operational characteristics of the stabilized toroidal ... 1958/papers... · calculation (fig. 9a)...

P/2488 USA

Operational Characteristics of the Stabilized ToroidalPinch Machine, Perhapsatron S-4

By J. P. Conner, D. C. H age r m an, J. L. Honsaker, H. J. Karr, J. P. Mize,J. E. Osher, J. A. Phillips and E. J. Stovall Jr.

Several investigators1"6 have reported initial successin stabilizing a pinched discharge through the utiliza-tion of an axial Bz magnetic field and conductingwalls, and theoretical work,7"11 with simplifyingassumptions, predicts stabilization under these con-ditions. At Los Alamos this approach has beenexamined in linear (Columbus) and toroidal (Per-hapsatron) geometries.

Perhapsatron S-3 (PS-3), described elsewhere,4 wasfound to be resistance-limited in that the dischargecurrent did not increase significantly for primaryvçltages over 12 kv (120 volts/cm). The minor insidediameter of this machine was small, 5.3 cm, and theonset of impurity light from wall material in thedischarge occurred early in the gas current cycle. Itwas tentatively concluded that in the small PS-3torus the flux of energy to the walls had reached anintolerable value. The resulting evaporation or sputter-ing of wall material then contaminated the dischargecausing the resistance of the discharge to rise. Forthis reason the next in the progression of toroidalmachines, Perhapsatron S-4 (PS-4), was constructed(see Fig. 1).

The machine has a quartz torus of 14.0-cm minorinside diameter, 218-cm mean circumference and wallthickness 0.6 cm. An aluminum primary, 1.25 cmthick, surrounds the quartz torus with minimumspacing, ~0.4 cm, and can be energized by 90,000joules, 20 kv at two feed points, permitting a maximumelectric field of 150 volts/cm. A two-ton iron core(laminations 0.002 in. thick) links the primary andsecondary and has a rating of 0.2 volt-sec. A solenoid,1.6 turns per cm, wound around the primary isenergized by a 2400 ¡d capacitor at voltages upjtoJS kvand produces an axial Bz magneticTfield up to~4000gauss. A split in the aluminum primary allows rapidBz field penetration.

ELECTRICAL CHARACTERISTICS

The typical behavior of gas current and secondaryvoltage at 25 kv is shown in Fig. 2. The current-voltage phase relation shows that the gas current is

* Los Alamos Scientific Laboratory, University of Cali-fornia, Los Alamos, New Mexico.

297

largely inductance-limited and not resistance-limitedas observed in PS-3. After gas breakdown about 80%of the condenser voltage appears around the secondary,in agreement with the ratio of source and load induct-ances. The rate of increase of gas current is at firstlarge, ~1.3xlOn amp/sec, until the gas currentcontracts to cause an increase in inductance, at whichtime the gas current is a good approximation to a sinecurve. The gas current maximum is found to riselinearly with primary voltage (Fig. 3), deviating asexpected at the higher voltages because of saturationof the iron core.

At the discharge current maximum, the secondaryvoltage is not zero, and if one assumes that there isno large change of inductance, the total resistance ofthe discharge (R = Vjl) is computed to be ~28milliohms.

EXPERIMENTAL RESULTS

Neutron Production

The total average yield of neutrons is ~4 x 106 perdischarge at 30 kv, and neutron yields as high as~107 per discharge have been recorded. No cir-cumferential asymmetry in neutron yield has beenobserved.

The average yield of neutrons is found to vary withpressure as shown in Fig. 4. The maximum neutronyield is found at a lower pressure (~ 15 fx) than withthe smaller machine, PS-3 (~30 /¿). The neutron yieldalso is observed to decrease more rapidly with in-creasing pressure than for PS-3 and is reduced toone-half of its maximum value at a pressure of 21.5 /¿.

