LLNL CompactTorusAccelerator 1990

UCRLi..7C-106121 PREPRINT

C. W. Hartman, J. L. Eddleman, J. H. Hammer, B. G. Logan,

H. S. McLean, and A. W. M61vik

This paper was Workshop on

and Fusion Applications

Acceleration of Compact Toruses

October 15-24, 1990

October 11, 1990

Varenna, Italy

”

./-

prepared for presentation at the Physics of Alternative Magnetic Confinement Schemes

This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or the University of California, and shall not be used for advertising or product endorsement purposes.

DISCLAIMER

Acceleration of Compact Toruses and Fusion Applications*

C. W. Hartman, J. L. Eddleman, J. H. Hammer, B. G. Logan, FL S. McLean, and A. W. Molvik

The Compact Torus (Spheromak-type) is a near ideal plasma

for acceleration. The fields are mcxstlygenerated

confinement conjuration by internal plasma currents, plasma confinement is toroidal, and the compact torus exhibits resiliency and stability in virtue of the “rugged=helicity invariant. Based on these considerations we are developing a coaxialrail- gun type Compact Torus Accelerator (cT’A). In the CT’A,the CT ring is formed between coaxial electrodes using a magnetized MarshaUgun, itis quasistatically “recompressed” in a conical electrode section for inductive energy storage, it is accelerated in a straight-mtid ekctrode section as in a conventional rail-gun, and it is focused to small S* and high energy and power density in a final “focus” cone section.

Abstract

Lawrence Livermore National Laboratory P.O. BOX 808,L-637 Livermore, CA 94550

The dynamics of slow precompression and acceleration have been

demonstrated experimentally in the RACE device with results in good agreement with 2-D MHD code calculations. Cl’ plasma rin~ with 100 pgrns mass have been accelerated to 40 ICJkinetic energy at 20% effidency with final velocity = 1 XI@ an/s (= 5 KeV/H+). Preliminaryfocus tests exhibit the

predicted dynamics of radius compression, deceleration, and bouncing. Compression ratios & 2-3 have been achieved.

lWorkperformedunderb auspkeaof theU.S.DqmtmentofEnergybytheUwrence LiwrmoreNationalLaboratoryundercontractW-740S-EIWM8.

A scaled-up 10-100 MJ ~A is predicted to achieve a focus radius of

several cm to deliver= 30 MJ fig kinetic energy in 5-10 nsec. This is sufficient energy, power, and power density to enable the CTA to act as a high efficiency, low cost ICF driver. Alternatively, the focused CT can form the basis for an magnetically insulated, inertial confinement fusion ~~ system. Preliminary Calculati-

of these fusion systems will be dkcussd.

The acceleration of magnetically confined plasma with subsequent

focusing offers the possibility of achieving very high power, power density and energy density with applications to soft x-ray generation, magnetically insulated ICF (MICF) and ICF. The mass of accelerated plasma, l~s to 10-2 gm, places this type accelerator intermediate between space-chargelimited accelerators (electron rina etc.) and conventional rail-gun accelerate=. Typical kinetic energy per nucleon is 10-100 keV, in the range of thermonuclear fusion requirements, while the total energy of accelerated plasma in scaled up accelerators maybe 10-100 ML in the range required for MICF and KY.

In this paper we discuss the Compact Torus Accelerator (~A),

the dynamics of accelerated Cl%, experimental studies of the CTA, and proposed fusion applications.

Introduction

The coaxial rail-gun type CTAtl~J dixussed here is shown

schematically in Fig. 1. The CI’ plasma ring acts as a moving short between

the coaxial electrodes and is accelerated by the } x k force as in the usual rail- gun. Four phases of operation of the CTA are shown. Fwt, the CI’ ring is formed using a magnetized plasma gun driven by a qaator bank dkharged across the outer two electrodes at the accelerator breach. The preestablished radial magnetic field shown in Fig. 1 is entrained by plasma and ~ field emerging from the gun to forrm after reconnection of the pdoidal field, an isolated CT plasma ring shown in the formation phase of Fig. 1. Formation

Compact Torus Accelerator Concept and Compact Torus Dynamics

.— .—. — ------ ------ ------ ------ -

Focusing

Formation

Acceleration

by helicity in@on

Following formation, an acceleration capaator bank is discharged

between the inner two ekctrodes at the breach and the ~ ring can be accelerated directly between straight coaxial ekctrodes or quasistatically precompressed in a coaxial cl-e have experimentally tested both direct acceleration and precompression.

section (compression region, Fig. 1). We

Fig. 1. Conceptual drawing of the Compact Torus Accelerator. The magnetized plasma gun utilizes the outer two coaxial electrodes at the accelerator breach.

can be fast (zfoma t~fim) as done early in our expedients, or slow (zfom z

%~ d-y>> T*)

as done presently in the experiments.

