GB2180943A

GB2180943A - Magnetic field screens

Info

Publication number: GB2180943A
Application number: GB08622277A
Authority: GB
Inventors: Peter Mansfield; Robert Turner; Barry Leonard Walter Chapman; Roger Malcolm Bowley
Original assignee: National Research Development Corp UK
Current assignee: National Research Development Corp UK
Priority date: 1985-09-20
Filing date: 1986-09-16
Publication date: 1987-04-08
Anticipated expiration: 2006-09-16
Also published as: EP0216590A1; GB2221540A; US4978920A; DE3650778D1; GB8919777D0; EP0365065B1; JP2515107B2; CA1282457C; GB2180943B; GB8622277D0; DE3689346D1; JPS62143012A; DE3689346T3; DE3689346T2; EP0216590B1; EP0365065A1; DE3650778T2; GB8919577D0; EP0216590B2

Description

1 GB 2 180 943 A 1

SPECIFICATION

Magnetic field screens

This invention relates to magnetic field screens and has application in N M R imaging apparatus.

Current carrying magnet coils are used fora variety of purposes in N M R imaging apparatus. Examples include large electro-mag nets designed to provide static magnetic fields to polarise nuclear spins, magnetic field gradient coils which superi m pose gradients onto the static polarising field and rf transmitter and receivercoils.

In many cases the design of a magnet coil is such as to optimise the magnetic field within a desired volume. 10

However the coil inevitably produces an extraneous magnetic field outside that volume, especially relatively close to the coil. In the case of large bore static electromagnets the high fields they generate will produce undesirably strong extraneous fields at distances outside the magnet corresponding to many magnet diameters. Such magnet systems therefore require much free and unusable space around their instal lation.

Stray magnetic fields maybe intolerable in hospitals because of iron structures positioned around the in- 15 stal lation site which vitiate the homogeneity of the magnetic field Additionally, electronic equipment may not perform well in an environment which has an extraneous magneticfield.

Furthermore, most N M R imaging systems utilise rapidly switched magnetic field gradients in their oper ation. A major problem especially where superconductive magnets are used, is the interaction of the gradient field with the magnet itself. Existing attempts to minimise this interaction include the use of conducting metal 20 screening sleeves. However, induced currents in these sleeves or in the heat shield of the magnet decay with uncontrolled relaxation times which make it difficu It or even impossible to implement some of the faster and more efficient N M R imaging methods. This is because the decaying current produces image fields superim posed on the desired gradient field. This uncontrolled time dependence introduces phase artefacts which can completely ruin the image.

In orderto provide adequate access for patients, and to improve gradient uniformity, it is desirableto maximise the diameter of the magneticfield gradient coils in an NIVIR imaging machine. However,this often causesthe coilsto be closeto other conductors, eitherthe surfaces of cryogenic vessels (in superconducting magnet systems), electromagnetic coil supports (in resistive magnet systems), orferromagnetic pole pieces (in ferromagnetic systems). When gradients are switched rapidly, as with many imaging techniques, eddy 30 currents are induced in these conductorswhich then contribute additional field gradients varying in time and potentiallyvery non-uniform in space. Typical time constantsforthe decay of the eddy currentvaryfrorn a few milliseconds to hundreds of milliseconds, depending on the type of main magnet and the specificcoil configuration.

The commonest solution to this problem isto tailorthe input applied to the amplifiers generating the 35 gradient coil currents in such a waythatthe gradient fields themselves followthe prescribed timevariation.

The inputvoltage and gradient coil currents are characteristically overdriven forthe initial part of the on period of the gradient. Butthis remedy has a major disadvantage. If the gradientcoils are placed closetothe coupled surfaces, so thatthe eddy currentfield gradients may havethe same uniformity asthe desired gradient, the gradientcoils become very inefficient and a large overcapacity in the gradient current amplifiers 40 is required, since the'reflected'fields will be large and in the opposite sensefrom the desired fields. If, on the other hand,the gradient coils are reduced in size,to avoid the amplifier capacity problem, then the reflected gradientfieldswill in general be non-linear overthe region of interest. Furthermore, in eithercase there are likelyto be reflected fieldsfrom more distant conductors in the main magnet structure, each with its distinct time constant and spatial variation.

The only effective solution is in some wayto reduce the gradient fields to zero at a finite radius outsidethe coils, so that no undesired conducting structures may be coupled to them.

Partially effective methods for magnetic screening in specific coil geometries have been proposed hitherto in particular U.S. Patent Nos. 3466499 & 3671902. These geometries are not generally useful in N MR and NIVIR imaging.

It is an object of the invention to provide more efficient and effective magneticfield screens for coil geo metries useful in NIVIR and NIVIR imaging.

It is afurther object of the invention to provide efficient magneticfield screensfor any coil design.

It is a still further object of the present invention to provide magneticfield screensfor any desired compo nent or components of a magneticfield.

According to the invention a screen for a magneticfield comprising a set of electrical conductors and means for supplying the conductors of the setwith electrical currents of magnitude such that a) the resultant current distribution approximates to the induced current distribution in a hypothetical continuous super conductive metal surface positioned in the place of said setso asto appear as a complete reflector of mag neticfield, and b) the resultant current distribution in this or otherscreens behaves alone or in a combination 60 with said otherscreens in such a way as to appearto selectively reflect and/ortransmit desired components& magneticfields of specific configuration through said screen-or screens.

Preferablythe current distribution localised to the surface of a hypothetical conducting sheet orsheets is determined bythe deconvolution of the magneticfield response function of the unit line elements of that current with the field to be screened; such problems being most conveniently solvedli n reciprocal space,

2 GB 2 180 943 A 2 which is defined bythose co-ordinates conjugate to real space used in appropriate integral transform.

More preferablythe problems are solved in Fourier space which is a particular example of reciprocal space.

The present invention also provides a method of designing a screening coil for selectively screening the field of a magneticcoil.

The present invention further provides a gradientcoil systernforuse in NMR apparatus including a main 5 coil designedto provide a gradientfield and a screen coil surrounding the maincoil.

In one preferred arrangementthe conductors of the setare regularlyspaced apartfrom each other.They may beconnected electrically in parallel and have differentvaiues of resistance in orderto producethe desired current distribution. In embodiments ofthe invention the differentvalues of resistance of thecon- ductors may be produced by different thicknesses of the respective conductors or constructing thernwith 10 different compositions having appropriate values of electrical resistivity.

In alternative preferred arrangements the conductors of the set carry equal currents but are spaced apart from each other by different spacings so as to produce the desired current distribution.

