Review of Controlled Thermonuclear Research at Los Alamos for … · 2008-07-29 · P/1860 USA...

P/1860 USA

Review of Controlled Thermonuclear Research atLos Alamos for mid 1958

By James L. Tuck*

At this first opportunity for open scientific dis-cussions on this subject we look forward with eagernessto exchanging experiences with others and hearing ofthe courses taken towards the common goal in thevarious laboratories of the world.

Early Development

At this laboratory, the peculiarly intriguing natureof the problem and the admirable consequences of itssolution have long been recognized. Lively discussionsof such matters as plasma drift in a torus and itseffect on achieving a laboratory thermonuclear reac-tion occurred between Fermi, Kerst, Landshoff,Teller, R. R. Wilson and the writer in 1946, and anunsuccessful search for neutrons from colliding Munroejets of metal deuterides was made at about the sametime, based on an earlier paper by Ulam and thewriter.

When the subject was reopened in 1951, thetoroidal pinch (as proposed, with a superimposed Bzfield, by the writer in 1948) was selected as theconfinement geometry for initial study and it passedthrough the usual vicissitudes and modifications—instability, linear dynamic pinches (Columbus),rf pinches, so called Bz and wall stabilized pinches;while parallel speculations and experimental forayswere made into cusped geometries (Picket Fence),spinning plasmas, shocks in axial and convergentgeometries and magnetic mirrors. Our ideas and planshave undergone profound changes during the lastseven years and are in process of undergoing another.As little as half a year ago, the chief obstacle to theachievement of a thermonuclear reaction via thestabilized pinch appeared to be contamination of theplasma by foreign atoms sputtered or evaporated offthe walls. Doubtless this particular obstacle is stillthere, but in the meantime a crevasse has opened atour feet, in the form of our new experimental observa-tions of high energy losses from the pinched plasma.If these turn out to be due to the newly predictedsurface hydromagnetic instabilities, then we know howto overcome these and the outlook may be better thanever. If the losses turn out to be due to plasma

* Los Alamos Scientific Laboratory, University of California,Los Alamos, N.M.

2

oscillations, as is feared, then the outlook for thestabilized pinch as a possible reactor seems grave.

Present Requirements

The outstanding need in controlled thermonuclearresearch at present is for reliable quantitative observa-tions on confined plasma, and the shortage of thesecan undoubtedly be blamed on the extreme mobilityof plasma, the variability of gas discharges, and theirsensitivity at high temperatures to impurities. It isonly recently that primary measurements on the pincheffect have been made, of quality such that worthwhilederivations of other quantities from them could bemade. At Los Alamos, the magnetic probe hasunquestionably been the most effective measuring tool,yielding (from the pinch) plasma pressure, plasmaelectrical conductivity and, most recently, plasmamass. The mean temperature of the plasma, involving(î'eiectron+î'ion)» has also been determined but notthe much-sought-after individual components of it.Obviously, if ion temperatures could be made highenough, the trivial neutron-producing processes whichbedevil us at present would also become trivial inyield, with the result that the thermonuclear yieldcould take its logical place as the ideal thermometerfor ions.

In order to bring this into play, there has been adirect effort at Los Alamos to produce an identifiablethermonuclear reaction, without regard for reactorimplications. Whether this has been achieved is stillindeterminate: of the five experiments producingneutrons, Scylla looks probable as a thermonuclearsource and is supported by a measurement of theneutron energy distribution, Columbus II neutronshave an energy anisotropy so small as to raise diffi-culties in interpretation by trivial processes, ColumbusS-4 neutrons seem well correlated with anew instabilityand therefore appear suspect, as do the PerhapsatronS-4 neutrons on account of a much larger energyanisotropy. Ixion neutrons seem to be of two kinds,trivial ones associated with sheath breakdown and lessdeterminate ones in a kind of tail of indefinite extent.

Obviously, the control of thermonuclear fusiondepends on answers to problems in basic plasmaphysics. For example, are the high plasma lossesobserved in the pinch a characteristic of all confined

SESSION A-7 P/1860 J. L. TUCK

systems? Until such questions are answered, thetechnological problems of a fusion reactor are surelyfar away. What engineering design for a thermonuclearreactor would survive an increase in plasma diffusionrate by an order of magnitude ?

As a matter of fact, some of the highly impulsiveschemes—Columbus and Picket Fence—might survivesuch an increase but, for the time being, at Los Alamoswe hope to steer clear of any large machine, keepingto a course of fairly basic plasma physics research inwhich practice and theory are intimately associated,around numerous modest-scale experiments.

In magnitude, our effort engages the activities offifty-one people, including twenty-four physicists, therest being engineers, technicians and secretariat. Thestaff is divided into two groups under the leadershipsof Dr. K. Boyer and Dr. J. A. Phillips.

THEORETICALStability

The theories of an infinite-conductivity pinchstabilized by an axial field—Kruskal and Tuck,1

Rosenbluth,2 and Colgate3 in the USA, Artsimovich4

and Shafranov б in the USSR, and Taylere in the UK<—have become largely supplanted in our minds by theenergy principle treatment7 by Suydam8 of the samegeometry with diffuse boundaries between axialstabilizing field Вг and confining field Be. In thistreatment the sign of 8W, a function of the displace-ment, is the criterion for stability. The study wascarried out by noting that the special character of theEuler-Lagrange equation of the variational principlepermits one to evaluate SW f or a minimal displacement(i.e., a displacement which satisfies the Euler-Lagrangeequation) for general configurations of plasma andfield, without obtaining a detailed solution to thisequation. If a minimum for bW exists, such a procedurewill find this minimum. However, certain configura-tions exist for which bW is unbounded below (henceunstable) and it has not been shown that the aboveprocedure will identify such cases. Thus a conditionhas been found which is necessary, but has not beenshown sufficient for stability. It is

¥/+4\^) > 0

where ¡i = Be/rBz and p = plasma pressure. Thisimposes restrictions on the radial gradient of densityin the pinch, such that it seems unlikely that a stablepinch with unidirectional Вг and Be exists. However,and here we differ from the older Rosenbluth criterion,stability is aided by an external-to-the-pinch reversedВг and Be. Much importance is attached to thisprediction, for although it adds complications to athermonuclear reactor based on a pulsed B^-wallstabilized, toroidal pinch (Pephapsatron) it reviveshopes for a continuous rf pinch using cyclic Вг and Be

magnetic fields, to which we shall return in the con-clusions. A computation of a stable configuration withthick boundaries and reversed Bz has also beenreported by Rosenbluth.9

A pinch current and plasma distribution has beenfound by Longmire10 (see also Bickerton11) which isstationary and in equilibrium with pressures anddiffusion, assuming isothermal plasma and ignoringJoule heating. It is unlikely to be observed in thelaboratory since it is unstable by the Suydam criterionabove, but has didactic value for the light it throws onthe compensation of the outward diffusion current-DVn by the inward drift cE/B.

Ixion GeometryThe axial magnetic field-radial electric field,

spinning plasma geometry (as variously proposed byLloyd Smith,12 Shipley,13 Luce,1* Baker" and Gow16}with the addition of magnetic end mirrors, is knownhere as Ixion. A mathematical analysis of the motion17

predicts a strong enhancement of the mirror confine-ment. In such a device, collisions are by virtue of theLarmor energy since the rotation does not lead tocollisions and, for ions created non-adiabatically in thesystem (as, for example, by ionization), the Larmorenergy is approximately the same as the drift energy,%mcz(B¡E)z. Thus, for example, with E = 10 esu/cmand В = 2000 gauss, the Larmor energy is 25 kevwhich is quite adequate for thermonuclear purposes.The current through such a device in equilibriumwould of course ideally be zero, and the plasmaconfinement time diffusion-dominated. A plasmacurrent does arise, however, by virtue of interactionbetween the rotating plasma and neutral atoms,either originally present or returning from the walls, aswell as by virtue of a differential drift, between ionsand electrons, due to the centrifugal force. In order,then, to achieve the long confinement time appropriateto a reactor, plasma drifting to the walls must bedisposed of by some kind of diverter (с/. Stellarator)action and, to minimize the centrifugal drift, the radiusmust be large.

The initial formation of the rotating plasma alsopresents a problem as follows. The displacement cur-rent which flows in setting up the rotation has amagnitude corresponding to the enormous dielectricconstant 4immc2/B2, i.e., of order of 106 amp. Thiscurrent, in flowing to the electrodes, would producelocal space charges (sheaths) which would screen outthe applied electric field from the bulk of the plasmaunless arrangements are made for a ready supply ofelectrons and ions at the appropriate electrodes.

RunawayRunaway is the term given to the production of an

accelerated directed velocity in some components ofthe plasma by an applied electric field. A theoryof immediate runaway in a fully ionized plasma oftemperature Г in a strong electric field has been givenby Dreicer.18 It turns out that the critical electricfield Ec required to produce such runaway is small andproportional to the ratio, density/temperature. Forexample, at particle density n = 1016 cm~3 and f kT ==100 ev, EB = 8 volt/cm. The theory has now beenextended to the more difficult case of weaker electric

CONTROLLED THERMONUCLEAR RESEARCH AT LOS ALAMOS

fields,19 where only part of, say, the electron distribu-tion runs away immediately. These theories do nottake into account the excitation of plasma oscillationsby the runaway which, it seems superficially obvious,will reduce the runaway to some extent.

The pressure balance equation much used in thelaboratory has also been modified by Dreicer asfollows:

where г, в, z are cylindrical coordinates, 2?w is theradius of the outside wall, В is the magnetic field,B% = Bz

2 + Be

z, and Prv, P e e are elements of themomentum flow tensor,

P e e =

¥„ =Here, v is the electron drift velocity parallel to B;the mean square random thermal speeds are assumedto be equal in the в and v directions.

The new term,

Гis the centrifugal force due to electron runaway. Thequestion now arises, how much the very encouragingvalues for nkT deduced experimentally in this labora-tory have been exaggerated by the neglect of this term.We shall return to this in the discussion.

OscillationsThe literature on plasma oscillations is voluminous,

and we mention among the early contributors, thenames of J. J. Thomson,20 Tonks and Langmuir,21

Landau,22 Bohm and Gross,23 and Vlasov.24 Morerecently, the subject of the excitation of plasmaoscillations has been reported on by Akhiezer andFaynberg,26 Akhiezer and Polovin,26 Luchina,27t28

Gordeyev,29 and, very recently in the USA, Bune-mann.30>31 These papers discuss the excitation ofplasma vibrations by an electron beam or drift in anapplied electric field, and they show that by a co-operative space charge interaction (without collisions)between ions and electrons, somewhat resemSh'ngbulk Helmholtz instability, the electron and ionosculations can grow. Experimental confirmation ofthis process comes in an entirely different connection,namely the so-called double-beam traveling wavetube,32>33 in which amplification of space charge wavesoccurs by interaction between electron streams ofdiffering velocities. (The identity of these two pro-cesses was pointed out by Bunemann.)

