US2969308A

US2969308A - Method of producing energetic plasma for neutron production

Info

Publication number: US2969308A
Application number: US753846A
Authority: US
Inventors: Persa R Bell; Jr Robert J Mackin
Original assignee: Individual
Current assignee: Individual
Priority date: 1958-08-07
Filing date: 1958-08-07
Publication date: 1961-01-24
Anticipated expiration: 1978-01-24
Also published as: DE1165776B; FR1234901A; GB880124A; CH370493A; BE581270A

Description

Jan. 24, 1961 P. R. BELL ET AL METHOD OF-PRODUCING ENERCETIC PLASMA FOR NEUTRON PRODUCTION Filed Aug. 7, 1958 momDOm ZO Jan. 24, 1961 P. R. BELT. ETAT. 2,969,308

METHOD OF PRODUCING ENERGETIC PLASMA FOR NEUTRON PRODUCTION Filed Aug. 7, 1958 2 Sheets-Sheet 2 MOLECULAR ION SOURCE BEK LOW ENERGY NEUTRAL SOURCEl B \PRESSUR|ZED WATER A N K E T E, TURBOl v GENERATORP :ELECTRIC v Y POWER -q E l STEAM END HEAT lEXCHANGER PLATES l INVENTORS Perso R. Bell Rober-T J. Mock/'n Jr.

BY f Fig. A/ber Simon ATTORNEY United States Patent F METHOD OF PRODUCING ENERGETIC PLASMA FOR NEUTRON PRODUCTION Persa R. Bell, Albert Simon, and Robert J. Mackin, Jr., Oak Ridge, Tenn., assignors Vto the United States of America as represented by-the United States Atomic Energy Commission Filed Aug. 7, 1958, Ser. No. 753,845

5 Claims. (Cl. 204154.2)

This invention relates to a novel device for producing energetic neutrons and for heating a plasma and method of operation thereof.

Prior work in this ield which laid the groundwork for the devices described herein consisted of the development of high-current or energetic arc discharges such as disclosed in the applications of John S. Luce, Serial No. 738,242, tiled May 27, 1958, now Patent No. 2,920,234, issued January 5, 1960, and Serial No. 748,771, led July 15, 1958, now Patent No. 2,927,232, issued March 1, 1960; the development of a method for trapping atomic ions in a magnetic field by dissociation of injected highly energetic molecular ions by an energetic arc discharge, as disclosed in the application of John S. Luce, Serial No. 728,754, filed April 15, 1958; and the development ofthe method of fburnout by ionization of neutral particles in a plasma producing device as disclosed in the application of Albert Simon, Serial No. 732,770, filed April 28, 1958.

The apparatus set forth in the application of Albert Simon, aforementioned, is useful and capable of producing an energetic plasma, but the size of the plasma produced is limited due to the relative small size of the apparatus. In order to provide a device in which a larger plasma may be obtained, it is necessary to make the de` vice much largerthan that set forth by Simon. However, iii a very large device, it is impractical to achieve burnout of the residual neutral particles, which is a prime necessitybefore a plasma can grow and thus reach a size where it produces a substantial energization of the plasma. Burnout is impractical in a larger device because suiciently large molecular ion beam currents are not readily obtainable.

Another problem which is inherent in the Simon method is the existence of the arc within the plasma boundaries. This'arc may be thought of as constituting a body which introduces impurities which'tend to cool the plasma and itfco'ntains'ions which'kare 'cooler than the plasma by several -ord'ers vof' inaig'nitiide'y The injection of highly energeti'c-io'ns 'isf'vry effective in cleaning up these impurities, but it is quite costly to feed sucient energetic fuel to a large device at a rate as fast as it is being burned.

With a knowledge of the above problems related to the apparatus set forth in the Simon application, aforementioned, in the production of substantial energization of the plasma, the problem of cleaning up impurities in such an apparatus and the feeding problem in a large device, it is a ,primaryl object of this invention to provide a controlled plasma and neutron producing device in which burnout can be achieved, a plasma grown, and a substantial quan tityof neutrons can'be produced. p

It is another object of this invention to provide a controlled plasma and neutron producing device in which the heat drain and the impurities inherent in the arc ignition can tbe disposed of.

2,969,308 Patented Jan. 24, 1961 device in which some electrical power can be produced from the reactions which take place in the plasma which is produced in the device.

These and other objects and advantages will be apparent from a consideration of the following detailed specifications and the accompanying drawings wherein:

Fig. 1 shows a longitudinal cross-sectional view of one embodiment of a controlled plasma and neutron producing device.

Fig. 2 shows a cross-sectional view of another embodiment of a controlled plasma and neutron producing device,

, and

The primary object of the invention is provision of a I method for producing an energetic plasma and for pro- Fig. 3 shows a schematic diagram of a method for converting heat from the reactions in the device of Fig. 1 into electrical power.