It is a further object of the present invention to reduce acoustic vibration in MR gradient coils by using the active screening hereinbefore described.

In examples of carrying outthe above invention a set of conductors are arranged on a cylindrical former and with appropriate spacing can be fed with equal currents. The spacing of the conductors of the set and the magnitude of the currents are calculated using the currents induced in a flat superconductive screen asthe starting point.

Additionally according tothis invention thetheoretical current distribution in a continuous superconduct- 20 ive cylindrical shield positioned in the place of the aforementioned set of electrical conductors is calculated.

Such a calculation enables an improved screen to be provided, especiallywhere a cylindrical screen is re quired.

The calculations described herein represents an analytical formulation of the problem, enabling afully general calculation of the currentdensity in a cylinder required to cancel outside the cylinderthe magnetic fields generated bycoils inside. The results obtained are firstly applied to passive shielding, using athick high-conductivity or superconductive cylindrical tubeto solvethe reflected fields problem without sacrificing gradient uniformity. The conclusions arrived atcan then be applied to active shielding; the calculated current densitieswithin the skin depth of athickcylinder or in a superconducting cylinder are mimicked using a suitable arrangementof a setof wires supplied with currents of appropriate magnitude.

For passive shielding using a normal conducting cylinderto be effective, the skin depth er in the shield atthe lowestfrequency represented in the particular gradient switching sequence must be much smallerthan the thickness d of thewall of the cylinder. For an echo planar switched gradientjor instance, with afundamental frequencyofl KHz, this entails a wall thickness of -10 mm of aluminium. For switched gradients such asthat used for slice selection, where there is a non-zero d.c. component of the fields atthe cylinder surface, passive 35 shielding is not appropriate.

Whenthe criterion of ald << 1 is met, the time dependence of reflected fields will be identical to that of the applied field, and it is only the spatial non-u niformity of the net magnetic field which is of concern. Analytic calculation of the ensuing fields enables the necessary corrections to coil spacingsto be made.

By Lenz's law, a magneticfield screen constructed in accordance with the above design criteria produces a 40 magneticfield which opposes thefield generated bythe primary magnetic coil that it is designed to screen.

Fora given current in the primary coil the resultant magneticfield generated within the volume embraced by the coil is reduced and its spatial variation is also changed by the presence of the screen currents thus intro ducing undesirable variations in the primary field.

It is therefore a further object of the invention to provide a screening coil arrangement in which the above disadvantages are overcome.

Accordinglythe present invention also provides a magnetic coil surrounded by two active magnetic screening coils, namely an inner screen and an outer screen, each respective screen comprising a set of electrical conductors and means for supplying the conductors of the setwith electrical currents of magnitu- des such thatthere is no appreciable magnetic field outside the outer screen and the field within the inner screen substantially corresponds to the field thatwould be provided by the said magnetic coil if the screens were not present.

In orderthat the invention may be more fu lly u nderstood reference will now be made to the accom panying drawings in which:

Figures lto 10 are explanatory of the underlying theory; Figures 11to 17 illustrate in diagrammatic form various em bodiments of the invention; Figure 18 shows a cylindrical co-ordinate system used in calculating the magnetic fields produced by currentflowon a cylindrical surface; Figure 19 illustrates saddle-shaped coils used as magnetic gradientfield coils;

Figure20 illustrates the configuration of one octantof a setof screening coils in accordance with the 60 calculations described herein; Figure21 shows curves for optimising the positions of the arcs of the saddle coils of Figure 19; Figure22 illustrates diagrammaticallythe magneticfield produced by an unscreened primary coil inthe form of a single hoop; Figure23 illustratesthe same hoopwith a double screen embodying the invention; 3 GB 2 180 943 A 3 Figure 24 is a graph showing the magnetic field at different radial positions that is produced by the Figure 23 arrangement;

Figure25is a perspective viewof a double saddle coil used to produce transverse gradientfields which is screened by a double screen embodying the invention;

Figures26to 33 illustrate ways of providing varying current distribution over a desired area; Figure34shows a parallel band arrangement; Figure35shows a series arrangement; Figure36shows various arrangementsfor assisting in reduction of acoustic vibration in MR coils bya gradientwire with (a) a wire pair (b) a wire array (c) a pair of conducting plates used to nullifythe main field in the neighbourhood of the gradient coil and (d) a double active screen arrangement; Figure 37shows winding strategies for screening wires about gradient coils of the (a) standard circular design and (b) saddle design; and Figure 38 illustrates the screening of one coil from the magneticfield of another.

The basictheory and ideas are developed from the simple case of an infinite straightwire parallel to an infinite flat conducting sheet. Figure 1 shows along straight wire carrying a currenfl. The magneticfield B,, at 15 a point Pwhich is ata distance r normal tothewire is given by B(, = (1,0) 21 47r r (1) If the current is changing with angularfrequency wand the wire is nearto an infinite conducting sheetas shown in Figure 2 (also if the current is static and the sheet is superconducting), the magnetic field undergoes distortion atthe metal surface. Let us assume no field penetration into the screen, i.e. the angularfrequency(O and the metal conductivity a are sufficiently high, then the boundary conditions for the magnetic field at the 25 surface are BX = 0 BY= BY B, = 0 (2) The detailsof thefield ata point Pclueto a wire ata distance dfrom the sheet may be conveniently calculated asshown in Figure 3 using the method of imageswhich assumes awire ata distance d from the othersideof the sheet carrying a current 1.

In general, current in the sheet surface is directly related to the tangential field Hy. The total field B. at P, 35

Figure 4, is given by Equation (1) and maybe resolved into components Bx and By in the x and y directions respectively By = (1,0) 21 cos) 41T r so (3) 40 21 sin( BX = (1,0) 41T r (4) Takingthe imagecurrent -1 intoaccount, Figure 5, we obtain the total ydirectionfieid BTOTatpoint Pfora currentl atpointO and its imagecurrent - 1 ata pointO'.

image BTOT = By + BY = OAR) 21 cos4) _ cos (18 1 0-( 41r 111r r 1 We also note f rom Figure 5 that y = r sin( = r'sinO and r cos( + r cosO = 2d If P is on the conducting sheet su rf ace r = r' in which case, see Fig u re 6.

