Feasibility of electromagnetic separation of irradiatednuclear reactor fuel-rod components

J. Penman, B.Sc, Ph.D., C.Eng., M.I.E.E., and A.C. Williamson, B.Sc, Ph.D., C.Eng., M.I.E.E.

Indexing terms: Magnetic devices and properties, Magnetic fields

Abstract: Possibilities of electromagnetic separation of the metallic components of spent nuclear reactor fuelelements, according to the materials from which they are made, are investigated. This has advantages in thereprocessing and disposal cycle of fuel management. A design study for a prototype separator, involving nomoving parts, is described, and practical problems involved in handling hazardous materials considered.

1 Introduction

The radioactive-waste management associated with theirradiated-fuel cycle of a commercial nuclear reactor is amajor undertaking in both economic and technical terms.It is also one of the most sensitive areas of the civil nuclearprogramme, for not only must waste reprocessing andstorage be totally safe, it must also be accepted as beinghazard-free by the population at large. Here the authorsaddress themselves to one aspect of the problem of treatingspent fuel elements, in an attempt to improve the waste-storage stratagem for a civil Magnox reactor.

In the case under consideration, the fuel elements arefabricated from metallic uranium clad in a Magnox jacket.In addition to these components, the fuel units havestructural members made from graphite, zirconium, andstainless steel. There are also further Magnox assembliesthat act as separators of coolant gas flow. These auxiliarycomponents lie in the neutron flux of the reactor through-out the useful life of the fuel element, and consequentlybecome radioactive to an extent dependent on the nuclearcross-section to thermal neutrons of the material. Structuraland cladding materials are ordinarily chosen so as to havea low cross-section (in the nuclear sense), and preferenceis given to materials that do not become radioactive asa result of neutron capture, or for which the inducedradioactivity is low (unenergetic gamma radiation), orthe half life is very short. In the main, these criteria aremet by the materials mentioned above. However, stain-less steel will contain chromium and nickel, each ofwhich has intermediate values of nuclear cross-section;also the nickel may be contaminated with cobalt, whichhas a very high value of cross-section and the inducedisotope Co60 has a half life of 5-3 years, with an energeticgamma ray. Zirconium may contain traces of the elementhafnium, which has a very high nuclear cross-section.

Because these various components have differing levelsof induced radioactivity, and storage and disposal techniquesare to some extent dependent on this, it would be advan-tageous to separate them, depending on the material fromwhich they are fabricated.

When a spent fuel-rod assembly is removed from thereactor, it is usually consigned to the cooling ponds for100 days or so, to allow fission products of short half life,and beta activity, to decay almost completely. The spentfuel and the primary cladding are then sent for reprocessing,

Paper No. 877B, first received 2nd April and in revised form 9thJune 1980Dr. Williamson is and Dr. Penman was formerly with the Depart-ment of Electrical Engineering & Electronics, University ofManchester Institute of Science and Technology, Manchester,England. Dr. Penman is now with the Department of Engineering,University of Aberdeen, Aberdeen, Scotland.

IEEPROC, Vol. 127, Pt. B, No. 5, SEPTEMBER 1980

where the Magnox jacket is mechanically removed and thefuel treated chemically. Left behind are the various struc-tural components, and it is the separation of these withwhich this paper is primarily concerned. For completeness,the properties of metallic uranium are also considered. Theproblem is, therefore, to accept these components, whichhave been subjected to mechanical stripping and guillotininginto a manageable size, and to separate them in a radio-logically hazard-free way. Of primary importance is theseparation of the zirconium and stainless steel from theMagnox for the reasons outlined earlier. A further compli-cation is that, as a result of the mechanical handling, thecomponents have very different and variable geometries;the graphite tends to become a large-grained aggregate,while the zirconium and stainless steel reduce to box-typesections about 15 cm long. The Magnox flow splitters haveextremely variable shape, as they are fabricated from aneasily deformable thin ribbon of the material with spot-welded cross pieces. Initial consideration of the problem-added a further constraint. In order to minimise main-tainance and to ensure a high degree of containment for theprocess, it was decided to design a system of separationinvolving no moving parts. This leads naturally to theconsideration of electromagnetically driven systems.

