X-RAY SOURCE WITH AN ELECTROMAGNETIC PUMP

Abstract

A liquid metal jet X-ray source including an electromagnetic pump for pumping the liquid metal. The electromagnetic pump includes a core having a core diameter and an outer yoke with a thickness of at least 20% of the core diameter. Preferably, the thickness of the outer yoke is at least 20% of the core diameter plus 6% of a radial distance between an outside of the core and an inside of the yoke.

Claims

1. A liquid metal jet X-ray source, comprising: a nozzle for providing a liquid metal jet; an electron source for providing an electron beam to interact with the liquid metal jet such that X-ray radiation is generated; an electromagnetic pump for providing liquid metal to the nozzle; wherein the electromagnetic pump comprises a core having a first diameter and an outer yoke with a thickness of at least 20% of said first diameter.

2. The liquid metal jet X-ray source of claim 1, wherein there is a distance between an outer periphery of said core and an inner periphery of said outer yoke, and wherein the thickness of the outer yoke is at least 20% of said first diameter plus 6% of said distance.

3. The liquid metal jet X-ray source of claim 1, wherein said core and said outer yoke comprise iron or magnetic steel.

4. The liquid metal jet X-ray source of claim 1, further comprising a collector for collecting material forming the liquid metal jet and transporting it to an inlet of the electromagnetic pump.

5. The liquid metal jet X-ray source of claim 1, wherein the electromagnetic pump comprises: a conduit arranged in windings around said core for transporting the liquid metal from an inlet to an outlet; a permanent magnet, arranged concentrically with said core, providing a radial magnetic field through said conduit; a current source for providing an electrical current through the conduit in an axial direction along said core and substantially perpendicular to said magnetic field.

6. The liquid metal jet X-ray source of claim 5, comprising at least a first and a second segment along an axial direction of said core, wherein a first permanent magnet is arranged in the first segment and a second permanent magnet is arranged in the second segment, said first and second permanent magnets being arranged with opposite magnetic field orientations, and wherein the conduit winding direction in said first segment is opposite to the conduit winding direction in said second segment.

7. The liquid metal jet X-ray source of claim 5, wherein liquid metal is allowed to flow both inside and outside of a wall of said conduit.

8. The liquid metal jet X-ray source of claim 5, wherein said conduit is immersed in an incompressible medium.

9. The liquid metal jet X-ray source of claim 5, wherein said conduit is made from a non-magnetic material.

10. The liquid metal jet X-ray source of claim 1, wherein the electromagnetic pump is configured to provide liquid metal to said nozzle at a pressure of at least 100 bar.

11. The liquid metal jet X-ray source of claim 1, wherein said X-ray source is arranged to provide the liquid metal jet as a freely propagating jet from said nozzle.

12. The liquid metal jet X-ray source of claim 1, further comprising a vacuum chamber, wherein the nozzle, the electron source, and the electromagnetic pump are comprised within the vacuum chamber.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The above, as well as additional objects, features and advantages of the present inventive concept, will be better understood through the following illustrative and non-limiting detailed description of different embodiments of the present inventive concept, with reference to the appended drawings, wherein:

[0071] FIG. 1 schematically illustrates a first conduit section and a second conduit section;

[0072] FIG. 2 schematically illustrates an electromagnetic pump in a cross-sectional view;

[0073] FIG. 3 schematically illustrates an embodiment of a first conduit section and a second conduit section in a cross-sectional view;

[0074] FIG. 4 schematically illustrates a further embodiment of a first conduit section and a second conduit section in a cross-sectional view;

[0075] FIGS. 5a and 5b schematically illustrate a further embodiment of a first conduit section and a second conduit section in cross-sectional views;

[0076] FIG. 6 schematically illustrates a further embodiment of a first conduit section and a second conduit section in a cross-sectional view;

[0077] FIG. 7 schematically illustrates an X-ray source comprising an electromagnetic pump;

[0078] FIG. 8 schematically illustrates core and yoke geometries of an embodiment; and

[0079] FIG. 9 is a cross sectional view illustrating dimensions and sizes of an embodiment.

[0080] The figures are not necessarily to scale, and generally only show parts that are necessary in order to elucidate the inventive concept, wherein other parts may be omitted or merely suggested.