The objects stated above have been achieved in the present invention by providing mirror coils which provide a temporary magnetically confined subvolume region, said coils at startup having, for example, about one-fifth their normal operating values, initiating a plasma within this region by, for example, injecting high-energy molecular ions in an amount in excess of the critical input current for burnout (see the Simon application, supra, Fig. 2) into the temporary region into the path of an energetic arc such as disclosed in the aforementioned Luce applications, where a portion of the injected molecular ions are l dissociated into atomic ions, which are trapped by the temporary mirrors will be increased, say by a factor of.

about 5. Simultaneously, the arc is shut olf, high-energy injection is discontinued and injection of cold fuel at an angle greater than the critical angle for containment and through the mirror region, for example, is begun. Cold fuel as used herein is fuel of a temperature below that for optimum reaction rates, as fully discussed below. The addition of suicient cold fuel causes the temperature of the plasma to fall. The injection preferably continues until the temperature falls to that corresponding to the maximum reaction ratel for a given machine. At that time the cold feed is adjusted to maintain the optimum reaction temperature. Alter the subvolume is filled with a hot plasma, the reacting volume is gradually increased by proper manipulation of current in the magnetic coils surrounding the device and the fuel feed controlled until the entire working volume of the device is filled with an energetic plasma. Finally, the plasma temperature is reduced to an operating value corresponding to the injection of fresh fuel as rapidly as fuel is lost and burned.

A brief description of the subject matter of the aforementioned applications will now be Agiven to provide a better understanding of the operation of the instant invention. Y

In the application of John S. Luce, Serial No. 738,242, filed May 27, 1958, now Patent No. 2,920,234, issued January 5, 1960, there is disclosed an apparatus for producing an energetic carbon arc discharge suitable for dissociation of molecular ions into atomic ions. In that application, an energetic carbon are is produced between widely spaced carbon electrodes disposed in an evacuated chamber and in a strong magnetic field. At startup, gas is K fed to the face of a bored cathode, a R.F. voltage source is temporarily applied between the electrodes and a varialn the applications of John S. Luce, Serial No. 748,771;

filed July 15, 1958, now Patent No. 2,927,232, issued March 1, 1960, andPersa R. Bell andrJohn Sr. Luce, serial N0. 750,834,"1ei July 24,4 1.953, new. nare/rit ne. 2,920,235, issued January 5, 196`Q, `t`here are'disclosed apparatuses for producing ank energetic deuterium arc discharge which also suitable `for *dissociationh of niolecf` ular ions into atomic ions. VVAIn those applicationshan energeticV gas disch-arge isproduced` between a hollow elongated cup-shaped cathode electrode ancla hollow anode electrode disposed in an evacuated Chamberland in anstronglmagnetiefield. Deuterium gas is fed to the inside f .at least @ne Qf. .Sadhollow electrodes @inthe base thereofV at a controlled rate such that nearly coinplete spaceicharge neutralination occurs within thehollow cathodeandhcaduses 4the arc dischargeAto terminate froml within the hollow cathode. As in the carbon arc,rdescribed above,an. `R.F. voltage source is used to help initiate the discharge and is then disconnected. .Avatiable. `@patatinaiwtential isalSQ connected, across theA electrodes'. The deuterium arc depends upon cross` iield emission withinwthe hollow cathode. `This cross-held emissionin thevathode and the cup-shaped configuration, ofthe anode causesufeed gas to be completely ionized before it leaves the electrodes. It is this complete ionization of thehfeecl` gas` that permits the discharge to be very energetic nand to be operated under low pressure condi,-V tio ns`. Arc currents of VL00 amperes and above arcob-l tainable with this arc discharge using deuterium as a feedaas. M H In the applicationofi` JohnSLuce, Serial No. 728,754,` led,Apri ltill5-i19-5i8, there isvdisclosed ,a system for igf uiting a plasmzhofV high-energy; ions and containing the' plasma in a s trongfmagnetic field. .-In the device described in thatvlapplication, llighfenergy `molecular ions1 such as. B2i-,arei injected Vinto a confining magnetic field perpendicular to the lines `of magnetic force. At some point in the orbit of these ions in the magnetic eld, a portion of them are caused to be dissociated and/or ionized by an energetic `arc dischargeto form atomic ions.- These resu1tantatomic ions haveA one-half the momentum of the original` molecular ions,1 when said molecularions are diatomic-,Handg hencehlgtave one-half the .radiuscf curvature in theeld. VIfV thecenter of ,the orbits of these atomic ions coincides with the axis of themagnetic field, the ionscwill circulate in aringf.-` If.the centerof the orbits andthe: axisof the'machine do not coincidet the" atomic ,ion orbit center` will precess aboutthe magnetic axis., rIfhepions` will-,circulate until.a-charge exchange occurs with one of the neutral. gas atoms in the system or until some other4 process causes the ions to be lost. A

`ln the application of Albert Simon, Serial No. 732,770, field April 28, 1958, Athereis disclosed a method for de-V stroying neutralparticles `in a thermonuclear device such asw disclosed` in` the" Luce application,y Serial No. 728,754, aforementioned. In order for'plasma` to build up and becomehot, the residual neutral atoms or panticles in the device have to be destroyed and new neutral particles have to beidestroyed as fast as `they flood into the system. ATherefis a, critical: value furthe-input current of the injected. molecular ionsat which the ions burn out or ionize theneutralparticlesfas fast as they are ilooding into the plasma.` Sincewburnout is an important step in the devices,.described...herein,a detailed discussion f this principlexwillbe given below. .A

In the Simon application,` the apparatus at startupwill have, large numbers of neutral 'particles in it and these neutral particles'cwill remove hot ions from the system because of the charge exchange process. The cross sectionffor charge exchange -is a steeply decreasing'vfunction of the atomic ion velocity above about 30 kev.

