retardation of charge recombination is facilitated by the insertion of a thiophene moiety between the π-bridge and the acceptor units. The estimated cold electron injection efficiencies deploying the Onsager–Braun theory, that rely on the computations of cold electron injection lifetime and cold electron lifetime, show a linear correlation with the experimental photovoltaic parameters of the DSSC comprising short-circuit current density, open-circuit voltage, and power conversion efficiency. The outcomes of the present investigation establish a basis for unraveling the mechanism of intricate dynamical processes upon photoexcitation of the sensitizers, as well as devising plausible routes for functional DSSC materials.

14 SOLAR ENERGY↗

DOE OSTI2024

Surface Deformation and Seismicity Linked to Fluid Injection in the Raton Basin

Abstract It is suggested that in addition to seismicity deep fluid injection may cause surface uplift and subsidence in oil and gas‐producing regions. This study uses the Raton Basin as an example to investigate the hydromechanical processes of surface uplift and subsidence during wastewater injection. The Raton Basin, in southern central Colorado and northern central New Mexico, has experienced wastewater injection related to coalbed methane and gas production starting in 1994. In this study, we estimate the extent and magnitude of total vertical deformation in the Raton Basin from 1994 to 2020 and incremental deformation between the years 2017 to 2020. Results indicate a modeled uplift as much as 15 cm occurring between 1994 and 2020. Between 2017 and 2020, up to 3 cm of uplift occurred, largely near the northwestern injection wells. Most modeled uplift between 1994 and 2020 occurred near the southern wells, where the greatest cumulative volume of wastewater was injected. However, modeled subsidence occurred around the southern and eastern wells between 2017 and 2020, after the rate of injection decreased. Modeling indicates that while the magnitude of modeled uplift corresponds to cumulative injection volume and maximum rate in the long‐term, short‐term incremental deformation (uplift or subsidence) is controlled by changes in the rate of injection. The number of yearly earthquake events follows periods of rapid modeled uplifting throughout the Basin, suggesting that measurable surface deformation may be caused by the same injection‐induced pore pressure perturbations that initiate seismicity.

Geology↗

DOE OSTI2025

Design considerations for optimizing the transient CHI injector on QUEST

Transient coaxial helicity injection (transient CHI) on the QUEST (Q-shu University Experiment with Steady-State ST) spherical tokamak (ST) has recently validated the floating biased electrode configuration for solenoid-free plasma startup. In support of a significant divertor upgrade on QUEST, the details of the transient CHI injector geometry on QUEST have been examined more closely using tokamak simulation code (TSC) simulations. QUEST uses a HIT-II-like (Helicity Injected Torus) injector configuration in which the injector region is comprised of coaxial injector electrodes located in the lower part of the machine. TSC simulations indicate high injector flux operation may benefit from an increased gap between the coaxial electrodes. This is the first study to examine the differences between an open and closed electrode configuration for solenoid-free plasma startup using transient CHI. Results show that both configurations can generate similar levels of closed flux, but the closed configuration may be easier to implement in some ST designs as a much smaller portion of the injector needs to be close to the injector flux coil. Results show that increasing the electrode gap width from the present 10.8 cm to about 15–20 cm would increase the closed flux fraction by about 40%. The results presented in this paper are generally applicable to the CHI design for other STs.

coaxial helicity injection↗

DOE OSTI2024

Innovating the next generation of commercial smart building software

Nearly 30% of commercial building energy use is wasted due to equipment faults and HVAC controls problems. The result is increased emissions, compromised comfort and productivity, and less reliable coordination of building power needs with a clean grid. The energy impact alone represents $17 billion in potential savings. Today’s smart building software provides a robust solution to address these operational deficiencies. Energy management and information systems (EMIS) are saving up to 9% on average, with two-year paybacks. They are being incorporated into energy management processes, commissioning services, and utility programs. As effective as they are, two barriers prevent even deeper benefits; limited personnel to fix problems once they are identified, and the expense and time to manually implement changes in control systems. In partnership with the research community, the EMIS industry is developing new capabilities to overcome these barriers. Moving beyond siloed products for either fault detection and diagnostics, or optimal control, these new capabilities empower users to not only automatically identify faults, but also to push corrective action, and control improvements to their buildings. In this paper, several areas for enhancements are documented: ‘one-time’ correction of faults such as setpoints, schedules, and economizer lockouts; short-term active testing for automated proportional integral derivative (PID) loop tuning and functional testing; and continuous supervisory control for demand flexibility and year-round efficiency. Results are presented from a pair of partner implementations out of a dozen providers integrating these enhancements into their products, including field tests from across the country, and insights into operator acceptance and integration into operations and maintenance practices.

