Confinement of a fusion plasma by a cold gas blanket

BOYE AHLBORN De/)rrrfrnenr ({f'Physics, The U t ~ i ~ ~ e r : ~ i f ~ l ~f'Bt.iri.sh Colrrmbicr, Vc~ncor ,~ ,er , B . C . , Ctrrroda V6T 1 W5

Received January 14, 1977

The particle end losses from a linear magnetic fusion reactor can be suppressed by establishing an ablation front in a cold gas blanket. The power density W(W/cmZ) to drive the thermal front may be drawn from inside (energy end losses) or outside (auxiliary heating). With W below lo9 W/cm2 and a D-T blanket the particle outflow is retarded. With higher W values the flow is completely stopped and the fusion plasma is recompressed by a shock wave traveling inwards from the ends.

Les pertes de particules aux extremites d'un reacteur i fusion rectiligne i~ confinement magnet iq~~e peuvent etre eliminees en etablissant un front d'ablation dans Ltne couche de gaz froid. La densite de puissante W (M'/cm2) requise po~rrmaintenirle front thermique peut etre tiree de I'interieur (pertes d'energie par les bouts) ou de I'exterieur (chauffage auxiliaire). Avec W au-dessous de lo9 R'/cm2 et une couche D-T, I'ecoulement de particules vers I'exterieur est retarde. Avec des va1e~11.s plus elevees pour W. I'ecoulement est completement stoppe. et le plasma de fusion est recornprime par une onde cle choc se propageant vers I'interieur ir partirdes extrCniites.

Can. J . I ' I1yb . .55 . 1047 (1977) [Ttxduit pal le journal]

I. Introduction There is a growing interest in a fusion scheme

initially suggested by Dawson et 01. (1971), in which a high beta plasma is confined by a straight magnetic field and heated up t o fusion tempera- tures by the absorption of CO, laser radiation. In a prototype of such a device a 10 keV plasma with an electron density of 1 2 , = 3 x I O l 7 would be confined by a 500 k G magnetic field of - 1 cin2 cross section and - 10%m length. CO, lasers within the reach oftoday's technology could deliver the power to heat this underdense plasma. Theoretical and experimental studies have shown that the laser beam can be confined to the axis (Steinhauer and Ahlstrom 1971b; Burnett and Offenberger 1974), and that the total volume can be quickly heated to high and uni- form temperatures by a laser pulse of increasing intensity, which drives a supersonic radiation

-. - front along the axis.(Steinhauer and Ahlstrom 197 In; Steinhauer 1975 ; Burnett and Offenberger 1976; Vagners et al. 1976).

The large length of the reactor is required mainly in order to reach in an open ended con- figuration the Lawson condition for a confine- ment time of about I Ins. However, much shorter reactors would suffice if it were possible t o elimi- nate the particle end losses. Most recently it has been suggested t o close temporarily the reactor ends by solid walls or by a 'plug' or a blanket of cold gas of density p t and first experiments and

inodel calculations have been reported (Johnson and Chu 1976; Steinhauer 1976; Schaffer 1976; Coin~nisso et 01. 1976; Malone and Morse 1976). I t is easy to see how such a cold gas blanket could prevent the plasma from escaping: When the cold gas is brought in contact with the plasma, the nearest layer will quickly be heated to high temperatures. This increases the pressure p , in the heated layer, launching a shock wave which travels into the cold gas, similar to the manner in which a shock wave is often produced by laser heating of a solid target. If p , is chosen high enough and the heat flux W is large, the pressure p , in the heated region will rise above the pressure p, in the fusion plasma. In this case another shock wave will propagate backwards into the plasma providing additional heating and c o ~ n p r e s s i o ~ ~ . In fact it is the thrust created with its own heat losses that keeps the fusion plasma temporarily confined. If p , and (or) W are low, p , will stay below p, and a flow field develops like that in a pressure driven sllock tube with a hot driver gas (the fusion plasma), where a rarefac- tion wave moves into the driver medium and the contact surface between driver and test gas (the cold blanket material) moves outwards pushing a shock through the blanket gas. Only for a particular blanket gas density p ,* , which de- pends 011 the power flux W, can one obtain p , = p,. For this case of 'pressure matching' the fusion plasma is neither shock co~npressed nor

