• 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
    (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.
    Fig. 1. (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.
    Fig. 2. 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.
    Fig. 3. 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.
    Fig. 4. 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.
    Fig. 5. 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.
    Fig. 6. 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.
    Fig. 7. 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.
    Fig. 8. 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.
    Fig. 9. 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.
    Fig. 10. 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.
    Fig. 11. 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.
    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 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 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 2. Radius, circumference, gap, impedance, and inductance of the ten MITL segments used in the SCREAMER calculations.
    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
    Table 3. Listing of B-level MITL parameters from SCREAMER calculations for a variable-impedance MITL.
    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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