Superconducting magnet design for open gradient magnetic separation

Superconducting magnet design for open gradient magnetic separation J. G e r h o l d Anstalt for Tieftemperaturforschung, Steyrergasse 19, A-8010 Graz, Austria Received 26 March 1986; revised 4 July 1986

Well designed superconducting magnets seem to be especially promising for use as open gradient magnetic separators. Specific magnetic force densities in the region of 100 MN m -3, which are appropriate for the industrial treatment of paramagnetic matter, may result. The magnets can be optimized by choosing a proper winding geometry as well as by using a beneficial superconductor layout. These two optimization procedures may be carried out almost independently from each other by means of dimensionless parameter functions. The geometric design has to be planned with regard to the required force field type, e.g. katadynamic or anadynamic force field, and with regard to an efficient use of the superconducting material. The superconductor design has to be planned with regard to achieving a high magnetic force density, which is correlated with a high Lorentz-force density within the winding. High overall current densities are required. The optimum flux densities are in the region of 5 T with NbTi.

Keywords: superconducting magnets; magnetic fields; magnetic separation; magnet design

Open gradient magnetic separators (OGMS) may be characterized by comparatively long-range magnetic forces. These forces favour continuous separation processes where the particles to be separated are deflected according to their susceptibility ~. The duty factor can be taken as unity. By way of contrast, recognized high gradient magnetic separators (HGMS) are characterized by very short-range forces. Consequently, the separation is effected by capturing the magnetic particles. The captured particles have to be flushed out after matrix loading. Non-superconducting HGMS as used in the kaolin industry, for instance, exhibit duty factors of only 4 0 - 5 0 % 2"3. The duty factor may be enhanced to > 60% when using a double matrix canister system with superconducting magnets 3. Even higher duty factors emerge with carousel machines. These machines have the disadvantage of having rather complicated mechanical auxiliary equipment. Superconducting magnets have been proposed for them but have not, as yet, been discussed in detail 4. Superconducting magnets are especially suited to producing high magnetic field strengths with rather moderate field gradients. The latter are essential for long-range magnetic forces. This fact renders superconducting magnets especially interesting for industrial OGMS processes, where large separation volumes are needed. For economical reasons the magnets should be optimized. The background for optimization is discussed in the following text and is illustrated with typical examples,

tic forces, Fm should be counteracted by forces, F~, e.g. mass forces. Figure 1 shows a schematic separation process using gravity for the counteracting forces. Other mass forces, for instance inertia forces, have also been proposed 5. Centrifugal mass forces may be esflecially suitable for the separation of fine grained matter U. The long-range magnetic forces acting on a weakly magnetic particle

are given by the particle susceptibility, K, and particle volume, Vp, and by the specific magnetic force density fm= grad ~m

To obtain efficient separation of magnetic particles from less magnetic or even non-magnetic particles, the magne0011-2275/86/100523-08$03.00 (~ 1986 Butterworth & Co (Publishers)Ltd

(2)

The specific magnetic potential equals the energy density of the magnetic field with flux density B according to the equation ~m = -

1 .B 2 2~--~

(3) &

l

l

l

1

l

I

l

I

I

. . - . . . .•. . .. . .. . ... . .. .',... . -. -.. °..,.="" .-,:: -Concentrate ":'~*i'i° .": " . * • . • . °". o.." . . , .' . " . • ' " . "" " """ ,";" '" ,e~.~-s~ ...... F~*d .....:*'...**" °"'°'° . . ". . " ° l" o ..... '.. ~ ... ...... a

•

"

•

•

•

•

• .o

Open gradient magnetic separator scheme

(1)

Fm = K'Vp'fm

•

=.