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1048 C A N . J. PHYS. VOL. 55. 1977

expanded by a rarefaction wave. The contact surface is at rest and the particle velocity on either side of it is zero. Although the scheme of plugging the open ends of a linear fusion reactor with cold gas does not exactly eliminate particle motion in axial direction but rather substitutes the end losses of the fusion plasma by the end losses of the shock compressed blanket gas, it suffices for temporary confinement, which can be made to last for many milliseconds. Since the scheme requires only that the blanket gas density and the power losses from the fusion plasma are sufficiently high, it may apply in general to other open ended high beta fusion systems.

In order to assess the constraints placed on heat flux and blanket gas density for successful cold gas plugging of a fusion reactor, we have developed an analytical model using the concept of a step heat wave (Ahlborn and Strachan 1973) for the description of the shock compressed zone. Since the shock velocity depends in a simple way on the power flux absorbed in the blanket, the results may also be used to infer the reactor heat losses from a measurement of the shock front velocity.

11. The Heat Wave Model The problem at hand is to prevent the motion

of hot plasma of high pressure by a 'wall' of cold gas of density p,. The flux of power, W, (W/cm2) from the plasma to the blanket gas will heat suc- cessive layers of the cold gas to high tempera- tures, so that Twill vary steadily from the maxi- mum value in the fusion plasma to room tem- perature outside. Since the thermal conductivity increases strongly with T, there must be a very rapid temperature drop over a short distance somewhere in the blanket gas. The place where this happens may be considered as the front of a thermal wave, or heat wave, and we will approxi- mate the temperature profile of the heat wave by - -

--"" "2 step fundtib'n'. The quantity IV is the net power flux which is absorbed in the heat wave and be- comes hydrodynamically effective. W includes power which is delivered by radiation and by thermal conduction of electrons, hydrogen ions, and alpha particles. Photons and particles (fusion neutrons) which are not absorbed in the ablation front do not contribute to W, but W could be augmented by external heat sources. Since the strong lontigudinal magnetic field grossly inhibits all transverse particle motion we assume strictly one-dimensional motion in x-direction throughout. This assumption should

be well satisfied where the induced shock ionizes the stopper gas completely. It is only an approxi- mation for high blanket gas densities (see later). Depending on the magnitude of the parameter I v p , the heat wave may be of the subsonic or of the supersonic type. For the purpose of elimi- nating the end losses of a fusion reactor it is essential to establish a subsonic heat wave with its leading shock. One must strictly avoid cre- ating a supersonic heat wave since the outflow of hot plasma cannot be avoided with this type of wave. The subsonic heat wave is always cre- ated together with its shock, but we will later sometimes consider the heating zone by itself and refer to it as the 'ablation front.' This name is appropriate because due to the heating the specific volume of the blanket gas is greatly in- creased at this place, resembling the ablation of atoms from a solid under the influence of power absorption.

In the real physical situation the cold gas blanket would be injected, possibly by puff fill- ing, so that the density would increase gradually in space and time from the reactor density, p,, to the blanket density, p,. The full wave struc- ture, consisting of the ablation front and the leading shock would develop into a steady state during a start-up phase. The situation is idealized here by neglecting the initial phase and assuming that at a time to a fusion reactor plasma of pres- sure p, and enthalpy 11, is suddenly brought into contact with a cold blanket gas of density p, (Fig. la). A steady power flux W is assumed to enter the blanket gas, establishing without delay an ablation front and the leading shock. All fronts are assumed to be narrow and plane step discontinuities as indicated in Fig. Ib. We as- sume further that we can apply the integral con- servation equations of mass ~nomentum and energy across each front. These equations are written in the front frame of reference, where the region ahead of the discontinuity is labelled with the index a and the region behind it with the index b