DETAILED DESCRIPTION

[0081] Referring to FIG. 1, a first conduit section 102 and a second conduit section 104 are illustrated. The first conduit section 102 here comprises a tube or pipe, and is arranged as a right-handed helix, and the second conduit section 104 here comprises a tube or pipe, and is arranged as a left-handed helix. The first conduit section 102 may be fluidly connected to the second conduit section via an intermediate conduit 157. The direction of a magnetic field B generated by a magnetic field generating arrangement (not shown), a current direction I, and a flow direction P within each conduit section are illustrated. As can be seen, a direction of the magnetic field B, the current direction I, and the flow direction P, are all mutually orthogonal.

[0082] FIG. 2 illustrates an electromagnetic pump for pumping an electrically conductive liquid 100 in a cross-sectional view along a main axis A of the electromagnetic pump 100. The electromagnetic pump 100 here comprises four conduit sections 102, 104, 106, 108. It is however to be understood that the electromagnetic pump 100 may comprise at least a first conduit section 102 having an inlet 110 and an outlet 112, and a second conduit section 104 having an inlet 114 and an outlet 116, wherein each one of the conduit sections 102, 104 is arranged to provide a flow of the liquid from its inlet to its outlet. The outlet 112 of the first conduit section 102 is further fluidly connected to the inlet 114 of the second conduit section 104. The further conduit sections 106, 108 illustrated in this embodiment may be seen as a repeat of the first and second conduit sections 102, 104, i.e. subsequent to the first and second conduit sections 102, 104, yet another first and second conduit section 106, 108 are arranged. The terms “first conduit section” and “second conduit section” may in this regard be seen as a reference to a type of conduit section, rather than a specific conduit section.

[0083] The electromagnetic pump 100 further comprises a current generator 120 arranged to provide an electric current through the liquid in the first conduit section 102 and the liquid in the second conduit section 104 such that a direction of the electric current is substantially perpendicular to the flow of the liquid in the first conduit section 102 and in the second conduit section 104. The direction of the electric current and the flow of the liquid in the conduit sections are more clearly illustrated in FIG. 3. It should be noted that the current generator 120 may be connected to other points than illustrated in FIG. 2.

[0084] The electromagnetic pump 100 further comprises a magnetic field generating arrangement 122 arranged to provide a magnetic field passing through the liquid in the first conduit section 102 and the second conduit section 104 such that a direction of the magnetic field is substantially perpendicular to the flow of the liquid and the direction of the electric current. Similarly to the above, the direction of the magnetic field is more clearly illustrated in FIG. 3.

[0085] The first conduit section 102 and the second conduit section 104 are configured to provide an orientation of the flow of the liquid in the first conduit section 102 that is opposite to an orientation of the flow of the liquid in the second conduit section 104.

[0086] Further, the electromagnetic pump 100 may comprise a main inlet 124 and a main outlet 126 for respectively receiving and ejecting the liquid. Further, a yoke 128 encasing the first conduit section 102 and the second conduit section 104 may be comprised by the electromagnetic pump 100. The yoke 128 comprises a ferromagnetic material. Further, the yoke 128 here comprises end pieces 130, 132, arranged, respectively, before the first conduit section of the electromagnetic pump 100, here being the first conduit section 102, and after the last conduit section of the electromagnetic pump 100, here being the second conduit section 108. The terms “before” and “after” in this regard are made with respect to a main flow direction M, defined by a flow vector between the main inlet 124 and the main outlet 126. In particular, the term “before” may be interchangeable by the term “upstream”, and the term “after” may be interchangeable by the term “downstream”. The end pieces 130, 132 of the yoke may provide routing of the magnetic field. A core 129 is also arranged in the electromagnetic pump 100. The magnetic field may thus go from the inner pole of the magnetic field generator 122, pass radially through the conduit of the first conduit section 102, go through the core 129, the end piece 130, and the yoke 128 into the outer pole of the magnetic field generator, thus completing a closed magnetic circuit.

[0087] The electromagnetic pump 100 may further comprise lids 136, 138 configured to be connected to the yoke 128. The lids 136, 138 may provide mechanical support and feed-throughs for the electrically conductive liquid 124, 126 and the current I. In particular, the lids 136, 138 may be configured to withstand a pressure generated via the forces acting on the electrically conductive liquid by the electromagnetic pump 100.