[

1 I

,

• = • . *o . + o • °, '*, ' ' ° ,• % * o

~ [ 1 ~ I

Tailings

1

Rgure 1 Continuous magnetic separation process

Cryogenics 1986 Vol 26 October

523

Superconducting magnet design: J. Gerhold The mass forces on the other hand are proportional to the mass density, p, of the particles and to the particle volume. From this

z* = Z/~o ~*= ~/~

(outside the winding) (winding coordinates) (7)

leads to

Fm/Fc pc I

(4)

comes out, where ;( is written for the mass susceptibility of the particles. The aim of an ideal magnetic separation process is the net separation according to the mass susceptibilities, Xl and X2, of a particle mixture to be separated. Separation takes place theoretically either for -

F¢ > 0

for

> Xo

(5)

or

r" ( z ' , ; ' )

=

(8)

Fo = Fo/~

(9)

From this, the specific magnetic potential emerges, according to Equation (3), as

1 J'Bo" FF--:o.F*.~

4'm = -

(10)

From

Fro2 - Fc < 0

for X2 < ;(o

with X0 as a type of critical susceptibility. Such an ideal separation process is only possible for the separation of magnetic particles from essentiall), non-magnetic particles with today's industrial separators'. Special isodynamic OGMS devices have been used, however, for the selective separation of particles with different but similar susceptibilities on a laboratory scale s. To make OGMS viable for the industrial treatment of weakly magnetic matter having mass susceptibilities below 10 -5 m 3 kg -~, superconducting magnets must be used. These magnets can bring about high magnetic flux densities which are not limited by iron saturation. Transforming Equation (2) and (3) by vector algebra into

fm= 1 .B-grad B

(6)

shows clearly that a force density of > 10s N m -3 may be possible with moderate flux density gradients. This allows the use of large separation volumes,

Analysis Superconducting magnets used for OGMS should be optimized with regard to the actual separation process. This optimization can be carried out by means of a set of dimensionless parameter functions and by means of optimum layout of the superconductor, Generally, the flux density anywhere in a magnet without iron is proportional to the overall current density, J, times the vacuum permeability, ~ , and to a geometric function, x9. The maximum flux density, Bo, as seen at the superconductor, arises within the winding at a coordinate ~ , which is correlated with Fo. Using reduced space vectors (see Figure 2)

<)~

S'= ~IT.

grad ¢Pm = O~Pm = O~bm ~z ~z'~

(11)

the specific force density is obtained from

Bo.J fro=

a

2

F"

~z" ( ~ "

Bo.J F')=

.'/"

(12)

2 ,/" is a pure geometric function of the reduced space vectors defined by Equation (7), which do not depend on the actual magnet size. The term B J is correlated with the maximum Lorentz-force density arising within the winding. Equation (12) brings the Lorentz-force density in relation to the specific magnetic force density acting on the magnetic dipoles to be separated. The maximum force density depends on the magnet size, the superconductor performance and the actual winding techniques. Any optimization procedure should consider the geometric function as well as the Lorentz-force density term. For a real separation process the whole space outside the windings can never be used; only a limited volume, v, can actually be utilized. Within this limited volume a maximum value of the specific magnetic force density, fmax, may arise at Zmax. Using fm~ as a reference value of the separator magnet gives

0 {Z*) =fro {z')lfm~x

(13)

By means of the force-field shape function, 0 {z*}, the geometric function, y', may be split further into ~,. {~',z*} = 0 {z') g) {~*,Zm~} (14) This formal splitting can be done at least approximately and may be very useful for design purposes. The forcefield shape function has to be accommodated to any particular separation process. It determines the magnet type, e.g. straight or circumferential multipole, racetrack magnet, split coil, etc. But for any magnet type there exists a variety of actual winding shapes. This variety is expressed by the force density efficiency, ~. This is defined by

z'= Z/]'o =

winding Figure 2 Reduced space vectors for separator magnets

524

Cryogenics 1986 Vol 26 October

fmx/82"J

05)

The force density efficiency can also be optimized. The force density efficiency is one of the most important criteria. But there are other criteria too, which should be considered. For instance, large intereoil forces,

Superconducting magnet design: J. Gerhold Fic, must often be handled. These forces determine the mechanical structures. To assess the structural requiremeats, it seems to be useful to consider the figure of merit. This is defined by the integral of the specific magnetic force density over the separation volume and may be correlated directly with the capacity, M, e.g. for dry separators of the 'falling curtain type 1°. From

M oc ffrn'dv

(16)

v

one type of relative figure of merit, ~rfm, can be derived according to ~rfm = I fm "dr/Fic v