We now propose still another process for the ex-citation of plasma oscillations, depending on two-body interactions between ions and electrons as

follows.34 For a plasma consisting of ions of densityщ cm~3 and of electrons, both at temperature T, anelectric field Ea has induced a displacement of theelectron velocity distributions in the x direction as awhole, so that the electric velocity distribution issymmetrical about a point vx (henceforward called v).The so-called dynamical friction force36 between theelectron and ion distributions has been calculated onthe above model by Dreicer.18

+0.6

+0.4

+0.2

0

-0.2

-0.4

Figure 1. Dynamical friction for displaced Maxwell distribution.Straight line section through origin, Lz_>o0(z), leads to Tf law of

conductivity

Figure 1 gives the form of the function ф(г) wherethe dynamical friction is treated as giving a fictitiouselectric field of magnitude Ееф(г) ; the abcissa, z, is theratio: drift velocity/mean thermal speed. At themaximum on the curve, ф{г)Ес = 0.425.

For drift speeds larger than the mean thermal speed,we see that the slope of the dynamical friction curvebecomes negative, in fact ф(г) ос z~% for large z. Foran applied electric field, E&, we write down the equa-tion of motion of the electrons, taking into account thedrag force:

+V ^EE^(z)]

-

- ^ 3 -2 -1 fL

i0 1 2 3 Z .

1860.1

where Ea is the restoring space charge field related tothe electron density n by:

I 2 = Mno-n)

and the equation of continuity is

We discuss a small sinusoidal modulation in the driftvelocity, which oscillates with the characteristicplasma frequency, wp = (4тгие2//х)*, where ju. is thereduced electron mass.

The effect of the negative slope of ф(г) is to introducea negative damping, and we find the growth constantfor small electron oscillations to be 4eEceTlmvos

where vo = mean drift velocity. A numerical exampleof the growth constant for the following values of theparameters: plasma density n = 10 ie electron/cm3,temperature T = 100 ev, z = 2eT¡mv0 = 2, v0 = Ю9

cm/sec, Eo = 90 volt/cm, £ a = 19 volt/cm, e = e/300

SESSION A-7 P/1860 J. L. TUCK

= 1.6 x 10-ia, is Wg = 7 x 101?. we see that the growthis such that large amplitudes could develop in a fewmicroseconds.

For identification, we shall refer to this as theviolin-string mechanism (the mechanism is closelyanalogous to the setting into vibration of a string bythe nonlinear friction of the bow).

For the large osculations, we must refer to the limitcycle of the nonlinear equation, the maximum down-ward excursion of the velocity for z = 2 beingobtained by equalizing the two shaded areas, fromwhich we see that the amplitude can become largeenough to move the particles against the field in thepeaks.

The external manifestation of the process as des-cribed might be a small increase in plasma resistance(but not enough to bring it above the f power lawvalue) and an increase in the Maxweffization rate—cf.Langmuir's paradox.36 These longitudinal oscillationsdo not radiate but numerous cross-coupling pos-sibilities for transition into radiative modes exist—asfor example via the fluctuating electron centrifugalforce in moving along curved magnetic field lines. Forthe violin-string mechanism, the critical value of the zparameter is 1, but it has not yet become clear howlarge the fraction of the electrons having z > 1 must befor growing waves to-exist. The ratio z is, of course, acritical parameter for the other mechanism also, forwhich still larger growth rates have been predicted, sothere is some doubt which of these will be dominantfor the plasma oscillation phenomena concerned.

A theoretical analysis37 has also been made of theeconomics and stability of the plasma confinementprocess, variously called electrostatic36 or inertial39 inwhich electrons are inwardly projected over the surfaceof a sphere, the resultant turning point near the centerforming a space charge well for positive ions. It turnsout that a modest thermonuclear reaction mightconceivably be maintained in a few mm3 in this way,for experimental purposes, but no economic thermo-nuclear reactor seems to be possible from this geo-metry in the electronic form. However, an alternativearrangement,40 with the ion and electron rolesreversed, and which technically we do not know howto construct, looks quite promising.

EXPERIMENTAL

(The order is in historical sequence of development)

Columbus II 4 1

This is a high power linear pinch apparatus with thefollowing properties: ¿#6e-diameter, 10 cm; length, 30cm; material, Mullite; condenser-ca.Tpa.dty, 25 x 0.8 ¡JS;voltage, up to 100 kv; peak current, 800 ka; time tocurrent peak, 2.2 /¿sec. The condensers (Fig. 2) are atthe periphery of a low inductance transmission lineconnected to the discharge tube by a singleeight-plate subdivided vacuum spark gap.42 At 50 kvtube voltage, the neutron pulses from this machine, ofduration ~ 1.5 /¿sec, contain 3 x 108 neutrons per pulsefor zero Вг and 2 x 107 for 200 gauss B z.

4 3 The yield atlarge В г has proved to be susceptible of improvement

BRASSSTADUSS STEEL

•TEFUJNCERAMIC

1860.2

Figure 2. Columbus II apparatus, schematic


0

0

16

8

d24

16

8

0 12

J

(Ь)

_J ,л

(с)

ft r r t

16

Lu

Щ

n,

1П

20

III

и

г1

—

:

j

Г

Г

2

Ip

2.

17

27:

1) g o

r.

us s

1 •t

п

581

LtrtJ55t

J"

i ^i

4?24 2

1100 gauss

500 gauss

1

cw

8 2E n (Mev) 1860.3

Figure 3. Columbus II neutron energy distributions

by a conditioning treatment of the tube, together witha reduction of tube voltage from 50 to 40 kv. Nuclearemulsion measurements of the neutron energy dis-tributions have been obtained up to 500 gauss Bz.Results of such measurements are shown in Fig. 3.

Neutron YieldThe neutron yield falls with increasing Bz (Fig. 4),

at first sharply and then more slowly. The neutronenergy anisotropy also falls from the value (expressedas the energy of deuterons moving towards thecathode, assumed to react with stationary deuteron)of 57.5 kev at Bz = 0 to 7.2 kev at Вг = 500 gauss.Equivalent deuteron radial velocities appear fromnuclear emulsion studies in other experiments to belower than the velocities towards the cathode. If weassume that the primary neutron source is, in reality,monoenergetic and centered on the peak of theobserved smooth neutron energy distribution, we canproceed to calculate the current of deuterons (havingthe appropriate energy from the observed center-of-mass velocity) incident on stationary deuterons at thecompressed pinch density consistent with the observedyield. At low Bz, this gives a reasonable answer, e.g.,at Вг = 0 and deuteron drift energy 57.5 kev,deuteron current ~103 amp. However, at high Bz,say 500 gauss, and deuteron drift energy 7 kev, thedeuteron current is 6 x 106 amp: this is absurd, both onenergetic grounds and also because it is larger than thetotal tube current ~5 x 106 amp. (These currents arenot dissimilar but it should be remarked that afraction of the tube current—nearly all of it in a torus,

IOIOо

о_ l

YIE

rRO

N

эшZ л

060:

M,

40

| 30

ш 20

10

n

\

\

\

\

\\

V ." — • — .

- _

(

——

~ 2 X 106

4500

0 100 200 300 400 500 600 700 800 900 1000Bz (gauss) 1860.4

Figure 4. Columbus II neutron yield and energy anisotropy asfunctions of axial magnetic field B2

where the net plasma momentum is zero—is carriedby the electrons.) In speculating on the origin of thesehigh Bz neutrons, none of the usual instabilitycharacteristics are present, voltage signatures or sharpneutron peaks, and the discharge is conventionallystable in the m = 0 mode.

A simple explanation, in terms of a general thermo-nuclear reaction throughout the pinch, can likewise beexcluded since it is not energetically possible for thewhole plasma to have the required drift velocity. Someprocess is needed which would increase the deuteron-deuteron relative velocity in a small fraction of theplasma while maintaining in it the 4.1 x 107 cm/secdrift towards the cathode. At first sight, a Fermi-typemechanism, i.e., acceleration by reflections betweenmoving magnetic discontinuities, might seem the mostlikely but in such a case more neutrons from deuteronsmoving away from the cathode should be observed.Ordered motion of the required kind can be imaginedin a shock moving toward the cathode, as proposed byPhillips (the neutrons are known to be emitted uni-formly along the pinch except in the vicinity of theanode). Another suggested process is a constrictionmoving towards the anode and having in it an in-creased Bz. The conservation of flow through such aconstriction involves acceleration of the deuterons intothe constriction, accompanied by conversion of longi-tudinal motion into Larmor energy by the increasedВг field, the required relative velocities being thusproduced without calling on a collision process.Future experiments with the Columbus II apparatusinvolve a search for a relation between neutron pulselength and tube length, and a further attempt to applythe magnetic probe. The latter has so far proved toofragile, both mechanically and electrically.

Columbus S-4 44-48

This is a medium power linear pinchmachine havinga ¿w&e-diameter, 13 cm; length, 61 cm; material,

SESSION A-7 P/1860 J. L TUCK

BxlO

1860.5

Figure 5. Columbus S-4 radial distribution of pressure and magnetic field strength Bz, Bgand pressure(left) showing so-called hollow pressure distribution and (right) Suydam stability criterion for the

foregoing: unstable between 2.5 and 5 cm

alumina (Mullite); condenser-capacity, 75 /if; voltage,20 kv; peak current, 250 ka; time to current maxi-mum, 6 /*sec.

Light EmissionThis apparatus has been used in a series of funda-

mental studies of the pinch, and from it have comemost refined and reproducible observations. Import-ant, rh the achievement of cleanliness from impuritiesand reproducibility of operation, has been a condi-tioning of the tube by repeated discharges, withmonitoring of the emitted impurity light and gasformation. In the clean state, the total visible light is< 1 % of that emitted from normal tubes, and nomarked emission of gas into the pumping system isobserved after a 250 ka discharge. Remaining changesin the performance from one discharge to the next were"traced to fluctuation in pressure due to pumpinginstability, and were eliminated by a gas flow controlservo operated from a Pirani gauge. In the final state,readings of Вд and Bz (except when instabilities arepresent) are reproducible to within a few percent.

Emission of Up light occurs in a brief flash, fallingto zero for the main duration of the discharge. Si n

4128 Â line intensity, used as an indication of wallimpurities, does not appear until the second halfcycle.

Behavior of Current SheathThe magnetic probe measurements show (Fig. 5)

that the currents flow in a well developed sheath in theinitial stages (0-3 /¿sec), with a good r"1 dependencefor Вд, indicating negligible currents outside thesheath. From the equation for static hydromagneticpressure balance,

we evaluate nkT. At 2.5 /¿sec, this is peaked at theradius of the current sheath and falls to zero on theaxis. This hollow nkT distribution has been predictedfor some time to occur as a consequence of the accumu-lation of the swept-in gas at the sheath (snow ploweffect) and its joule heating, but was never observedin earlier experiments with smaller diameter tubes. Itturns out to have important consequences for theinterpretation. Figure 5 also plots the two sides of theSuydam inequality from which we see that the pinchis unstable for radius >2.5 cm. After three or fourmicroseconds, the azimuthal symmetry of the pinchis generally lost, in a manner depending on the magni-tude of the initial Bz stabilizing field. For low Вг, аhelical deformation is found, such as would be pre-dicted for m = 1 instability. Higher Вг fields effec-tively eliminate such gross motions but a "fluttering"


motion of the plasma boundary appears: correlationstudies, of the signals from sets of closely spacedmagnetic probes, indicate this motion to be turbulentin nature with related motion limited to regions of 1-2cm extent. Figure 6 shows magnetic probe traces ofthe Be signal as the fluttering boundary reaches theprobe radius set at 4 cm, together with the neutronsignal. This figure also gives the signal from a probeoriented to detect radial components of the magneticfield. Such probes detect the onset of instabilitysensitively. Neutrons are emitted from Columbus S-4in a characteristic long pulse coinciding with flutteringand seen only when the clean state is achieved andfluttering is present. It seems reasonable to attributethe fluttering and the neutrons to the boundary layerinstability of the kind predicted by Suydam.