BY = ('-) 41 cos4) 47r r (5a) (6) (7) 60 (8) 65 4 GB 2 180 943 A 4 1 5 r 2 = d 2 + y2 (9) and cos( = d/r (10) From Equations (9) and (10)we obtain d BY = (N) 41 2 + Y2 47r d (11) z Consider now the line integral of the magnetic field in and close to the metal surface, Figure 7. ByAmpere's theorem we have ^A 1 = 1JyAs (12) is where JY is the surface current density and ds an area element and dl a path element. For a short path 1 parallel to the surface H. is constant. The line integral is therefore HY1 - HyA + (H>, + H' W = Jyl (13) But in the metal W= 0 and H,,= H'yielding fordl --> 0 Y X HY = JY (14) 25 The surface current distribution is therefore 1 41d j y J 1 (d) (15) This f unction is plotted in Figure 8.

To determine the field produced by the su rface cu rrent density distribution, let us assu me we have a 35 su rface distribution JY within a flat metal sheet as in Eq uation (15). Consider an element of surface d 1 with current 8i, Figu re 9. This cu rrent is g iven by Bi = (1) 41d dy 47r c12 + y2 (16) 40 The elemental field at point P which is a distance rfrom the element and distance d from the sheet is

BH = Bi) 27rr (17) so The tangential component of which is:- 8H = Bi sind) = Si d 21rr 27r r 2 (18) =.11d2( 1) 2 dy 2)2 7r 41T (d + y (19) Thetotalfieldis f '21c12 (1) dy Hy=2 0 ir4w (d 2 + V2)2 (20) GB 2 180 943 A 5 whichyields B, = 1 (1,0) (21) d 47r 5 Thus the field at point P distanced from the surface current distribution is equivalent to a mirror current of -1 at distance 2d from P.

The total surface current 00 ly=f My = 1 -00 (22) The results derived above suggestthat instead of using a metal plate to screen alternating fields, an active 15 screen comprising a mesh of wires may be used in which a current pattern is externally generating to mimic a desired surface distribution. This situation is shown in Figure 10. Wires at positions Y1, Y2.... Yn in the y direction all carrying an equal current 1 are spaced at different discrete intervals corresponding to equal areasA underthe Ji curve of Figure 8. For equal currents in the wires, the wires must be unequal ly spaced with 20 positions yn which satisfy the relationship 1 2N Y' (n+)=f-1 J1(y)dy 0 (23a) for an even array of 2N wires spread aboutthe y origin. Foran odd array of 2N + 1 wires with one wire atthe origin we have (2N+1) Yn n J1(y)dy 0 (23b) 30 where n = 1, 2,3... Alternatively, wires may be equally spaced with different currents chosen such that nAy In =f J1 (n.Ay)dy (n-l)Ay (24) In either case, since we have arrangedto satisfythe original boundary conditions on the surface of afictitious 40 plate,the magneticfield in the half plane (x,-ty) approacheszero. The degree of screening depends ultimately onthe number of wires used in the active screening mesh.An example of such an activescreen isshown in Figure 11 fora distribution of currentcarrying conductors corresponding to Figure 10 all carrying an equal current I.Thefield B onthe opposite side of thescreen is effective iy zero.

If two parallel screens are used, each will have primary current distributions of Jl(dl) andJ,(d2) given by 45 Equation (15). This is shown in Figure 12. However, each induced current distribution will inducefurther changes inthe distribution in the opposite plate represented byadditional terms Jn(dn). This is equivalenttoa setof multiple reflections, Figure 13,which correspond to an infinite setof images. When d, = c12 = d,image currents occuratx = 2nd, n = 1, 2... Thetotal induced surface current in each sheet isthe sum of J(d) = In Jn(d,).

The boundary conditions atthe metal surface ensurethatthe normal laws of reflection apply. However, when active currentscreens are used,the reflection laws may be selectively changed to reflect any images using the Jn(d)'s corresponding to particular distances d.

An example of a gradient active screen is shown in Figure 14fora single circular hoop of diameter2a. Let this bescreened by an active current mesh in theform of a cylinderof radius a + d. In a metal cylinder,image 55 hoops appearat radii r = b + cl, 3b-td, 5b d, etc. However, sincethe effect of these distant images diminishes quite rapidly, it is reasonableto approximate a screen with Jl(d) corresponding tothe plane sheetcase, Equation (15). Better approximations may be obtained by an iterative numerical approach. Although exact solutions forthe surface current in a cylinder exist, when actual wire screens are constructed,the numerical approach is preferred since it automatically takes accountof thefinite number of wires and their discrete 60 spacing.

The screen currentis N212 (L1) 2.(x Nj I, r2 6 GB 2 180 943 A 6 where N2 is the number of screen wires in the mesh of radius r2 each carrying a current 12 and Nj is the number of turns in the primary coil radius r, carrying a current I,. The factor oL is of the order of unity and is chosen to optimise the screening. The whole optimisation procedure is accomplished by a computational process which generalises to applying m in imisation of the total field over a limited region of space. Mathematically this is conveniently achieved by a least squares method. For practical ease, it is desirable to have both coil and 5 screen driven from the same current source. Since the total screen current is less than the primary current it will in general be necessary to take parallel combinations of the screen mesh so that the tota I system maybe driven in series. However, a parallel arrangement is also possible in which the screen wires are varied in resistance andlorimpedance in such away that when driven from a voltage source appropriate currents flow.

Because of the screening effect the inductance of both versions of the coil system should below.

Sets of screened hoops maybe used to construct screened magnets producing uniform magnetic fields.

The presence of the screen around one hoop is approximately equivalent to an image hoop with negative current producing an opposing field. Fora Helmholtz coil pairthe intercoil spacing equals the coil radius a.

When screened, however, the spacing must be changed so as to make the second derivative of the field B, with respect to z vanish for the combined coil system. Similarly fora Maxwell pair designed to produce a linear magnetic field gradient, the intercoil spacing is ideally a 3. This is shown in Figure 15. The two hoops forming a Maxwell pair are screened by a concentric pair of screening meshes offset axia I ly from each other.

The combined screen current distribution is also shown. Again, however, when screened coils are used, a new spacing obtains which makes the third derivative of B,, with respecttoz vanish for the total coil system.

The process of optimisation of coil geometry can be done analytically for simple coil structures as discussed 20 above. For more complicated systems such as screened saddle geometry gradient coils, it is preferable simple to find by computational means the position where the chosen derivative vanishes, or is minimised.

For N M R imaging systems using superconducting magnet coils it is convenient to use saddle coils to produce the transverse gradients aB, and aB, ix- ay In some imaging techniques, at least one of the gradients can be very large making interaction with the main magnet potentially serious. Figure 16 shows one half of a Gx screened gradient coil system. A screened single 30 saddle coil is shown in end view at (a) and plan view at (b). The dotted lines correspond to the screening mesh.