(17)

The dimensionless relative figure of merit is determined by geometric relations and is independent from the actual magnet size. One of the most crucial design parameters for superconducting magnet systems, on the other hand, may be the stored magnetic energy, Era. It can be found from the integral of the specific magnetic potential over the whole space. A comparison of this stored energy with the specific magnetic work to be done on particles which must be separated seems very enlightening. The specific work depends on the magnetic forces and the displacement, x, of the particle according to the equation

W m = ffm.dx

(18)

x Only magnetic force components fitting the counteracting forces, F~, should be taken into account. The specific work can be integrated over the separation volume. Dividing this integral by the stored energy leads to the dimensionless energy efficiency ap = f( f fm'dx)" dv ] Em

(19)

v This may be used for an estimation of the capacity of a separator compared with the magnet costs,

analytically using the current sheet approximation. The force field of a circumferential muitipole with p pole-pairs (see Figure 3) is given by 14 0i = (r*) 2p-3 forp I> 2 (inside the current sheet radius r0)

(20)

0o, " ~ - (r*) -2p-3 for all p (outside the current sheet radius r0)

(21)

where r" = r/ro. The stored energy, Era, is halved at to. Radial-symmetric straight muitipoles have been proposed as so-called cusp-coil systems 13 for instance• These systems show a force field diminishing in a way that is similar to r*o outside the magnet. But, in addition, a considerable variation can be seen in the axial direction. M o r e recent design concepts use n o n - c i r c u l a r multipoles 1°,15,16. The racetrack magnet for the 'falling curtain' dry magnetic separator may be of special interest. This magnet can be built very long to obtain a large separator capacity. The principal force-field shape in the horizontal plane of symmetry for a long vertical racetrack magnet can be seen in Figure 4. All these multipole magnets have a principal drawback that can be seen in Figure 4. The force density exhibits its highest value just where the magnetic potential is lowest. These force fields have been classified by Frantz s as katadynamic and prevent a selective separation of particles with different but similar susceptibilities. There exists no position within the separation volume where a stable equilibrium arises between the magnetic forces and the counteracting forces. The consequences may be illustrated for the principal separation process shown in Figure 1. A vertical katadynamic force field, similar to that indicated in Figure 4, is assumed. Then the magnetic particles entering at the lower border of the separation channel are subjected to the lowest magnetic forces but should exhibit the largest displacemeat and vice versa. Therefore, the separation effect may be influenced considerably by random effects, e.g. initial position and size of the particles. To obtain a selective separation, stable equilibrium conditions should be achieved. Figure 5 shows a so-called anadynamic force field which can be brought about near the midplane of a simple split-coil system ~7 (see Figure 6); cusp-coil systems may be used to thns end, too . Particles which are subjected to such a magnetic force field and to •

Magnet optimization To get an economic design of separator magnets the different parameter functions have to be considered reciprocally and weighted. First of all, a proper force-field shape function must be chosen. It must match the particular separation process. Then a proper winding geometry has to be found leading to a high force density efficiency. The last step may be the optimization of the superconductor. This determines the flux density, Bo, within the winding, the magnet size and the level of the specific force density. The last variable must fit some minimum requirements due to the susceptibility of the matter to be separated.

Force-field shape function There exists a lot of force-field shapes that can be used for separation. Early separator design concepts ~-13 used mainly radial-symmetric force fields. These force fields may be brought about by means of straight or circumferential muitipoles. The latter ones can be treated

~

, l ' I " - ' - " " "x / / I . \ ~ // , . - , ~ , _ _ ~ ~ " a~mXz " J ' h ~ / . / ~ x ~ N , x ~ ~

17

/

"x~ \ f l u X [i 13e s / - - - [.~~ , . x. .\ . . ~ T i / ' /.. ~,£t~---,~..., / /'l[I i ~'x~.' ~/~ i .t 11,,x x, "--" 4 ~ ~ ~"-" ~ - . - . 4 i ~] ,~ ~'*'~. ' ~, , - / .N'-L, ~ \x \ ~ / ' / ~'//~ \ " ~ \ \ ~' / / - , ~ , / ," :~...,\ x ~/_.,-" ¢. ~ / ( ~ ,,, \~-----current sheet