The energy source term W,,/p,V, has to be in- cluded only at the ablation front, i.e., we assume here W,, = W,, = W,, = 0. V, and Vb are the

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,fusion plasma ,cold D T g a s

AH LBORN

h eat wave

contcct surface \ [shock <L,fJ <3CS <i?>

P ; P q ( b )

FIG. I. Uniform fusion plasma, region f, confined by a cold (D-T) gas blanket, region I in the case of pressure matching, p4 = PC. (0) Initial condition for pressure p , density p, and temperature T. (6) Wave structure obtained for pressure matching p4 = pr. (1,2) shock wave, (3,4) sitbsonic heat wave, (4,f) contact surface. 1 1 : particle velocity.

flow velocities relative to the nearest discon- tinuity (a,b). p, y , and k are density, pressure, [3b] --- PO P b - l + g a ~ . ' ( l - f i )

and enthalpy respectively. In addition the equa- tion of state where

is used, which contains all the thermodynamics of dissociation and ionization in the numerical value of the enthalpy coefficient, g, which is here considered to be constant. If required this am- biguity could be eliminated by a simple iteration (Ahlborn 1975). This set of equations will now be used to describe the parameters of the heat wave as function of the (free variable) density p, of the blanket gas and the (possibly unknown)

- - power density W. We leave W a s a free param-

.I -. .. eter ij7 Z d e r to study ~ts'influence on the motion so that the best value for p, may be selected later. The procedure followed here is very similar to the study of radiation fronts behind windows (Ahlborn and Zuzak 1969). Initially the equa- tions are solved formally for the ratios of pres- sure and density across the discontinuity:

and

E vanishes for any one of the three conditions g, = gb, M,2 << 1, and M: >> 1, and will be neglected in the following. Equations 3a and 3b contain the well known shock jump relations assuming WOb = 0, M: >> 1 and choosing the + sign in front of the square root, namely

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1050 CAN. J . Pt lYS. 1

The Chapman-Jouguet conditions in which the ablation front has managed to catch up to the leading shock are obtained with [ ~ C I ] and [3b] when the square root is zero, so that W = W,,. The subsonic heat waves which are of prime con- cern here, are found assuming M 2 << 1 and choosing the negative sign in [3a] and [3b]. How- ever, in most calculations we will not use the quadratic equations but apply linear approxima- tions, which are valid as long as

For the many iinportant situations where this is satisfied we can expand the square root in [3n] and use the linear approximations

Notice that p, -- p, since the second term in [IOa] is sinall compared to 1 as long as [7] is satisfied. One can also show that the pressure ratio must be confined t o the range

The lower limit of this ratio is attained when the ablation front has caught up to the shock, i.e., in the case of a Chapman-Jouguet heat wave. With these solutio~ls of the conservation equa- tions we will now investigate the problem of axial confinement of fusion plasmas.

111. Pressure Matching One of the objectives of this study is t o find

-- -.the reginit -of blanket gas density in which the fusion plasma can be confined by the thrust created with its own heat losses. One of the limits of this confinenlent regime is found with the con- dition that the pressure in the exhaust gases of the ablation front (region 4) rises exactly to the pressure p, in the plasma

In this case of perfect 'pressure lnatching' the contact surface (4,f) must be at rest and the particle velocity on either side 11, and u, must be

zero. Only the shock compressed blanket mate- rial in region 2 is in motion. It has a bulk velocity zi2 in +x direction, as indicated in Fig. lb. The intake and exhaust velocities of the two fronts are related as

The stopping gas density required to attain this condition is indicated by an asterisk, pl* . (1,2) is a strong shock, and (3,4) a subsonic heat wave, which is in a wide regime well described by the linear approximations [8] to [lo]. Notice that pressure, density, and enthalpy are the same in regions 2 and 3, i.e., p , = y , , = li,, and p 2 = p , , but the relative particle velocities V2 and V , are different because the exhaust velocity from the shock V 2 is referenced to the front (1,2), but the intake velocity of the heat wave V 3 is referenced to the front (3,4).