Casillas, Armando↗

DOE OSTI2021

FESS Design Simulations: methods, tools, & issues for the edge/scrape-off-layer region

This topic describes the plasma and neutral particles in the transition boundary region between the hot core plasma and the surrounding material walls. A key geometrical transition that occurs in this region is where the equilibrium magnetic field changes topology from a set of closed, nested magnetic flux surfaces inside the magnetic separatrix to flux surfaces, and therefore magnetic field lines that intersect material walls. Because the plasma exhaust heat flows very rapidly along the field lines, these intersection locations can have heat fluxes much higher than the walls can withstand. The most promising strategy pursued here to avoid this problem is injection of moderate-Z impurities that radiate the exhaust power over a much larger surface area on the walls, thus keeping the peak heat flux at or below the goal of 10 MW/m 2 . Further, the intrusion of injected and wall-sputtered impurities into the core region must be kept below certain limits to prevent degradation of the fusion power generated in the core.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Cavity evolution and void swelling in dual ion irradiated tempered martensitic steels

Microstructural evolutions in two variants of the F82H 8 wt%Cr tempered martensitic steel under dual (He + plus Fe 3+ ) ion irradiations at 500 °C have been characterized by transmission electron microscopy. Emphasis is on understanding the combined effects of displacements per atom (dpa) and the helium/dpa ratio (He/dpa) on cavity evolution and void swelling (f v ). The dual ion database includes 231 alloy-dpa-He/dpa conditions for irradiations up to ~ 82 dpa and 3700 appm helium. Here, we hypothesize that the large “scatter” observed in the f v data is primarily due to local microstructural variations, especially those that shield regions at shallower depths from the effects of injected interstitial atoms, which would otherwise reduce f v . More generally, our hypothesis is that the highest f v data, at a specified dpa and He/dpa, provides the most appropriate estimate of swelling for fusion neutron irradiation conditions. The dose dependence of f v can be described by an incubation dpa i , marking the onset of significant void growth, and a post-incubation swelling rate, f v ’ = Δf v /Δdpa. Both dpa i and f v ’ decrease with increasing He/dpa. The f v ’ data are quantitatively consistent with a simple model for defect partitioning between evolving bubble, void, and dislocation sinks strengths and biases. Most notably, the model correctly predicts both the incubation dpa i , and the subsequent f v ’, in spite of the fact that they reflect somewhat different physics. Our analysis also suggests that defect recombination is modest at 500 °C. Along with other considerations, this supports the hypothesis that, even at high dpa rates, dual ion irradiations can be used to reasonably emulate void nucleation and growth for a range of fusion-relevant neutron irradiation service conditions. A companion paper incorporates the results of this study in a reduced-order, data-driven void swelling model.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Instability seeding mechanisms due to internal defects in inertial confinement fusion targets

Performance degradation in laser-driven inertial confinement fusion (ICF) implosions is caused by several effects, one of which is Rayleigh–Taylor instability growth. Defects in ICF targets, such as internal voids and surface roughness, create instability seeds in the shell as shocks propagate through the target. A comprehensive understanding of seeding mechanisms is essential to characterize the impact of target defects on inflight shell integrity and mass injection into the central, lower-density vapor region. An analysis of early-time behavior of both single-mode shell mass modulations and isolated voids is performed by examining the evolution of the acoustic waves launched by these target imperfections. A systematic study of localized perturbation growth as a function of defect placement and size is presented. Furthermore, the use of low-density ablator materials (such as foams) is suggested as a potential mitigation strategy to improve target robustness against the impact of defect-initiated growth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Applicability of alkali beam emission spectroscopy on NSTX-U

Understanding fast pedestal dynamics and turbulent transport in the edge and scrape-off layer (SOL) plasma of spherical tokamaks is crucial for the design and operation of future fusion reactors. The alkali beam emission spectroscopy diagnostic technique offers a means to measure the absolute electron density radial profile and fluctuation amplitude in these regions. Here, in this study, we demonstrate that injecting a sodium neutral beam radially into the plasma and analyzing the light emission from its 3p–3s atomic transition using near-orthogonal viewing angles allows for accurate measurement of the electron density profile and fluctuations in the National Spherical Torus Experiment (NSTX) Upgrade spherical tokamak. Our findings indicate a peak signal-to-noise ratio of 118 in the pedestal and 12 in the SOL under typical NSTX plasma conditions. The spatial resolution for the electron density profile is estimated to be between 2 and 8 mm, while for fluctuation measurements, it ranges from 12 to 15 mm.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Divertor detachment characterization in negative triangularity discharges in DIII-D via 2D edge-plasma transport modeling