/

"I/fl I \ " "---"--" / I I

\,. ~

I

1"13O g n e t i c f o r c e s RllUm 3 Force field and flux patterns of a sine-distributed currentsheet quadrupol (2p=4)

Cryogenics 1986 Vol 26 October

525

Superconducting magnet design: J, Gerhold

Vj

b,

¢,~= constant horizontat._ distnnce x .... I -

Figure 6 Isopotential traces of a split-coil system; separation volume border at 30 ° angle of magnetic forces

'

.._X2 < XO

Figure 4 Force field and specific magnetic potential in the horizontal plane of symmetry for a vertical racetrack magnet

counteracting centrifugal mass forces, for instance, are

Rgure 7 Selective separation by ring-shaped anadynamic magnetic forces and counteracting centrifugal mass forces

either captured in a stable position (X~ > Xo) or extracted

Particles with X2 < Xo are deflected to the flat potential

(;(2 < Xo)- This is indicated in Figure 7. This separation process, which may be realized by means of a continuously rotating disc, seems to be very selectiveTM. For the selective separation within dense particle streams, which are typical for high capacity separators, a so-called isodynamic force field may give the best results. This produces a stable equilibrium over the whole separation volume for the critical susceptibility, ;(o, only. In general, isodynamic force fields are defined by~

region and particles with ;~1 > 7~ are deflected to the deep

grad B~ = constant

(22)

potential region. In a more rigorous sense, Equation (22) matches only counteracting forces which are constant over the separation volume. For varying forces, such as centrifugal mass forces, the magnetic force field may be adjusted to them. Isodynamic force fields can be brought about approximately within a limited separation volume. Superconducting split-coil systems or cusp-coil systems seem especially suited to achieving this end tT.

Force density efficiency

1~ ~

,

i

~

l~

r'*=x- . . . . . . . .

L--/~r ~

.

.

.

rL

Figure 5 Ring-shaped anadynamic force field and specific magnetic potential wall

526

Cryogenics

1 9 8 6 Vol 26 O c t o b e r

It has been mentioned already that many winding shapes exist for any particular force field. This can easily be explained for the circumferential multipoles giving purely radial magnetic forces [see Equations (20) and (21)]. Any real multipole has to be built with a winding thickness rou-ri, as may be seen in Figure 8. The maximum flux density limiting the overall current density of the supercOnductOr tO T be used h e arises has r awithin be d i theu winding" s , corresponding to, to calculated from r,,, and ri. Figure 8 gives some calculated force density efficiencies19. The outer radius, r,,u, and the inner radius, r~, respectively, have been taken for the reference coordinate, Zma x, These theoretical force density efficiencies are surprisingly high within thick multipoles. In practise, a thermal insulation is needed between the winding surface and the separation volume border ~s Lower practical force

Superconducting magnet design: J. Gerhold ~ ~

~

~

Relativefigure of merit

~g/.

The relative figure of merit relates the separator capacity with the intercoil forces of the magnet. It is of interest for the layout of muitipoles and racetrack magnets, as well as split circular-coil systems. From the data given in Reference 10 for racetrack magnets, a relative figure of merit ranging from 0.2 up to > 2.0 may be derived. This seems to be surprisingly high. The split-coil systems shown in Figure 9 exhibit considerably lower values.

" ~*~ '

~-I

Energy efficiency 05

~,, 0 0'2

0~

~ 0'~ 01, ; r~/r, Figure 8 Forcedensity efficiency of circumferential multipoles density efficiencies therefore emerge. The prototype quadrupole for the CERN intersecting storage rings for instance 2°, with its 173 mm warm bore diameter, would yield a force density efficiency of = 20% when used for separation. This level may be taken as typical of several other magnet types too, e.g. racetrack magnets, Systematic investigations have been carried out with split-coil systems for anadynamic force fields21. Figure 9 gives calculated force density efficiencies in the midplane over the relative coil distance, do/ro;do and ro are defined by the maximum flux density, B0. There are no restrictions due to thermal insulation requirements. The thermal insulation is in fact around the coils but does not interfere with the separation volume in the midplane. This volume is mainly given by the direction of the magnetic forces which are perpendicular to the isopotential traces indicated in Figure 6.