[0088] Referring now to FIG. 3, a first conduit section 102 and a second conduit section 104 are illustrated in a cross-sectional view. A main flow direction is here indicated by the direction M in the figure. The main axis A is also indicated. The first conduit section 102 and the second conduit section 104 are here consecutively arranged along the main axis A.

[0089] The first conduit section 102 comprises a first coil 140 wound in a first direction around the main axis A, and the second conduit section 104 comprises a second coil 142 wound in a second direction around the main axis, the second direction being opposite the first direction. In other words, the first conduit section 102 comprises a first coil 140 being either of a right-handed and left-handed coil, and the second conduit section 104 comprises a second coil 142 wound in a second direction around the main axis, i.e. being the other of a right-handed and left-handed coil. From the illustrated cross-section, the specific orientation of the conduit sections 102, 104, i.e. whether they are left-handed or right-handed coils, cannot be deduced. In contrast, what is of relevance is that the first and second conduit section 102, 104 respectively have opposite orientation.

[0090] In the illustrated cross-section, the flow of liquid in the first conduit section 102 is indicated by flow directions 144 and 146, while the flow direction in the second conduit section 104 is indicated by flow directions 145 and 147; the flow propagates either out of (indicated by points) or into (indicated by crosses) the illustrated plane.

[0091] A direction of an electric current I through the liquid in the first conduit section 102 and the second conduit section 104 is indicated, the direction of the electric current I being substantially perpendicular to a flow of the liquid in the first conduit section 102 and in the second conduit section 104.

[0092] The electromagnetic pump 100 further comprises a magnetic field generating arrangement, which here comprises a first magnetic field generator 148 arranged to at least partially enclose the first conduit section 102, and a second magnetic field generator 150 arranged to at least partially enclose the second conduit section 104, wherein the first magnetic field generator 148 is arranged with a type one magnetic pole 152 (in this example the south pole S) facing radially towards the first conduit section 102 and a type two magnetic pole 154 (in this example the north pole N) facing radially away from the first conduit section 102, and wherein the second magnetic field generator 150 is arranged with the type one magnetic pole 152 (in this example the south pole S) facing radially away from the second conduit section 104 and the type two magnetic pole 154 (in this example the north pole N) facing radially towards the second conduit section 104, the type one and type two magnetic poles 152, 154 being opposite magnetic poles. Owing to the arrangement of the first and second magnetic field generators 148, 150, the magnetic field generated by the respective magnetic field generators 148, 150 are mutually closed by means of each other.

[0093] A magnetic circuit provided by respective magnetic field generators 148, 150 passes through the liquid in the first conduit section 102 and the second conduit section 104 respectively such that a direction of the magnetic field is substantially perpendicular to the flow of the liquid and the direction of the electric current I.

[0094] The yoke 128 encasing the first conduit section 102 and the second conduit section 104, as well as the core 129 are also visible in the illustrated cross-section.

[0095] An intermediate reservoir 156 is fluidly connected to the outlet 112 of the first conduit section and the inlet 114 of the second conduit section 104. The intermediate reservoir 156 is here formed by the core 129, an outer wall 158, and at least part of the first conduit section 102 and at least part of the second conduit section 104. The electrically conductive liquid (not illustrated) may thus flow from the first conduit section 102, via the intermediate reservoir 156, into the second conduit section 104. The electrically conductive liquid being located in the intermediate reservoir 156 may also serve to pass the electric current I from the first conduit section 102 to the second conduit section 104. It is further envisioned that an intermediate conducting element, such as an electrically conducting cuff (not illustrated) may be arranged between the first and second conduit sections 102, 104. The intermediate conducting element may extend around the main axis A, thus increasing a contact area between the intermediate conducting element and the first and second conduit section 102, 104 respectively. One embodiment of such an intermediate conducting element may be represented by an open cuff, wherein the opening in the cuff forms part of the intermediate reservoir 156.

[0096] The outer wall 158 may be electrically insulating, and/or made from an electrically insulating material.