JUS* ' • >.-....

."•

I " f

i

1Figure 6. Columbus S-4 neutron emission coincident with flutter-Ing of plasma boundary: Top - Br, showing onset of fluttering;middle - neutron emission; bottom - Be at 4 cm radius: B. =

1000 gauss; trace speed, 3 /¿sec per division

Microwave RadiationObservations made with a microwave detector,47 at

A = 3 cm, in the axial and radial directions show (1),an intense pulse of radiation in the first microsecond,(2) a quiet period 1 to 3 /¿sec and (3) a burst of radiationcorrelated in time with the fluttering. As the pressurebalance calculations are extended to later times, thesheath which was well defined at 2.5 / sec, becomesintermixed at a discouraging rate so that, at 6 jusec, thedistributions are found to correspond to jB and j zcurrent densities uniform across the tube.

Carrying the probe observations to the. end of thefirst half current cycle resulted in the observation ofentrapped currents in the pinch. Such currents havebeen reported before48" 49 and occur in a theory ofimperfect sheath formation.60 At the time when thetotal tube current has reached zero, approximatelyone third of the original maximum current ~6x 104

amperes may still be flowing in the axial region, andback along a thin region adjacent to the wall. Thephenomenon is, of course, due to the appreciablediffusion time for the internal currents to reach theexterior, together with the conductivity at the wall ofsome of the expanded gas in the pinch, which effect-ively screens the interior from the reversal in the

applied voltage. Such reversed current distributionshave some practical interest; a sufficient increase inthe reversed current leads to a reversal of Be. Suydam'scriterion for stability can be met by a reversal in Be,and a stable pinch configuration involving reversed Bghas been deduced by Tayler.6

ConductivitiesReturning to the plots of Be and Вг versus radius—

using VxB = 477J, we can derive В and j . Fromthree plots separated in time, using cV x E = —BB/dt,we determine E, the electric field at all points. Know-ing B, j and E at all points allows the evaluation of theparallel and perpendicular conductivities, <rB and a x .Figure 7 shows the results obtained for a discharge at60 ¡i deuterium pressure, 200 ka peak, Вг = 2000gauss.

Highly peaked currents, / e and Jz, at intermediatetimes indicate a well developed sheath. Note that Ee issmall at the-wall (it should extrapolate to zero at 7.2cm for conservation of Bz flux). The parallel con-ductivity is seen to rise with time, reach a maximum(at t = 1.8 /¿sec and / = 3.5 cm) of 800 mho cm"1, andsubsequently decline to a uniform lower value of ~ 150mho cm-1. The perpendicular conductivity is notplotted in Fig. 7 as its value within the experimentalerror turns out to be zero, except at the same point inspace and time as the maximum in o-n, where itreaches the value 20 mho cm"1.

Plasma InertiaThese parallel conductivities correspond to electron

temperatures, of 12 ev for 800 mho cm"1 and 5 ev for150 mho cm-1. In the Fig. 7 plots of pressure versusradius, an anomalous plasma pressure is observedwhich alternates between the inside and outside ofthe current sheath. Suspecting that this was due toan inertia term, a careful plot of radius versus timerevealed a small sinusoidal oscillation during thecontraction (Fig. 8).

A calculation of the mass density in the sheath, usingthe accelerations measured from Fig. 8 and theanomalous part of the pressure plot, agrees, within theexperimental error, with the total mass of containedgas that would be swept in by the sheath. Subse-quently this was done more simply by noting that thesmall oscillation frequency about the equilibriumradius of a thin heavy shell of surface density, ps,under the particular external circuit conditions of Bzand I conserved, is

where В = Bg = Вг is the magnetic field strength atthe shell surface. An experiment to observe thisoscillation frequency (Fig. 9) using а Вг probe on theaxis, over a range of gas densities, confirms that theoscillation frequ' ncy varies as the square root ofthe gas pressure and that the Bz oscillation amplitudeincreases with gas pressure, as it should since thesheath velocity in Columbus S-4 is only slightlydependent on gas density at the selected operating

10 SESSION A-7 P/1860 J. L. TUCK

t «2.6 pesa

Ю000

4tnho/dit

Hoo-

IOO0 •

8 0 0

600

400

200

! ir»cm.

^ ^ о

2 ï 4 i

l i l i l í1 2 3 4 6 6

цет.', 2

l i l i3 4 S 6r, em.

3 4- 0 i 2 3 * В « ^ 0 I Z T ^ 6 01860.7 r,em. non. r,cm

Figure 7. Columbus S-4 magnetic probe results and derived data. Вг, 1500 gauss; Da pressure, 60/¿ Hg;potential, 14 kv; peak current 200 ka

¿

parameters. The evaluation of pa in this way fills whathas been a conspicuous gap in our knowledge of thepinch—namely, the completeness of the insweeping ofthe initial gas filling (since Columbus S-4 is apparentlyfree from impurities during the first half currentcycle).

TemperaturesThis, together with the observed dependence of cur

on initial gas filling density, leads to the furtherconclusion that no significant contribution to thedeuterium gas filling occurs by desorption or removalof monatomic films of deuterium from the wall, or

CONTROLLED THERMONUCLEAR RESEARCH AT LOS ALAMOS 11

fi, cm

3.0

Figure 8. Columbus S-4 sheath radius vs. time (for parameters of

Fig- 7)

detachment of the sheath from the wall, as has beenfeared. We next attempt to apply the knowledge of p s

obtained from the osculation frequency, to the nkT inthe sheath, deduced from the pressure balanceequations, in order to extract T. We take a peakednkT distribution (Fig. 5) for example (see the dis-cussion for the justification of this), and proceed toguess a density distribution in the sheath. The lowesttemperature we can obtain throughout the sheath is bymaking it isothermal and matching the point densityto the pressure. Dropping the inertia! part of p in Fig. 7and normalizing the resulting integral over the pointdensity to the measured ps, we obtain the temperatures(Г е + Ti) of 6 ev at 1.4 /¿sec and 13 ev at 1.8 /¿sec. Wecannot do this at 2.6 /¿sec since we have no check onpB, and, furthermore, the distribution is not hollowthen. We can assume the peak in p contains all theinitial filling gas, however; in which case, we obtain for(Te+Ti) at 2.6 /¿sec the value 33 ev. Substitution inone of the expressions for the rate of equalization oftemperature between electron and ion Maxwelldistributions, shows, for particle density n ~ 10ie cm~3

and Te ~ 10 ev, that (a) if Te > Ti, there is insufficienttime for Ti to approach Te, and (b) if Te < Xi,equalization will be close in a fraction of a micro-second. Accordingly, Te ^ Ti > 0, and Te lies be-tween the values quoted above and half those values.The best agreement with data is for TÍ = 0.

The first two temperatures assumed to be Te are inexcellent agreement with the parallel conductivities,and at 2.6 /¿sec, the conductivity goes down. Weobviously suspect a breakdown of the confinement andwe shall refer to these observations in the discussion.

Future experiments with Columbus S-4 might be (a)most urgently to attempt to make the system Suydam-stable, perhaps by using programed Bz and Be; (b) asearch for radiations in the plasma. oscillation fre-quency region, i.e., 2 x 1012 sec"1, for the violin stringmechanism, and 1011 sec-1 for the Akhiezer et al.-Bunemann mechanism.

Perhapsatron S-4 5 1

This toroidal wall-and-Bg-stabilizedpinch apparatus,shown in Fig. 10, is the scaled-up successor of Per-hapsatron S-3.62 The parameters are: torus diameter,7 cm; major diameter, 35 cm; torus material, quartz;number of feed points, 2; condensers, 2 x 225 /¿f at 20

1860.9

Figure 9. Columbus S-4 radial oscillations as a function of pressure.Deuterium pressures, from top to bottom, 30, 60, 120 and

400 n Hg; scan, 1 /¿sec per division

kv; peak pinch current, ~320 ka; time to currentmaximum, 12.5 /¿sec. Figure 11 shows a characteristicoscillogram of voltage per turn, current, neutronintensity, and Sin 4130 À light intensity.

In general, we see that the current and voltage aremore nearly тг/2 out of phase, than for the S-3machine, indicating that the current is limited byinductance rather than resistance as in the latter. Theneutrons aré emitted in the vicinity of the currentmaximum, and are more reproducible in intensitythan has been previous experience. A mean neutronyield at 15 kv condenser voltage is 5 x 10e. The maxi-mum yield observed is slightly in excess of 107 neutronsper pulse. The impurity light intensity is seen to riserapidly during the neutron emission. The rise becomesearner and steeper as the power (condenser voltage)is increased. Thus, impurities are probably an import-ant factor in the performance of Perhapsatron S-4 at

LAMINATE!) IRON CORE

POLYETHYLENEINSULATION

SECOND FEED POINT FLANSE

FIRST FEED Р0МГ FLANSEi

COAXIAL CABLES TO,CAPACITOR ВДГ

DISCHARGE REOION

QUARTZ TORUS

ALUMINUM PRIMARY

Figure 10. Perhapsatron S-4 apparatus


times later than the maximum in the neutron intensity.

Magnetic BehaviorMagnetic probe measurements of Be and Bz were

made by a probe inserted along the radius at one pointon the outside edge of the torus. The determination ofp from such records in toroidal geometry requiressome explanation. From the BQ and Bz vs. timerecords, we map BQ and Bz over the plane of the minoraxis as a function of time. Then p in this plane isobtained from the equation

where x is the radius from the major axis, a is the radiuswhere BQ = 0, and the constant С is evaluated fromsome point where p is known.

This derivation assumes only that the magneticfield is symmetrical about the plane of the minor axiscircle and that there are no variations of field alongthe axis. The magnetic closed curves need not becoaxial with the minor axis, or with one another.

By analysing the probe data in this way, plots suchas those shown in Fig. 12 may be obtained. In gen-eral, sheath detachment from the walls is imperfect.Bz shows only very minor negative values at the outeredge so m = 1 spiral instabilities are not significantlypresent. The pressure distribution shows a hollow onthe axis as late as 10 /xsec, but with substantialflanks which reach the walls at all times. At later times,the pressure distribution becomes wild, and it seemslikely that the pinch is moving (a) from side to side inthe plane of the mirror axis and (b) above and belowit. The latter motion invalidates the pressure balanceequation assumptions so we cannot decompose thepressure distribution into its pressure and inertialcomponents as was done with Columbus S-4.

The reproducibility of the data is insufficient toallow deduction of ah and of the pressure distribu-tions—only one is zero on the axis, that at 3.75 /¿sec.We take this one and estimate T from neT by equatingthe particles in the sheath to those that could beswept in from the original filling gas, and emerge with(Ге+Ti) ~130ev.

Since the voltage around the discharge is finite whenthe pinch current is passing through its maximum, wecan estimate a gross resistance of the pinch, whichturns out to be 2.8 x 10~2 ohms. To obtain theconductivity of the plasma, we need to estimate thecurrent path and, approximating this as a 45° spiral,we obtain the value 2.5 x 102 mho cm"1, correspondingto a temperature of 5.5 ev.

