We describe herein a system of self-magnetically insulated vacuum transmission lines (MITLs) that operated successfully at 20 MA, 3 MV, and 55 TW. The system delivered the electromagnetic-power pulse generated by the Z accelerator to a physics-package load on over 1700 Z shots. The system included four levels that were electrically in parallel. Each level consisted of a water flare, vacuum-insulator stack, vacuum flare, and 1.3-m-radius conical outer MITL. The outputs of the four outer MITLs were connected in parallel by a 7.6-cm-radius 12-post double-post-hole vacuum convolute. The convolute added the currents of the four outer MITLs, and delivered the combined current to a single 6-cm-long inner MITL. The inner MITL delivered the current to the load. The total initial inductance of the stack-MITL system was 11 nH. A 300-element transmission-line-circuit model of the system has been developed using the TL code. The model accounts for the following: (i) impedance and electrical length of each of the 300 circuit elements, (ii) electron emission from MITL-cathode surfaces wherever the electric field has previously exceeded a constant threshold value, (iii) Child-Langmuir electron loss in the MITLs before magnetic insulation is established, (iv) MITL-flow-electron loss after insulation, assuming either collisionless or collisional electron flow, (v) MITL-gap closure, (vi) energy loss to MITL conductors operated at high lineal current densities, (vii) time-dependent self-consistent inductance of an imploding z-pinch load, and (viii) load resistance, which is assumed to be constant. Simulations performed with the TL model demonstrate that the nominal geometric outer-MITL-system impedance that optimizes overall performance is a factor of $3 greater than the convolute-load impedance, which is consistent with an analytic model of an idealized MITL-load system. Power-flow measurements demonstrate that, until peak current, the Z stack-MITL system performed as expected. TL calculations of the peak electromagnetic power at the stack, stack energy, stack voltage, outer-MITL current, and load current, as well as the pinch-implosion time, agree with measurements to within 5%. After peak current, TL calculations and measurements diverge, which appears to be due in part to the idealized pinch model assumed by TL. The results presented suggest that the design of the Z accelerator's stack-MITL system, and the TL model, can serve as starting points for the design of stack-MITL systems of future superpower accelerators.
We have developed a semianalytic expression for the total energy loss to a vacuum transmission-line electrode operated at high lineal current densities. (We define the lineal current density j ' B= 0 to be the current per unit electrode width, where B is the magnetic field at the electrode surface and 0 is the permeability of free space.) The expression accounts for energy loss due to Ohmic heating, magnetic diffusion, j  B work, and the increase in the transmission line's vacuum inductance due to motion of the vacuum-electrode boundary. The sum of these four terms constitutes the Poynting fluence at the original location of the boundary. The expression assumes that (i) the current distribution in the electrode can be approximated as one-dimensional and planar; (ii) the current IðtÞ ¼ 0 for t < 0, and IðtÞ / t for t ! 0; (iii) j ' 10 MA=cm; and (iv) the current-pulse width is between 50 and 300 ns. Under these conditions we find that, to first order, the total energy lost per unit electrode-surface area is given by W t ðtÞ ¼ t B ðtÞ þ t B ðtÞ, where BðtÞ is the nominal magnetic field at the surface. The quantities
The Total Immersion Particle [B. M. Marder, Math. Comput. 29, 434 (1973)] code has been used in several two-dimensional geometries to understand better the measured dynamics of annular, aluminum wire-array z-pinches. The areas investigated include the formation of the plasma sheath from current-induced individual wire explosions, the effects of wire number and symmetry on the implosion dynamics, and the dependence of the Rayleigh–Taylor instability growth on initial sheath thickness. A qualitative change in the dynamics with increasing wire number was observed, corresponding to a transition between a z-pinch composed of nonmerging, self-pinching individual wires, and one characterized by the rapid formation and subsequent implosion of a continuous plasma sheath. A sharp increase in radiated power with increasing wire number has been observed experimentally near this calculated transition. Although two-dimensional codes have correctly simulated observed power pulse durations, there are indications that three-dimensional effects are important in understanding the actual mechanism by which these pulse lengths are produced.