2 Method of electromagnetic separation

2.1 Consideration of alternatives

Levitation comes to mind immediately when consideringpossible alternatives for the electromagnetic separation ofmetallic components of varying geometry and materialproperties. It is relatively simple to design a levitator tolift a given component a small distance, but it is not simpleto do this in a stable manner if the component geometryis irregular and variable. There is a possibility that a levitatordesigned for one specific component may attract anotherand, for levitation to heights of several centimetres (whichwould be required in this case), there is the further possi-nility that some components may melt. These aspects oflevitation are discussed in Reference 1 and 2 (the latterreference giving an extensive list of 124 other references),and lead to the conclusion that levitation is not a practicalsolution to the present problem.

A second alternative is to use coils supplied witha.c. toproduce a travelling field which will give rise to varyingforces on components according to geometry and materialproperties. If components are given a feed velocity into thesystem, either by conveyor or by gravity, then a transverseacceleration imparted by means of the travelling fieldwould cause deflection of components from the feeddirection in a selective manner.

277

0143-7038/80/050277 + 10 $01-50/0

A third alternative is the use of a d.c. field system. Thefield is distributed and angled in such a manner that thepassage of a component through it induces currents in thecomponent, which interact with the field to produce forcestransverse to the feed direction. The varying deflections canbe used for separation, as in the a.c. case.

The choice between the a.c. and d.c. alternatives is in-fluenced by the following factors:

(a) A magnetic field of a given amplitude can be estab-lished with much lower VA requirements by using d.c.rather than a.c.

(b) A consequence of (a) is that the coils producing thefield will be simpler in construction and require only alower level of insulation.

(c) A d.c.-produced field is more easily controlled inamplitude (by means of a controlled rectifier bridge)than an a.c. field.

(d) The magnetic circuit of a d.c. field system may besimpler in construction than that of an a.c. system, sincethe latter would require a completely laminated circuit.

(e) Containment of radioactive material is a prime con-sideration and will require a substantial enclosing structure;the use of an a.c. system might cause problems with eddy-current losses in such structures. The factors above militateagainst the use of a.c. systems, and encouraged the authorsto pursue the study of the d.c. system described in thispaper.Having decided to use a d.c. system, the possibility ofusing permanent magnets must be considered. Althoughpermanent magnets do not require expensive windings, andare now available with great stability and high energydensity, they do suffer the disadvantage of having noinherent mode of control. In the scheme proposed, it willbe advantageous to have control over the field strengtn inorder to adjust the transverse deflections of components; afurther advantage will be the ability to reduce the field tozero in order to release any ferrous materials which may,

by accident, appear in the feed stock. A permanent-magnetsystem would require some form of moving belt or wiper tofree it, and moving parts should be avoided, if possible, inthe radioactive areas.

2.2 Principle of angled d.c. field method

Fig. 1 defines co-ordinates used in later analyses, andalso illustrates the principle used. A component ofdimensions L x W moves, under the action of gravity,in the y direction (i.e. vertically) through a steady magneticfield. The field, which is substantially normal to the planeof x and y, varies in amplitude, in a direction z between+ B and — B, over a wavelength X. Note that the directionz is not orthogonal to x and y but is a direction in theplane of JC and y at an angle 9 to y. A line of constantB (the 'axis' of the field) is at right angles to the z direction,along the co-ordinate direction s.

If the component is nonmagnetic, the only electro-magnetic force acting upon it will be produced by aninteraction between the field B and currents induced inthe component by its motion through the field. Currentswill only be induced by the component velocity z in thei direction, since the quadrature component s is along linesof constant field strength. Hence a force F will only beproduced in the z direction by components of inducedcurrent in the s direction. F will have a component F cos 6opposing motion under gravitational acceleration, and atransverse component F sin 6, which will give an accelerationin the horizontal direction, and hence cause a transversedeflection of the trajectory.

It is shown later, in Section 3, that, for an idealisedcomponents and field geometry, the force per unit mass,or electromagnetic acceleration in the z direction, is given by

F_Ayr

M

B2 1

pa

Fig. 1 2-dimensional co-ordinate system for angled field method

278

Ki and K2 are factors each dependent only on componentand field geometries, pa is the product of electricalresistivity and density for the material of the component,and, all other things being equal, will determine the deflec-tion of the component. The values of p, a and the paproduct for those materials to be separated, plus uranium,are given in Table 1.