The dependence of the average neutron yield fromPS-4 on the initial axial Bz magnetic field (Fig. 5a)exhibits a striking similarity to that reported for PS-3with an optimum value of Bz giving the maximumyield. It is also found that the optimum value of Bzvaries with the applied primary voltage as shown inFig. 5b. Again a comparison with PS-3 can be madein that a smaller value of Bz is required in the largermachine to optimize the neutron yield for a givendischarge current. It is of further interest to note thatfor the Bz field adjusted for optimum neutron yieldat various primary voltages, the yield experiences

298 SESSION A-10 P/2488 J. P. CONNER et al.

350

Figure 1. Photograph of Perhapsatron S-4 showing the torus, iron

cores, electrical feed points and a section of the vacuum system

essentially a linear rise with increasing primaryvoltage. These data are summarized in Fig. 6.

The average times of onset, cessation and durationof neutron emission are shown in Fig. la and 7b. Asthe primary voltage is increased the neutrons appearearlier in time and their duration grows shorter. Theonset of neutrons at a fixed Bz field may well beassociated with a critical value of discharge current(~180ka) so that the more the primary voltage isincreased, with the resulting increase in the rate ofrise of gas current, the earlier will this critical currentbe reached and neutrons emitted. The termination ofthe neutron burst is correlated with the appearance ofradiation from wall materials. At the lower voltages(20 to 24 kv), neutron emission occurs almost sym-metrically in time about the current maximum withlittle or no impurity light (Si II) emitted in this time

25 5.0 7.5 I0.0 Í 2 5 15,0'вез Primary Bank Voltage (kilovolts)

Figure 3. Peak gas c u r r e n t as a function of p r i m a r y voltage

1.0

17.5

10 20 3 0 4 0 50 6 0 70 8 0Deuterium Gas Pressure (microns)

90

Figure 2. M u l t i p l e beam oscilloscope traces of ( a ) secondary

voltage, and (b) gas discharge c u r r e n t . Initial c o n d i t i o n : p r i m a r y

voltage = 30 kv; axial magnetic field B 2 = 1 7 0 0 gauss, P = 12.5 ц

Figure 4. N e u t r o n yield vs. d e u t e r i u m gas pressure

P r i m a r y voltage = 3 0 kv, axial magnetic field B z = 1 7 0 0 gauss.

Each point represents t h e average yield of t h r e e discharges; t h e

standard error for this average is approximately ± 2 0 %

interval. At the higher voltages (>24 kv), impuritylight comes in earlier with an apparent quenching ofthe neutrons, thus leading to shorter burst duration.

The region of emission of neutrons in the torus hasbeen measured with a large paraffin collimator used

OPERATIONAL CHARACTERISTICS OF PERHAPSATRON S-4 299

О 400 800 1200 1600 2000 2400 2800 32002488.5o В г Axial Magnetic Field (gauss)

Figure 5a. Neutron yield as a function of axial Bz magnetic field.Primary voltage = 30 kv

in conjunction with a fast phosphor and photo-multipHer detector. The results of the measurementare shown in Fig. 8. Within the experimental errors,the results for the horizontal and vertical scan acrossthe minor diameter are the same, and it is concludedthat the source is probably symmetric about the minoraxis. From a knowledge of the resolution of thecollimator, these data have been obtained with theaid of a 704 computing machine. The results of thecalculation (Fig. 9A) show that the neutrons areproduced in a hollow cylinder, ~2 cm id and ~3 cmod, with some contribution between 8- and 14-cmdiameter. The data, however, are not inconsistentwith neutrons being produced uniformly in a rod3 cm in diameter with a small contribution betweenthis rod and the torus wall, Fig. 9B.

The energy distributions of the emitted neutronshave been measured in two directions tangential tothe major circumference: one in the direction in whichdeuterons are accelerated by the induced electricfield, and the other opposed. An expansion-type cloudchamber, 30 cm id, filled with CH4 at a pressure of1.5 atmospheres placed one meter from the torus wasused as the detector. A paraffin collimator betweenthe cloud chamber and the torus limited the neutronsaccepted to those emitted tangentially from the torus.To minimize X-ray background a 0.6-cm thick leadshield surrounded the cloud chamber. The high relativeneutron yield from this machine has made it possibleto obtain ~870 usable tracks in ~1600 expansions.The results with the machine operating at 27.6 kv,1500 gauss Bz field and 12.5 [x D2 gas pressure, areshown in Fig. 10 together with a calibration run made

4 0 0 800 1200 1600 2000 2400Bz Axial Magnelic Field (gauss)

2800

Figure 5b. Axial Bz magnetic field for optimum neutron yield asa function of primary voltage. Deuterium gas pressure = 12.5 ¡L

' 02488.6

8 12 I6 20 24 28Primary Voltage (kilovolts)

32 36

Figure 6. Neutron yield vs. primary voltageAxial Bz magnetic field adjusted for optimum neutron yield at

the individual data points. Deuterium pressure = 12.5 JU.