Light ion beam ICF is a concept in which intense beams of low atomic number ions would be used to drive ICF targets to ignition and gain. Three dimensional analytic approximations indicate that at least twelve beams would be required to drive an indirect drive target with adequate symmetry. Here, results from two dimensional numerical simulations are presented describing the ion deposition and drive symmetry aspects of such a target for which the ion beams are approximated as ring sources. For adequate symmetry in the two dimensional calculations, the simulations required six ring sources and two pole sources during the low power `foot' pulse and four ring sources during the main ion beam drive pulse. If each ring represents five individual beams, this corresponds to 32 beams in the foot pulse and 20 beams in the main pulse. The corresponding two dimensional integrated LASNEX calculation, simulating the target from ion beam input to ignition and burn in the same code run, produced 591 MJ of thermonuclear yield with lithium ion beam sources containing a total input energy of 16 MJ.
We have designed and tested a 10-nH 1.5-m-radius vacuum section for the Z accelerator. The vacuum section consists of four vacuum flares, four conical 1.3-m-radius magnetically-insulated transmission lines, a 7.6-cm-radius 12-post double-post-hole convolute which connects the four outer MITLs in parallel, and a 5-cm-long inner MITL which connects the output of the convolute to a z-pinch load. IVORY and ELECTRO calculations were performed to minimize the inductance of the vacuum flares with the constraint that there be no signi6cant electron emission from the insulator-stack grading rings. Iterative TLCODE calculations were performed to minimize the inductance of the outer MITLs with the constraint that the MITL electron-flow-current fraction be 17% at peak current. The TLCODE simulations assume a 2.5 cm/W MITL-cathode-plasma expansion velocity. The design limits the electron dose to the outer-MITL anodes to 50 J/g to prevent the formation of an anode plasma. The TLCODE results were confirmed by SCREAMER, TRFL, TWOQUICK, IVORY, and LASNEX simulations.For the TLCODE, SCREAMER, and TRlFL calculations, we assume that after magnetic insulation is established, the electron-flow current launched in the outer MITLs is lost at the convolute. This assumption has been validated by 3-D QUICKSILVER simulations for load impedances 10.36 ohms. LASNEX calculations suggest that ohmic resistance of the pinch and conduction-current-induced energy loss to the MITL electrodes can be neglected in Z power-flow modeling that is accurate to first order. To date, the Z vacuum section has been tested on 100 shots. We have demonstrated we can deliver a 100-ns rise-time 20-MA current pulse to the baseline z-pinch load. We have produced a 1.9-MJ x-ray yield; the project goal was 1.5 MJ. We can reproduce the peak MITL current to within rt1.6%. Power-flow measurements indicate the vacuum section performs as expected until peak current.Afterward, measurements and simulation results diverge. TLCODE calculations indicate elimination of this discrepancy may increase by 20% the kinetic energy delivered to the pinch.
Ab s t ra c tWe hiwe imploded a 17.5 mm diameter 120-tungsten-wire a m y weighing 150 U g h n onto a 1 mrn diameter silicon aerogel foam weighing 650 pgfcm, using the pulsed p o u a driver SATURV. . 4 p& current of 7.0 M-4 drives a 18 N impiosiou to strike time followed by S N cf foam compression until stagmtion. Thc tungsten strikcs the foam ivitti n 50 crn'us implosion veIocity. Radiation tempcnrures \sere measwcd from thc sidc nnci nfong the nsis with fiItered x-ray diode arrays. There is evidence of ndintion [rapping by thc optically thick tungten from crystal spec~oscopy. The pinch is open to lcss dian n 1 rnm diameter xs measured by time-resolved s-ray fnming camens. The radiation brisfitncss tempenturc in the foam reaches 150 eV before the main radiation b u n t or stagmtion.
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