0,3 / /

//~/" ~" /././

. .e-

l!

/

"~

~/

0,1

.

0,02

.-~,

"-

&-

/

-

J .

/x //\

0

Figure 9

... I "

~'-----~

0.5

~

(23)

0{r'} = (r/ro)-3

//

/~////

Any optimization of the lorentz-force density term, BoA is strictly related to the assessment of the type of superconductor, as well as of the winding technique. It is also related to the level of the specific force density and the magnet size, respectively. The principal optimization procedure can be illustrated by means of a very simple example, that is a straight single conductor or radius ro, which is shown in Figure 10. The maximum flux density, Bo, arises at the conductor surface and limits the overall current density, J¢. It must never exceed the critical current density of the superconductor times the filling factor. Outside the conductor there exists a gradient field, B{r}. The maximum specific force density arises at the conductor surface with

and the force-field shape function comes out as

/ 0,2

Lorentz-force density

fm~x = Bo JJ2

/ /

High energy efficiencies can be assumed with katadynamic force fields only. The CERN quadrupole 2° already discussed yields an energy efficiency of = 10%; a similar figure may be assumed for racetrack magnets. This is partly due to the potential of feeding a particle stream through on both sides of such a magnet, e.g, with the 'falling curtain' separation process 1°. Anadynamic or isodynamic force-field magnets exhibit a considerably lower energy efficiency. This may be considered to be a penalty for the feasibility of a selective separation process. Figure 9 may give an impression of energy efficiency for split-coil systems.

d./r.

1

~_~

l ,~

0.01

~1

0

Force density efficiency, relative figure of merit and energy efficiency of a split coil system

(24)

The force density efficiency has to be taken as unity for this conductor. It equals half the maximum Lorentz-force density. The actual level of the force density can be adjusted by varying the maximum flux density and is correlated with the conductor radius, to. Figure 11 shows this for the superconductor given in Figure 10. A broad maximum of ~ 800 MN m -3 arises at a relatively moderate flux density, Bo, of ~ 5.5 T. The corresponding conductor diameter of 55 mm may be attributed to a linear size factor, 0t=l. Sometimes more full use of the superconducting material may be sought. This can be achieved by matching up the local current density, J¢{r), to the local flux density, B{r}, within the conductor. The matching can have a considerable effect on fm,x as may be seen from Figure I1. The position of optimum flux density is not changed considerably. The local matching up may be of economic interest, especially for complicated magnets which consist of several coils.

Cryogenics 1986 Vol 26 October

527

Superconducting magnet design: J. Gerhold

~

0,

j

c,oss,~,ioy"

current den- / ~ sity matches local flux ~ density /'"

./

L/ /"

./"

/

/

6o0

I ./'/" o Rgure 11

4oo

"~l

~

~ a.

i

ar

Lorentz-force density term

Discussion 2oo

b , 2

°0

, 4

~r -~ Figure 10 (a) Straight conductor model. (b) Overall critical current density of the straight conductor model. 2:1 copper/ NbTi at 4.2 K

For any separator magnet a diagram similar to that shown in Figure I1 can be realized. It can be useful to define a linear size factor by z 0t = (25) z{0t= 1} In addition, a current density factor, ~, which is a function of (x as well as of the superconductor = J~{0t=l)

(26)

Jc{Ot} is introduced. I~ has to be evaluated from the critical current density characteristic of the superconductor, With the help of the size factor and the current density factor, any data about the actual separator magnet may be found easily, especially the force density level for a given size fm(0t}

=

~2. 0t "fm{0t=l}

(27)

It should be pointed out that the diagram in Figure 11 is valid for all of the magnets to be built with this particular superconductor. To get a first estimation for an actual design, an c-scale may be superimposed onto the flux density scale. Then the range of economic sizes and force density levels can be found easily,

528

;