It can be seen from Table 1 that the differencesbetween the values of pa for those materials expected inthe mix are sufficiently great to encourage further investi-gation of the possibility. The pa products for uranium andstainless steel are very similar, but since the geometries ofthe components will be very different in the unlikely eventof uranium being present in the mix, the possibility ofsuccessful separation remains.

3 Electromagnetic forces and deflections

It will be assumed that the field is sinusoidally distributedalong the z-axis, given by B = B sin (2TTZ/X). This willunderestimate forces, since additional currents inducedby space harmonics of B will be neglected. It will also beassumed that induced currents are resistance-limited; thiswill certainly be valid for stainless-steel and zirconiumcomponents of the dimensions expected and will notintroduce serious error for the Magnox components.

IEEPROC, Vol. 127, Pt. B, No. 5, SEPTEMBER 1980

Table 1: Material properties

Material

MagnoxZirconiumStainless steel

Reactor graphite

Uranium

Density (a)

kg m"3

1-64X 103

6-5 X 103

80 X 103

1-75X 103

18-7 X 103

Resistivity (p)

ftm4-2 X 10"8

450 X 10"8

800 X 10~8

/ perpendicular ^I to grain 1020

| parallelto grain 680

V 330 X 10~8 ;

i

I 8500 X 10~8

I

po

6-9 X 10"s

2930 X 10"s

6400 X 10"s

15000 X 10"s

6150 X 10"s

3.1 Ignoring end effects

Let the component be a rectangular plate of dimensionsL and W (as shown in Fig. 1), which are very large com-pared with the wavelength X, and of uniform thickness h.Further, let the plate move at velocity i through the B-distribution, as shown in Fig. 2.

At any point in the plate there will be a motionaUyinduced electric field, the distribution of which will reflectthe distribution of B, given by

E = Bz (1)

As a result of the assumptions, the electric field will beabsorbed locally in ohmic voltage gradient Jp, where Jis the local current density. Thus, in element bz of the plate(Fig. 2), there will be a current

67 = Jhbz = —bz = — zbzP P

(2)

This current element will react with the local flux densityto give an instantaneous force per unit length 5/, opposingvelocity i , and given by

5/ = Bbl = zbzP

(3)

The instantaneous force per unit length, over a wavelengthX, is given by

rA B2hz hzB:

f =\ — - dz =Jo n o

2nzr* . 2 znz\- sin2 — dzJo \ XJ (4)

The result of integrating between these limits is to givea constant force per unit length per wavelength of

F =hzB2

(5)

L

J = B sin(2itz/A)

° z • velocity= z

Fig. 2 Configuration analysed for infinite plate

If this force is divided by the corresponding mass M of theplate per unit length over a wavelength, the result is

FM 2po

(6)

This result is independent of the sizes of the componentand field system, but only applies in the case of dimensionsL and W much greater than X.

3.2 Longitudinal end effects.

Allowance is readily made for the effect of the length W(in the z-axis), together with the effects of a central hole inthe plate. Such a shape is chosen for its generality andapproximate likeness to the deformed Magnox components.The transverse length L is again assumed to be very long,but the cross-section of the plate is now assumed to be asshown in Fig. 3, the two sections being joined at the ends.Appendix 10.1 derives the ratio of the average force tomass for this configuration as:

FM

B2

2 pazKx (7)

where the factor Kx depends only on the ratio of span W towavelength X, and the ratio r of hole span to W. Kx isplotted against W/X for various values of r in Fig. 4.

3.3 Transverse edge effects

The analysis of the previous Section is valid, provided thatthat transverse length L of the plate is very long, when the

Fig. 3 Inclusion of longitudinal end effects

1EEPROC, Vol. 127, Pt. B, No. 5, SEPTEMBER 1980 279

resistance of closing paths for the transverse currents can beneglected. If the length/, is not long, the current distributionis complex and not readily calculated.

Solutions are available for the current distribution forthe case of a short plate in the transverse sense, but with aninfinite number of wavelengths in the longitudinal sense.Such a solution, given in Reference 3, can be used to showthat the force on the finite plate will be K2 times that onan infinite plate, with K2 given by

and

,. , , ,TTL

K7 = 1 tanh — (8)

and plotted against L/\ in Fig. 5.The validity of this factor is dubious if the dimension

W is less than a wavelength, since the current distributionis constrained accordingly. Consequently, it is proposedthat, for those cases where 2W<\, the factor K2 beestimated for a fictitious wavelength equal to 2 W.