[0097] Each conduit section 102, 104 may further comprise an interconnecting arrangement. The interconnecting arrangement may be configured to allow the electric current to travel within each one of the conduit sections. In particular, the interconnecting arrangement may be configured to allow the current to travel in a direction being perpendicular to the flow direction within each conduit section. The interconnecting arrangement may be configured to conduct electrical current.

[0098] Referring now to FIG. 4, a similar arrangement as described in conjunction with FIG. 3 is shown. For the sake of avoiding repetition of already discussed features, like elements between the embodiments described in conjunction with FIGS. 2, 3 and 4 will not be further discussed in the following sections. The main flow direction is indicated by the direction M.

[0099] The magnetic field generating arrangement here comprises a first magnetic field generator 148 arranged on an inlet side 111 of the first conduit section 102, arranged with a type two magnetic pole 154 facing axially towards the first conduit section 102 and a type one magnetic pole 152 facing axially away from the first conduit section 102. A second magnetic field generator 150 is arranged on an outlet side 113 of the first conduit section 102 and an inlet side 115 of the second conduit section 104, wherein the second magnetic field generator 150 is arranged with the type two magnetic pole 154 facing axially towards the first conduit section 102 and the type one magnetic pole 152 facing axially towards the second conduit section 104, the type one and type two magnetic poles 152, 154 being opposite magnetic poles. The term “axially” is here referring to the main axis A. Further, the first magnetic field generator 148 is here a cylinder having a first diameter 160 being smaller than a first coil diameter 161 of the coil of the first conduit section 102. Similarly, the second magnetic field generator 150 is a cylinder having a second diameter 163 being smaller than a second coil diameter 165 of the coil of the second conduit section 104.

[0100] The first magnetic field generator 148 is arranged to provide a magnetic field passing through the liquid in the first conduit section 102 such that a direction of the magnetic field is substantially perpendicular to the flow of the liquid and the direction of the electric current I. The second magnetic field generator 150 is arranged to provide a magnetic field passing through the liquid in the second conduit section 104 and the liquid in the first conduit section 102 such that a direction of the magnetic field is substantially perpendicular to the flow of the liquid and the direction of the electric current I.

[0101] In the illustrated cross-section, the flow of liquid in the first conduit section 102 is indicated by flow directions 144 and 146, while the flow direction in the second conduit section 104 is indicated by flow directions 145 and 147; the flow propagates either out of (indicated by points) or into (indicated by crosses) the illustrated plane.

[0102] Magnetic field circuit lines are illustrated in FIG. 4, and the magnetic field provided by the respective magnetic field generators 148, 150 passes through the liquid in the first conduit section 102 and the second conduit section 104 respectively such that a direction of the magnetic field is substantially perpendicular to the flow of the liquid and the direction of the electric current I.

[0103] An intermediate conducting element 162, for example an electrically conducting cuff, is arranged between the first and second conduit sections 102, 104. The intermediate conducting element 162 is here also arranged before the first conduit section 102. The intermediate conducting element 162 may extend around the main axis A, thus increasing a contact area between the intermediate conducting element 162 and the first and second conduit section 102, 104 respectively.

[0104] The outlet 112 of the first conduit section 102 may be fluidly connected to the inlet 114 of the second conduit section 104 by means of an intermediate reservoir as described in conjunction with FIG. 3, and/or by an intermediate conduit (not shown). The intermediate conduit may extend substantially the same distance from the main axis A as the first and second conduit sections.

[0105] Referring now to FIGS. 5a and 5b, a further embodiment of a first and a second conduit section 102, 104 is illustrated. For the sake of clarity, some parts of the electromagnetic pump are here omitted from the illustration. It should be noted that the illustrated figures are merely schematic and not necessarily to scale.

[0106] Referring first to FIG. 5a, a cross-sectional view illustrates several conduit sections 102, 104, 106, 108. An interconnecting arrangement 158 is arranged to allow the electric current I to travel, within each one of the conduit sections 102, 104, 106, 108 and from the inlet to the outlet of each one of the conduit sections, a distance being shorter than the liquid path. The liquid path of a first conduit section 102 is here illustrated by the path P, and the distance of travel of the electric current from the inlet to the outlet of the first conduit section 102 is indicated by the distance D. Each conduit section in the illustrated embodiment may have a meander shape.