Cryogenics

1986 Vol 26 October

Any separator design should begin with some approximate but principal estimations. It has been shown before that a specific force density level of 10a N m -3 may be taken as a reliable base. This sets a lower limit for the mass susceptibility of the matter to be separated. This susceptibility should not be much lower than 10 - 7 m 3 kg-l; otherwise sophisticated magnet techniques must be used, e.g. an expensive cooling to 2 K. But then HGMS may often be a more economic solution. In a second step, an appropriate separation process has to be chosen. Here the required quality of separation has to be weighed against a high capacity. The separation quality is determined to a large extent by the kind of force field, whereas a high capacity can be related to a high energy efficiency. High energy efficiencies can be brought about easily with katadynamic force fields. But then more than one single pass may be needed for a selective separation 5. This lowers the final capacity considerably. On the other hand, anadynamic or isodynamic separators may achieve a selective separation in a single pass. But these separators exhibit a rather low energy efficiency; especially when the specific force density must be high, the energy efficiency may only be ~ 1%. Since the capacity of separators in general may grow with tim//2 up to fro5 ."2 3", the influence of the force density level has to be carefully balanced against a low energy efficiency. For the last step, three particular procedures have to be carded out. The first procedure should lead to winding types which guarantee the required force-field shape. The mathematics for a straightforward calculation have been developed recently24; special computer programs may be available in the future. Second, a particular winding resulting in a high force density efficiency has to be picked out. Finally, a high Lorentz-force density must he achieved. To this end, an appropriate type of superconductor, together with a matching winding technique, has to be chosen. A high overall current density should be the result. Then a high force density level can be expected. Setting the specific force density level via the superconductor determines simultaneously the size of the magnet. But this determination is only two-dimensional. It does not hinder the construction of large separator magnets a priori. The straight model conductor or any

Superconducting magnet design: J. Gerhold multipole may be built to a considerable length for instance, to ensure a large separator capacity. Therefore, separators with a capacity of 100 t h -1 may sometimes be a most reasonable size assumption. An overall size limit is enforced because of the well-known adverse effect of the stored magnetic energy on the current density2s. Not only katadynamic muitipoles but also anadynamic split-coil systems may be built in large units. The split-coil systems shown in Figure 9 may exhibit a peak specific force density of > 100 MN m - 3 when the coil radius is 1 m. According to market requirements, however, more medium-sized selective separator units, with a capacity of several tons per hour, seem to be of interest 6"7. This coincides with the aim of high current densities in the windings; adiabatically stabilized and impregnated coils may be appropriate for these magnets ~7. The limited optimum flux density coming from the high Lorentz-force density requirements should be seriously considered. Concerning the magnet, the internal mechanical stresses which are directly proportional to BoJc increase with the size factor, ct. This makes large magnets rather uneconomical. But for the separation process the flux density level should also be limited. High flux densities favour magnetic agglomeration. Agglomeration interferes with a selective separation and is due to dipolar attractive forces between magnetized particles, The agglomeration forces, Fag, a r e highest when the particles are touching each other. For spherical particles with radius Rp and volume susceptibilities K1 and ~:2

grained matter should be separated with lower flux densities than larger particles. Figure 12 illustrates this for a special case. In a more general manner the non-agglomeration requirement limits the spatial range of the magnetic forces, too. Limiting the admissible flux density inevitably enhances the necessary flux density gradient [see Equation (6)]. Fortunately, a separation process for small sized particles may need a considerably smaller separation channel width than a process for large particles. Following the first approximate magnet design, which must make evident the practicability of a superconducting OGMS for the particular separation problem, a detailed layout has to be prepared. This layout must incorporate the specific physical properties of the particular matter to be separated. Even for nominally equivalent materials these properties may vary over a broad range 7. Prospects

The agglomerates tend to be aligned in the magnetic flux direction. They may be strongly separated when the difference in the separating force which acts on them exceeds Fag

From the present state of development of superconducting OGMS two main tendencies can be seen. First, very large separators have been designed or tested in part. These large separators have a capacity of = 100 t h -1 but use katadynamic force fields only. They are suitable for the separation of magnetic particles from non-magnetic particles. Then there are the selective separators which may be constructed using anadynamic or isodynamic force fields. The economic size of selective separators may be in the capacity range of several tons per hour. These separators are appropnate for the industrial separation of weakly magnetic matter with only slightly different magnetic properties. Compared with conventional separators, for instance the Jones separator, these superconducting systems have to be either less expensive or significantly superior in performance to become economically attractive.