I I I I I I I I I I I Г

•Time of cessationof neutrons

I I I I IV I 6 17 18 19 20 2l 22 23 24 25 26 27 28 29i88 7e Primary Bank Voltage (kilovolts)

32 33 34 35

Figure 7a. Time, during gas current cycle, of onset and cessationof neutron emission, and time on onset of Si II 4128 Â line as afunction of primary voltage. Axial Bz magnetic field adjusted for

optimum neutron yield at the individual data points

on a Cockcroft-Walton accelerator. It is seen that theneutron energies measured in the direction in whichdeuterons may be accelerated in the machine arehigher than those in the opposite direction, withpronounced energy peaks at 2.59 Mev in the forwarddirection and 2.37 Mev in the backward direction.The widths at half-maximum of the neutron energypeaks are 0.3 and 0.35 Mev and only slightly largerthan that of the calibration run, ~0.2 Mev. Theseenergy shifts show that the center of mass of thereacting deuterons is moving in the direction of theinduced electric field with a velocity of ~5xlO7

cm/sec. If the assumption is made that fast deuteronsreact with deuterons at rest, the peak of the neutronenergy distribution implies a deuteron energy of10 kev.

Magnetic Field and Pressure Distributions

The Be and Bz magnetic field distributions havebeen measured across a minor diameter of the torusin the horizontal plane. If the assumption of symmetryof the discharge about the horizontal plane is correct,then only two components of the magnetic field,Be and Bz, need be measured as Br is zero. Subsequentto these measurements, other results12 at Los Alamosin cylindrical geometry indicate a gross bodily move-ment of the discharge with the resulting inference thata more detailed program of measurements includingthe third component (radial) in toroidal geometry isrequired.

The magnetic fields are measured by previouslydescribed techniques,4 and the resulting calculated j zand je current density distributions at 30 kv primaryvoltage and 1700 gauss Bz stabilizing field are shownin Figs. 11 я and 116, respectively. The dischargeappears to be confined by the pinch field and isconcentrated about the axis with little or no currentnear the walls after the initial pinching at about onemicrosecond.

The discharge current along the axis is not zerowhen the total secondary current passes through zero.

ью-Í9l e

1 б

24

_ v29.8kv о

-22.4 kv

34.0 kv

3 -

2 - a Primary Voltage =34.0 kv_о Primary Voltage =29.8 kvA Primary Voltage=22.4 kvi-

I J_О

24887 b

I _L3500700 1400 2100 2800

В г Axial Magnetic Field (gauss)Figure 7b. Duration of neutron burst as a function of primaryvoltage and axial Bz magnetic field. Deuterium pressure, 12.5 ¡j.

This phenomenon has been observed in the lineardischarge machine, Columbus S-4,12 and is of coursedue to finite velocity of diffusion of currents throughthe conducting medium.

Pressure and current distributions were calculatedfrom a knowledge of the magnetic fields measuredalong a minor diameter of the torus. The equationused for calculating the pressures along this diameter

where R is the major radius to the point underconsideration, A is determined by the conditionBe = 0 at R = A, and the arbitrary constant С isdetermined at some point where the pressure is known.The quantity (R2-A*)I2R is the minor radius of thetoroidal coordinate surface through the point. Theequations for the current distributions along thediameter are

and

y i e - ¿ ^ + ^pBa) (2)

(3)1 (3BZ В

Typical results of the pressure calculations are shownin Fig. 12.