However, even at 300 kev. it has a value (for deuterons is readily lost `to the system.. `The `ionization caused by thefast ion will remove many neutrals by.,.this means, since the ionization` cross section;A about 4 `1`( )1'1 om?, is more than 20 times largeas' fl'oif` charge exchange at' 300 ktv.A As statedn above, there.,is', a`criticalvalue for the input atomic current at `which the ions burnout the neutrals as fast asl they are ioodi'g-irit the plasma. Once this valuel is exc eeded ,Witheniodnsi get ahead of the neutrals and the plasma buildsy up Within the volume of containment produced by the magnetic mirror coils, hence burning out additional neutrals* Iand` the system cleans outithe n'eutrals in the plasma interior. i

To determi-ne the actual magnitude of ciiitioal current,V pressure, and other controlled condi tio1`1s,r the effect of burnout by energetic ions has` been investigated numeri'- cally. The buildup of 4ion density inthe plasma in a minier-type device such as disclosed in` the Simon application, andalso the sub-volume formed by the temporarymirros in the instantsapplication, can be expressed by the' time-dependent equatidns'i anti "0:1 u a Smic sion, current. 0f @react plasma r ensitywof neutralsuin external manifold, which is P- he probability gifu scattering into the` escape cone,

,approximately equal to LlT-cos 0c K=volume occupied by the plasma locityiofjons i,

v0 hernial Vvelooityof neutrals:4 2,..

rpoulombcross section. in the` plasma.fonscatteiingv by multiple small-angle collisions through degrees cxharae exchange. cross section' a, 4ionization cross section region bounded bya surface formingavnangle,withthe iiilul, @the critical angle-fernuntainment. This' critical angle (0) is obtained from the expression:

v ercual to the `mirror ratio; that isgthe ratio, ofhtlie in magnetic iield strength inl the mirror region, (o the axis:insideftheV rnirr'cils) tor the in 1- i i Athe Iral regionbetweii the` 4ritiirror e ex fil-'ai iajfanifld, fffrea tiliiitei fN" ab `hat,region external t6,` i .iinnei'fchinlieigbounded' by iniiei liner 7, bfies 3;' and biics'V 4, in the Simon kev., for example. The coulomb cross-section values may be computed from the formula where e is the charge on the electron, and E, is the average energy of anion in the plasma.

In the iirst equation above, the rst term on the right represents the constant source input; the second term takes into account mirror losses; and the third term represents loss by charge exchange. In the second equation above, the first term on the right represents the streaming of lneutrals into the plasma; the second term represents the outstreaming from the plasma; and the third term shows the eects of neutral burnout by ionization and charge exchange.

As discussed above, burnout occurs at the critical point at which the neutrals are being ionized at a rate equal to the rate of their entry into the system. The average number of neutrals ionized by a fast ion before the ion itself is lost can be expressed as Therefore, the critical value of input current to obtain this critical point may be expressed approximately as:

where I is the total current of neutrals streaming into the plasma as defined by the formula:

The input current Ic used is the value of atomic ion current produced as a result of dissociation and/ or ionization of the molecular ion beam. Since the neutral instreaming varies linearly with pressure, the value of critical current also varies linearly with pressure.

, Burnout is not a suddenly occuring phenomenon as the current is increased, but rather a smooth transition over a relatively narrow range of current. It has been shown that for currents well above the critical value, the steady-state neutral density, no, can be expressed as:

This shows that the neutral density approaches zero as I+ becomes very large.

Referring now to Fig. 1, which illustrates one apparatus in which the principles of this invention may be carried out, a cathode 8 `is mounted in member 33 and an anode 9 is mounted in a breeding blanket 1. It may be desirable to place the anode at the extreme right end of the reactor, outside the permanent mirror and thus to run the arc over the entire length of the machine. Gas fnom ya source 34 is fed through a tube 35 to the inside of cathode '8. An arc-initiating-assisting means such as a R.F. voltage source 36, which may be a conventional welding source, is connected at one side to cathode 8 by leads 37 and 38, and is connected at its other side to anode 9 by lead 39, switch 40, lead 41, and lead 42. An arc operating potential, such as a variable direct current source 43 is connected at one side to the cathode 8 by

leads

44 and 38, and is connected at its other side to anode 9 by lead 45, switch 46, lead 47, and lead 42. An energetic arc discharge 10, which passes through opening 28 in end plate 14, opening 29 in breeding blanket 1,v and follows the magnetic field lines as set up by the magnetic mirror coils as shown, may be initiated and sustained by apparatus such as disclosed in either of the aforementioned Luce applications.

' The reaction chamber 26 is defined by the breeding blanket 1 which is surrounded by magnetic mirror coils 6 2 and 3 and by a plurality of solenoid coils 17 disposed in end-to-end relation between the mirror coils 2 and 3,l Iand a pair of end plates 14 and 15 which are mounted by electrica-

l insulators

31 and 32, respectively, to the outside chamber wall 21. The end plates areA thus insulated so that they may become charged by ions and repel further'ions back 4into the reaction volume, and so that a current may be drained therefrom to obtain electrical power directly. The solenoid coils 17 are also used to provide the temporary mirror regions. The reaction chamber 26 is evacuated by vacuum pumps, not shown, through

tubular members

24 and 25. An outer vacuum chamber 30 which encloses the reaction vacuum chamber 26, is evacuated'by vacuum pumps not shown through

tubular members

22 and 23. High energy molecular ions, for exampleD2+ of 600 kev. energy, are injected from a source 4, through an accelerator tube 5, through tube 48, yand through an opening 16 in one of the solenoid coils 17 and the blanket 1, and then into the path of the energetic arc discharge 10, where a portion of them are dissociated to form a magnetically trapped circulating ring 7 of atomic ions in a manner set forth in the aforementioned Luce application, Serial No. 728,754. Heat from the reactions that take place in the chamber 26 and the nuclear reactions that take place in the breeding blanket 1 will be removed by circulating a pressurized liquid through tubes 18 disposed in the blanket 1, through tubes`20 disposed adjacent to the end plate 14, and through tubes 19 disposed adjacent to the end plate 15. Fig. 3 shows a schematic system forl converting this heat into electrical energy.