From [8] and [ l l ] and with the help of the strong shock relation [46] one finds

and with the strong shock relation [5] it follows

and further from [9]

In addition one can show that p217, = p4h4 so that

I t can be seen from [lob] that the pressure drop across the ablation front is very small in the en- tire subsonic regime. The upper limit is of interest here, and assuming that the pressure is matched in regions f and 4 we have

1161 P2 134 = Pf

Equation 13 is now used t o determine the density p l * necessary to obtain perfect pressure match- ing for the heat flux W.

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and with [12] we find the shock front velocity in the case of pressure matching

The stopping distance 1 = V,*t , namely the dis- tance through which the shock travels during the confinement tinie t is now easily found with [IS]. It is also of interest t o see how high the enthalpy 11, rises due to shock compression. I t can be found froin [6] once VlS : is available. All these parameters are shown as functions of Win Fig. 2. In this case g, = 513 and g2 = 1.2 were chosen but the results are not very dependent on the magnitude of g,. As long as the shock is de- tached from the subsonic heat wave, the pressure in regions 2 and 4 and hence the conditions for pressure balance can be determined without knowledge of the enthalpy behind the heat wave in region 4. However, as W is increased the ablation front will catch up to the sliock and the region 2 will disappear. When this has happened the wave has the properties of a Chapman- Jouguet detonation, the speed of which depends uniquely upon the enthalpy behind it:

The pressure behind the Chapman-Jouguet heating front is

and the power input W = WcJ is found fro111 [7a] as

The lowest density p,$: for which the pressure behind the heat wave can be brought up to pf is found for the maximuln velocity or the highest enthalpy 17, behind tlie wave. The limit must be h, = 17,, and one finds in this case p,*(min) = 1.5 x g/cm3, bVCJ = 10" W/cm2, and Vc, = 1.3 x 10' cm/s. These values are shown as end points in Fig. 2. The dashed sections are interpolated to colinect the region where the linear approximations apply. One has p 4 = pf on the curve p,*(l.V). T o the left o f i t one

FIG. 2. Blanket gas density p," for press~lre matching p, = pl = loJ atm, pl = 1.2 x l o d G g/cm3, shock front velocity V," , and enthalpy /12* as f ~ ~ n c t i o n s of net power CV absorbed in the heat wave. FLIII circles: CJ values for which p4 = pr and 11, = / ir = lo9 J/g.

hasp , < p, and the fusion plasma acts like the hot driver gas in a pressure driven sliock tube. On the right of it one hasp, > y, so that tein- porary confinenient by a cold gas blanket is pos- sible.

1V. Temporary Confinement with Shock Compression

If one chooses a blanket gas density which is higher than p," for a given power flux, the shock will travel slower tlian V," but the pressure p , will rise above the value p,. In this case a re- flected pressure wave niust start from tlie contact surface, and travel into tlie fusion plasma. I t will be a shock if p , >> y,, and a new zone of sliock compressed plasma (region 5) will be created, see Fig. 3. The additioiial shock heating ]nay be a beneficial side effect of providing axial confine- ment with a cold gas blanket. Of course if p, < p,* is chosen, a rarefaction wave will travel into the reactor plasma, and one has a (somewhat re- tarded) escape of fusion plasma out of the ends.

In order to study the conditions in the region of confinenient we assume that a weak shock (5,f) with a front velocity V, is established. In all likelihood this will not be an adiabatic shock but there should be some absorption of power W,,,

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1052 C A N . J . PHYS.

Contact Surface

<f.5> <45> (3.0 (1.2)

FIG. 3. (a) Wave structure for p, > 11, at time ti. Re- gions 1, 2 ,4 blanket gas. Region f, 5 fusion plasma. (1,2> and (f,5> are shocks, (3,4> is the subsonic heat wave, and (4,s) is the contact surface. (b) Space time diagram. -- + particle path lines.

in this front. However, since the magnitude of this source term is hard to assess we will neglect it altogether so that we may obtain a t least a qualitative description of the resulting wave motion. Letting W,,, = 0 we obtain from [5] and [6] the weak shock relations for the discon- tinuity (5,f)

where

Again the leading discontinuity ( 1,2) is assumed to be a strong shock and the heat wave (3,4) is imbedded between the region of shock com- pressed blanket gas and the ablation products. The transition across it is again described by [8] to [lo].

