Title: Development of five-moment two-fluid modeling for Z-pinch physics

Abstract

The Z-pinch m = 0 instability as well as its stabilization by radially sheared axial flow is studied using the nonlinear ideal five-moment twofluid (5M2F) model with an extension of that model to include Braginskii heat and momentum transport. Using the ideal 5M2F model, linear growth rate results are compared with prior work using MHD and Hall MHD. At small normalized wavenumber, $1<ka<4$, where a is the effective pinch radius, 5M2F results agree with Hall MHD within 20% in scenarios without radially sheared axial flow. With the sheared flow and focusing on ka = 10/3, agreement with Hall MHD is excellent. In the limit of small ion inertial length, results also match with MHD. A comparison with PIC modeling of shear-free m = 0 stability focuses on a plasma scenario based on recent experimental results. In a scan of mode wavenumber, ideal 5M2F results are qualitatively similar to PIC: the growth rate rises to a peak at a moderate wavenumber and declines at a large wavenumber in contrast to MHD results, which show the saturation of the growth rate with the increasing wavenumber rather than a decline. The peak normalized 5M2F growth rate is $\gamma {\tau }_A=1.5$, where sA is the Alfven transit time across the pinch. The peak occurs at normalized wavenumber ka = 10. For comparison, PIC results have a peak growth of $\gamma {\tau }_A=0.77$ at ka = 5. Including Braginskiibased closure of the 5M2F model does not qualitatively change the ideal results in this particular case. Nonlinear saturation is studied using the 5M2F model with the dissipative Braginskii-based closure in cases with pinch-edge sheared-flow speed equal to half the Alfven speed. Nonlinear mixing due to the sheared flow yields a quasi-steady state after modest losses of pinch ion inventory and pinch thermal energy, approximately 30% and 10%, respectively. 5M2F modeling captures the essential physics of m = 0 instability and offers a computationally tractable route to high-fidelity modeling of 3D Z-pinch behavior, including m = 1 instability.

Authors:

Meier, E. T.  ^[1];

• Search DOE PAGES for author "Meier, E. T."
• Search DOE PAGES for ORCID "0000-0001-6825-9842"

Shumlak, U.  ^[2]

• Search DOE PAGES for author "Shumlak, U."
• Search DOE PAGES for ORCID "0000-0002-2918-5446"

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+ Show Author Affiliations

1. Zap Energy, Inc., Seattle, WA (United States)
2. Zap Energy, Inc., Seattle, WA (United States); Univ. of Washington, Seattle, WA (Aerospace and Energetics Research Program)

Publication Date:

Wed Sep 22 00:00:00 EDT 2021

Research Org.:

Univ. of Washington, Seattle, WA (United States); Zap Energy Inc., Seattle, WA (United States); Univ. of California, Oakland, CA (United States)

Sponsoring Org.:

USDOE Advanced Research Projects Agency - Energy (ARPA-E)

OSTI Identifier:

1848201

Grant/Contract Number:  

AR0000571; AR0001010; AR0001260; AC02-05CH11231; FA9550-15-1-0271

Resource Type:

Accepted Manuscript

Journal Name:

Physics of Plasmas

Additional Journal Information:

Journal Volume: 28; Journal Issue: 9; Journal ID: ISSN 1070-664X

Publisher:

American Institute of Physics (AIP)

Country of Publication:

United States

Language:

English

Subject:

70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Physics; Plasma confinement; Plasma waves; Equations of fluid dynamics; Viscosity; Computational models; Flow instabilities; Magnetic energy; Plasma instabilities; Magnetohydrodynamics; Fluid flows