Neglecting the plasma pressure (fkcl),

the ring equation of motion is

approximately,

Mp- = L:ne lz/2- dUrn/dP - Fdrag

(l.)

where p is the ring position measured along the cone, L&e 12/2is the force

of the accelerating Bgfield generated by accelerator current I with cone

inductance per unit length L&w H/cm,Urnis the magnetic energy of the

rings, dUm/dPis the component of the radial equilibrium force along the cone, a sin8 where O= 9(P) is the cone angle and Fdrag is the drag force on the

ring exerted by the ektmdes. s Oand the component of the radial equilibrium force along the cone

For quasistatic compression Mb and Ftig are

dUm/dPis in near balance with the force of the accelerating Be field LA

12/2.Recompression Canbe SIOW(tmpion

5 %~ dmy) allowing the USe

of low voltage, low power capaator banks to store energy inductivelyprior to acceleration. On the other hand, for efficient direct acceleration without precompression dUm/dP= Oand for efficient couplin~ the arcuit time

constant~~must

be about the same as .eCTringtransit

time ~&/Vnng leading to low capacitance,high voltage driver banks because of the high velocity V*

and low m-.

After precompression the ring enters the straight coax acceleration phase of Fig. 1. Here the equilibrium force is orthogonal to the electrode surfaces so that dU~~dp = Oand acceleration takes place limited by eddy current drag on the electrodes @drag in Eq. 1I and trailing plasma emkided force which can be applied to the on the accelerating field. The no~~albd

CT ring for acceleration, K= (l-~cc12/2)f(Urn/Lring).

(B ~@&,

K<l by “blowby” of the acceleratingfield near the center electrode. The “blow-by”condition K= 1 has been obtained by 2D MHD numerical computation and verified experirnentiy. A lower upper limit on Ks 0.4

has km predictedbased on the destabilizationof shear stabilized Rayleigh- Taylor ballooning modes of the CI’ rin@J however, no clear evidence of this effect has been obtained experimentally.

is limited to

ACT ring undergdng accelerationis predicted and observed to change

shape as the poloidal field at the rear of the ring is compressed. in addition, during uniform acceleratio~ the plasma “slumps”to the rear of thering assuming an exponenti~ atmosphere distribution for the density P = I@)

exp(- inz/c~)where < =T(Y)/miJz~41 Variation of the acceleration can

provide strong heating of ions through “sloshing”of the plasma through interpenetratingion orbits or shock waves at small mean free path.

After acceleration, the high velocity ring is injected into a conical focusing region at the muzzle of the accelerator as shown in Fig. 1. Here the

terms Mp”and dUm/dPin Eq. 1 are dominant and the ring is decelerated converting the kinetic energy into magnetic energy of the CT ring with the ring velocity going to zero at a radius compression ma %tRf = 1 + Uk/Um where ~ is the radius during acceleration, Rf is the stagnation radius, and uk and Urnare the ring kinetic and magnetic energy at the entrance of the focus cone. Since U@rn G 100 is predicted, a large impression ratio can be achieved on the short timescale determined by me fig velocity to achieve very high power and energy density as shown in Fig. 2 Since the CT ring dwell time on the focus cone is very short, inertia prevents significant motion of the cone during focusing when *e ring fiel~ greatly exceed the usual material stress limits. For Fig. 2 the ring is assumed to be adiabatic so that focusing is self-similm which leads to further increases in energy and power density because of shortening of the ring length..

III.

ek-~~lon&Xa~d-20aD.

We have carried out experimental demonstrations of the CT accelerationin the RACE (for Plasma _~g &elerator ~xperiment) facility

shown in Fig. 3. The magnedzed ring-formation gun with inner and outer solenoidsis driven by the 200 KJ fast bank shown md more reoently a 260 KJ, llkVslowbar& Located inside the gun center electrode is an accelerator electrode which passes through a shielded accelerator feed insdati and Mm extends 4 m at 20 cm diameter with a 2 m cone. The outer acceleratorek?ctmde is 50 cm diameter andascon@ured in Fig.3alsoh- cone. l%e electrode assembly is located in a 5’ — base p~

in the low l@7 torr range. For plasma formation, 1-10 Atm- cms

vacuum tank with a

anwitha2mfocw

a4mstra@t

Experimental Studies of the ~A in the RACE Facility

of gas (usually Hd is admittedby 8 fast acting pulse gas valves located midway along the gun electrode as shown in Fig. 3.

focusing.