The contact surface (4,5) now nlust move to the left and the particle velocity on either side of it, u4 = u,, is negative. This particle velocity can be linked either to the velocity of the reflected

shock (5,f), or to the velocities at the heat wave, namely

Since the pressure drops very little across the heat wave and must re~nain constant across the contact surface one hasp, - p,. This indicates that p, the ratio of plasma pressure and mag- netic field pressure is constant in the entire flow regime if the magnetic field has the same strength in the reactor and the end zone.

If the pressures are eliminated by the help of [5] and [22] one finds:

where

A second equation between V, and Vf is ob- tained by combining [4b], [8], [23], and [24]. One can solve for

so that the velocity of the reflected shock be- comes

The correction t e r m F , and 1 + F, approach 1 if both shocks are very strong. Equations 26 and 27 have been solved by successive iterations to obtain the shock velocities as functions of p, and W, assuming g, = g, = gf = 513. Lines of constant V, are shown in Fig. 4. If V, is large enough, the shock compressed gas will be fully ionized so that the approxilnation of one- dimensional flow should be quite good. In order to ionize the gas completely the enthalpy jump must provide at least the ionization energy E and dissociation energy D for each particle. One finds approxi~nately Vl i - J3(E + D/2)/1?1 (Ahlborn 1974), where n1 is the particle mass. For a D-T mixture one has Vli cz 4.4 x lo6 cm/s. Below

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AHLBORN

FIG. 4. Confinement region for a fusion plasma (with pr = 1.2 x lo-' ggicm3, = lo4 atm, a n d h, = 10"/g) a n d lines of constant shock velocity V , . p, = p , " is obtained withp, = pr; P I = p ~ , ~ , is obtained for a CJ detonation wave with 11, = A,. F o r p , i p,*, p, , , , a rarefaction wave will travel into region 4. If, is f i~nction of W only.

this velocity the shocked gas is only partially ionized. Values for V,, which depends only on W, are given on the upper scale of the graph. Using [26] we obtain the pressure and enthalpy in re- gion 2 :

- - The . . -- constants .% . e C,, aild Cz are of the order unity. They depend only on-the enthalpy coefficients. The equations 26 to 29 give a good qualitative understanding of the flow field parameters of cold gas plugging of fusion reactors. The numeri- cal values for V , and V, obtained from these equations and depicted in Fig. 4 should be used with a certain measure of caution, because we have neglected possible power absorption in the surface (5,f) and also because the linear approxi- mations [8] to [ lo] used in the derivation are only poor approximations close t o the Chap- man-Jouguet limit.

V. High Power Limit of the Confinement Regime

When the power flux becomes very large every heat wave will turn supersonic and the pressure behind it will then be independent of the power input and it will accelerate particles in its direc- tion of propagation. The limit of the supersonic regime is given by the Chapman-Jouguet con- ditions [19] to [21]. The higher the enthalpy h, the higher the power t o reach the Chapman- Jouguet conditions. The rnax i~nun~ value again will be h, = / I , , so that V,, = 1.3 x 10' cm/s. A Chapman-Jouguet detonation of this velocity can be reached with different conlbi~lations of p , and W, determined by [3c] so that

p,,,, and p,* are both plotted in Fig. 4 as func- tions of W. These two curves limit the regime in which a fusion plasma of p , = 1.2 x g/cm3, = lo4 atm, and lcT, = 10 keV can be

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1054 C A N . J . I'tlYS.