The accelerator tube 5, referred to above, may be energized by a conventional high voltage generator. A suitablehigh current source of molecular ions from source 4 may be provided by apparatus such as set forth on pake 18 of if it is desired to impart energy to the fuel, and through entrance conduit 49 into the plasma region. In a mirror type machine, such as illustrated in Fig. 1, it is difficult to inject Icold gas into the interior of a plasma at an angle less than the critical angle for containment due to the short life of a cold atom. The mean life of an atom in a plasma is: v

t=- nav where n is equal to the ion density, v is equal to the ion velocity, and r is equal to the ionization cross-section. The cross-section (a) is about 1016 cm.2 for the device in consideration, and t is then equal to about 10- sec. It therefore follows that the mean distance a room-temperature atom can penetrate into the plasma before it becomes ionized is -a fraction of a centimeter. Since a cold ion is incapable ofrcrossing the magnetic eld, cold atoms injected rfrom the side are prevented from reaching the plasma interior. A solution to this problem is to inject the cold fuel particles (neutrals and/or ions) through one of the mirrors at an angle greater than the critical angle for containment. This critical angle is obtained from the formula:

where R is equal to the mirror ratio as discussed above and in the aforementioned Simon application. Upon ionization, the injected particle is then trapped between the mirrors and will move into the plasma along the field lie'which it is on. Theneutral atom'trajectory may be chosen' so that this field line is an interior field line of the plasma.'A

It has been determined that a mirror ratio ofv about 3.5 to l" is required for insuring the production of a copious quantity of neutrons when a 50-50 mixture of deuterium' and tritium is used as cold fuel feed, and the magnetic field must everywhere be strong enough toy .contain most of the alpha particles' produced in AtheD-T reaction. A

D-D reaction is not possible in magnetic mirror machines withoutextremely highmirror' field ratios, which makes such a machine uneconomical;

The problem'of tritium conservation in a DT device" requires -that almost exactly one' tritium atom can be produced for every neutron produced in a` 50-50 D-T mixture. It will, in fact, be desirable to breed extra tritium to the maximum extent possible. This would necessitate surrounding the reaction tube with a blanket 1 consist -mostly of lithium. In addition to the lithium, the blanket 1' would consistof water, beryllium, andiron".

The water is used to moderate the neutrons rapidly, while the beryllium produces extra neutrons by (n, 2n) reactions. separately. The tritium thus produced in the blanket may then be recovered by conventional methods.

, VIn the apparatus, illustrated in Fig. 1, the reaction tube radius is 60 cm., the blanketthickness is 60l cm., theinner diameter of the coilsis 240 cm., the outer diameter of the coils is 480 cm., andthe length of the reaction chamber is 50 meters. 17 are not shown vin theirrtrue perspective with respect tothe radius of ,the reaction chamber 26 because of space' limitation on, the drawing.

In the initial stage of operation of the. apparatus of Fig. 1 -haying the4 dimensions referred to above, a sub-volume o f .theentire device is isolated magnetically by suitably energizing` different sections of the coils 17. An additional' temporary mirror is produced about one meter from `the mirror 2 with a mirror ratio of 3.5 to l. The temporary mirror formed by the coils `17 is shown by the dashed, bowed-in` field lines in' Figure 1. The sub-volume formed bythe temporary mirror and the permanent mirror is then Substantially equal to the reaction Vchamber of the aforementioned, Simon application., The entire eld strengthy in thisregion ,isestablishedr at aA value about 1/s of its normalgoperating value; Thus, tlie field in the' midplane of: the subfvolumeisabout 6 kilogauss on the axisV and is 21- kilogauss in the coils. .The next section of eld coils immediatelyfollowing thetemporary mirror is reversed in current direction. This is done in order to obtain some eld lines which run up into the wall region as shown by dashed lines on the drawing.

A high-energy vacuum carbon arc or hi-gh-energy deuteriumarc is now struck :between the cathode 8 and the anode9 in a manner as set forth in the aforementioned Luceapplications. Once the archas been struck, injection ofkmolecular D21' `or DT+ ions at energies of about 6O0Nkev, and a current of about one ampere or greater is begun by use of a cascade accelerator as discussed ahora The initial pressure ini the reaction chamber 26 is maintained at atvalue of about l06 mm. Hg. The injected molecular beam 6 is passedthrough the arc dischargel wheireka portion, for` example, 25%,. of the molecular ions are dissociatedand `are trapped by the magnetic field and forni` a `circulatii1g- `beam 7, of atomic ions.

The initial condition which must be attained is Vthat of burnout The pressure is low enough and the trapped beam is large enough so that the neutral particles which are ooding into the active volume are ionized by ionizationnand ,charge exchangeas fastras they enter. The

The iron is used to contain the lithium and water The width of the blanket 1 and of the coils.

. lowed by the formation of a hot plasma in the sub-volume.