To a first approximation, the screen current profile is Jl(d). Better screening maybe obtained by an iterative procedure which minimises the field outside the screen.

Figure 17 shows a screened rectangular Gx gradient coil set with 1/2 screen. Again, if a d<<2a,Jj(d) maybe used as a good approximation for the screen current distribution. For better results other reflections can be 35 included orthe iterative procedure used to minimise fields outside the coil.

N M R imaging systems require rf coil systems to deliver rf pulses to the specimen and to receive signals induced in the sample. Because of then u m ber of other coil systems required for field gradients, there is always a problem of space. With normal rf coi I arrangements the field outside the coil drops off ratherslowly.

In orderto minimise coi I interactions which can lower the Q value, rf coil diameters are often chosen to be around 0.5 to 0.7 of the gradient coil diameter. With shielded rf coil designs, it maybe possible to utilise more of the available space without loss of performance.

A systematic procedure for reducing extraneous magnetic fields outside the active volume of static mag nets, field gradient coil systems and rf coils has been described. In N M R imaging, reduction of stray fields in all three types of coil structure is extremely important. The method utilises active magnetic screens and has 45 the advantage that such screens operate independently of frequency down to dc. Some price is paid in terms of reduction of field in the active volume compared with that of the free space value. With time dependent gradients, the price is in general acceptable since for fast NMR imaging schemes employing rapid gradient switching, active coil screening maybe the only way in which such imaging schemes maybe made to operate in the relatively close confines of an electromagnet.

In what has previously been described, iterative and least suqares approximation methods are used to obtain actual screening wire positions. It is possible to obtain these positions directly using analytical methods. If the gradient coils and screens are located on cylindrical formers, it is natural to use cylindrical co-ordinates p, (, z in orderto retain the symmetry of the system. The z axis is taken to lie along the axis of the cylinder as shown in Figure 18.

The vector potentialA, is used to describe the magnetic field. This has the components AP, A,, A, given by

AP=R.f Jb,(r)dv'sin()-(5') (25) 4,,, Ir-el 60 g. J4,,(iJ) dv'cos(( - A4, = Zf Ir - iJI (26) 7 GB 2 180 943 A 7 Az = N J,,(e) dv' T, f ir-,-1 (27) whereJisthe current densityand dv'is a volume element corresponding tothe position vectorr'.There isno 5 current flow in the radial direction in many problems of interest so J has only z and) components.

It has been assumed that currents induced in the shield are confined to the surface of a cylinder of radius b. The gradient coilsto be shielded are mounted on a cylindrical former of radius a which is coaxial with the shield. The currents can then be written as J= F(z,))8 (p -a)+ f(z,4))3(p -b) (28) 10 where Fdescribes the current in the gradient coils, f describes the current induced in the shield and 8 is the Dirac delta function. It is possible to derive relationships between Fand f from the condition that the radial component of the magnetic field is zero on the surface of the shield. The other constraint which is used isthe equation of continuity, which, in the absence of charge accumulation is 15 7.j=0 (29) The vital step in the analytical treatment of this system is the use of the Green's function expansion 1 = -1 ms T dk e'-(b-)')e Mz - z') I m(kP<Wm (kp>) Ir-el 7r m - 00 -00 (30) where m is an integer and p< (p>) is the lesser (greater) of p and p', and lm(z) and Km(z) are modified Bessel functions. To use equation (30) in equations (25), (26) and (27) it is helpful to define a type of Fouriertransform of f and Fasfollows:

fnlk) ' f 7d4) e-'"T dz e -ikzfz(4>, Z) (31) 30 z -7-r -7r m 1 1T OC ikz f,,(), Z) f) (k) = 21T f iT d.e-'m'bf dze- (32) 35 wherethe quantities F', (k) and IF',5 (k) are defined in an analogous way. The components of A thus become (e.g. for p> b):

[10 00 00 40 Az -i7-r m Y. 0 f ', dk e'" e ikz KM%) [bi,(kb)fT(k) + alm(ka)Fm(k)l z z (33) 45 A4,=-E-0- ='Y'.O"fwdk e'-4e'kz[b(im-l(kb)Km-l(kp) 4, m - -1 so + lm+l(kb)K.+,(kp))f'lk) 50 + a(im-l(ka)Km-l(kp) + 1m+1 (ka)Km,l (kp))F'1k)l (34) 55 -iKo 00 00 AP= 4m = 1 cc Ld.ke'mlbe"(z[b(lm-l(kb)Km-l(kp) - lm+l(kb)Km+l(kp))fnlk) + a(in,-,(ka)Kn,-,(kp) 60 -]m,, (ka)Km,l (kp))Fnlk)l (35) 4) 8 GB 2 180 943 A Similar expressions can be obtained when p< a or a <p<b.

Now letthe boundary condition that the radial component of the negative field BP= Oat p= b be applied. This is equivalent to

1 aA, 1 aA. 1 b ab p=b az p=b Equations (33) and (34) are now used and terms varying as ei'4) are equated. This gives 8 (36) 2m Km (kb) [bl,,(kb)f m (k) + ai,,(ka)F m (k)l = fm) (k)b[ln-l(kb)Krn-l(kb) +]m+l(kb)Km,l(kb)l + FM (k)a[lm-l(ka)Km-l(ka) +]m+l(ka)Km+l(ka)l (37) 20 This equation can be simplified using the relations derived from the equations of continuity, 1 af,5 af,. - 25 U -ab -5 z (38) forthe currents in the shield, and 1 a F, aF, a a4) az (39) forthe currents in the gradient coils. 35 These equations are equivalentto f m (k) kb f m (k) (40) m z 40 and F m (k) ka Fm (k) 4) m z The recurrence relations for Bessel functions are also used, from which can be derived the identity so (41) 45 Im-1 (zl) Km-1(Z2) + lm+l(zl) Km+1(Z2) + (2M2/Z1ZA lm(zj)KjZ2) = 21m'(z1) Km'(Z2) (42) Here the prime denotes the derivative. 55 Equations (37), (40), (41) and (42) can be combined to obtain the elegant expressions, m m a 2 1,j(ka) z z l(kb) f m (k) F9k) a In,'(ka) b I m'(kb) (43) (44) 9 GB 2 180 943 A These identities provide the means of calculating fields due to any combination of currents constrained to flow on the surface of a cylinder inside a conducting shield. This will now be illustrated with an example.