3.4 Calculation of trajectory

The previous Sections have shown that the average electro-magnetic force on a component is given by

F = MAz

where

M = mass of component

z = velocity

10

0-5

(9)

0-5 10 1-5 20

Fig. 4 Longitudinal end-effect factor K,

10 r

Fig. 5 Transverse end-effect factor K2

280

A —B2

7po

is a parameter which is fixed for a given component andfield system, depending only on the geometry (for Kx andK2), field strength and the pa product for the material.Eqn. 9 is in a very convenient form for determining thedynamical behaviour of a component falling under gravitythrough the field.

Fig. 1 showed the co-ordinate system used in analysisof the trajectory, and the following equations of motioncan be written:

Mg cos 0 — F = M'z

Mg sin 0 = Ms

Substituting for F, from eqn. 9, gives

z = #cos 0 — Xz

s = g sin 0

If (i)0 and (s)0 are the initial velocities atthe solutions to eqns. 11 are:

1 ,.

(10)

= 0, z = 0,

s = (s)ot + %gsind.t2

To determine the trajectory in x and y co-ordinates, thefollowing transformation must be applied:

x = s cos 0 — z sin 0

y = s sin 0 + z cos 0(13)

If the initial velocity is v, in the y direction, at x — 0,y = 0, then applying the transformation gives

y = L\El -•-|2 I 2

- l +e~ p )cos

-{(l-e-p)cos20+psin20}/A.

(14)

where

p = At

The parametric relationship between x and y of eqns. 14was used to plot trajectories for various values of A, andfield angle 0, for the two values of v = 0 and !) = 4m/s.An example is given in Fig. 6 for 0 = 45°; from severalsuch computations the curves of Fig. 7 were obtained.Figs. 6 and 7 indicate the importance of the parameterA; for values of A greater than about 50 the path becomesalmost parallel with the field axis after falling only about200 mm through the field. For low values of A, maximum

IEEPROC, Vol. 127, Pt. B, No. 5, SEPTEMBER 1980

transverse deflection is obtained with the field axis atabout 37-5° to the horizontal. It can also be seen thatmaximum deflection (x) for a given fall (y) requires theinitial velocity to be as low as possible.

50

Fig. 6 Trajectories for 0 = 45°a Initial velocity = 0 ms" *b Initial velocity = 4 ms"'

4 Construction of the angled field

4.1 Alternative magnetic systems

The previous analyses have assumed a field varying be-tween ± B over a wavelength X, and have shown the import-ance of the value of X compared with component dimen-

03,.

L. 02

0-1

A =10

A = 5

A = 1

0 15 30 45

0,degrees

Fig. 7 Effect of field angle 8 on transverse deflection

initial velocity = Oms"1

initial velocity = 4 ms"!

B=01T

•5000A

-5000A

V/.

airgap

Vslot wedges. •"

a • •

5000 A

-5000A

conductor '

-tooth

<t-slot

' , i \ . \ \ \ X

Fig. 8 Alternate polarity field system, \—100 mm

a Double-sided arrangementb Lines of equal vector potential at equal intervals

IEEPROC, Vol. 127, Pt. B, No. 5, SEPTEMBER 1980 281

sions. Practical considerations require an airspace, throughwhich components fall, of at least 60 mm. There is aconflict between the advantage of a low value of X (toincrease factors Kx and K2 and hence the parameter A)and the difficulty of obtaining a high value of B in a largeairgap with a small value of \.

The variation in B can be obtained in two ways;either by

(a) alternating polarity m.m.f. distribution, or(b) a ripple superimposed on a mean value of B.

Alternative (a) is illustrated by Fig. Sa where the fluxvariation is achieved by coil sides of opposite currentsense in adjacent slots, thus giving adjacent teeth alternatemagnetic polarities. A double-sided system is shown toincrease B at the airgap centreline. A flux plot, assuminginfinitely permeable iron, is shown in Fig. 86 and illus-trates the difficulties with such a short wavelength. Cross-slot leakage flux will be much greater than crossgap flux,leading to saturation of the teeth. Even if saturation isignored, the arrangement of Fig. 8 requires very highcurrents per slot to give appreciable flux-density variationsat the midgap; for example, to obtain B = 0 1 T wouldrequire about 5000 A per slot, which, with a slot widthof about 25 mm, is close to the electric loading of present-day turbine generators. An important practical disadvantageof this scheme is that the coils are close to the radioactiveregion of the airgap, so that rewinding in the event of a coilfailure would be very difficult.