[0107] The flow of the liquid in the first conduit section 102 is here indicated by flow direction 144. For the sake of clarity, a positive direction is also indicated by an arrow with a (+)-sign. It can thus be seen that the flow of the liquid in the first conduit section 102 substantially follows the positive direction. The flow of the liquid in the second conduit section 104 is indicated by flow direction 145. The orientation of the flow in the second conduit 104 is opposite the orientation of the flow in the first conduit 102, i.e. the flow direction 145 in the second conduit section 104 is substantially opposite the indicated positive direction. This arrangement and resulting flow is partially made possible by the arrangement of the magnetic field generating arrangement, which will be further described in conjunction with FIG. 5b.

[0108] Referring now to FIG. 5b, a cross-sectional view of the further embodiment of the first and second conduit section 102, 104 is illustrated. The cross-sectional view is perpendicular to the cross-sectional view illustrated in conjunction with FIG. 5a.

[0109] Several conduit sections are here illustrated. Each conduit section is associated with a respective magnetic field generator. For example, a first magnetic field generator 148 is arranged to at least partially enclose the first conduit section 102. The first magnetic field generator 148 is arranged with the type one and two magnetic poles 152, 154 such that magnetic field circuit pass through the conduit and the liquid in the conduit substantially perpendicular to a direction of the electric current I. Furthermore, the arrangement of the magnetic field generators 148, 150 may serve to close the magnetic field circuit between the two magnetic field generators.

[0110] Referring now to FIG. 6, a further embodiment of a first and a second conduit section 102, 104 is illustrated. For the sake of clarity, some parts of the electromagnetic pump are here omitted from the illustration. It should be noted that the illustrated figures are merely schematic and not necessarily to scale.

[0111] Each conduit section in the illustrated embodiment may be formed as a spiral shape in a single plane. For example, a first conduit section 102 may be formed as a spiral shape in a single plane S.sub.1, and a second conduit section 104 may be formed as a spiral shape in a single plane S.sub.2. The first and second conduit sections 102, 104 preferably have the same orientation, i.e. being both either clockwise or counter-clockwise turning spirals. However, the orientation of the flow of the liquid in the first and second conduit sections 102, 104 respectively is opposite in that it flows from an outer part of the first conduit section 102, radially towards an inner part of the first conduit section 102, and from an inner part of the second conduit section 104, radially towards an outer part of the second conduit section 104.

[0112] Further, an outer electric current conductor 164 and an inner electric current conductor 166 is here provided. The electric current I is directed from the outer electric current conductor 164, via the conduit sections and optionally interconnecting arrangements configured to allow the electric current to travel within each conduit section, to the inner electric current conductor 166. The electric current hereby passes from one side of a conduit, via the electrically conducting liquid, to an opposite side of the conduit, and further to a nearby part of the conduit, optionally via an interconnecting arrangement.

[0113] A magnetic field generating arrangement may comprise a first magnetic field generator 148 arranged on an inlet side 111 of the first conduit section 102, wherein the first magnetic field generator 148 is arranged with a type two magnetic pole 154 facing axially towards the first conduit section 102 and a type one magnetic pole 152 facing axially away from the first conduit section 102, and a second magnetic field generator 150 arranged on an outlet side 113 of the first conduit section 102 and an inlet side 115 of the second conduit section 104, wherein the second magnetic field generator 150 is arranged with the type two magnetic pole 154 facing axially towards the second conduit section 104 and the type one magnetic pole 152 facing axially towards the first conduit section 102, the type one and type two magnetic poles being opposite magnetic poles.

[0114] An intermediate conduit 157 is here arranged between the first conduit section 102 and the second conduit section 104, wherein the intermediate conduit 157 provides a fluid connection between the outlet 112 of the first conduit section 102 and the inlet 114 of the second conduit section 104.

[0115] Referring now to FIG. 7, which illustrates an X-ray source 170 comprising: a liquid target generator 172 comprising a nozzle configured to form a liquid target 174 of an electrically conductive liquid; an electron source 176 configured to provide an electron beam interacting with the liquid target 174 to generate X-ray radiation 177; and an electromagnetic pump 100 according to the inventive concept. The liquid target 174 may be a liquid jet. Accordingly, the electromagnetic pump 100 of the inventive concept may be configured and/or suitable to provide a liquid jet. The X-ray source 170 may further comprise a low pressure chamber 178, or vacuum chamber 178. A recirculating path 180 may also be arranged in liquid connection with a collection reservoir 182 for collecting the liquid being ejected from the liquid target generator 172, and in liquid connection with the liquid target generator 172. The generated X-ray radiation 176 may exit the X-ray source 170 via transmission through an X-ray transparent window 184.