The resultant ion density, isdetermined by the balance between trapped currentand mirror losses, `with theV proviso thatl/z. The term is defined as the ratio of plasma pressure `to magnetic field pressure. The unit used for these pressures is dynes per square centimeter. The

ratio of these two pressures may be obtained from the equation f-nkT/ (B2/811), where n is the particle density,

T is the temperature'in K., k is Boltzmanns constant,`

and B is the magnetic eld strength in gauss.'Y It is hoped that for values oft less than 1/2 the plasma will be held in stable equilibrium by the magnetic tield. With a field of l0 kilogauss, P=0.l5and with an input trapped current of 200 ma., the particle' density is limited by =1/z condition for energies of the order of 100 kev. or greater.

Hence, the input current may be reduced immediately after goes to 3f0kilogauss. Simultaneously, the arc is shut off,`

burnout so asuto end up, with ai plasma with a l/z.

The term P, referred to above, is the probability ofV scattering into the escape cone, as discussed above, and is approximately equal to l--cos 9c, or

For a mirror ratio of 3.531,'` which is the case for the apparatus illustrated in Fig. l`, then" P=0.15.

Immediately following the formation of the hot plasma, the .magnetic fields in Vall regions (including the temporary mirror) will b'e'inc'reased by a factor of about 5.`

Thus, the end mirror andten'iporary mirror rise `to 105 kilogaus's while' tlie rriidplane field` of the subvolumeA high-energy injection is discontinued and injection of cold` fuel.` of a l5045() mixture of deuterium and tritium is begun from source 11 and'at an angle greater than the critical angle for containment as discussed above.

, The principle reason for increasing the magnetic fields perature of the plasma to fall.

maximum reaction rate (calculated as being about 78` kev.) for the device described hereinafter. At that time; the cold feed is" adjusted to maintain the temperature It should be noted that any impurities lin the plasma that are due to the arc ignition technique will vanish rapidly after cold-fuel injection of deuterium and tritium gas is begun.

If the average energy of the plasma is above a first steady operating point (plasma temperature corresponding to thermally stable steady-state operation) and below a second steady operating point (between kev. and 122 kev. for P=0.`l5), there is an intrinsic tendency for the plasma to heat itself up. On the other hand, if

the system, this has a tendency to depress the temperature olf th'e plasma. By balancing these two effects, it is possible to ma'intaain'theaverage energy at a xed level and to .increa's the total fuel in the volume steadily. The

next stepwill than be the gradual motion of the tempor'ary mirror to the right (Fig. 1) by selective adjustment of curernt t'o the solenoid coils 17, by means, not shown, with a consequent filling of the entire working volume. This adjustment of current to the solenoid coils compriseslincreasing thecurrent t0 a coil 17 to the right of the temporary mirror region to a value so as to provide a new temporary mirrior region having a eld strength of 105 kilogauss while at `the same time reducing the curent to the coil 17 which formed the initial temporary mirror region to a value which provides a field strength of 30 kilogauss. This procedure is repeated step by step until the temporary mirror eld is finally moved adjacent to the mirorr field provided by coil 3, after which the temporary mirror field is removed by reducing the current to the coil 17 adjacent to mirror coil 3 to its normal operating value so as to provide a field `strength of 30 kilogauss. YThe hot plasma is then confined in the entire magnetic volume provided between mirror coils 2 and 3 and solenoid coils 17. As discussed below the entire device can be lled in about 45 seconds and the temporary mirrors provided by coils 17 will need no special windings, since a temporary overload of a section of winding for an interval of this duration should be of no consequence. The final step is the reduction of the plasma temperature to the rst steady operating point (calculated to be about 60 kev.);

`1 Thevtheory of the mode of operation for the balancing effect mentioned in the preceding paragraph is developed below:

Assume that the magnetic pressure remains constant and that the plasma pressure also is kept lixed. In this case, the rate of change of the number of particles in the plasma is:

Here n denotes the total ion density (n=nU-l'nT), ac is the coulomb cross section for 90-deg. scattering by repeated small-angle collisions, and v is the relative collision velocity. The injected particle current of ions is denoted by I, and V is the total volume of the plasma.

f Similarly, the time rate of change of the energy of the system, is given by the equation:

=VnDnTUDTvtEa 1 P) 2E] VMMP- Pmm, Vn%f (s) where Ea(=3.5 mev.) is the energy deposited in the gas bythe He4 reaction product, and Pbrems is the bremsstrahllklngloss.` The last term on the right represents the Workfdone against the magnetic iield by the plasma. The pressure, on the assumption that the electron and ion temperatures are equal, is 4/3n. At constant pressure,

as follows from Equation 5 by' multiplication by 7/3.

On comparison with Equationv 8, this showsthat Hence, neutral gas must be fed in at a rate specified by Equation 10, which is greater than the loss rate if f 1` The volume will increase exponentially with a .time constant T which is Naturally, by Eq. 10, the neutral feed will necessarily increase exponentially as well.

For our conditions,

f0.84 sec. and

T= 6.5 sec.

The total expansion of volume required to lill the entire device is of the order of 103. Hence, the time required is about Tm: 6.79T=45 sec.

a plus the energy needed to heat incoming cold gas particles to the temperature of theA system. The energy depositedper unit volume per unit time is nD=deuterium ion density nT= tritium ion density aDT=nuclear cross section v=relative velocity Ea=energy of charged alpha particle (=3.5 me'v.)