Neutron Emission

The reproducible and relatively high neutron yieldfrom Perhapsatron S-4, together with its small size,gives sufficient neutron intensity for a survey to bepossible of the neutron emitting region. Using a lead-paraffin collimator and small plastic scintillationdetector, the resulting source distribution proves to bewell centered on the minor axis of the torus, when

20 40TIME

60 80

Figure 11. Perhapsatron S-4 voltage, current, neutron intensity,Si114128 Á intensity

Bz = 1700 gauss, p = 12.5/Lt Hg (D2) , primary voltage = 30 kv

viewed from two directions at right angles. Using anIBM 704 computer, the radial source primary distri-bution has been calculated from the experimentalobservations and the measured collimator resolvingpower. This gives the surprising result that the best fitto the data is for a source predominantly in a thin shellat the radius 1.3 cm. This is also the most probableposition for the sheath from the magnetic probe data.The reliability of the data is such that a solid cylindersource cannot be excluded altogether for these measure-ments. Better statistics will easily resolve this pointwhen the machine returns to the laboratory from theGeneva exhibit.

Figure 13 shows the neutron energy distributionsfrom Perhapsatron S-4, from proton recoil counts in acloud chamber neutron collimator system aimedrespectively in the two directions tangent to the minoraxis circle from a point in the plane of the torus.

The anisotropy corresponds to 10 kev deuterons,moving in the direction of gaining energy in the appliedelectric field, incident on stationary deuterons.

The distributions from the Perhapsatron are verylittle wider than the calibrations from a mono-energetic source, suggesting that the deuterons re-sponsible are fairly monoenergetic. A small secondarypeak 0.75 kev below the main peak of each distribu-tion can be conveniently attributed to an inelasticscattering resonance by the iron core.

Microwave EmissionA superheterodyne microwave receiver 53 tuned to

Л = 3 cm, when applied to the probe aperture,detected an extremely large signal some orders ofmagnitude outside the range of thermal radiationintensity appropriate to a black body radiation atkilo volt temperatures. The results are quite preliminary


but can obviously be ascribed to the plasma oscillationprocess mentioned above. Measurements in theelectron plasma frequency region, Л = 0.1 mm, are inpreparation.

Effect of CrowbarBy shortcircuiting the condenser supply at the

moment of maximum current, the high current can, inprinciple, be extended, changing the time dependenceof the current from a sinusoidal to an exponentialdecay. This procedure is known as crowbarring, a termborrowed from the Radiation Laboratory of theUniversity of California. By substituting a very largecapacitor or battery, for the short circuit, whosepotential is equal to the dissipative potential drop,RI, the duration of the current maximum can beextended still further or indefinitely. The device is thenknown as an amplified or power crowbar. It has provedpossible to apply the power crowbar to PerhapsatronS-4, using one 100 ¡Л condenser connected, viaignitrón, across each 7.5 ¡d, 20 kv condenser in themain supply. The power requirements of the pinchhave proved to be so large that, in order to stay withinthe safe rating of the crowbar condenser (3.5 kv), themain condenser has had to be operated at a potentialreduced from 14 kv to 7 kv. This reduces the neutronyield under normal operation to ~2xlO5. Thecrowbar extends the duration of the current maximumso that approximately 28 josec of essentially constantcurrent operation are observed, throughout whichneutron emission takes place, increasing the yield to~2xlO e (Fig. 14). Magnetic probe measurementsduring the constant current period show an intermixeddistribution which stays approximately constantuntil the end of the period. As a technical achieve-ment, the crowbar is very satisfactory but the con-clusions to be drawn from its behavior are disquieting.During the constant current phase, the current has thevalue 180 ka and RI has the value 5 kv, of whichthe resistive drop in the primary is negligible. (Theoscillograms are somewhat complicated by thesaturation of the iron core). Consequently it appearsthat the resistive drop in the pinch amounts to 5 kv at180 ka.

A simple calculation of the conductivity, assumingonly parallel conduction along the magnetic field

I -4 -2 0 2 4 6nu.ii Minor Radius-cm.

-4 -2 0 2 4 вMinor Radius-cm

14

12

s1°

"о

ssu

re-

I 4

г

о

: /I Ui

1 ji«^ '

г h?\ j

1

л//Г7л• 4 - 2 0 2 4 6Minor Radius-cm

100-

90-

80

7O

60-

eg 501

Ï40

20

1

§140-

120

100-

80

60

40

20

:—BACKWARD1 DIRECTION

(431 TRACKS)

—FORWARDDIRECTION

(441 TRACKS)

i OB

COCKCROFT-WALTONCALIBRATION

(431 TRACKS)

10 12 L4 IS L8 20 22 24 2.6 28 30 32 3.4 3.6NEUTRON ENERGY (Mev)

Figure 12. Perhapsatron S-4 radial variation of Bz, Be and pConditions as in Fig. 11

Figure 13. Perhapsatron S-4 neutron energy distributions, bycloud chamber

Conditions as in Fig. 11

Unes, gives the same value as before, 250 mho-cm"1,corresponding to 5.5 ev. The temperature by theresistivity is thus inconsistent with that derived fromthe pressure balance.

Further, the neutron emission and resistivityremain constant during the crowbar phase, duringwhich period 27 kilo joules are deposited from thecondensers, which would be sufficient to add 5.5 kevper electron to the plasma. The conclusion that theinput is balanced by some dissipative process seems tobe forced. -

Ixion 17

The arrangement in which most of the Ixion ex-periments were conducted consisted of an axiallysymmetric magnetic mirror. The magnetic intensitywas seven kilogauss in the median plane and rose to amaximum of 16 kilogauss at the throats of the mirrors.The radial electric field was approximately one kv/cm.

' The diameter of the outer electrode was 24 cm and thedistance between mirrors about 70 cm. The innerelectrode was, on occasion, either a metallic rod 5 cmin diameter or a cylindrical region of injected plasma,roughly 3 cm in diameter. The gas was usuallydeuterium, admitted at a pressure of 1 /*, Hg.

A typical oscillogram of the discharge current andvoltage (Fig. 16) reveals that, for the first hundredmicroseconds, Uttle current is drawn. Next a pulse ofcurrent is seen, which has a peak value of about 20 kaand lasts about 25 jusec, during which time the voltagedrops about 50%. During the next 500 jusec thevoltage decays exponentially to zero.

14 SESSION A-7 P/1860 J. L TUCK

Si H

20 40 60 80IM0.14 Time

Figure 14. Perhapsatron S-4, oscillograms in the crowbarredstate. (From top to bottom: current, voltage, neutron Intensity,

S F 4128 À light Intensity)

During the initial low current period there areindications of the presence of an anode sheath wheremost of the voltage drop occurs. The current pulseoccurs when a rotating plasma is developed. Ex-perimentally it appears that about one-fifth of thecharge transferred to the device by the current pulse isassociated with the polarization of the plasma causedby the tangential drift. The ion kinetic energycorresponding to the drift motion is about 30 ev asmeasured by the Doppler shift, assuming that theemitting atoms have acquired the plasma drift speedby collision or charge exchange. The subsequentexponential decay of the voltage is attributed to lossof plasma to the walls; the rate of decay is not in-consistent with the mechanism mentioned earlier.

If higher electric fields than 1 kv/cm are applied tothe device at the time of breakdown, the dischargebecomes completely dissipative, producing neutrons atthe same time, and no lasting rotary drift is induced.This limiting electric field is much smaller than wouldbe expected from an elementary analysis based on theequilibrium of a rotating plasma with the magneticfield. It appears that reasons for the present limitationon the voltage are rather to be found in the processesoperating during the breakdown period, one of whichis certainly the catastrophic evolution of gas from theelectrode surfaces. It is planned to focus attention onthese processes in the near future.

Columbus T-l 54

This is a long (6 m) linear pinch discharge tube of 15cm diameter, having 1.6 cm thick aluminum wallsdivided into insulated sections 5 cm long. It was builtprimarily to test the Harwell (UK) group's concept ofquasi stabilization of the pinch by conducting walls.The main interest in the results lies in the picture (Fig.17) it gives of a particular mode of a spiral instability,

VALVE

NANODE

46UIDE FIELD

LENOID

Figure 15. Ixion apparatus

ELECTRIC-E

MAONETIC-B

1860.15

at large amplitude in steady state motion or, alterna-tively, as a laboratory demonstration of a largeamplitude transverse Alfvén wave. This complicatedconfiguration was unravelled by a magnetic probeanalysis in three dimensions.

55, 56

Scylla uses a rapidly rising axial magnetic field toionize and compress a deuterium plasma in mirrorgeometry. Such arrangements have been proposed,with and without mirrors, as for instance by Post57

and Wilson 68 in the USA and Terletski 5» in the USSR,and studied experimentally in Jug,80 Collapse,61 andTotem Pole62. e3 and by Kolb.«4

The coil is energized from a bank of ten 0.88 /ifcondensers, and the inductance of the system is suchthat about half the 70-75 kv condenser voltage ap-pears at the terminals of the single turn coil. The

BREAKDOWN

VOLTAGE APPLIED

CURRENTf

VOLTAGE I

\:¿

1.0

0.8

0.6

0.4

0.2

0

1 1 !

- — • — Sj SOUTH- — x — Bz NORTH_

-

---_

/

. 1 -t-+~"íl -

/11

/•

-rj

/

i

1A\

/ Vni

\

1 1

Vv \

VV\

i

D --__

----

-

4262 4264 4266 4266 4270

1860 16 WAVE L E N G T H , ANGSTROMS

4272

Figure 16. Ixion, oscillograms of current and voltage, alsoDoppler shift in D Y


t ROTATION

Figure 17. Columbus T-l, structure of large amplitude plasmaperturbation

condensers are switched by individual 4-electrodespark gaps specially designed to have high precision infiring (Fig. 19). The tube is made of alumina (Mullite).Figure 20 is an oscillogram of the current togetherwith the signal from the scintillator. The current is inthe form of a damped oscillation of frequency 200 kc.The first sharp peak is due to X-rays and occurs at thevoltage maximum and the three subsequent peaksdue to neutrons are coincident with the currentmaxima. Neutrons do not appear in the first currenthalf cycle, presumably on account of incompleteionization; this hypothesis is supported by the observa-tion that the first neutron peak passes to the third andfourth current maximum as the gas pressure is re-

10 TRIGGER CABLES - 4 METERS LONG

CHARGING(+ 70 KV )

\

5 cm

VZTh-10 cm -

Figure 18. Scylla, coil with measured magnetic field lines

duced. The maximum neutron emission (22 May) is2 x 107 per pulse.

The magnetic field can be shaped in a very simpleway, by adjusting the internal cross section area sur-rounded by the coil, since, for the short times of theexperiment, the magnetic flux through all sections isthe same. The yield proves to be quite sensitive to themirror ratio. For uniform fields, no neutrons areobserved, and a maximum is found for (area of center)/(area of neck) ~ 1.1.-Higher mirror ratios, made byincreasing the cross section at the center, reduce theyield, presumably by reducing the maximum magneticfield at the midpoint and consequently the com-pression. The neutron yield is sensitive to impuritiesand the base pressure achieved in the vacuum system,and after a long series of shots under the same condi-tion, becomes quite reproducible.