An examination of the pressure profiles revealsseveral outstanding features. (1) The center of thedischarge as defined by BQ = 0 does not moveappreciably during the first half-cycle of gas currentbut is localized within less than ±1.0 cm along the


! I 1 I I I I I I I I I I I I

-7 -6 -5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 72488.8 Col I i ma tor Position Relative to Torus (cm)Figure 8. Results of neutron collimation experiment; A, verticaltraverse (each data point is obtained from averaging 10 dis-charges); B, spatial resolution of col I i mated detector for a line

source of neutrons from a Pu-Be source

axis. (2) A pressure minimum occurs on the axis andpersists during most of the first half-period. Twopressure peaks of varying amplitude are present oneach side of the pressure minimum at a radius of~2 cm. (3) Appreciable pressures of varying ampli-tude are present at the inside and outside walls.

These pressure distributions were unexpected asthey have not been obtained in toroidal machinesheretofore. The possibility exists that the assumptionsmade in the derivation of Eq. 1 are not valid and acomplete mapping of the fields is required. It isinteresting to note, however, that one possible con-figuration for the radial distribution of the emittedneutrons (see Fig. 9A) is a thin shell and thatconsequently, this shell will be found on the pressurepeaks at radius ~2 cm.

At. least three possible explanations exist for thelarge pressures calculated at the walls: (1) The dis-charge moves bodily about the tube and large inwardand outward accelerations are present as has beenobserved radially in the linear system12 (the presentdata are not sufficiently precise at this time to make amore detailed analysis); (2) High-energy runawayelectrons are contributing to the pressure by theircentrifugal force; or (3) Errors in field measurementsexist near the walls or near the probe openings in theprimary shell.

Powered Crowbar OperationFor some conditions it has been found possible to

sustain the current maximum for times as long as30 /¿sec. The current is maintained by switching an

-7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 52488,9 Torus Minor Radius (cm)

Figure 9.-Summary of analysis of data presented in Fig. 8

100

90

80

70

60

(/>50

840ш

¡£20

¡iojШ

m

g 140120

100

80

60-

40

20

—BACKWARDDIRECTION

(431 TRACKS)

—FORWARDDIRECTION

(441 TRACKS)

COCKCROFT-WALTONCALIBRATION

(431 TRACKS)

3.2 3.4 3.64)6 08 10 12 1.4 L6 1.8 20 22 24 Z6 282488.10 NEUTRON ENERGY (Mev)

Figure 10. Neutron energy distributions measured tangentially tothe torus circumference in the direction of the accelerateddeuterons and in the direction opposite to that of the accelerateddeuterons. Also pictured is a calibration measurement performedwith a monoenergetic source of neutrons from a Cockcroft-

Walton accelerator


3 0 0

-7 -6 -5 -4 -3 -2 -I 0 I 2 3 4 5 62488 il Torus Minor Rcjdius(cm)

Figure 11a. Contour plot of axial jz current density (amp/cm2) asa function of radius and time. Operating conditions: primary

voltage = 30 kv, axial Bz field = 1700 gauss, P = 12.5 p

additional 24 mf of capacitance (1.1 x 105 joules at3 kv) in parallel with the primary energy supply at thetime of the current maximum. Because of the un-expected high impedance of the discharge, the dis-charge current could be held constant by the crowbarbank only at the level corresponding to a total primaryvoltage of < 14 kv. If switching takes place at thecurrent maximum with initially 7 kv and 3 kv on theprimary and sustaining crowbar supplies respectively,the results shown in Fig. 13 are obtained. With aninitial applied secondary voltage of ~13 kv, it isobserved that the discharge current is held relativelyconstant, ~180 ka, for ~30 /xsec by the crowbarsystem.

The Вв and Bz magnetic field distributions havebeen measured as a function of time with a sustainedcrowbar operation, and the corresponding currentdensities, j z andje, calculated (Fig. 14a, b). Pressureprofiles have also been calculated. It is surprising thatfor times as long as 32 /xsec after the first currentmaximum the magnetic field distributions vary aslittle as they do. It is apparent that the axial dis-charge current remains separated from the walls for~48 /xsec after the initiation of discharge current.