[0116] As illustrated in FIG. 7, the electromagnetic pump 100 can be arranged inside the vacuum chamber 178 in comparatively close proximity to the electron source 176. Hence, it may be advantageous to take measures so that the pump does not interfere magnetically with the electron beam. An embodiment that takes this into account will be discussed with reference to FIG. 8.

[0117] A schematic cross-sectional view of two sections of an electromagnetic pump according to the present disclosure is shown in FIG. 8. FIG. 8 is similar to FIG. 3 and the same reference numerals are used in this discussion. However, in order not to clutter the view, some reference numerals are omitted in FIG. 8. The liquid metal is transported in tubes, e.g. thin-walled stainless steel tubes, that are wound around a central core. The flow direction of liquid metal in the tubes is indicated by points (flow out from the plane of the view) and crosses (flow into the plane of the view).

[0118] In some embodiments, liquid can also be allowed to flow outside the tubes, thereby reducing the pressure difference across the tube wall. More generally, the tubes (i.e. the conduits for the liquid metal) may be immersed or embedded in an incompressible medium. Such incompressible medium may be a parallel flow of the same liquid metal as inside the tubes, or it may be another liquid that is separated from the liquid metal inside the tubes. It is also conceivable that the incompressible medium is, for example, an incompressible potting compound such as an epoxy. The incompressible medium may also provide electrical connection between adjacent tube walls.

[0119] In order to maximize the magnetic field through the liquid metal and thereby maximizing the pumping power, the inner core C and the outer yoke Y are preferably made from a ferromagnetic material. Both the core and the outer yoke can thus comprise iron, magnetic steel, or the like. In the embodiment of FIG. 8, the magnetic field generators are permanent magnets which are arranged between the core and the yoke. Permanent magnets can be advantageous since no electrical feed-throughs are required for generation of the magnetic field, which enables a less complex design.

[0120] The length of one section is indicated by the arrow b in FIG. 8. A permanent magnet is located in each section, as illustrated in the figure. The length b of one segment is limited by the saturation magnetization of the (iron) core. If a circular symmetry is assumed (which may be typical), this condition can be written as

[00001]$\pi {\varnothing }_C\frac{b}{2}B\le \frac{\pi {\varnothing }_C^2}{4}{B}_S$

which can be re-written as

[00002]$b\le \frac{{\varnothing }_C}{2}\frac{B_S}{B}$

where B is the magnetic field strength provided by the magnets, B.sub.s is the saturation magnetization of the (iron) core, and Ø.sub.C is the diameter of the core.

[0121] A corresponding argument for the outer yoke Y gives a minimum thickness of the yoke in order to contain the magnetic field. Again, for circular symmetry with an inner diameter of the yoke being Ø.sub.1 and an outer diameter of the yoke being Ø.sub.2, the following condition applies

[00003]$\pi {\varnothing }_1\frac{b}{2}B\le \frac{\pi \left({\varnothing }_2^2-{\varnothing }_1^2\right)}{4}{B}_S$

which can be re-written as

[00004]${\varnothing }_1^2+{\varnothing }_1\frac{2b}{B_S}B\le {\varnothing }_2^2$

[0122] By inserting the upper limit for b from above, which corresponds to utilizing the largest possible magnetic flux in the core, this expression reduces to

Ø.sub.2.sup.2≥Ø.sub.1.sup.2+Ø.sub.1Ø.sub.C

and for the limiting case where the inner diameter of the yoke approaches the diameter of the core, this reduces further to

Ø.sub.2>√{square root over (2)}Ø.sub.C

[0123] Thus, the thickness of the yoke may, in the same limit, be written as

[00005]$\frac{{\varnothing }_2-{\varnothing }_1}{2}>\frac{\sqrt{2}-1}{2}{\varnothing }_C\approx 0.2{\varnothing }_C$

[0124] It can be understood that the thickness of the yoke should be at least 20% of the core diameter. In many embodiments, the magnets will have a non-negligible thickness and a gap is required between the core and the yoke to make room for the tube that carries the liquid metal. If the radial distance from the outside of the core to the inside of the yoke is denoted t, then the following applies.