< - 60 KV

154

CHARGING(+70KV)

— 10 UNITSC*0.88pf( 100 KV RATING)

1860.19

-INPUTTRIGGER

«-8 CABLES,4 METERS LONG

[OIL IMMERSEDJUNCTION

COMPRESSION COIL

Figure 19. Scylla circuit

16 SESSION A-7 P/1860 J. L TUCK

COIL г-TRAVELING WAVE ACCELERATOR

Figure 20. Scylla, oscillograms of coil current, neutron andgamma (X-ray) intensity, and general light intensity; timing

marks at 2.7 ¿isec

For an initial D2 pressure of 100 ¡1 Hg, thermo-nuclear neutron production would require a fullyMaxwellized temperature of 1100 ev to give the ob-served yield and satisfy a pressure balance equation.

With this small source and appreciable neutronyield, the neutron and X-ray brightness is high andexperiments yielding images of the neutron and X-rayemitting regions are a definite possibility. At presentthere seems no reason to doubt that a thermonuclearreaction is taking place, the difficulty at present beingthe usual one of not knowing whether the mean energyof the deuterons is high enough to give the observedyield, or whether some small group have an appro-priately larger energy. The time of emission of theneutrons and the clear separation of X-rays andneutrons are all very favorable indications, but adecision must be deferred at least until the neutronenergy distribution has been measured. The neutronemitting source has already been identified as close tothe coil axis, and nuclear emulsions have been ex-posed. An important experiment with this apparatuswill be to study the neutron emission while the currentis sustained at its maximum by a crowbar procedure.Another experiment currently in progress is todetermine, by a time-of-flight and momentumanalysis, the nature and energy of the particles escap-ing from the mirrors at the time of maximum com-pression.

РАМ 65

This is an experiment to study the acceleration ofplasma, both for its own interest (and possible applica-tion to thermonuclear reaction studies by collision)and as a method of translocating plasma auxiliary toother machines. For example, Ixion receives itsplasma by axial injection of plasma from such adevice, while efforts are being made in Columbus T-3to achieve pinches, at densities several orders of magni-tude below those achieved hitherto, by the aid of suchinjection. The novel feature in these experiments is theimmediate ionization, before dispersal, of a puff of coldgas injected into an evacuated tube which in most cases

PENDULUM PUMP

FALLING HAMMER STRIKES ANVIL BLOCK~OF FAST ACTING VALVE

-IGNITRÓN EXCITES Br WINDING

HAMMER SIGNAL ARRIVES AT VALVE, TRAVELING"AT SPEED OF SOUND IN STEEL VALVE STEM;

VALVE OPENS

IGNITRÓN EXCITES•PREIONIZING SHOCK COIL

ГSPARK GAP EXCITES.TRAVELING WAVE COIL

О 100 200 300 400 500/i SEC

1860.21

Figure 21. РАМ apparatus and timing sequence: (above) plasmaacceleration system, schematic; (below) typical timing sequence

is provided with an axial magnetic field (Fig. 21). Theinitial ionization is either by a pinch, with axialexpansion into the vacuum, or a tangential electricfield from a one-turn coil connected to a high voltagecondenser. Any neutral gas ahead of the expandingplasma is expected to be overtaken, ionized, andcarried along, or left behind so that the plasma can beobserved thereafter in vacuo.

The plasma has been successfully accelerated furtherby a traveling magnetic wave injected into a solenoidaltransmission line. The velocity of the plasma ismeasured from the transit time between fast photo-multipliers while the total momentum is measured bythe classical ballistic pendulum. At the time ofwriting, the plasma velocity is 5 x 106 cm/sec, plasmaimpulse 90 gm cm/sec. There seems no reason to doubtthat the present techniques will permit the finalvelocity and mass accelerated to be increased by abouta factor of ten.

Picket Fence 6 6

This and the following experiment are in a lessdeveloped state than the foregoing.

A test of the confinement properties of the cuspedmagnetic field configuration can very simply be madeby using the fast Scylla condenser bank in combinationwith a suitable coil. Such a coil has been made, Fig. 22,which shows the measured magnetic field lines.Ultimately, when the technique of the crowbar hasbeen extended to Scylla, it should be possible tomaintain the field at its maximum strength and toobserve the loss of plasma as a function of time. Adirect comparison of the loss rates from mirror machine


versus Picket Fence geometries should thus bepossible.

Columbus T-2 5 4

The range of densities over which good observationsof the pinch effect have been made (taking into accountthe scaling laws for similar discharges) is very small.Indeed it seems that the densities studied have beendictated by considerations of obtaining breakdown.A properly chosen preionization system should allow,for example, the production of a pinch at, say, 1/100 ofthe usual particle density per cm length of the tube,which would bring down the pinch current by a factorof 10 or, alternatively, allow much higher temperaturesto be confined at the same current. However, the most

10 CM

Figure 22. Picket Fence, coil and measured magnetic field lines

striking advantage of such an arrangement is ex-pected to be the complete isolation of the wall fromthe initial bombardment ; the pinch, in an arrangementsuch as this, being created in free space.

Figure 23 shows the large Columbus T-2 dischargetube, 90 cm in diameter and 3.6 m long in its new form.This has an all-metal wall consisting of a thin stainlesssteel bellows which conducts in parallel with thedischarge.

Such an arrangement has been proposed byThonemann.67 The pinch is formed by injecting a

plasma column along the axial magnetic field lines: onbridging the two ends, it becomes the pinch. Thisapparatus has been operated only in an unsatisfactoryform with subdivided conducting wall. The pinch isindeed formed in the predicted way, but the laterphenomena are overshadowed by arcing between wallsections and arcing from wall to pinch. The newconducting wall may still develop arcing to the pinch,in which case, an insulating wall will be used.

TECHNOLOGY

Magnetic Probe

Our most serviceable tool for plasma physics hasproved to be the magnetic probe.44' 6 8 The technique isstraightforward. A small coil (2 mm diameter, 20turns) enclosed in an electrostatic shield, is mounted inthe closed end of a tubular sheath of quartz oralumina, which projects radially into the dischargetube, and the coil is adjusted to the required radius andorientation. The integration of the resulting voltagesignal is by an RC network (which has been preferredto the more sensitive electronic methods of integrationon account of its great working range since the voltagesdeveloped by the coil can reach kilo volts). Care has tobe taken that the frequency responses of all com-ponents of the system are adequate. Twenty mega-cycles is used for test. Doubts have been expressed asto the validity of magnetic field measurements madeby a probe immersed in a plasma.69 For the ColumbusS-4 measurements, the validity of the probe measure-ments in the presence of plasma have been establishedbeyond all question as follows: the Bz in this apparatusis produced by a low frequency condenser dischargethrough a solenoid wound on the exterior of the cylin-drical return conductor of the discharge tube, reachingthe tube interior by diffusion, and is measured in situ,in the absence of plasma, by standard laboratorytechniques. The probe, whose integration timeconstant is too short to observe the slow rise of BZ} iscalibrated ballistically using standard magnetic coils.From a set of probe measurements of Bz vs. timesat different radii, for a pinch under carefully main-tained constant condition, the usual Bz vs. r curves

ДО VACUUM PUMP

STAINLESS STEEL BELLOWS

MAGNETIC COIL / FEED CABLE N/VIEWING PORT

1860.23Figure 23. Columbus T-2 apparatus


COMPRESSION SCREW

AIR INLET FORTFOR FLUSHING

TUNGSTEN MACHINABLEALLOY INSERT

GLAZED CERAMICINSULATOR

AIR OUTLET PORTFOR FLUSHING

YOKE(PHENOLIC PLASTIC)

100 KV 0,8 Jif CONDENSER(TOBE DEUTSCHMANN)

OUTPUT ELECTRODE

IRRADIATION GAP

TRIGGER ELECTRODE(SPARK PLUG)

TRIGGER INPUT

CENTER ELECTRODE

CORONA RING

HVELECTRODE

Figure 24. Four-electrode spark gap1860.24

are constructed for different times. The integral

2irrBzdr, taken over such curves, should be con-Jostant provided that no flux leaked in through the outerconductor (conservation of Bz flux). For a set of suchcurves, taken with special care on a Columbus S-4pinch which included plasma pressures up to 4 x 106

dynes/cm2, the Bz was conserved to within 98% of itsinitial value. Note also the zero value of Eg at the wallin Fig. 7. Normal data shows 90-95% flux conserva-tion.

Small probes, as described above, show remarkablylittle perturbation of the pinch so that, for example, atraverse along a diameter through a pinch column,from one side, gives a symmetrical record within theexperimental error (provided that the pinch is stable).Obviously, some perturbation must result, however;in Perhapsatron S-4, a reduction of neutron intensitycan be detected in the vicinity of a magnetic probe,the rest of the torus being unaffected. Unfortunately,as higher temperatures and longer confinement timesare reached, the contamination and local cooling bythe probe will inevitably become significant, andultimately intolerable, and this useful technique willhave to be abandoned.

Elaborate experiments have been made to find someother probe technique. Electron beams up to 400 kvproved quite useless for pinch currents > 10,000 amp.Highly energetic proton beams have frequently beenproposed, but the measurement quality is likely tosuffer greatly, and interpretations become verydifficult as consequences of the complicated deflexionpath through the pinch. A highly collimated micro-wave beam probe for the evaluation of electron density

is immediately practical for many geometries, but notfor the present high density pinches; these require aninterferometer arrangement at say Л = 0.1 mm, whichis certainly beyond microwave technology at thepresent time. Furthermore, there is some indicationthat the pinch itself may radiate more strongly thanany contemplated generator at Л = 0.1 mm.

Switch Technique

Switch techniques play an important part in highpower pulse discharge research. For discharges atmedium voltages (up to 20 kv) and times to peakcurrents of as little as 6 /¿sec, specially developedignitrons are used to connect many condenserssimultaneously across the load. The ignitrons showconsistency in triggering of approximately 0.1 /¿sec.As might be expected, the safe current carrying capac-ity per ignitrón depends on the duration of the currentimpulse. Characteristic maximum ratings for a halfsine wave current pulse are: (GE 5550ignitrón) 18,000amperes peak, duration 60 ¿tsec; 4000 amperes peak,duration 2 msec. A spoüed ignitrón has a low break-down voltage. The spoiling process is believed tobe associated with development of an arc spot on themetal walls of the tube. Installations of this kind areemployed on Columbus S-4, Perhapsatron S-4, andIxion and for Bz supplies universally. For extremelylow-inductance high-voltage high-power applications,such as Columbus II and Scylla, ignitrons cannot beused. Two kinds of spark gaps have been developed.

Vacuum spark42—The operation of Columbus IIhas depended on the success of a vacuum spark gap(visible in the upper half of Fig. 2) which was developedto meet the following requirements: trigger in less than


1 fisec, have an inductance < 3 x 10~8 h and be ableto hold off 70-80 kv, after having passed currents of106 amp. A simple vacuum gap readily holds off 70 kvbefore use but ceases to be able to do so after onedischarge. Potential grading, using 8 diaphragms,solved this difficulty; capacitative subdivision of thepotential between the diaphragms proved adequatefor an applied potential rising to full value in 100 ¿¿sec.The choice of Teflon (polytetrafluoroethylene) for theinsulators turns out to have been a happy discovery,for it has self-cleaning properties, after exposure to themetal vapor of the vacuum spark, so far unique to thismaterial. In our experience, normal materials, e.g.,porcelain, are quite impracticable for vacuum sparkgaps, becoming coated by a metal film after a fewdischarges. Brass electrodes withstand the erosion of5 x 105 amp discharges well, the original Columbus IIgap being still effective after many thousand dis-charges.' The eroded surfaces have a highly polishedappearance.

