• Matter and Radiation at Extremes
  • Vol. 4, Issue 2, 27402 (2019)
R. B. Spielman* and D. B. Reisman
Author Affiliations
  • Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623-1299, USA
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    DOI: 10.1063/1.5089765 Cite this Article
    R. B. Spielman, D. B. Reisman. On the design of magnetically insulated transmission lines for z-pinch loads[J]. Matter and Radiation at Extremes, 2019, 4(2): 27402 Copy Citation Text show less

    Abstract

    Many papers have been published on the theory of magnetic insulation and the use of Zflow analysis of magnetically insulated transmission lines (MITLs). We describe herein a novel design process using the circuit code SCREAMER for a real-world MITL for z-pinch loads based on the Zflow model of magnetic insulation. In particular, we design a 15-TW, 10-MA, 100-ns double-disk transmission line using only circuit modeling tools and Zflow analysis of the MITL. Critical issues such as current loss to the anode during the setup of magnetic insulation and the transition from a non-emitting vacuum power feed to an MITL play a large role in the MITL design. This very rapid design process allows us for the first time to explore innovative MITL designs such as variable-impedance MITLs that provide a significantly lower total inductance and improved energy delivery to the load. The tedious process of modeling the final MITL design with highly resolved 2D and 3D electromagnetic particle-in-cell codes occurs as a validation step, not as part of the design process.
    Zvac=VI=LC.(1)

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    Zflow=Va(Ia2Ic2)1/2.(2)

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    E/cB=Zr/Zvac.(3)

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    E/cB=Zr/Zflow.(4)

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    IaMC(V)=V/Z0fMC(V)[2fMC(V)1]1/2,(5)

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    IcMC=21/2(1fMC)1/2fMC(2fMC1)1/2VZ0,(6)

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    ZfMC(V)=Z0fMC(V),(7)

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    fMC(V)=(gmc28 eV1)+[(gmc28 eV1)2+(gmc22 eV1)]1/2(gmc22 eV1),(8)

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    h(Zf)=Zf3Z0Zf2+(gmc2V2eIa2V2Ia2)Zf+Z0V2Ia2=0,(9)

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    Zdisk=μ0ε0h2πr,(10)

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    R. B. Spielman, D. B. Reisman. On the design of magnetically insulated transmission lines for z-pinch loads[J]. Matter and Radiation at Extremes, 2019, 4(2): 27402
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