A control theory approach on the design of a Marx generator network

A Marx generator is a well-known type of electrical circuit first described by Erwin Otto Marx in 1924. It has been utilized in numerous applications in pulsed power with resistive or capacitive loads. To-date the vast majority of research on Marx generators designed to drive capacitive loads relied on experimentation and circuit-level modeling to guide their designs. In this paper we describe how the problem of designing a Marx generator to drive a capacitive load is reduced to that of choosing a diagonal gain matrix F that places the eigenvalues of the closed-loop matrix A+BF at specific locations. Here A is the identity matrix and B characterizes the elements of the Marx generator and depends on the number of stages N. Due to the special structure of matrix F, this formulation is a well-known problem in the area of feedback control and is referred to as the structured static state feedback problem. While the problem is difficult to solve in general, due to the specific structures of matrices A and B, various efficient numerical algorithms exist to find solutions in specific cases. In a companion paper by Buchenauer it is shown that if certain conditions hold, then setting the natural frequencies of the circuit to be harmonically related guarantees that all the energy is delivered to the load capacitor after a suitable delay. A theorem formalizing this result is presented. Earlier aspects of this research have been published in two theses

Transient phenomena on ZT-40

Two aspects of fluctuations in the ZT-40 reversed-field pinch are examined. First, the polarization of the magnetic fluctuations in the outer (vacuum) region is discussed. This in turn provides information on the wavevectors associated with the turbulence. The results provide some clues about the location (in minor radius) of the singular surfaces which are customarily associated with fluctuations. Second, the density fluctuations are studied using a multichord interferometer. The spatial distribution (in major radius) of the chord-averaged fluctuations are also described

Four-feedplate operation of ZT-40 with passive crowbars

This report summarizes the measurements made on the ZT-40 reversed-field pinch during the start-up on October 5, 1979, until May 1980, when the power crowbar circuitry became operational. The material contained herein pertains to the operation of ZT-40 with four current feedpoints, passive crowbars, and a nonconducting, high-purity alumina liner. The plasma properties are given for reversed-field pinches obtained either by aided or self-reversal and for nonreversed-field (stabilized) pinches. It is demonstrated that ZT-40 was capable of being ohmically heated to approx. 100 eV electron temperatures during the approx. 0.1 ms rise to peak current. Operation is obtained in which the fluctuations during start-up are observed to decrease later in the discharge, producing quiet periods of approx. 0.1 ms

Performance of the ZT-40M reversed-field pinch with an Inconel liner

Modifications made to ZT-40 have substantially improved plasma parameters: pinch resistance has decreased by more than an order of magnitude, T/sub e/ has exceeded 300 eV, and with power crowbar operation > 20 ms steady-state discharges have been obtained. With a ..beta.. of approx. 0.1, and the assumptions of modified Bessel function magnetic-field profiles and classical ohmic heating the energy confinement time, approx. 0.2 ms, is close to that expected for the measured temperatures and discharge currents. A relaxation process (dynamo) sustains RFP profiles extending discharge lifetimes beyond the limit predicted by classical resistive diffusion. If the process continues to operate, a steady-state RFP is possible. Extension of the toroidal current risetime to the experiment's design limit (1.5 ms) indicates that RFPs can be formed at still longer risetimes with reasonable voltsecond and energy inputs facilitating the design of future experiments. These results represent a significant advance for the RFP concept toward a viable ohmic-heated magnetic-fusion system

Initial reversed-field pinch experiments on ZT-40 and recent advances in RFP theory

The ZT-40 reversed-field pinch (RFP) has been operated in several modes: (1) without reversed toroidal field, (2) with self reversal, and (3) with aided reversal. An analytic ohmic heating and ignition model both confirm and provide guidance for transport codes. Nondissipative formation schemes have been analyzed and ideal MHD stable evolution and burn scenarios have been found. Particle and fluid simulations have produced qualitative agreement with respect to the nonlinear behavior of m = 0 resistive g-modes. Helical ohmic reversed field states are produced by a 2-D dynamical simulation, and nonlinear analytic work describes the final state. A fast resistive MHD code for linear stability has clarified the relations between several kinds of resistive instabilities. Ballooning modes and g-modes in systems with arbitrary magnetic shear including resistivity and viscosity, have been studied in a unified treatment with growth rate vs wavenumber showing the existence of important cutoffs

Local drift parameter, j/n/sub e/ and resistivity anomaly measurements in CTX spheromaks

In a spheromak, the magnetic fields confining the plasma are generated primarily by internal currents rather than external coils. In order to provide information on the possible existence of current-driven microinstabilities, localized measurements of the ratio of the drift velocity of the electrons generating the internal current to their thermal velocity, V/sub d//V/sub th/ proportional to j/n/sub e/..sqrt..T/sub e/ (known as the drift or streaming parameter), and j/n/sub e/ (proportional to V/sub d/) are needed. These microinstabilities are in some theories associated with an increase in the resistivity anomaly factor (eta/eta/sub Spitzer/). We present results on local measurements (at the magnetic axis) of the values of V/sub d//V/sub th/ and eta/eta/sub Spitzer/ by combining data from the spatially-resolved diagnostics employed on the CTX spheromak experiment, coupled with current density profile information from equilibrium measurements. The values of V/sub d//V/sub th/ and j/n/sub e/ appear to be correlated with local variations in eta/eta/sub Spitzer/, and can be changed by varying the plasma density. Data sets are presented for three values of n/sub e/