Edge fluid modeling of the first divertor-plasma detachment experiments in negative triangularity (NT) discharges in the DIII-D tokamak is presented using the 2D multifluid edge transport code UEDGE, including cross-field particle drifts. Experiments were performed where the lower single-null magnetic equilibrium had a strong NT (δ≈−0.5), that is, where the magnetic X-point is at a larger major radius than the core magnetic axis. Divertor-plasma detachment was induced by increasing the core plasma density in DIII-D via intrinsic gas puffing. Here density scans are performed with UEDGE to reach a detached plasma and to quantitatively recover the experimental rollover of the ion saturation current on the outer divertor target plate. The simulations cover experiments with both signs of the toroidal magnetic field, B T , where the ion magnetic Grad-B drifts are directed into (forward B T ) and out of (reverse B T ) the divertor region. Consistent with experiments with neutral beam power injection, the NT simulations reproduce: 40% higher density is needed to reach detachment onset with forward B T compared with reverse B T , and the absence of deep detachment is found with reverse B T . Similarly, comparison between Ohmic discharges in NT and positive triangularity (PT) shaping confirms that a substantially higher density is needed to achieve detachment in NT than in PT, with NT requiring an line-average density of at least the Greenwald density or higher. Simulation results suggest that higher densities are needed to reach detachment in negative compared to PT because these discharges have a shorter midplane-to-target distance along the total magnetic field B, a shorter outer divertor poloidal leg length (0.06 m vs 0.2 m), and reduced radial transport [near-scrape-off layer (SOL) D ⊥ /χ ⊥ =0.3/0.5 vs D ⊥ /χ ⊥ =1.0/1.0, all in (m 2 /s)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Pulsed Neutron Capture for monitoring CO2 Storage with Enhanced Oil Recovery in Northern Michigan

Pulsed neutron capture (PNC) logging has been used as part of the Midwest Regional Carbon Sequestration Partnership (MRCSP) monitoring of CO2 injection and storage during assessment of enhanced oil recovery (EOR) in several northern Niagaran trend reefs in Michigan. A total of four reefs were selected for these studies to monitor CO2 migration and to test the viability and effectiveness of the PNC technology on reefs in various stages (depleted, active and new reefs) of CO2-EOR activities.

Bagley↗

DOE OSTI2020

Structural Characterization of Potential Carbon Dioxide Reservoirs and Adjacent Strata within the Llandovery Silurian to Middle Devonian Strata of Ohio

The Midwest Regional Carbon Sequestration Partnership (MRCSP) has incorporated the work of geologic research teams (Geoteams) in its regional characterization, project planning and carbon dioxide (CO 2 ) injection implementation work since the partnership was established by the U.S. Department of Energy (DOE) in 2003. Over this 16-year period, the cohort of Geoteams has grown from five to ten states and has contributed to the characterization of geologic sequestration opportunities, refinement of reservoir and seal data, and supported injection efforts through both predictive and post-injection assessments. This report details the work led by the Ohio Department of Natural Resources, Division of Geological Survey to evaluate the structure of nine formations in the Appalachian Basin of Ohio to assess seal integrity and whether carbon dioxide (CO 2 ) migration pathways could pose a potential risk. As part of Phase II MRCSP work, the Pennsylvania Geological Survey led the characterization of the Llandovery Silurian (“middle Silurian”) to Middle Devonian regional geologic characterization CO 2 utilization and storage. This preliminary assessment included generalized, regional-scale mapping, as well as the development of relatively coarse structure and isochore maps of stratigraphic intervals of interest for the Appalachian Basin. Because this stratigraphic interval offers several enhanced oil recovery targets and secondary targets for CO 2 storage, the Ohio Geological Survey undertook efforts in Phase III to characterize the Ohio’s portion of the Appalachian Basin more precisely and to resolve inconsistencies within Ohio’s formation tops. This study refined the subsurface correlations of the Silurian-through-Devonian stratigraphic section in Ohio. Higher-resolution isochore mapping of the CO 2 storage reservoirs and seals provides greater detail of potential high-porosity zones and potential structural influence on the interval.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2023

A Multiwavelength Investigation of PSR J2229+6114 and its Pulsar Wind Nebula in the Radio, X-Ray, and Gamma-Ray Bands

Abstract G106.3+2.7, commonly considered to be a composite supernova remnant (SNR), is characterized by a boomerang-shaped pulsar wind nebula (PWN) and two distinct (“head” and “tail”) regions in the radio band. A discovery of very-high-energy gamma-ray emission (E γ > 100 GeV) followed by the recent detection of ultrahigh-energy gamma-ray emission (E γ > 100 TeV) from the tail region suggests that G106.3+2.7 is a PeVatron candidate. We present a comprehensive multiwavelength study of the Boomerang PWN (100″ around PSR J2229+6114) using archival radio and Chandra data obtained two decades ago, a new NuSTAR X-ray observation from 2020, and upper limits on gamma-ray fluxes obtained by Fermi-LAT and VERITAS observatories. The NuSTAR observation allowed us to detect a 51.67 ms spin period from the pulsar PSR J2229+6114 and the PWN emission characterized by a power-law model with Γ = 1.52 ± 0.06 up to 20 keV. Contrary to the previous radio study by Kothes et al., we prefer a much lower PWNB-field (B∼ 3μG) and larger distance (d∼ 8 kpc) based on (1) the nonvarying X-ray flux over the last two decades, (2) the energy-dependent X-ray size of the PWN resulting from synchrotron burn-off, and (3) the multiwavelength spectral energy distribution (SED) data. Our SED model suggests that the PWN is currently re-expanding after being compressed by the SNR reverse shock ∼1000 yr ago. In this case, the head region should be formed by GeV–TeV electrons injected earlier by the pulsar propagating into the low-density environment.