A neutron yield of ~2 x 105 per burst under normal

-7 -6 - 5 - 4 - 3 - 2 - 1 0 I 2 3 4Torus Minor Radius (cm)

5 6 7

Figure 11b. Contour plot of transverse je current density (amp/cm2) as a function of radius and time. Operating conditions:primary voltage = 30 kv, axial Bz field = 1700 gauss, P = 12.5 ft

operating conditions with 13 kv applied secondaryvoltage increases with crowbar operation at 13 kv to~2xlO 6 per burst with duration increased up to<60ju,sec (Fig. 13c). The rate of neutron emissionremains relatively constant during this time. Thisresult apparently precludes explanations of neutronproduction which use shocks originating by rapid rateof rise of discharge currents or sudden applicationsof high voltages. It appears necessary that the neutron-producing mechanism be continuous for relativelylong times and that it involve no permanent break-upof the pinch structure.

During the sustained crowbar operation, a consider-able amount of energy (9.0 x 102 joules/ tsec) is beingtransferred to the discharge. No appreciable changes,however, are found during these times in the pressuredistributions. The conclusion is inescapable thatenergy is being lost by the discharge as fast as it isbeing received.

Spectral Observations

The intensities of the deuterium D^ and siliconSi II (4128 Â) lines vary with time as shown in Fig.15. The hydrogen line is initially relatively intense.Radiation from the discharge gas becomes much


-6 - 4 - 2 0 2 4 6 -6 - 4 - 2 О 2 4 6 - 6 - 4 - 2 0 2 4 62488.12 Minor Radius-cm. Minor Radius-cm. Minor Radius-cm.

Figure 12. Calculated pressure distributions as a function of radius at t = 5.0, 7.5 and 10.0 /xsec

weaker when ionization has taken place and thenbecomes very strong, presumably because theionization of hydrogen released from the walls. Thetime of onset of the silicon light is a function ofprimary voltage (Fig. la) and is associated with thebombardment of the walls by particles or radiation.

X-rays

For primary voltages above ~20 kv a short burstof X-rays, duration ~2 /¿sec, is detected outside thealuminum primary at the start of the gas current.Little or no X-ray emission of energy >50 kev occursduring the remainder of the discharge cycle. The meanenergy of the X-ray (s.) outside the aluminum primaryis 68 kev, as measured with film badges. With anapplied primary voltage of 30 kv, a maximum X-rayenergy of 0.6 Mev was determined by lead absorbers.The X-ray intensity varies widely from discharge todischarge with an average reading of ~1 mr perdischarge measured with a dosimeter placed alongsidethe torus primary.

DISCUSSION

From the above data some conclusions can bedrawn concerning the plasma confinement and heatingin Perhapsatron S-4.

Electrical Resistance

In the operation of PS-4, the electrical resistance ofthe discharge was found to be considerably largerthan expected. At the discharge current maximum(3 x 105 amp), for example, the secondary voltage was

measured to be 8.4 kv, which gives from Ohm's lawa total discharge impedance of 28 milliohms. From thejz and je current density distributions (Fig. lia, b)it would appear that there are no large fluctuations inthe current density distributions at the current maxi-mum (t = 12.5 /¿sec) indicating that at this time thereis little change in the secondary inductance and hencethe voltage drop is purely resistive. The currentchannel diameter, ~7.2 cm, is also defined by the j zdistribution. With the assumption that the electricfield is constant throughout the discharge, we calculatea resistivity of 4.0xl0~3 ohm-cm, 45° pitch of themagnetic field lines, and a corresponding electron

Figure 13. Muitibeam oscilloscope traces of sustained crowbaroperation: (a) gas discharge current, (b) secondary voltage,(c) neutron emission. Primary voltage = 14 kv, sustained crow-

bar voltage = 6 kv, Bz field = 700 gauss

304 SESSION A-10 P/2488 J. P. CONNER et ai

temperature of ~6 ev, assuming validity of theresistivity-temperature relation p = Зх 10-6/Г3/2.13

A second measurement of the discharge resistance isavailable from the performance of the dischargeduring the sustained crowbar operation. In this casethe discharge current was held essentially constantfor 30/xsec with little observed change in the j z

current distributions (Fig. 14a). The discharge currentwas 1.8 x 105 amp with a secondary voltage of ~ 5.0 kv.From the foregoing crowbar operating conditions, thetotal discharge resistance is calculated to be ~28milliohms in agreement with the calculation made atthe higher voltages and currents. At the reducedpower level required for crowbar operation the dis-charge remains remarkably free from impurityradiation for ~40 /¿sec. This enables us to rejectimpurities as a serious contributor to the highresistivity.