Alternative (b) is illustrated by Fig. 9, which again showsa double-sided system, each side containing slots which areunwound. Across the airgap, an m.m.f. drives a mean valueof B, upon which a spatial ripple is produced by the slotting.The amplitude of the ripple at the midgap plane can beobtained from Reference 4; for the geometry of Fig. 9, anamplitude of 0 1 T can be achieved with a mean density of0-9 T, requiring a m.m.f. of about 43 000 A. This largem.m.f. is produced by a coil which spans many wavelengthsof ripple and is not contained in the slots at the airgap. Thisis an advantage, for the following reasons:

(a) The slots at the airgap need not be as deep as in thealternate polarity system.

(b) More winding area may be available.(c) It is possible to arrange for access to the coil without

breaking into the radioactive region of the airgap.The above arguments favour the use of the flux-ripplesystem. In both systems, however, the flux-density varia-tions at the midgap plane are low, but this can be alleviatedas described in the following Section.

4.2 Inclined plane arrangement

So far it has been assumed that components fall verticallythrough the angled field, and consequently would experienceflux-density variations as they occur at the middle of thegap. There are significant advantages in allowing thecomponents to slide down an inclined surface. If this isdone, there is less likelihood of a jam developing, sincecomponents are less likely to tumble. The attitude of the

//A V///.

Fig. 10 Flex-density ripple amplitude

a Geometry of halfslot pitchb By at various distances from tooth tip surface

-y — o,

Fig. 9 Ripple field system

282

y = \/8y - x / 4

IEEPROC, Vol. 127, Pt. B, No. 5, SEPTEMBER 1980

components will be with their major dimensions in theplane of the surface, and this is an advantage with respectto the factors Kx and K2 • The most significant advantage isthat components will be forced to slide in close contactwith the ripple producing surface; this will result in muchgreater variations in B than at the midgap plane, with acommensurate increase in the parameter A.

There is no information available in the literature on thevariation in ripple amplitude across the airgap, consequentlythe authors have analysed the configuration shown inFig. 10a, using a finite-element approximation. AD and BC,tooth and slot centrelines respectively, are flux lines. Thetooth (DEFG) is assumed to have a relative permeabilityof 1000, and flux density is normal to AB and DC. Thesurface AB can be either the midgap plane between twosimilarly slotted members or the surface of a smoothsecondary. The dimensions chosen are indicated in Fig. 10a.

It was found that the ripple attenuates rapidly within ashort distance of the surface EF. This attenuation is illus-trated by Fig. 10b where the distribution of normal fluxdensity (expressed as per unit of the mean value) is plottedfor planes at various fractions of a slot pitch (or wavelengthX) from the surface. Since the attenuation is so rapid,Fig. 10b can be used to determine the flux-density rippleamplitude for any ratio of EA/\ greater than about 1. Fora slot width equal to tooth width, as assumed, the ampli-tude of the ripple at the surface is about 0 4 times the meanvalue. For a mean value of 0 9 T , this corresponds toB = 0-4 T (compared with 0-1 T in Fig. 9 at the midgap,and the same mean value). This represents a great increasein B and it would be little affected if the secondary member(surface AB) were very far removed, or even removedaltogether.

4.3 Form of magnetic circuit

Section 4.2 has shown that the ripple amplitude at theslotted surface is only slightly affected by the presenceof a secondary, and if a secondary is used, it can be plain(i.e., unslotted). The design problem remaining is to producea high level of mean flux density from the slotted surface,and a secondary is of benefit in this respect.