Fml - Fm2 > 1 Fag

Acknowledgements

(28)

F = V°'KVK2"B2

16['t°'Rp2

(29)

To this end the condition B / grad B > 8Rp (1/K2 - 1/r~)

(30)

should be met. Equation (30) may be taken as a very rough approximation but it clearly indicates the tendency: fine

The author gratefully acknowledges the help of J. "Schmidt for extended numerical calculations; work which has been supported partly by a grant from the Fonds zur Foerderung der wissenschaftlichen Forschung, Vienna, Austria. Thanks are also due to H. Kolb of Voest-Alpine and H. Fillunger and S. Gruendorfer of Elin-Union for stimulating discussions and comments.

0,05 ~

References

t~'.

1 Parker, M.R. J Physique (1984) 45 C1-753

l

2 3

C025

4 5

6 7 8 9 10 0 ~

1'

2

-

B

iT

Figure 12 Agglomeration limit. ~m = 50 MN m-a; K=0.0015 =

2K2

Watson, .I.H.P., Scnrlock, R.G., Swalu, A.W. and lioldm,

T.A. Proc ICEC 9 [PC Science and TechnologyPress, Guildford, UK (1982) 120 Riley, P.W. and Hocking, D. IEEE Trans Magn (1981) MAG-17 3299 Gerber, R. IEEE Trans Magn (1982) MAG-18812 Ko[~, 2. lnt J Mineral Process (1983) I@297 Kolb,H. Personal communication (1.984) Ste/mer,HJ. Lecture at Elin--Union, Vienna, Austria (1983) Fritz, S.C. US Patent No. 2 056 426 (1936) Breehaa, H. Superconducting MagnetSystems Springer-Verlag, Berlin-Heidelberg-New York (1973) Kopp, .L M79 Zurich, Switzerland (1985) 299

II

~ K., Sul~, A. and D~r, H., paper presented at rig t2th lnt Mineral Processing Congress, San Paulo, Brazil (1977) 12 Cohen,H.E. and Good,J.A. IEEE Trans Magn (1976) MAC,-12

503 13 HIR, E.C. IEEE Trans Magn (1982) MAG-18847

Cryogenics 1986 Vol 26 October

529

Superconducting magnet design: J. Gerhoid 14 Hughes, A. and Miller, T.J.E. Proc lEE (1977) 124 121 15 Jiingst, K.P., Ries, G., F6rster, S., Graf, F., Obermaier, G. and Lehmann, W. Cryogenics (1984) 24 648 16 Unkelhach, K.H. and Wasmuth, H.D., paper presented at the Superconducting Magnetic Separation Meeting, London, UK (1985) 17 Gerhold, J., Schmidt, J., Griindorfer, S. and Fillunger, H. MT9 Zurich, Switzerland (1985) 302 18 Gerhold, J. and Schmidt, J., paper presented at the 4th World Filtration Congress, Ostende, Belgium (1986) 19 Gerhold, J. and Hammerl, M. Design Conceptsfor Superconducting Magnetic Separators Anstalt fiir Tieftemperaturforschung, Graz, Austria (1981)

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Cryogenics 1986 Vol 26 October

20 21 22 23 24 25

Ansorge, W. et ai. Proc 6th lnt Conf Magnet Technology Bradslava. Czechoslovakia (1977) 480 Gerhold, J. and Schmidt, J. J Physique (1984) 45 C1-785 Schmidt, J. CYCLOP Anstalt for Tieftemperaturforschung, Graz, Austria (1983) Schubert, H. Aufbereitung fester mineralischer Rohstoffe Vol 2, VEB Dcutscher Verlag for Grundstoffindustrie. Leipzig, GDR (1978) Schmidt, J. Supraleitermagnetscheider Final report for project No. P5462 for the Fonds zur F0rderung der wisscnschaftlichen Forschung, Vienna, Austria (1986) Green, M.A. IEEE Trans Magn (1981) MAG-17 1793