Ø.sub.1=Ø.sub.C+2t

and thus

Ø.sub.2.sup.2≥(Ø.sub.C+2t).sup.2+(Ø.sub.C+2t)Ø.sub.C

which can be re-written as

Ø.sub.2≥√{square root over (2Ø.sub.C.sup.2+6Ø.sub.Ct+4t.sup.2 )}

[0125] In the limit where t is small (i.e. thin magnets and a narrow gap), this last inequality can be approximated as

[00006]${\varnothing }_2\ge \sqrt{2}{\varnothing }_C+\frac{3t}{\sqrt{2}}$

and in this limit, the thickness of the yoke can thus be written as

[00007]$\frac{{\varnothing }_2-{\varnothing }_1}{2}>\frac{\sqrt{2}-1}{2}{\varnothing }_C+\frac{3-2\sqrt{2}}{2\sqrt{2}}t\approx 0.2{\varnothing }_C+0.06t$

Hence, in a preferred embodiment the outer yoke has a thickness of at least 20% of the core thickness plus 6% of the radial distance between the outside of the core and the inside of the yoke.

[0126] Embodiments in which the thickness of the outer yoke is at least 20% of the core diameter, or preferably at least 20% of the core diameter plus 6% of the radial distance between the core and the yoke, as described above thus have the advantage that magnetic leakage is prevented or at least drastically reduced, and interference with the electron beam is thereby eliminated or at least drastically reduced. A thick outer yoke also has the additional advantage that it may sustain a higher pressure in and around the tube that carries the liquid metal.

[0127] In some embodiments of the present invention, it may also be preferred to consider the dimensions of the gap in the magnetic circuit. To avoid deterioration of performance at elevated temperatures, the gap in the magnetic circuit should be made as small as possible. However, making the gap smaller may decrease pump capacity. Considerations in this regard will be described below.

[0128] When designing an electromagnetic pump based on permanent magnets, the characteristics of the magnet material should be taken into account. Rare earth permanent magnets, in particular neodymium based, exhibit a reversible linear behavior over at least some parameter range. This makes them particularly suited for this kind of devices. However, when temperature is increased, the linear relation breaks down for high demagnetizing fields. This drawback may be avoided if the working point corresponds to a sufficiently high induced field. For rare earth magnets such as neodyumium magnets, the magnitude of the induced field should generally be higher than the magnitude of the demagnetizing field, i.e. B.sub.m>−μ.sub.0H.sub.m.

[0129] With reference to FIG. 9, for a cylindrical geometry and with the assumption that no fields leak to the environment, the following expression can be set up

[00008]$\frac{B_m}{H_m}=-\frac{L_{m}P}{A_m}$

where B.sub.m is the induced field, H.sub.m is the demagnetizing field, L.sub.m is the average length of the path in the magnet, A.sub.m is the average area of the magnet, and P is the external permeance, in this case the annulus between the cylindrical magnet and the core. By setting the relative permeability in the annulus to 1, magnet length to L, outer diameter of the magnet to D.sub.y, inner diameter of the magnet to D.sub.0, and diameter of the core to D.sub.i, the following expression is obtained

[00009]$\frac{B_m}{{\mu }_0{H}_m}=-\frac{L_m}{A_m}\frac{2\pi L}{\ln \left(\frac{D_0}{D_i}\right)}=-\frac{2\pi L{L}_m}{\pi D_{m}L\ln \left(\frac{D_0}{D_i}\right)}=-\frac{2\left(\frac{D_y-D_0}{2}\right)}{\left(\frac{D_y+D_0}{2}\right)\ln \left(\frac{D_0}{D_i}\right)}$

where D.sub.m represents the average magnet diameter. The above-mentioned condition B.sub.m>−μ.sub.0H.sub.m can thus be written as

[00010]$\frac{2\left(D_y-D_0\right)}{\left(D_y+D_0\right)\ln \left(\frac{D_0}{D_i}\right)}>1$