Fig. 11 shows the arrangement proposed, which consistsof an array of poles of pitch Tp, each with unwound slots,of pitch X, machined on the face, and each excited by coilsof alternate polarities. Appendix 10.2 shows that, ignoringmagnetic saturation, the presence of a plain secondarydistance g from the pole faces, will, for a given m.m.f.,increase the mean gap density by a factor (Tp/ng) providedthat Tp > g. In order to easily accept the componentfeedstock, the gap g requires to be of the order of 70 mm,

whereas Tp is flexible. Fig. 11 shows that the maximumflux density in the secondary, of thickness d, will be approxi-mately Tp/2d times the mean gap density Bg. If the pole-face slot width is half a slot pitch, the tooth density will beapproximately 2Bg. Hence, for equal secondary and pole-face tooth flux densities, Tp = Ad as an upper limit. Aconvenient value for d is 100 mm (4 inch plate), givingTp = 400 mm. The probable maximum value of Bg is about0-8 T, requiring an airgap m.m.f. per pole of about 45 000 A.For the same m.m.f. but without a secondary, the meanvalue would fall to about 55% of this value, representinga reduction of about 70% in the parameter A.

4.4 Choice of ripple wavelength

The choice of a value for X is determined by actual dimen-sions of components, and is a compromise between valuesof Kx and K2 and attenuation of ripple with distance fromthe surface. All components are expected to be of a sizeclose to or greater than a rectangle of dimensions 80 mm x10 mm, but the attitude of the component is not predictable.Fig. 12 plots the variation with X of the product KXK2

(obtained from Sections 3.2 and 3.3) for the two cases:L = 80mm, W= 10 mm; and L = 10mm, W = 80mm. Itcan be seen that the attitude has little effect on the productKi K2 and it is proposed that the mean of the two variationsis taken.

Owing to the shape and likely distortion of some com-ponents, the major active region could be as much as 5 mmfrom the surface along which they slide. Taking this distance,the analysis of Section 4.2 can be used to determine thevariation of ripple amplitude with X, and this is plotted inFig. 12. The parameter A varies as {B)2 KXK2 and thiswill vary with X in the manner shown in Fig. 12. It is appa-rent, that for the component dimensions assumed, a valueof 40 mm is the optimum for X. larger components, orcomponents closer to the surface, will give larger valuesof ,4.

5 Predicted deflections

Here it is assumed that the xy plane of the field system,which was previously considered to be vertical, is inclinedat 45° to the horizontal plane. The preferred angle is the

0 50-

Fig. 11 Magnetic circuit

IEEPROC, Vol. 127, Pt. B, No. 5, SEPTEMBER 1980

Aim

Fig. 12 Effect of ripple wavelength on parameter A

x A", Kf for W = 10mm, L = 80 mmo Kt K2 for W = 80 mm, L = 10 mm

283

minimum to ensure freedom to slide, but with a minimumof bouncing, and is best determined empirically withtypical surface finish and components. The angle of incli-nation affects the effective value of g in the equations forthe trajectory (eqns. 14), but small departures from 45°will not have a significant effect. Fig. 13 gives computedtrajectories for components entering the field system withzero initial velocity, the field axis being at an angle of37-5° to the horizontal (x-co-ordinate) of an xy planewhich is itself inclined at 45° to the horizontal plane.Fig. 13 enables transverse deflections to be obtained if theparameters! is known.

It is not possible to predict the value of A to any degreeof certainty owing to the variable distortion likely incomponents. However, some guidance can be obtained asto deflections by considering a rectangular plate of dimen-sions 80 mm x 10 mm, sliding at a height of 5 mm from thesurface. This gives a value of Kx K2 = 016 and, assuminga mean gap density of 0 8 T in the airgap, a value of B =0-2 T. The values of A for the materials in question can nowbe calculated, and these are given in Table 2.

Also included in Table 2 is the length of fall (>»-direction)to give a deflection of 0-25 m in the transverse (x) direction.These results were obtained for rectangular plates; inpractice, components will be distorted into complex geo-metries. It will be possible to approximate a component toan equivalent rectangle, with or without a central hole, in

x,m

y.m

25

Fig. 13 Trajectories on face of plane at 45° to vertical for zeroinitial velocity and Q = 37-5°

284

Table 2:

Material

MagnoxZirconiumStainless steel

Values of A for B = 0 2T, KK

A

46-51090-5

Fall (m) for

0-32-03-1

= 0-16

0-25m deflection

order to determine the factors Kx and Ki. It will not beeasy to estimate mean height above the surface, and it maybe necessary to increase the effective density a in the (pa)product to compensate for the contribution to total massof those parts of the component not in close proximity tothe surface. The uncertainty with respect to componentshape will be reflected in the values of .4.