10$

10’

10°

t (its)

10-’

Fig. 2. High energy density focus example. A ~ ring with M = Id grn, V = 109 cm/s, Uk = 5 MJ, R = 5.7 an. The ring is asswned to undergo self-similar

1 1

outer solenokt

.;'''''?2z2::

Gun canter electrode

Gun tier electrode

accdemtor @ , /

pfd

jijij*

///

-4

-..-..--- = uyopump

Acceleratorouter electrode~

‘d”

To gun capacitor bank

Turbomolactdar pump

To solenold capacitor bank

i~NCryopump

h% = 50-100 cm, Um= 2-10~, ~d V*

10.03 pfd,5kV,250W[

= 2G50

111 pfd,60kV,200kJ

hitial experiments demonstrated the MHD model of CT ring

formation with parme~ cm/ps. The CT ring mass tended to be in the several x I@ gm range, dominated by O and C impurities. After successive electrode surface improvemen~ by adding Ta liners and W spray mating and discharge cleaning CT rings with M G 10-20 pgrn could be formed and accelerated.(s) The low mass, dom.inantiyH+ ion plasm Mgs could be formed only within

Fig. 3. Schematic of the RACE faality at LLNL. The accelerator electrodes, shown with a CT ring undergoing acceleration, are 4 m long with a 2 m focus cone sectiom

a limited range of parameter space with a critical dependence on forming the gun discharge just as the inlet gas crossed the interelectrode spa~.

Acceleration of low m- CT rings was achieved with trajectory results shown in Fig. 4. Here, the ring position along the accelerator is measured by B=probes locatd at the outer electrode surface and the trajectory is compared with the current sheet position calculated from the accelerator inductance and the trajectory as calculated using the CD W4C code. The RAC code solves Eq. I using external circuit parameters, it accounts fir the CT ring field decay by calculating plasma energy flows to obtain the resistivity, and RAC utilizes an eddy current model for Fdrag. ne m ring mass is assumed to be co-t with M = 8 ygm used in Fig. 4, determined using a He Ne interferrometer at z = 120 cm. The agreement obtained in Fig. 4 shows that the the acderator current flows at the ring position and that the trajectory, well described by WC, the final ring velocity WaSVring-2 xl@ cds = 16 KJ as determined by the input energy to the accelerator and the RAC code.

is consistent with constant ring mass and a low drag force. For this shot

and the kinetic energy was uk

The B=and ~ fields measured at the outer electrode by a probe at z =

124 cm are shown in Fig. 5. The BOfield is seen to increase rapidly from t = 14

to 15 w indicating a diffuse current sheath flowing at the back of the ring as expected from the current sheet trajectory. Further, the gradient of Bz has been steepened,as predicted, by the applied acceleration force. Fig. 6 shows the chord-averagedekctron density for the same short shot indicating localization of the plasma density by the ring. For the conditions of this shot the plasma density both preceding and following the ring was below

detectability &S 3 X1012 cm-30”I’heresults given by F@ 4,5, and 6 confirm

the general 2-D, MHD model of CT ring acceleration.

Interferometer ~-

cone 7-

80 -

160 ”

240 ”

andUkG@~.

1’

Time (mkroeaconda)

O-D code resuttfor M=8pgm

Current sheet posltbn from accelerator 1,V

FWHMring posltlon from magneticprobes

Energy scaling studies have been conducted for direct acceleration with s m long acceleration electrodes. me studies were conducted over a number of shots in which the accelerator bank eneqy WaS gradu~~y increased. Clean up of the electrode surfaces made it possible to achieve conditions for acceleration without strong trailing plasma k~~rference both at higher bank energy and for early gas timing as well as late gas timing. For early gas timing more efficient coupling in the gun was achieved and Urns 10 KJ could be achieved. The energy scaling res~~ givm in Fig. 7 correspond to a constant effiaency of 20%up to tie mtimum bti voltige of 100 kV. At 100 kV the accelerated ring parameters are M g 100 Pgm, urns 10 KJ, Vring G l@ ads,

Fig. 4. CT ring trajectory. The barred data are BZat the outer accelerating electrode with 0s at peak B=and barr 1’s at 1/2 BZPk. Note the shift of peak Bz to the back of the ring during strong acceleration (t = 1618 ps). The current sheet position and trajectory calculated with the WC O-D code are also shown.