temporarily confined by a blanket of cold (D-T) gas. If for instance the heat losses from the reac- tor are W = lo9 W/cm2, and cold deuterium- tritium gas of 10 atln was injected as stopper gas (p, about g/ci1l3), a s ~ b s o n i c heat wave would be created. Since, however, the pressure p, would not rise t o the pressure p,, the fusion plasma would be able to escape in axial direction (shocktube mode). If the power losses were niuch higher but the experin~ent was operated in a regiine to the right of the line p, ,,,, a supersonic heat wave would be created. Since such a wave compresses the material a positive particle velocity L,, would be created behind the heat wave and the contact surface (4,f) would have t o move t o the right, again allowing the fusion plasma t o escape. The actual Dower losses from the fusion reactor inay be given as !,I/ = epfVE, where e N 1016 erg/g is the internal energy per gram, p, 'V g/cm3 the mass density, and VE a characteristic energy escape velocity, which we take to be larger than the thermal velocity n = 8 x lo7 cm/s of the fusion plasma con- sidered here. Hence an approximate value of W - 10" W/cin2 is found, indicating that a gas plug of any density would stop the outflow of fusion plasma under these conditions.

The outflow of plasma from an open ended high beta fusion reactor can be temporarily eliminated by a cold gas blanket since the thrust created by the heat losses produces an ablation front and one or two shocks thereby closing the end of the system. The lnechanism provides complete confineinent with negative outflow velocities and recompression in the confinement regime 10' I W 5 lo1, W/cm2 and attenuates the flow for smaller values of W (see Fig. 4). The power W driving the ablation front may be de-

., =riued from .the heat losses of the reactor or could be delivered from outside. Since the shock front velocity V , in the blanket gas depends in a

VOL. 55. 1977

unique way on the absorption, one may use a measurement of V , for the determination of W. Calculations were carried out for a laser heated solenoid reactor, but since the scheme requires only that the blanket gas density and the power loss froin the fiision reactor are sufficiently high, this model should apply also to other open ended high beta fusion systems. It should be observed that a substantial fraction of the energy lost t o the gas plug is recoverable. The directed flow in the shock heated regiine could be passed through an M H D generator section, and the hot gas itself could be used as working fluid in a ther- modynamic engine.

Acknowledgements Discussions about this topic with Drs. T. K.

Chu, A. Pietrzyk, and G. Vlases are gratefully acknowledged. AHLBORN. B. 1974. Phys. Lett. A, 49, 115.

1975. Can. J . Phys. 53. 976. AHLBORN, B. and STRACHAN, J. D. 1973. Can. J. Phys.51,

1416. AHLBORN, B. and ZUZAK, W. W. 1969. Can. J . Phys. 47,

1709. BURNETT, N. H. and OFFENBERGER. A. A. 1974. J . Appl.

Phys. 45,2155. - 1976. J. Appl. Phys. 47. 3377. COMMISSO, R. J . , EKDAHL. C. A, , MCKENNA, K . F. , and

Q U I N N . W. E. 1976. Bull. Am. Phys. Soc. Ser. 11, 21. 1035.

DAWSON. J . M.. KIDDER. R. E.. and HERTZBERG. A. 1971. A.E.C.L. Research and Development Report, MATT.- 782.

JOHNSON, L. C. and C H U , T. K. 1976. Bull. Am. Phys. Soc. Ser. II,21, 1036.

1977. Princeton University Report, PPPL-1331. Princeton University, Princeton, NJ.

MALONE, R. C. and MORSE, R. L. 1976. Bull. Am. Phys. Soc. Ser. 11.21, 1150.

SCHAFFER, M. J . 1976. Bull. Am. Phys. Soc. Ser . 11, 21. 1091.

STEINHAUER, L . C . 1975. P h y s Fluids, 18,541. - 1976. Bull. Am. Phys. Soc. Ser. 11,21, 1091. S T E I N H A U E R . L. C. and AHLSTROM. H. G. 1971rr. Phys.

Fluids, 14. XI. 1971h. Phys. Fluids. 14. 1109.

VAGNERS, J . , NEALE. R. D.. and VLASES, G. C. 1975. Phys. Fluids, 18, 1314.

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