For transverse field gradients it is common to use a saddle coil configuration such as shown in Figure 19. Two pairs of saddle coils are shown. One pair extends between -dl and -d2 along the z axis. The otherpart 5 extends between +dl and +d2 along the z axis. With energisation of the coils as marked a gradientfield is produ(:;id in the form of a magnetic field along the z axis which has a gradient in the x direction. The field produced by such coils extends widely outside the cylinder on which the coils are wound unless they are shielded by a conductive sleeve.

Forthe standard coil geometry with 120'arcs forthe saddle coils.

F,(),z) = 1{8(z-dl) + 8(z+dl) - 8(z-d2) - 8(z+d2)} 27r 21T {H(4) ±10 H(, H() -) (1 H (( + 5-)) 3 3 3 (45) where HM isthe Heaviside stepfunction. This hasthe Fouriertransform F m (k) = 2sin(mTr/3) 1 (cos(kdl) - cos(kd2)) Mir X (1 - elmI (46) This is zero form even or an integer multiple of 3. This leaves non-zero terms form= 1, 5,7, 11 etc.

The position of the screening arcs can now be determined as follows. First it is necessary to specify the continuous current distribution to which the arcs approximate asset out in equations (43) and (44).

The actual surface current density may then be written fe,(4),z) 8 a sin M7r 1 =--2- =1 S COSM( bm 5,7 m 00 coskz dk (coskdl - coskd2) In,'(ka) G'(kb) (47) 35 and f"((,z) 8a 5 sin M7r sin m(h 1 -7 b m=l, 5,7 3 00 (coskdl - coskd2) 1,n'(ka) sinkz dk bk ImUb) (48) 45 The next step is to determine the stagnation point of this current density, that is, the point S = (Qd) atwhich f(b and f, are both zero, around which the surface currentflows. By symmetrythis occurs at 1) = 0, and sincefz 50 (0, z) = 0 for all z, it may be found by solving f, (0, z) = 0, by successive approximation.

Having found S, the integrated surface current It crossing the line SP between S and an arbitrary point P on the cylinder (Figure 20) is given by lt(-,z) = gf,, (0,z)dz - b tf,.(,,z)d.

(49) 55 (using the surface version of the divergence theorem). Hence 1t4A 1 8 a sin MIT b m, 5,7 -m dk T-i(-k- k. b)k (sinkz cosm( - sinkd) (50) GB 2 180 943 A Thecontours of the induced surface current may now befound bysetting lt((, z) = constant. These maybe translated into positions of screening arcs in thefollowing way. Thetotal currentinthe cylinder lt(0,0) is divided by2N, where N isthe numberof screening arcs required, andthe Wth arcconsists of thecontour where lt(4),z) =(2 M - 1) 2N (51) In practice lt((5,z) is calculated overa grid of 50 X 45 points, andthe contours arefound by linear interpolation 10 between the calculated points.

To checkthatthese arcs indeed provide adequate screening of saddlecoil fringe fields, thetotal field can be calculated usingthe Biot-Savart Law, taking as line elements d/the intervals between successive calculated coordinate pairs along each arc.

Given a set of saddle coils with radius 0.31 m and arc spacings from the centre d, and d2 of 0.108 m and 0.404 15 m,the shielding produced at 0.55 m radius, using six screening arcs on a cylinder of radius b = 0.45 m, is as follows:

Maximum unscreened field =0.6x10-c) T/A-turn

Maximum screened field (z < 0.5 m) = 0.2 x 10-7 T/A-turn Maximum screened field (z < 1.0 m) = 0.47 X 10-7 PA-turn

For comparison, the maximum field at 0.55 m radius produced by an unscreened small scale saddle coil set (a = 0.16 m, d, = 0.56 m, d2 = 0. 206 m) is 0.86 X 10-7 PA-turn.

Figure 20 shows the configuration of one octant of the set of screening coils calculated above.

A larger number of screening arcs, orthe use of foil ratherthan wire conductors, will further reducethe fringefields.

Screening a set of saddle coils, the spacing of which has been optimised withoutthe screen present, inevitably reduces the uniformity of the gradients produced. The uniformity may be recovered however by adjust- ing the arc spacing as follows:

The z component of the magnetic field can be derived from equations (34), (35), and (44) to give

Bz Ka m=000000 dk e'-4e ikz k Fr.1k) 21r L. 35 {Km'(ka) _ Km'(kb)Im'(ka)} Im%) (52) Im '(kb) 40 This becomes,with substition of equations (45) and (46) 00 B, _.E.a L. dk kcos m4) cos(kz) Im%) 1T m= 1A7,. 45 x.!sin(m7,l3) 1 (cos(kd 1) - COSM2)) {K,,'(ka) IT m K,J(kb)l,J(ka)} ImUb) (53) It is now possible to optimise the gradient linearity by adjusting the arc positions of the saddle coils. The 55 termsfor m= 5 are of fifth order in x,y orz,whereasthere aretermsfor m= 1 which are of first order in xand of third order in x, y and z.

The optimum choice of the parameters d, and c12 is the one which removes the third orderterms. This gives the condition 4 00 dk k4 (cos(kdl) cos(kd2)) {K,'(ka) - Ki'(kb)W(ka)}=0 11'(kb) (54) 11 GB 2 180 943 A 11 There are now two unknown quantities, D, (=dl/a) and D2(=c12/a) and only one constraint, so it is not possible to give a unique choice of parameters. However it can be ensured that each parameter separately satisfies the equation 00 Ki'(Q01'M dt t 4 cos(tD) {K, 1(t) --- --- 11 ' (at)} (55) (with a = b/a) for this automatically satisfies equation (54).Values of D, and D2 as a function of CL are shown in Figure 21.

It is possible to improve on this arrangement by altering D, and D2 slightly (subjectto the constraintgiven by equation (55)) and minimising thefifth orderterms. Thefinal choice of values of D, and D2 depend on whetherthe x orzvariation is considered to be more important. The values of Dl(ct) and D2(OL) shown represent an excellent starting point in the search forthe optimum position of the saddle coils.

Referring nowto Figure 22 there is shown therein a magnetic coil in theform of a singlewire hoop 1 of 15 radius a carrying a current +1. In Figure 23 the same wire hoop 1 is surrounded bytwo active magneticscreens S1 and S2. Each screen comprises a set of electrical current carrying conductors butfor sim plIcity the screens are shown as sections of cylinders. Outer screen S1 is a cylinder of radius b and innerscreen S2 is a cylinderof radiusc.

With appropriate screen current density distributions screens S1 and S2 acttogether as a flux guide confin- 20 ing thefield lines in the manner indicated. The design criteria forthe current density distributions are setout below.