Four-electrode spark gap70—The principle of auto-matic irradiation of a spark gap by photons from asubsidiary spark, in order to achieve precise break-down characteristics, has been well described.71 Suchan auxiliary gap adds a fourth electrode to the con-ventional three-electrode gaps (which, for preciseoperation, also depend on irradiation producedin alessdirect manner.)

The principle has been extended to the wellknown 3-sphere gap as shown in Fig. 24. The centralelectrode is arranged by divider to float at a potentialmidway between the upper and lower electrodes. Theincoming trigger pulse charges the center high im-pedance electrode via a small spark gap which irrad-iates the upper and lower gaps through the axial hole.When the center electrode reaches the breakdownpotential of one gap, breakdown occurs, which im-mediately overvolts the second gap, completing thecircuit. The not negligible advantage of this systemis that, although the upper and lower electrodes are, ofnecessity, connected to systems of very low impedance,which would therefore require powerful trigger pulsesto influence, the center electrode is in a high impedancesystem, capable of being triggered by a low powerpulse.

An essential feature of this type of gap, to achievereliably precise timing, is that the irradiation gap isadjusted in length to be small enough that its ownunirradiated jitter never overlaps into the time whenthe center electrode potential reaches the breakdownpoint of one or the other of the main gaps. The jitterof these four-electrode spark gaps has not beenmeasured but is known to be less than 10~8 sec for thefollowing reasons: ten of the gaps are used in a parallelconnection (see Fig. 19) in the Scylla apparatus, wherethe inter-condenser signal transit time is 0.03 /¿sec.The aggregate spread in firing must be less than this orsome condensers will fire in anti-phase, with markedeffects on the oscillograms (and serious strain on thecondensers !). Such behavior is seen at 65 kv gap voltagebut the gaps are completely reliable at 70 kv with no

malfunction in several thousand operations. Theupper voltage limit of the present design is aboutHOkv, being a function of the selected gap spacingand insulator design.

DISCUSSION

Pinch Temperatures

Before we can discuss the measurements of theinterior of the pinch, we must deal with the correctionto the pressure balance equation due to runaway. Thiscorrection has the effect of making p seem larger thanit really is, and we have no direct knowledge of theamount of runaway in the Columbus S-4 and Perhapsa-tron S-4 pinches. It turns out, fortunately, that we candemonstrate it to be negligible, in certain special cases.For the correction, as has been pointed out by Lovberg,is monotonie in / (centrifugal force is always outward).Consequently, for pressure distributions with p zero onthe axis (so called hollow distributions), the runawaycorrection must be insignificant.

Let us consider the most precisely known of ourpinches, the Columbus S-4 measurements at 1.4, 1.8and 2.6 /¿sec shown in Fig. 7. When the corrections aremade for the small radial oscillation of the pinch, thefirst two of these become hollow distributions and forthe third, being such a small extrapolation from thefirst two, we shall consider the insweeping of thesheath to have continued and swept all the initialfilling gas into the shaded area of Fig. 7.

We can derive a temperature Tp, from the sheathdensity. pB and the pressure, by the following:

' gives pB,. p ос пТ-р

Г°Tn ОС (1/ps)

Jo

Next we derive an electron temperature, Ta, from theconductivity72

o» = 1.65 xio- 7 :

where T is measured in ev. Then we make an energybalance calculation in the sheath, obtaining the rateof temperature rise:

dT¡dt ocE-j/».

Table 1 shows the results obtained.

Table 1. Comparison of Pinch Temperatures Calculatedfrom Pressures and Conductivities

pmean,

pressuredyne/cm2

1.5x10»8.0 xlO6

.2.5 x 10e

91

mean B adensity

atoms/cm3

1.6x10"3.8x10"4.4 x 10"

nelectrical

condii£tivity',mho/cm

200800150

ev

61333

ev

5124

dTdt

evliisec

205

50

t

fisec

1.41.82.6

At 1.4 /¿sec and 1.8 jitsec we see very fair consistencybetween the three quantities Tp and Ta and dTjdt.


However, for the third time, Tv is too high to beconsistent with the conductivity and, although theheat input rate rises greatly, the conductivity tem-perature falls. Obviously some cooling process isrequired, starting between 1.8 and 2.6 /¿sec.

The later phases of Columbus S-4 and PerhapsatronS-4 show these inconsistencies to an increased degree.For example, in the crowbarred phase of the latter,the steady energy input rate is 900 megawatts, or 95 evper electron per microsecond, yet no steady rise ofpressure, neutron intensity or even impurity lightintensity is observed. It seems urgently desirable tointroduce the slit of an energy and momentum analyserinto the discharge tube wall to perform a definitiveexperiment. [We are indebted to Colgate73 forexperimental evidence for electron escape.]

Returning to the late time inconsistency betweenTp and Ta—we can reconcile this in essentially fourways:

(1) increase particle density by transport of matterfrom the walls (i.e., retain the high pressure butbring Г р down to Ta);

(2) eliminate the high pressure by assuming a largerunaway correction, again reducing T p ;

(3) retain the high pressure but reduce Tp by assumingthat the pressure is due to some other form ofenergy density, e.g., turbulence; or

(4) raise To to Tv by making some correction to the f-power law conductivity formula.

Let us deal with these alternatives in order.

(1) To bring consistency by means of extra atoms israther inconsistent with the observed freedom fromimpurity radiation in both these experiments.

(2) There is undoubtedly some runaway, for bothexperiments produce X-rays, but, to account for thehigh pressures by these alone requires, for example, arunaway of all the electrons in the system, at severalhundred ev, which is both current-wise and energetic-ally impossible.

(3) It turns out that the turbulence hypothesis is aperfectly reasonable way of explaining how highpressures can be observed without the necessity forhigh temperatures. Consider the 10 /¿sec measurementin the Perhapsatron S-4 of Fig. 12. To account for theobserved 2 atmos pressures would require an electrontemperature in the original filling gas with, say, a four-fold compression, of ~220 ev. The conductivity isconsistent with a temperature of 6 ev.

Let us assume that the pressure is given by ^nmv2,where v is the root mean square speed in the turbulence,and that Tv is in reality 6 ev. We now estimate therelaxation time for the decay of the turbulence intoheat, and, for this, we require a mean eddy size, Л.From considerations of the size of the sheath and theresolving power of the probe, we shall take Л = 0.5 cm.Then the relaxation time т (given by 4тг2о-Л2/са) turnsout to be ~ 1 /¿sec for о = 9 x 1013 esu. If now theinput energy primarily goes into turbulence, andescapes immediately as heat to the walls, the rate-

determining process is the turbulence-heat decayrate. The instantaneous energy density in tur-bulence is given by energy input rate x т. This turnsout to be ~ 4 x 106 erg/cm3, in reasonable agreementwith the observed 2 x 10е erg/cm3.

(4) For the last hypothesis, it could be that althoughgood consistency was found using the f-power law forthe conductivity at early times, this law might breakdown as say plasma oscillations develop. Indeed,Bunemann has argued that this happens. In such acase, we retain T p , and Ta can be large, or evenmeaningless. We still, of course, have to keep the lossprocess which is not affected by the argument.

At present there is insufficient experimental evidenceto distinguish between hypotheses 3 and 4.

Loss ProcessTurning now to the prime cause of the loss process,

two possibilities come immediately to mind, namely:(a) hydromagnetic surface instability of the Suydamtype, and (b) plasma osculations induced by theelectric field. Both Columbus S-4 and PerhapsatronS-4 are Suydam unstable (see Fig. 5) so it seems likelythat growing perturbations will be present. The lossprocess is seen to intervene at 2.6 /tsec in ColumbusS-4, before any fluttering has been detected but thiscould easily escape detection when just beginning. I t isa straightforward experiment to check hypothesis (a) :all that is required is to impose a Suydam stableconfiguration, and observe whether the conductivityor pressure rises. There are several ways of doing this,including the reversal of Be and Вг. So far, the pre-liminary experiments have involved reversed Bg andhave been ineffective in changing the conductivity butthe Bz programming equipment has been inadequate.The outcome of this experiment may be crucial for thefuture of the stabilized pinch as a reactor, so that itwill receive much study.

As for hypothesis (b), the criterion for the excitationof plasma oscillations seems universally that z, theratio of drift speed to thermal speed, be > 1. Lookinginto the measurements on Columbus S-4 and Per-hapsatron S-4, for complete runaway of all the localelectrons, the largest values of z we can find, where

z = (Jlne)(m¡2kT)K

are 10~a and 0.5 respectively. Since however theelectric fields in these devices are appreciably lowerthan Dreicer's values for total runaway, these valuesare probably strong underestimates, and we can becertain some fast electrons are present, since bothapparatus produce X-rays.

Thus, about all that can be said, at present, is thatconditions could easüy be favorable for the excitationof plasma oscillations by runaway.

Electromechanical Oscillations

The electromechanical radial oscillations of thepinch reported in the section on Columbus S-4 havesome interesting properties. For the case when theplasma is concentrated in a thin shell between the


pfc-io, t«of°2SOkc for r°IOcm<r»9xlOBESUBl6íinhoctlíl

f= 10 kc for Г-10 cm

<r«9xlOBESUsK5zmhooñ l

1860.25RADIUS, CM RADIUS, CM RADIUS, CM RADIUS, CM

Figure 25. Magnetic field in the interior of a solid cylinder of radius r0, conductivity a, from a magneticfield at the surface, of constant strength, rotating with frequency cu.82 = с2/4ячио2

central Вг field and the external Be field, we haveseen that the oscillation frequency is

The time т for this configuration to become smearedout by diffusion of the currents is proportional to2naRo2lcz. Consequently, the number of oscillations ofthis type we would expect to see is штт, which isproportional to RQ*. Thus, more oscillations shouldbe obtained in large diameter discharge tubes.

After a time of order of magnitude т, the configura-tion wiH have changed to one resembling a solidcylinder composed of plasma and Bz magnetic field,surrounded by Be magnetic field (in cylindricalgeometry, the density rises more rapidly on the insidethan on the outside of the shell). For this configura-tion, the oscillation frequency acquires a dependenceon the plasma properties. Thus, for small oscillations,we have

where subscripts e and i refer to electron and ionproperties taken separately and у is the ratio ofspecific heats. These are the usual bouncing oscula-tions, such as were noted by Bezbachenko et al?$These oscillations might be used for plasma heatingpurposes, by exchange between the radial and longi-tudinal degrees of freedom, in the manner proposedby Spitzer76 and Schluter76 (magnetic pumping).77

Furthermore, ye and yi must change in a complicatedbut predictable way (in general from 5/3 to 2 as thetemperature rises) from which some knowledge of Tmay be extracted.