Table 2 shows that, even with the uncertainty in value ofA, the Magnox components should be readily separatedfrom zirconium and stainless-steel components, but, for thelast two materials, difficulty may be experienced unless thelength of the field system is long.

6 Practical considerations

6.1 Mechanical construction

One pole of a multipole prototype system is shown inFig. 14, which illustrates the essential features of the design,together with the practical additions necessary to ensureproper performance of the magnetic circuit and an appro-priate degree of containment of the radioactive material.Not obvious from the Figure, is the fact that the slots cutin the solid pole faces must lie at an angle of 37-5° to the

face plate!(mild steel)

magnetic bolts

nonmagnetic struts(20x10x200mm) U>

see detail Bbelow

slotted polepiece

(mild steel)

backplate(mild steel)

magnetic bolt

welds to providecontainment

weld to providecontainment machined,

surface

15mm

20 mmnonmagnetic

wedgedetail B

Fig. 14 Proposed construction of prototype (one pole pitch)

IEEPROC, Vol. 127, Pt. B,No. 5, SEPTEMBER 1980

horizontal in accordance with the requirements of Section3.4. This is most readily achieved by skewing the completepolepiece, machining the ends as appropriate and windingthe exciting coil at an angle of 37-5°.

To ensure that the flux density in the gap is as uniformas possible along the complete length of a multipole array,it will be necessary to provide flux shunts at each end ofthe device. These shunts take the form of solid steel piecesthat securely connect the secondary to the base plateson which the poles are mounted, and they must have suf-ficient cross-section of area to carry half the total fluxproduced by one pole.

By wedging and welding the pole edges, as shown in thedetail of Fig. 14, the secondary and the pole faces presenttwo parallel solid surfaces between which the componentsmust slide. Side plates of nonmagnetic steel would be addedto complete the enclosure of the radioactive region. Notealso the use of nonmagnetic struts of suitable proportions,to withstand the magnetic pull between the secondary andthe pole face. This force which is easily calculated asF = h § B • HdA, is of the order of 5 tonne-force for thedimension chosen. It is essential that these struts arenonmagnetic as they lie within the extremities of theexciting coil.

6.2 Excitation requirements

In Section 4.3, it was determined that each pole requires anm.m.f. of 45 000 A, and this must be accommodated withinthe area allowed for the exciting coil. In order to achievethis level of excitation, without removing excessive materialfrom the main body of the pole, it will be necessary towater-cool the conductors in the coil. Choosing a rating of10 A/mm2 and a 60% space factor to allow for insulationand cooling duct, a 1 cm2 subconductor can carry 600 A.75 such subconductors would provide the required excita-tion in a reasonable area.

The nature of the power supply to the coil will dependupon whether the coil is connected in series or parallel,and for the extreme conditions of an all-parallel or anall-series connection, the requirements are 45 000 A at0-5 V or 600 A at 35 V, respectively. The second alternativeis more attractive but the choice depends on subconductoravailability and hydraulic considerations.

The ripple in the d.c. supply to the coil must be as lowas possible and may even require the use of a series inductor,for the poles are not laminated and eddy currents will beinduced in them by the supply ripple. The reduction ofripple should present no serious problems, however.

7 Conclusions

An appraisal has been made of alternative possible methodsof the electromagnetic separation of materials from a mixof radioactive components, and reasons given for a finalchoice. It has been shown that, by sliding the componentsdown an inclined plane, through an angled field, selectivetransverse deflections can be obtained. The preferred formof the field has been shown to be a low-wavelength flux-density ripple superimposed upon a much larger wavelength,alternate-pole system, and an optimum wavelength has beenderived.

Of the materials present, Magnox is the most readilydeflected and could be separated from zirconium, stainJess-steel, and graphite with modestly-sized equipment. Theseparation of zirconium from stainless steel is more difficult

and would require a much larger system. This paper hasindicated the main features required of a prototype sepa-rator and its design was arrived at with the practical require-ments of a final assembly in mind. It has the advantages ofno moving parts, simple construction in the active regionand it gives access to the excitation coils without disturbingthe integrity of the active region.