1-P=probability that the alpha particle is not emitted into the mirror loss cone If the plasma particles are distributed according to a Maxwell-Boltzmann law, the quantities a and v should be replaced yby av. This denotes the average of av overa Boltzmann distribution. In a mirror machine, however, there will be a peaking of the distribution toward the higher end, owing to the preferential loss of colder ions through the mirrors. For this reason, a and v will be i calculated -by assuming an isotropic one-velocity distribution of ions with an energy equal to the average energy of the plasma particles. In this casel v Hence we choose I where -=iaverage energy of an ion in the plasma MD=deuteron mass MT=trit`on mass ll By'sirnilarreasoning;'the effective bombading energy of the deuteron is The power lostper unit volume due to bremsstrahlungis Since at equilibrium the sum of the particle loss through the mirror and the loss by burning in the reaction must be equal to the input current, the input current per unlt volume is:

iiirsttrinon the right vaccounts for mirror lo'ss of fuel.

Thus, a@ is the Coulomb cross section for scattering through 90 deg., and the mirror escape probability per 90 deg. collision is denoted by P. Thesecond term accounts for fuel lost by nuclear reactions.- c

Notenthat' 'a1-mirror ratio" of 3:1` is too small to permlt operation at constant density: For amirror ratio of 3.5,- h'oweveri operation. at constantdensity is` possible at either =60 kev. or=l22 kev. Now theflower the operating temperature. of asys'tem, the' higher the: density forI fixed hi-gher'the'V specicpower in-the plasma. r[his is normally desirable, `since it results in smaller over-all devices and lwe'r capital costs.' For this reason, we choose the operation of our device to be yat =60` kev; with a mirror ratio of 3.5: l. Note also that the point f=0 is the true ignition temperature. The gas, at that temperature or above, will continue to `burn (though at a decreasing rate) in the absence of cold feed.

Once the operating temperature of theV system has been decided, the maximum density may be determined by specifying a value of the magnetic field. Assume that 3:30.000 gauss. Their B2 11cTg4-nil.;Tri/5'*` (18) where' is the maximum ratio of material pressure to magnetic pressure. Assume that a maximum value of @2f/ jean be achieved. Y Now if the electrons and ions are at the same temperature and have equal densities,

F'nnfm 19) 'Ille mean residence time in the mirror system is 1 rm (20) For P==0.l5, this yields 7:0.45 sec. (21) Finally, the specific neutron production rate is N :nDrnTcrDTv: l .5 X 1013cm.3sec.1

As the radius of the device is increased, the nuclear power yield per unit length increases as the square of the radius. On the other hand, the total magnet power required does not change as long as the ratio of outer coil radius to inner coil radius is kept fixed.

We consider the device to be a long solenoid. This approximation should be valid, except near the mirrors. In that region, the actual magnet power will be somewhat larger than that calculated by this method.

The magnetic field in a solenoid is given by the relation where J is the number of ampere turns per unit length.` If the'insideu andoutside radii of the coils are-denoted by ri` andr2, respectively, and s is' defined as a spaceV factor equal to the fraction ofthe gross cross section of thecoil which is occupied by solid conductor, then J 24. g (Timms where I is the current density in the conductor. Hence` 10B :4a-s (rg-r1) (25) The ohmic power in the coils per unit length of the sole noid'is` then` Pm=I2pV (26) where p is the resistivity ofthe conductor and V is the volumeV of the conductor per unit length of the' solenoid.

Novi V=1rs(r22r12) (27) Hence, by

Equations

25, 26 and 27, the magnet power per unit length of the solenoid may be written as wie e i Pm- 41:-(12-108 (28) The resistivity of copper at 20 C. is about 2x10 ohm-cm1. In addition, as will be' seen, the power density in' the coilsv will be quite low. Hence, thef space factor We assume' .910.8'. The' choiceof;`

canlbe fairly la'rge'. rZ/rl` is somewhat arbitrary. Large values of` this ratio yield low values of the total magnet power, but at the expense of large capital investments in copper. We' assume that r2/r1=2 will be a reasonable choice.

For a eld of 30 kilogauss, we obtain Average plasma energy 60 kev.

Mirror ratio 3.5 to 1. Fuel composition 50% D, 50% T. Ion density 1.35 1014 ions/cm3. Magnet field (solenoid) 30 kilogauss. 1/2 Meanresidence time 0.45 sec. Specific neutron produc- 1 tion 1.5 1013 neutrons/cm/see. Plasma `radius t 38crn. Reaction tube radius 60 cm. Flux A,on reaction tube v wall 6.05 X 1013 neutrons/cm/sec. Magnet power 1.34 mw./ m. Blanket composition Li, H2O, Be, Fe. Blanket thickness 60 cm. Coil LD. 240 cm. Coil O D. 480cm. Length 50 m. Total heat power 402 Vrn'w. Total magnet power 67 mw.

Total weight of copper 5.4)(103 tons.

The energetic plasma produced in the device of Fig. l will effect the production of a quantity of neutrons and a large amount of energy. In addition, energy is produced by the (n, 7) reaction in the lithium blanket. As has already been mentioned, this energy will be taken off in the form of heat from the blanket, tube wall, and end plates and will be put through a conventional heat cycle. Fig. 3 shows such a conventional heat cycle in which electrical power is produced.

For example, pressurized water ows through the coils in the blanket and those adjacent the end plates, and enters a conventional heat exchanger where it gives up its heat to generate steam. The steam drives a turbogenerator to produce electric power in the conventional manner.