A more precise and meaningful measurement of theresistivity of the discharge can be made with theknowledge of the Be and Bz distributions. The electricfields and current densities parallel to the magneticfield can be calculated throughout the discharge andfrom these data changes in the resistivity obtained as

a function of time. These calculations are now beingmade but no results are available at this time.

In summary, the experimental results indicate thatthe apparent resistivity of the discharge is large(4.0 x 10~3 ohm-cm) with a corresponding low, ~6 ev,electron temperature. It should be emphasized, how-ever, that these calculations use the simplified Ohm'slaw relation for the plasma,13 ignoring, in particular,velocity terms that would exist in the presence ofplasma waves or turbulent conditions.

Energy BalanceIt is instructive to account for the energy taken

from the capacitor banks during the discharge. WithPS-4 operating at 15 kv, the energy deposited in thevarious sections of the machine at a time of 6 /¿sechas been calculated. The results are summarized inTable 1.

If the remaining energy, 7180 joules, were used toheat all the gas initially present in the torus, a plasmatemperature of ~760 ev would exist at 6 /¿sec in thedischarge cycle. This result is clearly incompatiblewith the ~6-ev electron temperatures calculated fromthe resistivity.

i i i i i i i

Torus Minor Radius (cm)

Figure 14a. Contour plot of axial jz current density (amp/cm2) asa function of time and radius for sustained crowbar operation.Primary voltage = 14 kv, sustained crowbar voltage = 6 kv,

Bz field = 700 gauss, and P = 12.5 ¿t

-7 -6 -5 -4 -3 -2 -I 0 I 2 3 4 5 6 7Torus Minor Radius (cm)

Figure 14b. Contour plot of preliminary transverse ¡в currentdensity (amp/cm2) data as a function of radius and time forsustained crowbar operation. Primary voltage = 14 kv, sustained

crowbar voltage = 6 kv, Bz field = 700 gauss, and P = 12.5 /A


Table 1

Initial energy in condenser bank 50,600 joulesEnergy remaining in condenser bank a t 6 ftsec . . . . 28,200 joulesEnergy in external inductance 2,760 joulesMagnetic field energy associated with discharge,

S(Be2l87T)dV+S{Bz2l87r)dV-S(Bzo2l8<7r)dV 11,620 joules

Resistance losses 540 joulesEnergy in primary inductance 300 joules

Total 50,600 joules 43,420 joulesEnergy unaccounted for 7,180 joules

The sustained crowbar operation gives us additionalinformation as to the problem of heating the plasma.With a constant current of 1.8 x 105 amp the secondaryvoltage remains essentially constant at 5.0 kv for~30 fisec. Energy is then being transferred to thedischarge at the rate of approximately (1.8 xlO5)(5 x 103) x 10"6 = 900 joules/jLtsec. The calculatedcurrent density distributions (Fig. 14a, b) indicate thatthis energy is not appearing in the magnetic field sincethese distributions do not change appreciably duringthis time interval. The energy must then be given tothe gas at the rate of 95 ev per particle per /¿sec. How-ever, the calculated pressures during this time intervaldo not rise appreciably nor does the rate of neutronproduction increase as would be expected from asteadily increasing temperature.

These arguments lead to the obvious conclusionthat there are mechanisms at work by which energyis being continuously drained from the discharge. Themagnetic probe measurements indicate that the dis-charge current is at least grossly confined away fromthe tube walls, but the experimental results demon-strate that the energy transferred to the plasma is notconfined. The nature of the loss mechanism is not yetknown though it is suspected that loss by escape ofenergetic particles across the confining magneticfield, particle acceleration by the electric field, andloss by radiation generated by plasma waves andturbulence may be contributing factors.