8 Acknowledgment

The work described in this paper was carried out on behalfof Taylor Hitec Ltd., to whom the authors wish to expresstheir gratitude for assistance with information and theprovision of fuel-rod components in an unirradiated state!

References

1 LAITHWAITE, E.R.: 'Propulsion without wheels' (EnglishUniversities Press, 1966)

2 THORNTON, D.R.: 'Magnetic levitation and propulsion, 1975'IEEE Trans., 1975, MAG-ll,pp. 981-995

3 YAMAMURA, S.: 'Theory of linear induction motors' (J. Wiley& Sons, 1972)

4 FREEMAN, E.M.: 'The calculation of harmonics due to slottingin the flux-density waveform of a dynamo-electric machine',Proc. IEE, Monograph no. 523, 109, 1962, pp. 581-588

10 Appendix

10.1 Longitudinal end-effect factor

For the plate of Fig. 3, assuming the field is invariant overthe thickness h, and taking a reference frame with z fixedto the plate and the origin at the centre, the field will begiven by

B = Bsin{ — (z-zt)A

(15)

with the zero of time t defined in Fig. 2.Eqn. 15 is conveniently written in terms of new para-

meters e and y as

B = B sin (e - 7)

where

2-nz

(16)

e =

and

2nzt

The electric field induced by motion will have a componentonly on the s axis, and will be given by

dE_

dz

dB dE dB_

3 7

From eqn. 16, this gives

E = C + zB

with constant Cto be determined.

07)

(18)

IEE PROC, Vol. 127, Pt. B, No. 5, SEPTEMBER 1980 285

Assuming the two regions of the plate to be connectedat the ends through zero impedance, the electric fieldinduced will be locally absorbed as an ohmic voltagegradient Jp by the current density / . Thus

= '—I sin (e — 7)P P

and, since the total current must be zero

f hJdz = - f hJdtJ-b Ja

Eqn. 20 enables Cto be determined, giving

(19)

(20)

T & * I • / A i • (sin /3 — sin a . ,/ = — j s i n ( e - 7 ) + sin7( ^ ^ | | (21)

where

nW nrW(5 = and a =

A XThe instantaneous force per unit length on an element ofthe plate, of cross-section h. bz is given by

5/ = hJBbz (22)

and the total instantaneous force per unit length on theplate by

r-a ca

-l-h Jh(23)

Substituting for J and B in eqn. 22 and integrating betweenthe limits of eqn. 23 gives

/ = ^Yp (0 -<*)"I (s in20-s in 2a)x

sin 27(sin 0 — sin a)7

(3-a2 sin27 (24)

Now 7 is a function of time, so the temporal average forceper unit length is given by

(25)

The mass of the plate per unit length is given by

M = oh2(b-a) = oh2{$-a)—2n

Hence

B

M 2pa

where

Kx = 1 -

zKx

sin 0 — sin a

0-oc

(26)

(27)

(28)

is a longitudinal dimension factor, determined by the ratiosW/X and r. (Note that for a plate without a centre hole,r = O.)Ki is plotted as a function of W/\ and r in Fig. 4.

70.2 Effect of secondary member

For the array of poles shown in Fig. 11, the determinationof flux distribution in the air space is difficult. A closeapproximation to the effects of a secondary slab of ironcan be obtained, however, if the poles are replaced by aninfinite slab of iron of infinite permeability, with a surfacecurrent sheet of line-current density given by

Z7T= / sin (29)

This will give a maximum m.m.f. per pole of F = Tp/nJ.The maximum normal flux density will occur at x = 0

and will be given, from Ampere's circuital law, as

(30)A -

= 2 -

where

Si(x)

and

Hence

D —

Mo

Tp

•J.

Mo

2

* s

i

7T

2*

r

i n w

IT

ycbc

°)

(31)

When a secondary slab of iron is present, the maximumnormal flux density will be

Bo =g

(32)

provided that Tp is large compared with g.

Thus

t>2 _ 1P

5i TTg(33)

This estimate of the increase in airspace flux density at theprimary iron surface, due to the presence of a secondary,was obtained from consideration of a distributed currentsheet, but similar effects can be expected for the concen-trated excitation system shown in Fig. 11.

286 IEEPROC, Vol. 127, Pt. B, No. 5, SEPTEMBER 1980