Astronomy & Astrophysics↗

DOE OSTI2021

SECARB Post Injection Assessment Report

The Southern States Energy Board (SSEB) managed the overall Southeast Regional Carbon Sequestration Partnership (SECARB) Phase III project and The Bureau of Economic Geology (BEG), at the University of Texas at Austin, managed all activities associated with the Early Test field site near Cranfield, Mississippi (the Early Test or Cranfield Project). The SECARB project at Cranfield was focused downdip of the oil rim and on demonstrating the stacked nature of the storage potential at this location: enhanced oil recovery (EOR) up-dip and saline downdip. Because the injection for EOR continued after the SECARB project ended, no actual post-injection period occurred. However, information collected during the SECARB-monitored injection period, including pressure and CO2 plume position, was utilized in an EOR carbon lifecycle assessment. The carbon lifecycle assessment provided insight on tracking injection fronts and production efficiencies across the field. To complete the post injection assessment, taking into account the continuing EOR period after closeout of SECARB field activities, this report provides data and analysis done under another DOE-funded project. The follow up project focused on the carbon lifecycle of EOR and included an assessment of EOR at as-operated and under possible future scenarios. This work was published by Hossieni et al. (2018) and Hosseininoosheri (2019).

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2020

Assessment of Enhanced Oil Recovery Using Carbon Dioxide in Michigan Basin Silurian Pinnacle Reefs

The Midwest Regional Carbon Sequestration Partnership (MRCSP) has incorporated the work of geologic research teams (Geoteams) in its regional characterization, project planning and carbon dioxide (CO 2 ) injection implementation work since the partnership was established by the U.S. Department of Energy (DOE) in 2003. Over this 16-year period, the cohort of Geoteams has grown from five to ten states and has contributed to the characterization of geologic sequestration opportunities, refinement of reservoir and seal data, and supported injection efforts through both predictive and post-injection assessments. The Michigan team at Western Michigan University has provided technical analysis and support of the enhanced oil recovery (EOR) using carbon dioxide (CO 2 ) in the Northern Michigan Silurian Pinnacle reefs. With Core Energy, LLC as the industry partner, this project has assessed the potential for EOR in known fields in the Michigan Pinnacle reefs and the capacity for CO2 storage in the reef reservoirs as they are depleted and after reservoir abandonment. This project managed by Core Energy, LLC, involves the only commercial CO 2 Enhanced Oil Recovery floods within the MRCSP region. The Silurian pinnacle reef trend shows significant potential for CO 2 -EOR: this play is relatively new, with approximately 60% of the wells in the largest Niagaran fields still accessible. Most wells have modern logs and there are many cores, core analyses, pressure tests and produced water analyses available for study from these fields. These carbonate reservoirs in Michigan have produced sufficient oil to warrant evaluation for additional recovery efforts. The role of the Michigan team was to collect and analyze all relevant data about reservoir properties, including lithologic and depositional characteristics of the reservoir formations and porosity and fluid flow properties through different compartments in the reservoir. The team has also developed models that represent the geological and physical characteristics of the reservoir and seal system.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2020

Flow Z-pinch plasma production on the FuZE experiment

The Fusion Z Pinch Experiment (FuZE) investigates sheared-flow stabilization of classic m = 0 and m = 1 instabilities in Z pinches with an embedded axial flow. FuZE consists of a 100 cm coaxial plasma accelerator, where neutral gas is ionized and accelerated in a pulsed electrical discharge, followed by a 50 cm assembly region, where pinches are formed. Maintaining the pinch requires continuous plasma injection provided by a deflagration mode in the coaxial accelerator. Two discharge modes, with and without deflagration, are investigated on FuZE. Pinch formation is observed with deflagration only. Plasma velocities in the assembly region are found to match the E × B velocity estimated in the accelerator based on a 1D circuit model, indicating that a 1D MHD approximation may offer a valid description of the plasma in the accelerator channel. The velocity of magnetic field propagation is found to agree with the snowplow model based on momentum conservation, and the lifetime of the pinch is shown to be in agreement with constraints imposed by mass conservation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