For a single conducting screen S,the boundary conditions of the magneticfield 8(r-r) atthe surface of the screen require onlythatthe axial component B, (r-r', z'z') is considered which for a coaxial hoop is indepen- dent of azimuthal angle (b. for perfect screening it is required that IB,(r-a,z) + Bs(r-b,z) = 0 Z for r >band foraU z, where B,(r-aj) is the primary hoop field per unit current and B S (r-b,z) (56) is the total field generated by the screen. The screen field is the convolution of the su'rface current densityj,(z) with the hoop magnetic field response per unit current. Equation (56) may therefore be written as

0" 1 Bz (r-aA L.Bz (r-b,z-z')j(b(z')dz' Notethat F9q) = J' (q) = J (q) 1q); F' 4) Z z f%) = j9q); R(q) = j'(q) z z where q may be takento be korz.

The spatial Fou rier transform of equation (57) gives so 1 Bz(r-aA = - Bz (r- b,k)j4,(k) (57) 35 (58) 50 wherekisthe reciprocal space wave number.

Equation (58) maybe generalised for two screens with current densities j' (k) and j2 (k) as set out below. For zero field in the ranger --band the unperturbed hoop field for r -- cthere is obtained

1 B, (r-a,k) = -Bz (r-b,k)j (k) - Bz (r-c,k)j 2 (k) for r -- b 0 = Bz (rb,k)j 1 (k) + Bz(r-c,k)j 2 (k) for r -- c (59) (60) 12 GB 2 180 943 A 12 The current hoop fields are evaluated numerically along thez-axis onthe appropriate cylindrical surface usingthe Biot-Savart Law,then Fouriertransformedto k-space. This allows numerical solution ofthesimult aneous equations (59) and (60)yielding the k-space current densities. These arethen inversely transformed to yield the actual screen current density distributions.

In this example consider a primary hoop of radius a = 0.5 m shielded bytwo active screens S1, S2 with radii 5 b = 0.75 m and c = 1.0 m respectively. The hoop current is 1 A. Using the Computed distributions, thetotal magneticfield generated bythe screen system in the hoops plane (z = 0) is calculated as a function of r. This is shown in Figure 24 which is a graph of a calculated z-component of magneticfield B,(r,O) against radius in the plane of a doubly screened flat current hoop of dimensions as in Figure 23. The unscreened hoop field is shown bythe broken curve and is equal to Bjor r < 0.75 m. As expected for r < c, the field B, exactlyequals 10 that of the unscreened hoop. For r > b, the f ield B is zero. Between the screens, the field is wholly negative. The total screen currents are given by 11 = j' (0) and 12 = j2 (0). In this case 12 11 = 0.57 1. The results have been

41 1b produced by numerical methods using a computer.

The innerscreen S2 behaves like a complete absorber of the primaryfield. However, oncetrapped between 15 the screens, the field is completely internally reflected by S1 and S2. The screen S2 behaves like a perfect one-way mirror. Practical screens having these properties clearly cannot be continuous metal surfaces. Externally driven discrete wire arrays which approximate the calculated continuous surface current densities are used instead. For a common screen current, wires are placed at current positions corresponding to equal areas underthe current density distribution integrated over discrete intervals, as described in the above patent specifications.

Although active screening of a single hoop has been described in the above example, the principles of double screening applyto other geometries, for example f lat screens as well as more complex coil geometries, some of which are used to produce linear gradients in NIVIR imaging.

On the basis of the analytical expression forthe component of the magneticfield B, which is set out in 25 equation (52), equations (59) and (60) become, for k-space.

aill(ka) = -bil(kb)j 1 (k) - cl, (kc)j 2 (k), for r > b (61) 4) 30 0 = b K, (kb)j (k) + cK, W0 2 (k), for r < a (62) 35 which yieldthe current densities j 1 (k) = -1a]l(ka) 1 - 11 (kc) K, (kb) -l 40 (5 bll(kb) L 11(kb)Kl(ke 1 (63) and j 2 (k) = -j 1 (k) b K, (kb) c K, (kc) (64) For k=O, KiM)/K1(kc) = c/b and 11 (ka)/I1 (kb) = a/b from which it is deduced thatthe total currents 11, 12flowing 50 in S, and S2 are equal and opposite. From equations (63) and (64) there is obtained [. l 2 [ 1 _[ 11 =; -1 b bl 2 = -12 -1 (65) 55 (66) If a= Chereby making the primary coil and S2 Coincident, the condition b = aV2- makes 11 = -1 = =12 and 60 means thatthe coil and screens maybe placed in series. For discrete wire arrays chosen to approximate the required continuous current distributions, equations (65) and (66) become N.I.=Nill b 2 1_ [C] 21 [a] 1 b (67) 65 13 GB 2 180 943 A 13 and Nil, = -N212 (68) where N,[,, Nil, and N212 arethe ampere-turnsforthe primarycoil and screens S, and S2 respectively. A more 5 general series coil arrangement is possible byvarying both theturns and screen radii in equations (67) and (68).

AMaxwell pairof two hoopswith opposite currents may be usedto generate a z-g radient field. Since doublescreening produces the free space field forthe hoops inthe region r< a,the usual coil spacing aF3 obtains forthe most linear gradient along the z-axis.

Figure 25 shows a simple saddle coil of radius a used to produce a transverse gradient. Letthis be shielded bytwo active cylindrical screens S, and S2 with radii band c respectively where a --c< b. Fora standard saddle geometry with 120'arcs, the primary current is J,b (4),z) = 1{8(z-dl) + 8(z+dl) - 8(z-d2) - 8(z+d2)} X {H(4)+7r/3) [1 -H()-7r/3)1-H((-217/3)[1 -H(.+27r/3)1} (69) where H(o) is the Heaviside function. The Fourier transform ofequation (69)is Ak) = 2sin(m7r/3) 1[cos(kd2) - cos(kd,ffil -e imTr (5 MIT (70) This is zerofor m even or an integer of 3. Since there are now manyvalues of rn, equations (61) and (62) are generalised to givefortwo shields Jnlk)ai'(ka) =-bi'(kb)jl'm(k) ci'm(kc)j2,m (k) 4) m m( (71) (P 0 = bK'(kb)jl'm(k) + cCkc)i 2 ' m (k) m) m) (72) From equations (71) and (72) there is obtained the resultsthat j (k) = 5 j 1 ' m (k) = -Jrlk)!nM Im'(ke)Km'(kb) m bm x Im'(kb) 11 Im'(kb)Km'(k) -1 (73) 40 and 2 5 2,m by 1,m)Krn'(kb) j (k) j (k) j (k (b m -b cm (b K,'(kc) (74) These results evaluated at k = 0 give for each separate arc pair at dl and:td2the total azimuthal screen currents 11 and 12. The dominant components of these currents arise from them= ltermsandmaybe simplified by noting that atk = 0, 11'(ka)Al'(kb) = 1 and Kl'(kb)/K1'(kb)/K1'(kc) =C'/b 2 Thez-componentsof currentflowing in the screens may be calculated by noting that divil r =R= 0 (75) which expanded gives ahlaz = - 1 aj la.