The principles set forth above may be employed in a device which is toroidal in shape. This presupposes that current theoretical ideas for making a successful toroidal container are correct. Such a device is illustrated in Fig. 2. The device of Fig. 2 may involve the use of the energetic arc for substantially the full length of the re actor although operation of a shorter arc in the manner of Fig. l is also feasible. The arc is terminated after burnout followed by a magnetic field increase, and relatively low energy fuel injection is used to feed the plasma after burnout, in the same manner as set forth in the operation of Fig. l above. The arc electrodes are positioned in a region of widely diverging magnetic fields (a temporary condition) so that the field lines intersect the walls of the reaction tube. A temporary mirror region is established, as shown in Fig. 2, near the diverging region to form a static mirror region. This static mirror region is shown by the dashed bowed-in field lines adjacent to where tube 65 enters into the reaction chamber. In addition, a moveable mirror region is established to the right of the static mirror region as shown by the dashed bowed-in field lines. A small reacting plasma is initiated, by means described above for Fig. l, in the sub-volume between the static mirror and the moveable mirror. When burnout conditions have been achieved and the subvolume filled, the magnetic field is increased to the value necessary for the containment of reaction products, the arc is extinguished, cool fuel injection is substituted, and the moveable mirror is progressively moved away from the static mirror until it eventually is beside the opposite side of the diverging region. At this point, the field in the diverging region is returned to normal, and both of the mirror fields are removed. Alternately, the field in the diverging region may be returned to normal when the arc is extinguished.

In Fig. 2, a cathode electrode 55 is insulatingly mounted in a space in one of the solenoid coils 71, and anode electrode 56 is insulatingly mounted in one of the solenoid coils 71. These electrodes are so positioned that the'arc discharge 57 which is initiated between them passes through holes 75 and 76 in the blanket 70 and reaction tube 74 and then follows the magnetic field lines as shown by the dashed linesA in the figure. The reaction chamber 72 is formed by the tubular member 74 shaped in the form of a toroid as shown. This tube is surrounded by a breeding blanket 70. This blanket 70 is in turn surrounded by the solenoid coils 71. Additional coils, not shown, are provided to establish a system of transverse magnetic fields perpendicular to the axial confining field, to insure stability of the plasma. The direction of these transverse fields rotates with axial distance around the torus. A helical confining eld is Ia simple form of such transverse field, for example. Heat from the reaction tube and the reactions that take place in the blanket 70 is removed by pressurized fluid which is circulated through tubes 69 mounted in the blanket 70. This heat is then converted into electrical energy in the same manner as set forth for Fig. l above. The reaction tube is evacuated by vacuum pumps not shown, through

tubular members

67 and 68. Proper energization of the solenoid coils 71 provides the diverging magnetic fields and the temporary mirror elds as shown on the drawing. vHigh energy mo-V lecular ions are injected into subvolume 73 from a source 58, through accelerator tube 59, and through tube 60 in the form of 4a beam 61 which beam passes through arc discharge 57 where a portion of them are dissociated to form a magnetically trapped circulating beam of atomic ions 62. When burnout has been achieved, injection of high energy molecular ions may be stopped and injection ofcold fuel then started. This cold fuel during the time that a temporary mirror region exists, may be injected as a beam 66 and at an angle greater than the critical angle for containment from a source 63 through tube `64, and then through tube 65, as shown. The toroid is then filled with a plasma in a manner indicated above.

The `dimensions -for the device of Fig. 2 are substantially the same as those for Fig. 1 above and the device of Fig. 2 operates in substantially the same manner as that set forth for Fig. l above and therefore a detailed description of the operation of Fig. 2 will not be given.

If a hollow deuterium arc discharge, such as disclosed in the application of John S. Luce, Serial No. 748,771, now Patent No. 2,927,232, issued March l, 1960, aforementioned, is used in the devices of Fig. l and Fig. 2, then the magnetic mirror fields will cause the discharge to spread out in the region between the mirrors and the plasma will then be contained within the hollow arc discharge. This condition will prevent the instreaming of cold neutrals from the vessel Walls into the plasma.

This invention has been described by way of illustration rather than limitation and it should be apparent that the invention is equally applicable in fields other than those specified.

What is claimed is:

l. The method of initiating and sustaining an energetic plasma for the production of neutrons in an evacuated reaction chamber surrounded by a plurality of electromagnetic coils in end-to-end relation comprising the steps of selectively energizing some of said coils to establish a relatively large first value of containing magnetic field in a small portion of said chamber to form a magnetically contained sub-volume, said sub-volume being formed by two magnetic mirror regions spaced apart axially with a uniform magnetic field therebetween and having a mirror ratio of at least 3.5 to l; initiating an energetic arc discharge between two electrodes, said discharge passing through said sub-volume along the containing magnetic field lines; injecting a selected current of relatively highenergy molecular ions into the path of said discharge where a portion of said molecular ions are dissociated and/or ionized to form atomic ions which are trapped by said containing magnetic field to form an energetic plasma in which neutrons are produced within said sub-volume, said selected current being at least Igreater than that required for producing a current of atomic ions sufficient to achieve burnout of neutral particles in said sub-volume; increasing the magnetic field strength of said sub-volume to a value at least five times larger than said first value after said plasma is formed; simultaneously terminating said arc discharge and the injection of said high energy molecular beam, and then injecting relatively low-energy particles at a selective feed rate into said plasma until said sub-volume is filled with a plasma; then continuing said injection of said low-energy particles While at the same time periodically, step-by-step increasing the length of said magnetically contained sub-volume, each said step comprising decreasing the current flow through the coil forming one of said magnetic mirror regions to return -said one region to said uniform field strength, and simultaneously increasing the current ow through the next adjacent coil to thereby establish a mirror region in alignment with said next adjacent coil, until said sub-volume has been expanded to encompass the entire reaction chamber and is filled with an energetic plasma and a substantial quantity of neutrons.

doeegsos `2. The method set forth in' claim '1,l wherein. the reacf f tion chamber is cylindrical.

