Matter and Radiation at Extremes, Volume. 4, Issue 2, 27402(2019)

On the design of magnetically insulated transmission lines for z-pinch loads

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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    Figures & Tables(14)
    (a) Schematic of the full double-disk MITL that shows the insulator stack, the vacuum flare region, the MITLs, the post-hole convolute, the inner disk MITL, and the load region. (b) Schematic showing the dimensions of the two MITLs being modeled. The 1.5-Ω impedance value is only for the radius and gap at that point. The vertical scale is expanded four times for clarity.
    Calculated total current (black solid curve), A-level current (red solid curve), and B-level current (blue solid curve) as functions of time.
    Calculated currents in each MITL segment as functions of time. The differences seen in the time window from 120 ns to 140 ns reflect losses during the setup of magnetic insulation.
    Calculated voltages in each MITL segment as functions of time.
    Electron-loss currents in each MITL segment, where the largest current losses occur with the inner MITL segment 10. z-pinch stagnation is at ∼255 ns.
    Electron-loss current density in each MITL segment, where the largest current density losses occur with the inner MITL segment 10.
    Calculated total current (black solid curve), A-level current (red solid curve), and B-level current (blue solid curve) as functions of time.
    Calculated currents in each MITL segment as functions of time for the variable-impedance MITL. The differences in the various currents seen at ∼120 ns to 150 ns reflect losses during the setup of magnetic insulation.
    Calculated voltages of each MITL segment with time. The voltages decrease radially inward.
    Electron-loss currents in each MITL segment for the variable-impedance MITL, where the largest current losses occur with inner MITL segment 10. z-pinch stagnation is at ∼255 ns.
    Electron-loss current density in each MITL segment of the variable-impedance MITL, where the largest current-density losses occur with inner MITL segment 10.
    • Table 1. Listing of the MITL parameters from the ten MITL segments on the B level from SCREAMER calculations for a 2-Ω constant-impedance MITL.

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      Table 1. Listing of the MITL parameters from the ten MITL segments on the B level from SCREAMER calculations for a 2-Ω constant-impedance MITL.

      MITL segmentRadial location (cm)AK gap (cm)Zvac (Ω)Va (MV)Ec (kV/cm)Ia (MA)Zr (Ω)Zflow (Ω)Ic (MA)Ivac (kA)E/cBhsh (mm)hsh/gap
      1144.954.83521.282652.770.4621.9782.693770.2340.520.0108
      2132.854.43121.222752.770.4401.9802.701690.2230.450.0101
      3120.754.02821.172902.770.4221.9802.706640.2130.400.0099
      4108.653.62421.123092.770.4041.9812.712580.2040.340.0094
      596.553.22021.073322.770.3861.9822.717530.1950.290.0088
      684.452.81721.013592.770.3651.9832.723470.1840.240.0083
      772.352.41320.9663822.770.3491.9842.727430.1760.190.0080
      860.252.01020.9064512.770.3271.9852.732380.1650.150.0075
      948.151.60620.8555322.770.3091.9862.736340.1550.110.0071
      1036.051.20220.8036682.770.2901.9862.740300.1460.080.0068
    • Table 2. Radius, circumference, gap, impedance, and inductance of the ten MITL segments used in the SCREAMER calculations.

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      Table 2. Radius, circumference, gap, impedance, and inductance of the ten MITL segments used in the SCREAMER calculations.

      MITL segmentRadius centroid (cm)Circular centroid (cm)Calculated gap (cm)Local impedance (Ω)Local inductance (H) (×10−10)
      1144.2565906.43.6211.5056.0384
      2132.2295830.83.3451.5176.0858
      3120.2025755.33.0701.5316.1427
      4108.1755679.72.7941.5496.2122
      596.1485604.12.5181.5706.2991
      684.1215528.62.2421.5986.4109
      772.0945453.01.9661.6356.5600
      860.0675377.41.6901.6876.7689
      948.0405301.81.4141.7657.0822
      1036.0135226.31.1391.8967.6049
    • Table 3. Listing of B-level MITL parameters from SCREAMER calculations for a variable-impedance MITL.

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      Table 3. Listing of B-level MITL parameters from SCREAMER calculations for a variable-impedance MITL.

      MITL segmentRadial location (cm)AK gap (cm)Zvac (Ω)Va (MV)Ec (kV/cm)Ia (MA)Zr (Ω)Zflow (Ω)Ic (MA)Ivac (kA)E/cBhsh (mm)hsh/gap
      1144.953.6391.5051.2313382.920.4221.4792.7991210.2850.620.0171
      2132.853.3611.5171.1883532.920.4071.4932.8091110.2730.540.0160
      3120.753.0831.5311.1453712.920.3921.5082.8201010.2600.470.0151
      4108.652.8061.5481.1033932.920.3781.5302.829910.2480.400.0142
      596.552.5281.5701.0604192.920.3631.5492.840810.2340.330.0131
      684.452.2501.5981.0174522.920.3481.5792.850720.2210.270.0121
      772.351.9731.6350.9664902.920.3311.6172.858620.2050.220.0110
      860.251.6951.6870.9235452.920.3161.6712.867530.1890.170.0098
      948.151.4171.7650.8806212.920.3011.7502.876440.1720.120.0085
      1036.051.1401.8950.8297272.920.2841.8822.887330.1510.080.0070
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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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    Paper Information

    Category: Inertial Confinement Fusion Physics

    Received: Sep. 13, 2018

    Accepted: Dec. 12, 2018

    Published Online: Jun. 27, 2019

    The Author Email: Spielman R. B. (rbspielman@me.com)

    DOI:10.1063/1.5089765

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