R (76) 60 14 GB 2 180 943 A 14 Fou rier transforming equation (76) gives j m (k) = - --T j (k) (77) Z Rk 5 Equation (77) for R= b or c and equations (73) and (74) give on transforming to z-space the actual screen surface densities.

The above results have shown that by introducing a second active screen the spatial response within a primary coil can be made to be independent of the surrounding screens. The inner screen maybe positioned 10 to be coincident with the primary coil and still remain the above advantages. While in the above description two active magnetic screens have been employed it is possible to extend the principles of active magnetic screening of coil structures to multiple screens. Use of two or more than two screens has the advantage that the screens can be designed so as not to vitiate or change the character of the magnetic field spatial response from the primary coil structure being screened. This istrue even when the inner screen of a two or multiple screen structure is coincident with the primary coil structure.

The calculations and analytical expressions presented referto continuous currentdensity distribitions in the screens. Practical active screens require discrete wire arrays which simulate the continuous current den sity distributions. Discrete screens also allow exploitation of the selective transmissive and reflective prop erties of the active magnetic shields.

The object of a magnetic screen is to provide a spatial current distribution which mimics that which is theoretically induced in a real and/orfictitious continuous conducting sleeve around a coil structure in which the coil itself is producing a time-dependent magnetic field gradient. Equation 24 describes an arrangement in which wires are equally spaced by with currents chosen again to mimicthe induced surface currentdis tribution in a continuous metal screen.

Several methods of varying the current in these conductors are:

1. To include in each conductor a small resistor chosen to given required current.

2. To change the diameter orthe shape of the wire so as to affect its resistance in the right manner.

3. Change the composition of the conductorto affect its resistance.

These situations are covered in Figures 30 and 31.

[twill also be clearfrom the above discussion that when the conductor size is changed as in Figures 31 and in the limit of uninsulated touching wires, we have the situation shown in Figure 27. An alternative arrange mentto this is a profiled cross-sectional band of material as shown in Figure 26. Alternative ways of produc ing this band or its effect are shown in Figures 28 and 29. The thickness t of the band must be chosen such that the electro magnetic penetration depth 8 is less than tforthe highest frequency present in the currentswitch- 35 ingwaveform.

Itwill be seen thatthe above conductor arrangements 26 to 31 could be parallel arrangements or bands as in Figure 34fed with appropriate total current along the edges indicated. However, it is conceivable that one could manufacture multi turn band structures producing a series arrangement as in Figure 35.

An alternative approach using a constant standard wire section employs the wire arrangements in Figures 40 32 and 33. Here the wires are stacked in such a manner as to produce the desired current distribution. If the wires are uninsulated and touching this is an alternative method of producing the equivalent arrangement of Figure 26. However, if the wires are insulated and touching itwill readily be seen that all the turns may be in series. A series arrangement will have a much higher inductance but require only a small common current through each turn. The parallel arrangements discussed earlier requirethe driver circuitryto provide thetotal 45 field screen currentfor a one turn arrangement as in Figure 34.

In orderto obtain images by magnetic resonance it is necessaryto switch gradients rapidly. Fortypical magnetic gradient strengths the current 1 required is commonly around 150 Amps. These currents,when flowing in the staticfield B produce a force per unit length of is so F=1x8 onthewires carrying this current. For parts of the gradientcoll thefield 8 and the current/may be per pendicularthus maximising thisforce. The resultant motion of thewires causes acoustic noisewhich can be very loud if strongly coupled to the coil former. This problem is growing in severitywith the use of higher 55 staticfields. The situation isfurther exacerbated by used of larger gradient coils where the wire length is greater over which the force can act. Rapid imaging strategies can also create more noise.

Solutionsto the noise problem such as embedding thewires in rigid materials like concrete do help by lowering the natural resonances of the coil former and by absorbing some acousticenergy. Surroundingthe wireswith some softacoustic absorbing material such as cotton wall can also reducethe noise. Butthese 60 approaches treat the symptoms ratherthan the cause.

In afurther example of the use of the present invention the problem is solved at source by reducing the B fieldto zero in thevicinity of thewires. This eliminates the force on and hence motion of thewires. Aswell as solving the noise problem, the lackof motion of thewires removesthe possibility of progressive fatiguing and fracture of the conductors.

0 2 GB 2 180 943 A 15 In orderto dothisthewires on the gradienteoil are locallyscreened magnetically from B. This isachieved byusing the principles of active screening. Asingie screen arrangement is created byarranging thescreening wires in series. Different arrangements areshown in Figure36. With these arrangements the far field, i.e.

coordinates x, z fora point P a distance R >> awhere a isthe half separation of the screen pair (Figure36), is effectively unperturbed. For an infinite straight wire screen the interior and exterior screening fields B. and B 5

P (R >> a) are respectively B, Hol ira (78a) a (Z2-X 2) BP 21r---R4 where R2 = X2 + Z2 (78b) (78c) For small separation B. can be very large and BP small. This represents a netfall off rate which goes as 1/R 2. Forfinite wires the fall off is basically dipolar i.e. goes as 1/R 3. 20 For parallel infinite sheets the fields are

Bc = KOJ BP=0 (79a) (79b) where J is the current density per unit length. Forthe arrangements sketched in Figures 36a to 36c respectively the screening efficacy will lie between the cases covered in Equations (78) and (79). Becausethe screen produces a static field, perturbation of the main field can be eliminated with a shim set. The screen or counterfield generator need be active only during the experimental period.

To further reduce the extraneous staticfields produced bythe wire screening arrangement, a second active 30 screen may be used in addition to the f irst screen.

Such a double active screen arrangement is sketched in Figure 36. The wire W is roughly screened by a parallel plate arrangement S,. Residual farfields arising from non-cancellation outside the plates is annulled by a second active screen S2 comprising a set of conductors distributed appropriately. Figure 37 showstwo local wire screening strategies for a circular hoop (37a) and a saddle gradient (37b).

