| Significant improvements in fast Z-pinches driving imploding plasma have been achieved in recent years. One of the great achievements in fast Z-pinch technology was the successful design of the magnetically insulated transmission lines (MITL). MITL are used to deliver electromagnetic energy from large diameter water lines (several meters) to the small diameter of the load (several centimeters) with high power density (up to MW/cm2) and low current loss (less than 10%) in high current accelerators. Since MITL is one of the key components and the biggest technical challenges in such a facility, engineering-oriented theoretical investigation of MITL was addressed in this dissertation. This investigation based on two purposes: first, establishing general methods for calculating the electric parameters of circular-conical MITL system, laws for the performance of magnetic insulation and the basic means for analyzing the structural stabilization of the whole vacuum power transmission system; second, providing adequate and reliable criterions for engineering design.The electromagnetic performances of MITL include the relation between current and voltage of the MITL, correlative electric and magnetic field in the MITL (i.e. theory of magnetic insulation), and corresponding effects (thermal effect, mechanical effect, etc.) on the MITL under the action of the electric and magnetic field. Theory of magnetic insulation is the primary tool for describing the electromagnetic performances of a MITL. At present, theories describing MITL principle can be classified into stationary theories in steady state and non-stationary theories in unsteady state. Laminar flow theory is the best example for the former ones, which is usually adopted in engineering design and was adopted here. While the latter one is often used to analyze the local electron flow of the MITL.MITL can have distinct geometrical configuration. Circular-conical MITL, which is adopted in PBFA Z at Sandia National Laboratory, is a representative one. This dissertation focused on such a configuration. Circular-cone MITL configuration consists of vacuum insulator stack (VIS), outer MITL, Double Post-hole Convolute (DPHC), inner MITLs and load region. Outer MITL are the critical part for the performance of a MITL.From fundamental theory of electromagnetism, the capacitance, calculation formulas of inductance and impedance of three special shapes, which constitute the geometry ofcircular-cone MITL, were derived. The analytical expressions were examined with the Z parameters. The calculation values of the inductance and impedance are only 3% and 5% larger than the published values of Z, respectively.In order to design geometrical structure of the circular-cone MITL, characteristics of the magnetic insulation for three representative geometries (i.e. planar, coaxial-cylindrical and common-vertex conical) were studied. Maximum of space-charge limited (SCL) flow and the relations between the space-charge limited flow and conducting current in steady state, which related to the anode voltage, the conductor geometry and polarity for non-planar configuration, were investigated respectively. For the case without conducting current, generalized Poisson equations for these three geometries were deduced considering relative effects and with the assumption of space-charge limited flow, and the maximum of space-charge limited flow were acquired by numerically solving the equations. In the calculation, 8 degree polynomial fit was used, which is much more accurate than the power series fit given by published works (at 6 MV, accuracy is an order higher). For the case with conducting current, a conducting current factor was introduced into the generalized Poisson equation, so it can be used to describe the effects of conducting current on space-charge limited flow. The method calculation are available for several non-planar geometries besides planar one, and can be scale up to 6.5 MV (published works only treat the case of planar geometry below 1 MV).Electric parameters of circ...
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