—

tens of eV.

nmo (#s)

Axial magnetkfield at Z=124cm

Azimuthalmagnetk field at the same bcatbn

with BZup to 8 KG at the outw cl-e The rings undergostable, syrnmetic d-y

(~an

*---,

few x

Because of the axial locabtion

of the CT ring provided by the

precompression cone, after initial fast formation tests, slow ring fomnation@, ~fom= 50 ps, was employed. CT rings localized in the precompression cone have been _ entrance to the ~ne & = 12 ~. after the gun

turns offwithfdecay= 1oIS cm-s and the electron temperature infeIItd from t decay k a few

Typical chord-averaged density is &S

50 ~

Fig. 5. Axial (&) and timutid @e) fiekis measured at the surface of the Following energy scaling studies of direct outer electrode at z = 124 cm. as shown in Fig. 8 acceleration, the accelerating elaodes were r-figured to test the premmpression phase. The cone WaSdimetioned to provide 2:1 II .S to s.3 cm) and straight acderation sections 1 radial comp~ion

m and 2 m long were used. The accelerationelectrodes were made of copper and aluminum with W spray coating.

Fig. 6. Axial (Be) field shown in Fig. 5 and line-averaged electron density measured along a diameterat z = 124 an.

shot #256?

1.6 - — Axialmagnetk field

1.2 - ---

mdw

0.4 -

0.8 -

= u mN

*’

limo ( pa)

at Z=124cm

Chordaveraged

the same Iocatlon ,4

The dynamicsof precompressionare in good agreementwith ideal 2-D,

MHD modeling using the Lagrangian TRAC code.(~ A comparison of data with the TRAC code predictions is shown in Fig. 9. The data were obtained with 1 pH external inductance in the acmlerator bank circuit so that the current rises to peak current ins 10 P ( t = 49 ps, Hg. 9a). At t = M ps the BZ toc Oasthering iscompressed pastz=12cm. At field atz=12cmdecreases

t= 50 w the compressedring passes the small radius end of the cone (z =43 cm) and enters the accelerationsection where comparisons are made at z = 74 cm and z = 104 an. Good quantitative agreement is obtained confirming the validity of the 2-D MHD model of precompression and acceleration.

Compressed CT rings with M = 100 ~~, &2 few x 1016cm-3 B G 20 KG, kg=

30 cm have been formed and acaderated.

~ ,

i!j,:

J’

8’ #’ 1 ‘e

ukln~k-

=‘F14J-’

‘0 klnetiC’

203040506070&)

Acceleratorbank voltage (IN)

Late gas timing 0 Early gas timing

(1/25) km

Our general conclusion from the experimental studies conducted thus

far is that the compression and accelerationphases of the CTA can be described by the basic 2-D, MHD model &cussed in Section III. Preliminary tests of CT ring focusing with the electrode configuration of Fig. 1 have been inconclusive. The general dynamics of ring compression, deceleration, and bouncing in the cone are observed but the scaling of field strength and ring << ~~Om length with compression ratio for an adiabatic MHD model with ~ generallywas not observed. For the experiment~~ so that G 1/2-1/3 x~ nonadiabaticeffects can play a significant role. Further tests of focusingwill be made with a new electrode set under constructionwith kgs

Fig. 7. Energy scaling results with 5 m straight electrodes in RACE. For early gas timing gas is admitted 300 ~ before gun fire, for late timing 150 W.

Fig. 8. RACE gun and accelerator electrodes with a

precmmpressioncone.

IV.

:-i%.

Z(m)

0.s”

Uii-ii?

Isolondda

‘bL1-LJ

bank can be used.

CTA Scaling to High Energy and Fusion Applications

The MHD model of CT ring acceleration has been used to examine

‘I’heassumption is made

scaling of CI’A’S to high energy 1O-1W MJ or so. that technical problems associated with electrode surfaces, etc. can be overcome by maintaining the surface energy and power density at allowable values and by keeping the field ~lOW G 2W kG (ex@Pt for the fOCUSCOne where electrode destruction is expected each shot). A 100 MJ driver energy CTA has &en consideredwhich is predicted to produce 40 MJ kineticenergy CT rings which couldbe focused to d cm dimensions. Because of

precompression, a low voltage Mv=

‘l”he most signifbnt

cost item, the 500 kV, 100 MJ driver capacitor bank, has been estimated to crest 34M $u s in g o f f - t h e - s h e l f co m p o n e n s t o b e = 3$ /deliveredpule.