Using the wire screening arrangement described, the benefits of rapid switching of large gradients may be obtained within a high static magnetic field without acoustic noise.

Screening could also be applied to a Hal 1 probe to increase its sensitivity to small field variation by remov ing the main central field. 1

In addition to the application of active magnetic screening to electromagnet and gradientcoil designthere 40 are a number of possible applications in rf coil design. For example a fully screened series wound rf coil placed coaxially inside an unscreened coil would have zero mutual inductance. However an NIVIR sample placed insidethe screen coil would sensefields generated by both coils. The coilsthough coaxial therefore behave electrically asthough theywere orthogonal. This can have advantages in multi-nuclear irradiation and detection.

Aschematic example of one such possible configuration is shown in Figure 38 where an innercoil Cl is wound inside an outer coil C2. The inner coil Cl can be screened by providing a suitablywound screening coil CS between thetwo coils.Cl and C2. The screen coil CS is as shown connected in series with coil Cl to passthe same current. It is generally longerthan the coils Cl and C2 to provide efficient screening and is wound such thatthe current in coil CS opposes that in coil Cl. The exact positioning of the wires in coil CS is determined by 50 using the above approach.

Claims

1. A screen fora magneticfield comprising a set of electrical conductors and means for supplying the 55 conductors of the set with electrical currents of magnitude such that a) the resultant current distribution approximates to the induced current distribution in a hypothetical continuous superconductive metal surface positioned in the place of said set so as to appear as a complete reflector of magnetic field, and b) the resultant current distribution in this or other screens behaves alone or in combination with said other screens in such a way as to selectively reflect and/or transmit desired components of magnetic fields of specific configuration 60 through said screen or screens.

2. A screen as claimed in Claim 1 in which the current distribution localised to the surface of a hypothetical conducting sheet or sheets is determined bythe cleconvolution of the magnetic field response function of the unit line elements of that current with the field to be screened; such problems being most conveniently solved in reciprocal space, which is defined by those co-ordinates conjugate to real space used in an app16 GB 2 180 943 A 16 ropriate integral transform.

3. A screen as claimed in Claim 1 or Claim 2 in which the conductors of the set are regularly spaced apart from each other.

4. A screen as claimed in anyone of Claims 1 to 3 in which the conductors are connected electrically in 5 parallel and have different values of resistance in order to produce the desired current distribution.

5. A screen as claimed in Claim 3 or Claim 4 in which the different values of resistance of the conductors maybe produced by different thicknesses of the respective conductors or by constructing them with different compositions having appropriate values of electrical resistivity.

6. A screen as claimed in Claim 1 or Claim 2 in which the conductors of the set carry equal currents but are spaced apart from each other by different spacings in such a manner that the current in one wire is equal to an 10 integrated incremental theoretical surface current distribution such increment values to be equal for each wire so as to produce the desired current distribution.

7. Ascreen as claimed in Claims land 2 in which the number of screen wires is even and correspondsto the even arc integrated surface current distribution contours.

8. A screen as claimed in Claim 1 or 2 in which the number of screen wires is odd and corresponds to the 15 odd arc integrated surface current distribution contours.

9. A screen as claimed in anyone of Claims 1 to 8 in which the surface current distributions JY is defined by 1 41d J,= 20

10. A screen as claimed in anyone of Claims 1 to 8 in which the magnetic field is created by a current Fin gradientcoils and in which the current f defines the current in the shield and in which the Fouriertransforms of the currentf is defined as m 1 7r -im)- -ikz f z (k) = 17 f 7r d( e f dz e f.(4), z) m 1 ir -im)- f) (k) = 27r- f 17 d( e f dze- ikz f 4, z) -00 4) and wherein the quantities Fm (k) and Fmk are defined in an analogous way.

11. A screen as claimed in Claim 10 in which the relationship for the Fou rier components of the currents induced in the shield to that in the gradient coils is defined as m m a 2 Irn'(ka) f Z (k) F z (k) dpl(kb) f m (k) F m (k) a 1,'(ka) b Iffl'(kb)

12. A screen fora magnetic field created by a coil in which the coil is surrounded by two or more active magnetic screening coils, namely an inner screen and an outer screen, each respective screen comprising a set of electrical conductors and means for supplying the conductors of the set with electrical currents of magnitudes such thatthere is no appreciable magnetic field outside the outer screen and the field within the inner screen substantially corresponds to the field that would be provided by the said coil if the screens were not present.

13. A screen as claimed in Claim 12 in which the theoretical surface currents, ',m (k) 2,m (k) which lie on hypothetical cylinders of radii b &c corresponding to the outer and inner screen, are defined in FourierSpace 55 as C,n ,k)ai'm(ka) = Cbi'm(kb) -cl'm(k m (k) (71) f ( ( 0 W.'(kb) cK'rn(k)c), f 2,m (k) (72)

14. An active magnetically screened coil around which is a second unscreened coil such that the mutual inductance between the pair is zero, which coil system maybe used at rf frequencies as an NIVIR transmitter/ 65 17 GB 2 180 943 A 17 receiver orthogonal coil set, or as a double resonance transmitter coil set in which each coil maybe independently tuned to a different frequency.

15. A method of designing a screening coil for selectively screening the field of a magnetic coil comprising calculating the position of and current distribution within the wires of the screening coil such that a) the resultant current distribution approximates to the induced current distribution in a hypothetical continuous superconductive metal surface positioned in the place of said set so as to act as a complete reflectorof magnetic field, and b) the resultant current distribution in this or other screens behaves alone or in combination with said other screens in such away as to appear to selectively reflect and/or transmit desired components of magneticfields of special configuration through said screen or screens.

16. A gradient coil system for use in an NMR apparatus including a main coil designed to provide a 10 gradientfield and a screen coil surrounding the main coil the screen coil comprising a set of electrical conductors, means for supplying the conductors of the setwith electrical currents of magnitude such that a) the resultant current distribution approximates to the induced current distribution in a hypothetical continuous superconductive metal surface positioned in the place of said set so as to appear as a complete reflector of the magnetic field produced by the main coil and b) the resultant current distribution in this and/or other screens 15 behaves alone or in combination with said other screens in such away as to appear to selectively reflectthe gradient field and transmit a] 1 other fields through said screen or screens.

17. A screen fora magnetic field substantially as described with reference to the accompanying drawings.

Printed for Her Majesty's Stationery Office by Croydon Printing Company (UK) Ltd,2187, D8991685. Published by The Patent Office, 25Southampton Buildings, London WC2A 'I AY, from which copies maybe obtained.

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