Dynamically Stabilized Pinches

It has frequently been suggested that pinches withradio frequency currents might have advantages induration and stability over those with direct current,and rf pinches have been sporadically investigated

experimentally.78-80 The frequencies have to be high,so that the duration of the free expansion at the sur-face of the pinch, which takes place near the zero ofmagnetic field there, is insufficient to allow the plasmato reach the wall. Magnetic fields of several thousandgauss at megacycle frequencies require large expendi-tures of power, and the resulting economics of suchdevices takes them out of the field of possible thermo-nuclear reactors. Incidentally, the same seems true ofcavity confinement, although for experimental con-finement iot related to economic production of power,the rf cavity used in the strong focusing mode ofGood81 shows much promise.

Rotating Magnetic FieldsLater, have come proposals for rotating magnetic

field confinement where, since the confining field isnever zero, the required frequencies are lower.However, calculations of the stability of plasma-rotating magnetic field boundaries82- 8 3 have beendiscouraging. Nor is it hard to see why this has beenso. Consider an infinitely conducting pinch confined bya magnetic field of constant magnitude, but whosedirection at all points is along a tangent at the inter-facial plane, rotating with constant angular velocity.Such a configuration passes from the pure pinch {Bz inв direction) to the pure axial field confinementcyclically, and the modes of instability vary cyclicallybetween positive and negative values. Such systemsare characterized by Mathieu equations whosesolutions, except for restricted ranges of the para-meters, are badly behaved, i.e., divergent in amplitude.

It now seems that this treatment has led to anerror and an exaggeration of the degree of instability.Thin boundaries do not exploit the stabilizing proper-ties of the magnetic shear to the fullest possible extent.An example of this is to be seen in the effect of Вг

external to the pinch on its hydromagnetic stabilitywith thick and thin boundaries. As mentioned in the


theoretical section, with thin boundaries, external Bz

always diminishes the stability. For thick boundaries,a reversed Be can increase the stability.

For a rotating field, the magnetic fields take on alamellar structure which is qualitatively mostencouraging for stability. Solutions of Maxwell'sequations for the penetration of a rotating magneticfield into a uniformly conducting cylinder (withoutdynamics) exhibiting this are shown in Fig. 25. (Weare indebted to Riesenfeld84 for this solution.)

We see that for the currently observed pinch con-ductivities, ^/102 mho cm"1, frequencies in the range10-250 kc give appreciable penetration.

The next steps, of considerably greater difficulty,are to put in the plasma dynamics and then examinethe configurations for stability. It seems quite likelythat a moderate degree of interlaminar instabilitycould be tolerated in a constantly regenerated con-figuration of this kind but, at these low frequencies,surface instabilities would be fatal. Toroidal geometriesfor the excitation of pinches such as the above werediscussed some years ago at Los Alamos 8 S but droppedfor the reasons given above. Such geometries have acertain simplicity (Fig. 26).

For a simple verification of these speculations, effortsare being made to devise a ringing condenser systemto provide, for a brief time, the large (>100 Mw)alternating current power required.

Brute Strength ApproachSuppose it turns out that the losses from the

stabilized pinch are due to plasma oscillations ? In sucha case, since we have no idea how to prevent them, thestabilized pinch would seem unlikely to lead us to aneconomic thermonuclear reactor. Nevertheless, as anexercise, we can still in principle construct a pinchapparatus showing an energy profit. For this, wereturn to the old pre-stabilization Columbus Xconcept, of a single contraction pinch, whose size anddensity is such that the thermonuclear yield exceedsthe energy input. That this must be possible in princi-ple, we see as follows: consider a pinch which is formedarbitrarily rapidly, so that the losses are insignificantduring the contraction. The disassembly time for afixed optimum temperature is proportional to (com-pressed radius)/(sound velocity). Consequently thethermonuclear yield is given by

Y = АттгЪ%пЧЪг{т12ЩЬ.

The investment cost, where all magnetic fields, losses,etc., are absorbed into the constant, is

I = Bnt^kkT.

The efficiency, e = Y/I, is proportional to nr ;thus by making m large enough, e becomes >1. Toproduce a reactor this way is somewhat dismaying.Even using tritium-deuterium, the pinch currents are~109 amp, voltage gradients ~106 v/cm and thethermonuclear energy release takes the form of anexplosion of power equivalent to ~ 1 ton of TNT percm length of the pinch. Such impulsive confinement

sin ( « t + -£• )

1860.26Figure 26. Conductor arrangements for the excitation of arotating-field dynamically stabilized pinch (iron-cored torus)

arguments can of course equally be applied to picketfence and spherically convergent shock systems, butthe result is broadly the same. It would be an un-pleasant form of reactor, of course, but hardly more sothan the current proposals for thermonuclear powerfrom H bombs.

Plasma OscillationsWhile in this vein, we might speculate whether

plasma oscillations might grow on the transversecurrents (in the direction Vp x B) in the boundary ofa confined plasma. Qualitatively, we see that a smallelectron charge accumulation in the surface of such aplasma boundary produces an electric field which leadsto a ripple in the plasma surface, but does not relievethe accumulation of charge. Such a process wasdescribed by Alfvén.86

Although it can be shown that the charge drift in agradient of magnetic field is divergenceless; neverthe-less, a situation might easily arise in the sheath wherethe ripple would grow as follows. Figure 27 shows asheath having some trapped particles. The usualelectric field Ex, arising from the difference in Larmorradii of ions and electrons in the direction normal tothe interface, is present. If now Ex/Bz increasesoutward away from the plasma, any small accumula-tion of electrons introduces a perturbation in thedrift, which grows as it moves outward. The only self-consistent sheath analysis known to us87 is indeedunstable according to this.

It has been usual to take reassurance from the factthat charge can neutralize freely along the field lines.That this process is not always sufficient can be seenin the recent experimental observations88 of theinstability of a hollow electron beam traveling along


an axial magnetic field. The process is precisely thatdescribed by Alfvén above, and the beam breaks uptransversely to the magnetic field into parallelstreams, in cross section resembling a vortex street.

Non-pinch DevicesSo far we have discussed only the pinch. There

remain several other configurations, notably Scylla,Ixion, Picket Fence, and the electrostatic inertialsystems. We shall discuss these more briefly, since theyhave been studied less. We regard Scylla as anexperiment to make and study thermonuclearreactions, and it makes a substantial number ofneutrons. Before discussing these, we must have acriterion for a thermonuclear reaction.

The reason, of course, for the retention of the wordthermonuclear in the title of our subject is that inorder to produce an energy profit, we have to be ableto allow many Coulomb collisions for each nuclearreaction. Thus the Maxwell distribution is an essentialrequirement. All the neutrons reported so far havealmost certainly been produced by a small high energycomponent of a system whose average energy hasbeen small. Such neutrons are irrelevant though notuninteresting. Next we consider a system that doeshave a high enough average energy to make neutronsbut having all the particles with the same energy(8-function distribution). We see that this is notenough either. We must demonstrate that it can beconfined after it is Maxwellized. Thus the demonstra-tion of a thermonuclear reaction might progress in thefollowing steps:

(1) the neutrons must be produced under conditionswhere no violation of pressure balance, thermo-nuclear yield rates, etc., has occurred;

(2) the neutron energy distribution must exclude ahigh energy deuteron component as the neutronsource, and anisotropy in the distribution must beaccountable in terms of an overall plasma drift;

(3) a strong but not conclusive proof of a Maxwelldistribution would follow from neutron emission(even a rise of intensity) over many collision times(the loophole comes from the possibility of neutronemission from a cold deuteron plasma by photo-disintegration from Mev electrons); and

(4) a direct measure of F, the plasma distributionfunction, which would surely be conclusive: incertain cases, notably in mirror geometries, it mayeven be practical.

The preliminary energy distributions of the Scyllaneutrons indicate that Scylla is probably past stage2 above. The present time confinement is about onecollision time: the evidence for a thermonuclearreaction in Scylla is thus strong but not yet conclusive.

Ixion is an attractive geometry, especially as the"heating" process heats the ions selectively. It seemsdefinite from the Doppler shift of the radiation that anion drift and ion Larmor energy of about 30 ev hasbeen achieved. At present, the standing current acrossthe magnetic field is too large. For future experiments,

VACUUM BZO

I O N S ^1ЛЯ)То"0"в'в1Г<ППЛПге"0ТгеТ<ПЛГ

ELECTRON DRIFT s2- E x j

*0000ü000000(

PLASMACHARGE

ACCUMULATION

Figure 27. Possible Instability in a plasma-field interface

an increase of apparatus radius is indicated, togetherpossibly with initial ionization by condenser dischargeand maintaining of the current by dc supply, in astrongly pumped system with diverters.

Picket Fence is interesting mainly for its stronginherent stability. Since its losses would seem alwaysto be larger than those of the stable mirror machine,we regard it as a next-to-the-last-ditch reactorconcept (Columbus X is the last ditch!) to be broughtout if the mirror machine geometry is struck down byinstabilities.

The electrostatic inertial system is still only a paperspeculation.

CONCLUSION

A new surface instability of the Вг-wall stabilizedpinch has been deduced theoretically. It wouldrequire reversed Bz or Be to stabilize it.

Refined measurements have been made of theinterior of pinched discharges. The Вг-wall stabilizedpinch has been shown experimentally to have a largeenergy loss rate. The cause and mechanism for this isnot yet known but believed to be due either to the newsurface instability described above, or to plasmaoscillations excited by electron runaway. If the former,the outlook for the pinch is good; the instability can bestabilized, and there is even increased promise for acontinuously maintained dynamically confined pinch.If the latter, the outlook for the .B -wall stabilizedpinch as a reactor is poor.

Axial magnetic field-radial electron field systemsare shown to have much interest theoretically, and itappears that the confinement properties of mirrors canbe greatly improved. Experimentally, such a systemhas indicated qualitative agreement with theory, andan equivalent temperature of 30 ev.

A system for accelerating bursts of plasma intovacuum has been developed.

A rapidly rising axial magnetic field plasmacompression system in mirror geometry is producing> 107 neutrons per pulse, with a high probability ofbeing thermonuclear at a temperature of over 1100 ev(13х10в °K).

ACKNOWLEDGEMENTS

B.The valuable advice and support of J. IVKellogg ш this work is gratefully acknowledged.

In addition to those mentioned in the text, it is apleasure to acknowledge the generous cooperation of


the following: Gladys A. Alexander, William P.Basmann, Armand T. Brousseau, Heman L. Buey,Bruce E. Burkheimer, Charlie G. Charlton, Paul R.Greenbaum, Jano W. Haley, Richard D. Hicks,Stanley J. Hipwood, Robert O. Holm, Hugh K.Jennings, Ann Jensen, Edwin L. Kemp, Glenn H.

Livermore, Lawrence H. McDowell, Charles P.Milich, Elizabeth J. Pohlmann, Robert E. Pruner,Thomas M. Putnam Jr., Nicolas L. Salazar, Aldred E.Schofield, Jerald L. Sherwood, William В. С Smith,Francis K. Tallmadge, Carlos Val Verde, Fred E.Wittman and David A. Woodwell.

REFERENCES

l.

10.

u.

12.

13.14.

15.

16.17.

18.

19.

20.

21.

22.

23.

24.25.