‘I’heover-all system cost is estimated

2 -

200 -

100 -

m ’

1 - o F 1

g

Accelemtorcurrent

1 I

I I

(c)

tt 1I I

----” TRAC

: pre-compreaaor

6 - — Data 4 -

’---- TRAC ; :

Tllne(j8)

2 -

12 - — Data 10 - ----- TRAC 8 - 6 - 4 -

o~ ’

Fig. 9. A comparisonof data with the precompression cone with TRAC a 2D, MHD Lagrangiancode. Lack of coinudenm at z = 104 cm is probably due to too high ring mass in the code.

: Z= 104

A high energy CTA which delivers 1015 watts/crn2 of CT ring kinetic energy in 5-10 ns can act as a driver for an MKF8) or lCF fusionsystem(g). Interestin the CTA as a driver rests on high effiaency -40%, basic simplicity,and on low cost. The accelerator would employ roughly a 100 cm to 20 cm radius precompressioncone, a 30 m long acceleration section with Be <200 KG, and a 5 m long focus cone. The two fusion applications discus~d

here are shown in Fig. 10. Fig. 10a shows a “cannonball”MICF system. Fbr Xl@cm/s, MCT<50mgm this example a CTring with Uk = 100 MJ, V&2 and Uk/UrnG 5-10 is injected into a 1 cm radius cavity in the “cannonball” containment sphere. Shock waves generated by stagnation of the CT convert Uk into Up]asm at Tis 10 keV to initiate the DT thermonuclear bum. Since Uk/Um>>1, a transitionto P G UPlasma/Um>1 OCCUrSand the plasma pressure is supported by the walls forming the MICF configuration.

Fusion Applications

IV.

In order to achieve gain Q ~ 20-30, it is necessary to refuel the DT burn.

Refuelingin the examplegiven here would be accomplishedwith DT fuel injection plugs driven by neutrcmabsorption and heating of plug casings. Alternatively, high Q predicted by diffusive refueling if the containment chamber has an initial solid DT Inning. 70 is predicted for the system considered to produce a total fusion yield of -7 GJ. The containment “mnnonbal.1”is formed of Hg and has a thickness of several 14 MeV neutron mean-frepaths cannonball which vaporizes and expands into a containment chamber to form the working gas for an MHD generator cycle.

so that the yield is deposited in the

For a burn time ~e=1 ps a gain Q =

The indirectdrive ICF application shown in Fig. 10b is estimated to

require a 40 MJ kinetic energy Cf’ring. Because of the high CTA effiaency, a gain Q ~ 50 is adequateand a 2 GJ yield is estimated. Detailed design of the indirect drive capsule, including pulse shaping is currently under study.

~//

References

(1%7).

‘\ul

DT fusl Injactlon plugs

c1 from RACE vc~ 26X103luws 40MJ

~ CT from RACE v~m22 X103km/s lW MJ

Fig. 10. Schematic drawhgs of possible MCF @lg. systems driven by the ~A.

For MICF the fusion gain Q G 70, Ef~On E 7 GJ.

lea.) md ICF Wig. lob.)

The CT ring stagnation pressure is 100 Mb. For ICF Q c 50, E~~iOn2 GJ. CTA driver costs are estimated to be 70M $(M I C F) an d 35 M$ (IC~.

A. I. Morozov, “Equilibrium Configuration of a Uniformly Accderatin~

Axisymmetric Plasma Configuration; J. of T*.

Phys. 37, No. 1, p. 79

J. H. Hammer, J. L Eddleman, and C. W 30,1449 (1985).

Hartman, Bull. Am. Phys. Soc

C. W. Hartman and J. H. H~er,

phys Rev. htt. 48,929 (IW2).

J. H. Hammer, private communication.

J. H. Hammer, C. W. Hartman, J. L. Eddleman, and H. S. McLean, Phys.

Lett. 61,2843 (1988).

A. Hasegawa, et al., “MagneticallyInsulated and Inertially Confined

Fusion MICF: Nut. FUS-28, No. 3, p. 369 (1=).

T. Kammash, D. L. Galbrtith, “A Mgh Gak Fusion Reactor based on the Magnetically Insulated Inerdal Confinement Fusion (MICF) Concept”, J. NUC. Fus. 29, No. 7, p. lo~ (1989).

B. G. Logan, evaluation of MICF and ICF Systems.

T. R Jar-w, et al, Phys. Fluids B Z, 1342 (1990).

J. L Eddleman, et al, Bull. Am. Phys. SOC34,2051 (1989).

RW.

o f

T e c h n i c a l

C a l i f o r n i a

U n i v e r s i t y

L a b o r a t o r y

L i v e r m o r e ,

I n f o r m a t i o n D e p a r t m e n t

L a w r e n c e L i v e r m o r e N a t i o n a l