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The Pinch Effect Revisited

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The Pinch Effect Revisited Click here for Full Issue of EIR Volume 18, Number 6, February 8, 1991 The pinch effect revisited The late WinstonH. Bostick's 1977 groundbreaking examination qfthis aspect qfcontrolled thermonuclearfusion. Part 1 qf a series. We present here an historic scientificessay by Prof. Winston plasma pinch have been found to be essential in understand­ H. Bostick on the development of the plasma pinch from ing the tokamak itself. Furthermore, this deeper scientific its inception in early fusion energy research experiments comprehension has opened up prospects for realizing even through to 1977, which was first published in the Fusion more advanced typesof fusion reactors. But neither the toka­ Energy Foundation's International Journal of Fusion Ener­ mak nor these more advanced possibilities are being pursued gy, Vol. 1, No. 1, March 1977. Given his own role in the today, given the budget cuts now being implemented. development of this approach to magnetic fusion, the essay is necessarily semi-autobiographical. The pinch effect is the self-constriction of a column of de­ The following information will help the reader to put the formable conductor which is carrying an electric current.The essay in the context of developments since 1977. constricting effect on the column is produced by the magnetic In 1977, the United States had the world's largest and field pressure resulting from this current, or equivalently, by most advanced fusion energy research program. But during the Lorentz force produced by the currentflowing in its own the Carter administration, the program was essentially put magnetic field. Thus, in a controlled thermonuclear fusion on hold. Then, during the Reagan administration, fusion research (CTR) magnetic-containment device of the pinch­ energy research as well as nuclear power development in effect type, the containing magnetic fieldis generated chiefly general, were permitted to die on the vine, so to speak. Now, by the currentsflowing in the plasma itself. under the Bush administration, the fusion program is being In the sixteenth century the effect of a Lorentz force on completely destroyed by budget cuts. a movable, deformable plasma conductor was observed by Therefore, at the time Professor Bostick's paper was William Gilbert, the court physician to Queen Elizabeth I of published, the U. S. fusion program was relatively healthy England: He noted that a candle flame was deflected away and his critique of it was focused on the wrong-headed ap­ from a magnet when the magnet approached the flame. J.A. proach of centering the program on one single method, the Pollock and S.H. Barraclough at the University of Sydney tokamak. In the final outcome, both the tokamak and more reported in 1905 an analysis on a piece of lightning conductor general research were both cut back. For example, the last (a 1.8 cm-diameter, O.I-cm-wall-thickness copper tube) major step toward a tokamakfusion reactor was the Prince­ which had passed a lightning bolt about the year 1895. The ton TokamakFusion Test Reactor, which is currently in oper­ copper tube had been crushed by the "electrodynamic action ation. Planning for this large experiment was initiated in of the current," and if the tube was assumed to be rigid (not 1973 and initial design completed in 1976. No other major softened to plasticity by the heat) at the time of the passage project of similar size has been initiated since the Princeton of the current, it could be calculated that the magnetic pres­ TokamakFusion Test Reactor. sure had been about 400 pounds per square inch, and the In fact, experiments to date throughout the world have currenthad been about 100,000 amperes. Photographs of the demonstrated that the tokamakwould work as a power reac­ cross-section of the crushed ¢ylindrical shell are shown in tor. There simply has been no follow-through to actually Figure 1. Indeed a lightning stroke in the atmosphere is do that, despite the passage of the 1980 Magnetic Fusion a column of plasma whose diameter is influenced in some Engineering Act mandating just that. measure by the pinching electromagnetic forces. But this does not mean that Professor Bostick's critique In 1933, (when the neturon was being discovered and was offthe mark. ln fact, the same experiments which demon­ Hitler was on the rise to power), Willard Bennett wrote his strated the capabilities of the tokamak as a potential power famous paper on the steady-state pinch effect (published in reactor, have also shown that Bostick was correct in terms 1934). This article treated in a relativisticall y correct way the of the fact that the nonlinear dynamics demonstrated in the effect of the mutual attraction of electrons moving in one 20 Science & Technology EIR February 8, 1991 © 1991 EIR News Service Inc. All Rights