M. Kruskal and J. L. Tuck, The Instability of a PinchedFluid with a Longitudinal Magnetic Field, Proc. Roy. Soc,245, 222 (1958).M. Rosenbluth, Instability of the Pinch, Los AlamosReport 2030 (to be published).S. A. Colgate, Los Alamos Conference (1955).L. A. Artsimovich, Symposium on E. M. Phenomena inCosmical Physics. Stockholm (1956).V. D. Shafranov, The Stability of a Cylindrical GaseousConductor in a Longitudinal Magnetic Field, AtomnayaEnerg., 1, 33 (1956).R. J. Tayler, Hydromagnetic Instabilities of an IdeallyConducting Fluid, Proc. Phys. Soc., BIO, 31 (1957).I. B. Bernstein, E. Friedman, M. Kruskal and R. Kulsrud,Project Matterhorn Report No. S-25; Proc. Roy. Soc,A244, 17 (1958).B. R. Suydam, Stability of a Linear Pinch, P/354, Vol. 31,these Proceedings.M. Rosenbluth, private communication (1958).С L. Longmire, The Static Pinch, P/1861, Vol. 31, theseProceedings.R. J. Bickerton, Berkeley Conference on ThermonuclearReactions, TID 7536 (February 1957).Lloyd Smith, Basic Concepts in the Development of aThermonuclear Reactor, Washington Conference onThermonuclear Reactions, Washington Report No. 184(October 1954).E. D. Shipley, private communication.J. Luce, Ion Sources, Livermore Conference on Thermo-nuclear Reactions, Washington Report No. 289 (February1955).O. A. Anderson, W. R. Baker and J. M. Stone, Experi-ments with Two New Pinch Devices (Homopolar), BerkeleyConference on Thermonuclear Reactions, TID 7536(February 1957).D. Gow, Omnitron, private communication (1957).K. Boyer, J. E. Hammel, С L. Longmire, D. Nagle,F. L. Ribe and W. B. Riesenfeld, Theoretical and Experi-mental Discussion of Ixion, a Possible ThermonuclearDevice, P/2383, Vol. 31, these Proceedings.H. Dreicer, Runaway Electrons in a Fully Ionized Gas,Third International Gaseous Electronics Conference,Venice (1957).H. Dreicer, Theory of Runaway Electrons, P/2292, Vol. 31,these Proceedings. See also Proceedings of the TenthAnnual Gaseous Electronics Conference, Cambridge,Mass. (1957).

J. J. and G. P. Thomson, Conduction of Electricity ThroughGases, Cambridge University Press, p. 353 (1933).L. Tonks and I. Langmuir, Plasma Oscillations, Phys.,Rev., 33, 195 (1929).L. L. Landau, J. Exp. and Theoret. Phys. (USSR), 16574 (1946).D. Bohm and E. P. Gross, Plasma Oscillations, Phys. Rev.75, 1851 (1949).A. E. Ylasov, J. Phys. (USSR), 9, 25 (1945).A. I. Akhiezer and Y. B. Faynberg, On the Interaction of aBeam of Charged Particles with an Electron Plasma, Proc.Acad. Sci. USSR, 69, 555 (1949).

26. A. I. Akhiezer and R. V. Polovin, Theory of the WaveMotion of an Electron Plasma, J. Exp. and Theoret. Phys.(USSR), 30, 915 (1956).

27. A. A. Luchina, On Longitudinal Vibrations of Plasma I,J. Exp. and Theoret. Phys. (USSR), 28, 18-27 (1955).

28. G. Ya. Myakichev and A. A. Luchina, On LongitudinalVibrations of Plasma II, J. Exp. and Theoret. Phys.(USSR), 28, 28-37 (1955).

29. G. V. Gordeyev, High Frequency Oscillations of Plasma,J. Exp. and Theoret. Phys. (USSR), 24, 445 (1953).

30. O. Bunemann, Instability or Microwave Amplification inHigh Current Discharges, preprint (1958).

31. O. Bunemann, Instability, Turbulence, and Conductivity inCurrent-Carrying Plasma, Phys. Rev. Letters, 1, 8 (1958).

32. A. V. Haeff, Space Charge Wave Amplification Effects,Phys. Rev., 74, 1532 (1948).

33. J. R. Pierce, Increasing Space Charge Waves, J. Appl.Phys., 20, 1060 (1949).

34. J. L. Tuck, American Academy of Science Conference onMagnetohydrodynamics, Woods Hole, Mass. (June, 1958).

35. S. Chandrasekhar, Stochastic Problems in Physics andAstronomy, Revs. Modern Phys., 15, 1 (1945).

36. I. Langmuir, On the Energy Distribution of Electrons in GasDischarges, Phys. Rev., 26, 585 (1925).

37. W. С Elmore, J. L. Tuck and К. М. Watson, Electrostatic-Inertial Confinement in Spherical Geometry (to be pub-lished).

38. W. H. Wells (Bendix Aviation Corporation), private com-munication (1954).

39. P. T. Farnsworth (Farnsworth Electronics Company),private communication (1956).

40. J. L. Tuck, private communication (1956).41. J. W. Mather and A. H. Williams, Neutron Production in

Columbus II, P/2394, Vol. 32, these Proceedings.42. D. С Hagerman and A. H. Williams, High-Powered

Vacuum Spark Gap (to be published).43. D. С Hagerman and J. W. Mather, Neutron Production

in a High-Power Pinch Apparatus, Nature, 181, 226-228(1958).

44. L. С Burkhardt, R. H. Lovberg and J. A. Phillips,Magnetic Measurement of Plasma Confinement in a Par-tially Stabilized Linear Pinch, Nature, 181, 224-225(1958).

45. L. С Burkhardt and R. H. Lovberg, Field Configurationsand Stability in a Linear Discharge, P/2395, Vol. 32, theseProceedings.

46. L. С Burkhardt and R. H. Lovberg, New ConfinementPhenomena and Neutron Production in a Linear Pinch,Nature, 181, 228 (1958).

47. D. M. Slager, Los Alamos Scientific Laboratory, privatecommunication.

48. W. R. Baker, Conference on Controlled ThermonuclearReactions, Princeton, TID 7503 (October 1955).

49. S. A. Colgate, private communication (1957).50. S. A. Colgate and H. P. Furth, University of California

Radiation Laboratory Report, UCRL-5086.51. J. P. Conner, D. С Hagerman, J. L. Honsaker, H. J.

Karr, J. P. Mize, J. E. Osner, J. A. Phillips and E. J.Stovall Jr., Operational Characteristics of the Stabilized


Toroidal Pinch Machine, Perhapsatron S-4, P/2488,Vol. 32, these Proceedings.

52. J. L. Honsaker, H. J. Karr, J. E. Osher, J. A. Phillipsand J. L. Tuck, Neutrons from a Stabilized, ToroidalPinch, Nature, 181, 231-233 (1958).

53. D. M. Slager, Los Alamos Scientific Laboratory, privatecommunication (1958).

54. D. A. Baker, G. A. Sawyer and T. F. Stratton, LowVoltage-Gradient Pinches in Metal-Walled Systems,P/1025, Vol. 32, these Proceedings, and addendum toabove by K. Boyer, W. G. Elmore, E. M. Little andW. E. Quinn.

55. W. С Elmore, E. M. Little and W. E. Quinn, Neutronsfrom Plasma Compressed by an Axial Magnetic Field(Scylla), P/356, Vol. 32, these Proceedings.

56. W. С Elmore, E. M. Little and W. E. Quinn, Neutrons ofPossible Thermonuclear Origin, Phys. Rev. Letters,Vol. I, 32 (1958).

57. R. F. Post, The Mirror Machine, Bull. Am. Phys. Soc.,3, 196 (1958).

58. R. R. Wilson, Cornell, private communication (1953).59. la. P. Terletski, J. Exp. and Theoret. Phys. (USSR), 32,

927 (1957); Translation Soviet Phys., JETP 5, 755 (1957).60. J. W. Mather, Princeton Conference on Thermonuclear

Reactions, Washington Report No. 184 (reported by J. L.Tuck) (October 1954).

61. S. A. Colgate, Livermore Conference on ThermonuclearReactions, Washington Report No. 289 (February 1955).

62. F. R. Scott, Totem Pole, Berkeley Conference on Thermo-nuclear Reactions, TID 7536, Pt. II (February 1957).

63. F. R. Scott, W. P. Basmann, E. M. Little and D. B.Thomson, Magnetic Channeling of a Strong Shock, ThePlasma in a Magnetic Field, Stanford University Press,Palo Alto, California (1958).

64. A. C. Kolb, Naval Research Laboratory, private com-munication.

65. J. Marshall Jr., Acceleration of Plasma Into Vacuum,P/355, Vol. 31, these Proceedings.

66. J. L. Tuck, Princeton Conference on ThermonuclearReactions, Washington Report No. 184 (October 1954).

67. P. С Thonemann, private communication (1958).68. L. A. Artsimovich, A. M. Andrianov, O. A. Bazilevskaya,

Yu. G. Prokhov and N. V. Filippov, Investigations ofPulse Discharges at High Currents, Atomnaya Energ., 3,76-80 (1956).

69. S. A. Colgate, Washington Conference on ControlledThermonuclear Reactions (February 1958).

70. R. S. Dike et al. (to be published).

71. K. J. R. Wilkinson, Some Developments in High-PowerModulators for Radar, J. Am. Inst. Elec. Engrs., 93, Pt.I l l A., No. 6, 1090-1112 (1946).

72. L. Spitzer Jr., Physics of Fully Ionized Gases, IntersciencePublishers Inc., New York (1956).

73. S. A. Colgate, private communication (1958).

74. A. L. Bezbachenko, I. N. Golovin, D. P. Ivanov, V. D.Kirillov and N. A. Yavlinskii, Investigation of the Gas Dis-charge of a Very Strong Current in a Longitudinal MagneticField, Atomnaya Energ., 1, No. 5, 26 (1956).

75. L. Spitzer Jr., Bull. Am. Phys. Soc, Series II, Vol. 3196 (1958).

76. A. Schluter, Third International Conference on IonizationPhenomena in Gases, Venice (1957).

77. L. Spitzer Jr. and L. Witten, PM-S-6 (March 1953).

78. P. С Thonemann, private communication.79. W. L. Briscoe and T. F. Stratton, Livermore Conference

on Thermonuclear Reactions, Washington Report No.289 (February 1955).

80. A. A. Ware, Berkeley Conference on ThermonuclearReactions, TID-7536, Pt. II (February 1957).

81. M. L. Good, A Proposed Particle Containment Device,Berkeley Conference on Thermonuclear Reactions,Washington Report No. 146 (April 1953).

82. J. Berkowitz, Dynamical Stabilization of the Pinch, Pre-liminary Report of Conference on Controlled Thermo-nuclear Reactions held at Princeton University, TID-7503(October 1955).

83. R. J. Tayler, private communication.

84. W. B. Riesenfeld, Los Alamos Scientific Laboratory,private communication.

85. J. L. Tuck, Los Alamos Sherwood Conference (December1955).

86. H. Alfvén, Cósmica! Electrodynamics, Oxford UniversityPress, London (1953).

87. M. Rosenbluth and R. Garwin, Infinite ConductivityTheory of the Pinch, Los Alamos Report LA 1850(1954).

88. H. F. Webster, Breakup of Hollow Electron Beams, J.Appl. Phys. 26, 1386 (1955).

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