Pressure Balance Results

The pressure distributions calculated from themeasured magnetic field distributions in PS-4 show, ingeneral, a pressure maximum at a radius of ~2 cm.With a pressure minimum on the axis it can be con-cluded that the pressure difference between the peakpressure and the axial pressure is not a result offorces such as those produced by runaway electrons.The pressure differences between the peaks and theminima at the axis vary up to ~2.5 atmospheres withcorresponding energy densities of 0.25 joules/cm3.It is not clear whether this energy exists as gasturbulence, shock waves, plasma waves, or as thermalmotion of the gas particles. If it is assumed that allthe gas is confined uniformly in a rod of diameter3.5 cm, and that an energy density of 0.25 joules/cm3

is expended in thermal motion of the gas particleswithin the rod, then a temperature of 220 ev isdeduced from the pressure measurements. Thistemperature is perhaps low since considerablepressures are observed between 3.5 cm radius and the

wall, which indicates that all the gas may not beconfined within the 3.5 cm radius.

A temperature of 220 ev is not sufficient to explainthe PS-4 neutron yield based on thermonuclearreaction considerations although, as stated above, theresults of the collimated neutron observations across aminor diameter suggest that the neutrons are pro-duced in the measured high-pressure regions of thedischarge.

Neutron Energy DistributionsThe energy shifts in the neutron energy distribu-

tions described earlier in this report show conclusivelythat most of the neutrons are generated by reactingdeuterons having a center-of-mass velocity of~5x 107 cm/sec.

Two possible mechanisms representing extremes ofviewpoints can be considered by which the neutronsmay be produced with the observed center-of-massvelocity: (1) a simple acceleration process in which10-kev deuterons, which are a small fraction of thetotal deuterons present in the torus, react with theremaining deuterons at rest, and (2) a streaming ofdeuterons of velocity 5 x 107 cm/sec reacting witheach other by their relative velocities.

(1) In the acceleration process we can calculate thecurrent of 10-kev deuterons required to produce theobserved neutron yield. With an initial gas pressure of12.5 /x and an assumed compression of ten, a deuteroncurrent of ~ 370 amp is required to give the observedrate of neutron production of ~5 x 1011 neutrons/sec.(If a smaller compression is assumed, the current

Time Dependent Spectrum

Hydrogen (H^)

X = 4861 Â

Silicon И

X = 4I28 Д

4 0 50 60Microseconds

80 90 100

Figure 15. Intensity distribution of deuterium (D^, 4861 Â) andSi II (4128 Â) light as a function of time. Primary voltage = 30 kv,

axial Bz field = 1700 gauss, P = 12.5 ¿t


will increase inversely as the compression.) Thepercentage of the total number of deuterons presentin the torus which would contribute to this currentwould be small, ~0.02%, and the energy required toaccelerate them to 10 kev quite reasonable, ~ 8 joules.

Possibly the strongest argument that can be madeagainst this process of neutron production is that therequired deuteron current is too large. If conservationof momentum is to occur in the discharge, then theratio of the deuteron and electron currents should beinversely proportional to their masses. With a totaldischarge current of 300 ka, the deuteron currentwould be only 80 amp.

The above calculation of the required deuteroncurrent has assumed that all the accelerated deuteronshave an energy of 10 kev, corresponding to the peakin the neutron energy distribution. This may well bein error since comparable numbers of lower-energydeuterons may be present, which would not con-tribute much to the total neutron yield since thecross section is such a rapidly increasing function ofenergy. Unfortunately the cloud chamber data arenot sufficiently precise to permit a deuteron energydistribution to be calculated.

(2) If it is assumed that deuterons are streamingparallel to the axis of the torus it can be shown thatthe deuterons in the gas cannot all have the indicatedvelocity of 5xlO 7 cm/sec (~2.5 kev energy). Toaccelerate all the deuterons to this energy, a totalenergy of 1.2 xlO4 joules is required. In the energybalance consideration discussed above, only 7.2 x 103

joules are available for translational kinetic energy.One must then conclude that only a fraction, 60% atmost, of the deuterons could cooperate in this process.A difficulty arises in that this number of deuteronstraveling at a velocity of 5 x 107 cm/sec would producea current of 6.5 x 106 amp. In order to be consistentwith the observed current and momentum conserva-tion, the steady deuteron current must not exceed80 amp. The pressure distribution also establishes alimit on the maximum temperature and density whichcan exist. We must then conclude if hypothesis (2) iscorrect that in order to be consistent with current and

energy balance the reaction must proceed at largerelative deuteron velocities in a small fraction of thetotal gas. The necessarily high transient pressureswhich would then exist would not be observed by thepresent techniques. This highly localized source ofneutrons receives some experimental confirmation inthat, during the collimated neutron measurements, ata given coñimator position, the numbers of neutronsdetected on successive discharges frequently varies bya factor of three.