By setting the gap between the core and the magnet to δ/2, the above inequality can be re-written as

[00011]$\frac{D_y-D_0}{\left(D_y+D_0\right)\ln \left(1+\frac{\delta }{D_i}\right)}>\frac{1}{2}$

Under the assumption that the gap is small compared to the diameter of the core, this can be approximated to

[00012]$\frac{D_y-D_0}{\left(D_y+D_0\right)\frac{\delta }{D_i}}>\frac{1}{2}$

which can be rearraged to

[00013]$\frac{\delta }{2}<\frac{\left(D_y-D_0\right)D_i}{\left(D_y+D_0\right)}$

[0130] FIG. 9 illustrates the measures used in the expressions above, and also indicates a helical conduit provided inside the annular space between the magnet and the core. As will be understood, an actual embodiment will also include a yoke to complete the magnetic circuit, but such yoke is not shown in FIG. 9 for reasons of clarity. Embodiments with multiple sections having alternating polarity of the magnets and the winding directions of the conduits may be used to achieve the desired pump performance. In FIG. 9, the magnet is shown as a single radially magnetized hollow cylinder, but it may alternatively comprise a plurality of arc shaped magnets assembled to achieve a cylindrical configuration.

[0131] The pressure drop over the conduit decreases rapidly (to the fourth power) with increased diameter of the conduit. This would encourage implementations where the diameter of the conduit, and hence the gap in the magnetic circuit, is made large. However, the effective magnetic field will also decrease as the gap is made larger, thus making the pump less efficient. The decrease in magnetic field is a relatively weak function of the gap size. A preferred embodiment would have a gap size close to the limit δ/2 derived above.

[0132] The inventive concept has mainly been described above with reference to a few embodiments. However, as is readily appreciated by a person skilled in the art, other embodiments than the ones disclosed above are equally possible within the scope of the inventive concept, as defined by the appended patent claims.

LIST OF REFERENCE SIGNS

[0133] A Main axis

[0134] b Segment length

[0135] C Core

[0136] I Electric current

[0137] M Main flow direction

[0138] N Magnetic north pole

[0139] S Magnetic south pole

[0140] S.sub.1 Single plane

[0141] S.sub.2 Single plane

[0142] t Radial distance between core and yoke

[0143] Y Yoke

[0144] Ø.sub.C Core diameter

[0145] Ø.sub.1 Inner yoke diameter

[0146] Ø.sub.2 Outer yoke diameter

[0147] 100 Electromagnetic pump

[0148] 102 First conduit section

[0149] 104 Second conduit section

[0150] 106 Conduit section

[0151] 108 Conduit section

[0152] 110 Inlet

[0153] 111 Inlet side

[0154] 112 Outlet

[0155] 113 Outlet side

[0156] 114 Inlet

[0157] 115 Inlet side

[0158] 116 Outlet

[0159] 120 Current generator

[0160] 122 Magnetic field generating arrangement

[0161] 124 Main inlet

[0162] 126 Main outlet

[0163] 128 Yoke

[0164] 129 Core

[0165] 130 End piece

[0166] 132 End piece

[0167] 136 Lid

[0168] 138 Lid

[0169] 140 First coil

[0170] 142 Second coil

[0171] 144 Flow direction

[0172] 145 Flow direction

[0173] 146 Flow direction

[0174] 147 Flow direction

[0175] 148 First magnetic field generator

[0176] 150 Second magnetic field generator

[0177] 152 Type one magnetic pole

[0178] 154 Type two magnetic pole

[0179] 156 Intermediate reservoir”

[0180] 158 Outer wall

[0181] 160 First diameter

[0182] 161 First coil diameter

[0183] 162 Intermediate conducting element

[0184] 163 Second diameter

[0185] 164 Outer electric current conductor

[0186] 165 Second coil diameter

[0187] 166 Inner electric current conductor

[0188] 170 X-ray source

[0189] 172 Liquid target generator

[0190] 174 Liquid target

[0191] 176 Electron source

[0192] 177 X-ray radiation

[0193] 178 Low pressure chamber/Vacuum chamber

[0194] 180 Recirculating path

[0195] 182 Collection reservoir

[0196] 184 X-ray transparent window