Rescaling of equilibrium magnetically insulated flow theory based on results from particle-in-cell simulations

Abstract

By relaxing an assumption on the electron density in the flow layer used in magnetically insulated transmission line (MITL) theory, the theory is rescaled to match particle-in-cell (PIC) simulation results, providing a more accurate determination of the line voltage from the measurement of anode and cathode currents over a broad range of parameters. Results from the PIC simulations also show that self-limited flow is not determined by either a minimum-current or a minimum-energy condition, but rather is closer to saturated flow. In addition, analytic expressions are obtained for the first time for the self-limited flow impedance ZfSL(V)∕Z0 and the self-limited anode and cathode currents Z0IaSL(V) and Z0IcSL(V), where Z0 is the vacuum impedance of the line and V is the voltage. Similar expressions for both minimum-current flow and minimum-energy flow are also obtained. Results are compared with other models for MITL flow and show that this rescaled MITL flow model is most consistent with the PIC simulation results. Finally, it is shown that a matched load condition can never be satisfied for self-limited (or line-limited) flow.

Ion diode performance on a positive polarity inductive voltage adder with layered magnetically insulated transmission line flow

“…The experimentally measured voltage agrees reasonably well with the theoretical predictions developed in Sec. II, but not with the usual Mendel formula 6,9,11,15 developed for non-layered MITL flow. The measured ion current also agrees reasonably with the theoretical prediction developed in Sec.…”

“…11,[14][15][16] Here V is in MV, I a and I c are in MA, and Z f is in Ohms. Unless explicitly noted these are the units that are used throughout the paper.…”

“…Typically, IVA accelerators have a magnetically insulated transmission line (MITL) 4 and, consequently, also have MITL electron flow. [5][6][7][8][9][10][11][12][13][14][15][16] MITL electron flow occurs when the electric field stress on the cathode is high enough to cause electron emission from the cathode but the magnetic field (current) is large enough to magnetically insulate these electrons from reaching the anode, resulting in electron current flow in the vacuum region of the MITL as illustrated in Fig. 1.…”

Recyclable transmission line (RTL) and linear transformer driver (LTD) development for Z-pinch inertial fusion energy (Z-IFE) and high yield.

“…A low MITL impedance is advantageous for a z-pinch IFE system as it minimizes the inductance between the driver and the load; thus, the voltage generated by dI/dt (required to drive the z-pinch) is minimized [15]. The effective impedance of the MITL is described best by the flow impedance Z f , which is a function of both the geometry and the voltage [16][17][18][19][20][21][22][23][24] and is less than the vacuum impedance of the line Z 0 because of the distributed electron current. Additionally, high current resistively heats the electrode surfaces; when the anode surface is heated above T = 400° C [25][26][27][28][29][30], ions are emitted.…”

Modeling particle emission and power flow in pulsed-power driven, nonuniform transmission lines

“…The electron sheath layer alters the transmission-line impedance [4,6], and analytic models for equilibrium currents and impedance are actively being investigated [7]. The equilibrium values may be dynamically altered if the load impedance is less than the self-limited impedance of the transmission line.…”