Reserved. Reproduction in whole or in part without permission strictly prohibited. direction and the positive ions moving in the opposite direc­ tion. The correct relationships showing how the electric FIGURE 1 charge density depends upon the frame of reference (relation­ ships developed independently again by Budker in his doctor­ al thesis in 1956) were set forth by Bennett. Bennett calcu­ lated the equilibrium radial electron (and ion) density distribution to be where and JL�/87T = NkT (mksunits), Bz = 0, P = n.,kTe + njkTj, T = (Te+T)/2, 10 is the total current, the number of electrons and ions per unit length of column, Vz is axial electron drift and is constant everywhere, k is Boltzmann's constant, e is the electronic charge. It is rather incredible that such a sophisticated and perceptive paper on this phase of plasma physics should appear all by itself at this earlydate. Drawings of the cross­ About ten years later experimental work on the pinch sections of the copper effectin plasmas commenced with some work by Steenbeck, lightning rod that was who worked on induced, pulsed, high currents in a ring­ fa" crushed by the passage shaped glass tube. Cousins and Ware at Imperial College in of a lightning bolt. England performed experiments of this type from 1947 to 1951 and "were the first to demonstrate" that the current 4 channel (104 - 2 X 10 amps) did constrict. In 1951, due to classified weapons laboratories in those countries. security classification, this work was transferred to AEIRL Levine, Combes, and Bostick at TuftsUniversity showed at Aldermaston where extensive development was carried on in 1952 and 1953 that an 8,OOO-ampere pulsed currentin low in theproblem of arcing between the segments of the metallic pressure nitrogen gas produced a pinch which concentrated liners used in their discharge tubes. The employment of the the spectral line emission from singly ionized nitrogen, and applied magnetic field(in 1953) in the direction of the pulsed concentrated even more the lines from doubly ionized ni­ current led to the SCEPTRE program. Bill Baker at the Law­ trogen. rence Berkeley Lab (formerly the University of California In June 1952 at a meeting of the AmericanPhysical Soci­ Radiation Lab) in 1951 produced a pulsed, pinched high ety in Denver a special session on eTR was held under securi­ 5 current (10 amps) discharge between two electrodes in H2 ty classification for those interest�d physicists who held the gas and photographed the constricted (-3 mm diameter) appropriate security clearance. The "Matterhorn" project channel. Security classificationprevented Baker's work from from Princeton University under Lyman Spitzer described being published at that time. About 1950 at Los Alamos, their concept of the stellarator with its figure "8" configura­ planning of experiments (the Perhapsatron) on the pinch ef­ tion to obviate the "grad B drift," �md presented, in brief, the fect got under way under the direction of James Tuck. Appar­ theoretical work of Kruskal and Schwarzchild in which they ently the Soviets also started work on the pinch effect about predicted the sausage (m=O) and kink (m=1) MHD [magne­ the same time: The work on the H-bomb in the U.S.A., tohydrodynamics] instabilities tha,tthe pinch effect would be U.S.S.R., and United Kingdom had by this time rekindled expected to be subject to (see Figure2). These instabilities enough interest in controlled thermonuclear research to get were similar to the Rayleigh-Taylor instabilities of fluid me­ some experimental CTR programs under way at the security- chanics and could be classified as MHD instabilities because EIR February 8, 1991 Science & Technology 21 1954-63: practical schemes FIGURE 2 To locate the pinch effect among the various animals in m=O the CTR zoo we must recognite that the bulk of CTR thinking B has traditionally reasoned thal the pinch-effect magnetic field will impart energy to the pl�ma by adiabatic compression (in the dynamic pinch), by shock heating, by Joule heating, and by various instability meohanisms, and that in these pro­ cesses the plasma can be expected to acquire an energy densi­ ty approximately equal to that of the magnetic field. In the experimental investigation of the translation of this ( magnetic field energy into the plasma energy it has appeared that the plasma becomes more difficultto confineas it absorbs e the energy; that is, the instabiilities grow more rapidly in the energetic plasma, and the instabilities will very quickly and prematurely result in a loss of the plasma and its energy to the wall of the vacuum chamber. On the other hand, a sucaessful CTR magnetic contain­ ment device must have an energy containment time T and an m=1 ion density n sufficiently large so that an appreciable fraction of the fusionable fuel will be burned; that is the Lawson criterion must be satisfied (0'7'>10 14 for a deuterium-tritium (D-T) reactor).
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