' 3;'The'method set forth rin claim r1, wherein; the reaction chamberis a torcid. f

. 4. The method set forth in claim 1, vvherein` said reec'-` 5 rtion chamber is surrounded by a .tritium breeding blanket, f and wherein the saidl method includes'the further steps of` circulating a pressurized uid through tubes disposed inl f .saidblanket to thereby remove heat caused byy reactionsy in said chamber and nuclear reactions ywithin, .said blanket,

rand converting said removed heat into' electrical energy.. l f f f f 5. Thefmethod set -forth in claim 1, whereinr said lowenergyparticles includefboth ions'and neutral particles injected at `an angle greater than the critical angle for containment.

Project-Sherwood, `Amasa S. fBishopf,'Addison Wesley f Publ.y Co., Reading, Mass., September 1958, pages '132- l Atomics andl Nuclear Energy, February 1958, pp. 58,

Nucleoncs,-February'1958, pp. 90-93, 151-155 (204- Atom, No. 25, November `1958,`Mo`nthly Information' f Bulletin of` the United. Kingdom Energy Authority,

page 13.

Claims

1. THE METHOD OF INITIATING AND SUSTAINING AN ENERGETIC PLASMA FOR THE PRODUCTION OF NEUTRONS IN AN EVACUATED REACTION CHAMBER SURROUND BY A PLURALITY OF ELECTROMAGNETIC COILS IN END-TO-END RELATION COMPRISING THE STEPS OF SELECTIVELY ENERGIZING SOME OF SAID COILS TO ESTABLISH A RELATIVELY LARGE FIRST VALUE OF CONTAINING MAGNETIC FIELD IN A SMALL PORTION OF SAID CHAMBER TO FORM A MAGNETICALLY CONTAINED SUB-VOLUME, SAID SUB-VOLUME BEING FORMED BY TWO MAGNETIC MIRROR REGIONS SPACED APART AXIALLY WITH A UNIFORM MAGNETIC FIELD THEREBETWEEN AND HAVING A MIRROR RATIO OF AT LEAST 3.5 TO 1; INITATING AN ENERGETIC ARC DISCHARGE BETWEEN TWO ELECTRODES, SAID DISCHARGE PASSING THROUGH SAID SUB-VOLUME ALONG THE CONTAINING MAGNETIC FIELD LINES; INJECTING A SELECTED CURRENT OF RELATIVELY HIGHENERGY MOLECULAR IONS INTO THE PATH OF SAID DISCHARGE WHERE A PORTION OF SAID MOLECULAR IONS ARE DISSOCIATED AND/OR IONIZED TO FORM ATOMIC IONS WHICH ARE TRAPPED BY SAID CONTAINING MAGNETIC FIELD TO FORM AN ENERGETIC PLASMA IN WHICH NEUTRONS ARE PRODUCED WITHIN SAID SUB-VOLUME, SAID SELECTED CURRENT BEING AT LEAST GREATER THAN THAT REQUIRED FOR PRODUCING A CURRENT OF ATOMIC IONS SUFFICIENT TO ACHIEVE BURNOUT OF NEUTRAL PARTICLES IN SAID SUB-VOLUME INCREASING THE MAGNETIC FIELD STRENGTH OF SAID SUB-VOLUME TO A VALUE AT LEAST FIVE TIMES LARGER THAN SAID FIRST VALUE AFTER SAID PLASMA IS FORMED; SIMULTANEOUSLY TERMINATING SAID ARC DISCHARGE AND THE INJECTION OF SAID HIGH ENERGY MOLECULAR BEAM, AND THEN INJECTING RELATIVELY LOW-ENERGY PARTICLES AT A SELECTED FEED RATE INTO SAID PLASMA UNTIL SAID SUB-VOLUME IS FILLED WITH A PLASMA; THEN CONTINUING SAID INJECTION OF SAID LOW-ENERGY PARTICLES WHILE AT THE SAME TIME PERIODICALLY, STEP-BY-STEP INCREASING THE LENGTH OF SAID MAGNETICALLY CONTAINED SUB-VOLUME, EACH SAID STEP COMPRISING DECREASING THE CURRENT FLOW THROUGH THE COIL FORMING ONE OF SAID MAGNETIC MIRROR REGIONS TO RETURN SAID ONE REGION TO SAID UNIFORM FIELD STRENGTH, AND SIMULTANEOU-SLY INCREASING THE CURRENT FLOW THROUGH THE NEXT ADJACENT COIL TO THEREBY ESTABLISH A MIRROR REGION IN ALIGNMENT WITH SAID NEXT ADJACENT COIL, UNTIL SAID SUB-VOLUME HAS BEEN EXPANDED TO ENCOMPASS THE ENTIRE REACTION CHAMBER AND EXPANDED TO ENCOMPASS THE ENTIRE REACTION CHAMBER QUANTITY OF NEUTRONS.