Further experiments may reveal that the modelsdeveloped above are gross oversimplifications of thetrue mechanism for neutron production in PS-4.

SUMMARY

The preceding comments may be summarized asfollows:

(1) The discharge has been stabilized in a gross sense(the discharge current confined from the walls) fortimes ~48 /¿sec.

(2) From the measured resistivity of the dischargethe electron temperature is ~ 6 ev.

(3) By some as yet unknown mechanism, energy isbeing lost by the discharge at a rate of ~ 900 joules//¿sec under certain operating conditions.

(4) Maximum gas pressures of ~2.5 atmospheresare measured during the current cycle.

(5) There is a center-of-mass velocity of ~ 5 x l O 7

cm/sec of the reacting deuterons which produce theneutrons. The mechanism responsible for the pro-duction of these neutrons is not clear.

ACKNOWLEDGEMENTS

We wish to thank J. L. Tuck for helpful discussionsduring the course of this work and to acknowledge thecooperation of L. C. Burkhardt and R. H. Lovbergfor the magnetic probe assemblies, of J. W. Matherfor scientific assistance, of H. J. Longley, and T. L.Jordan for assistance with the calculations, of R. S.Dike for the engineering design, and of R. Holm andA. Schofield for the electrical design.

REFERENCES

1. P. С Thonemann et al., Nature, 181, 217 (1958).2. N. L. Allen et al., Nature, 181, 222 (1958).3. L. С Burkhardt and R. H. Lovberg, Nature, 181, 228

(1958).4. J. L. Honsaker et al., Nature, 181, 231 (1958).5. A. L. Bezbachenko et al., Atomnaya Energ., 1, No. 5, 26

(1956).6. S. Colgate, University of California Radiation Laboratory,

Livermore, California (private communication).7. M. Kruskal and M. Schwarzchild, Proc. Roy. Soc. A, 348,

223 (1954).

8. M. Kruskal and J. L. Tuck, Los Alamos Scientific Labora-tory Report LA-1716, Proc. Roy. Soc. (to be published).

9. R. J. Tayler, Proc. Phys. Soc. B, 70, 1049 (1957).10. M. Rosenbluth, Los Alamos Scientific Laboratory Report

LA-2030, Proceedings of the Venice Conference (1957).11. V. D. Shafranov, Atomnaya Energ., 5, 709 (1956).12. L. C. Burkhardt and R. H. Lovberg, Field Configurations

and Stability Studies of a Linear Discharge, P/2395,Vol. 32, these Proceedings.

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


Mr. Phillips presented Paper P/2488, above, at theConference and added the following remarks :

The first theory is that, although the pinched dis-charge has been grossly stabilized, there still remainlocal surface instabilities as observed by Burkhardtand Lovberg.12 This would be expected to increase theresistivity and give high local energy densities.Recently a possible stable configuration has beenderived, using the stability criteria of Dr. B. Suydamffor mixed BQ and Bz fields. The assumptions are

f Paper P/1364, Session A-5, Vol. 31, these Proceedings.

(1) uniform axial current density in the pincheddischarge and (2) a negative pressure gradient out-ward everywhere. The results show that a reverselongitudinal magnetic field outside the dischargemarkedly increases the pressure that can be confined.

The remaining theory is that the energy losses aredue to plasma vibrations excited by the electroncurrent, as discussed by Akhiezer, Faynberg, Luchinaand Gordayev in the USSR and, recently, by Bune-mann and Tuck in the USA. The disturbing implica-tions are that, if such plasma vibrations exist in gasdischarge systems, the stabilized pinch discharge isin serious difficulty.

operational characteristics of the stabilized toroidal ... 1958/papers... · calculation (fig. 9a)...

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