IL33204A - An improved ion-optical system - Google Patents

Description

An improved ion-optical System THE STATE 03? ISRAEL, ATOMIC ENERGY COMMISSION C, 30030 This invention concerns an improved ion optical system for use with, magnetic prisms such as, for example, the magnetic sectors used in mass separators.

With a good ion optical system, as in a light optical system, the achievement of a hig sharpness of the image, i.e. a high degree of resolution (of ions of different masses) should he combined with a high intensity of the ion beam. In contrast with analytical mass spectrometers in which the ion resolving power is of primary importance, in the case of mass separators the consideration of high intensity is not less important, since it determines the ion yield of the apparatus.

The relatively high intensity of the ion beam whic it is desired to obtain rules out the use of electrostatic "ion lenses" in mast* separators and, moreover, requires that the accelerated ions emerge from the ion source through relatively long (up to 10 cm) exit slits (or objeot slits), and that the ion beam will have a considerably wide aperture.

This requirement, however, of mass separators is in conflict with the requirement for optimal ion-resolving power, since a long exit slit and a large aperture angle of the ion beam adversely affect the image qualities of the ion optical system. The use of longe object slits and wider beam apertures introduces considerable "image errors", causing increased blurring o "smearing" of the image. As a consequence, the separating power of the system is reduced, i.e. an efficient separation of the ionB is prevented. This effect is even the more serious where ions of isotopes of higher masses are concerned, since in the magnetic-sector type instruments the distance between the images of ions of successive masses In order to understand more clearly the theoretical eonsldera iocs which give rise to the invention,, reference is made to Figures 1, 2a and 2b of the accompanyin drawings of which ©few; Fig> 1 shows a schematic plan view in the median (x»y)-plane o the ion optical system of a magnetic sector type mass separator* showing the main geometrical parameters; Fig. 2a is a schematic representation of the left-hand part of the view shown in Fig. 1, showing the "radial aperture angle" a of one trajectory of the ion beam originating at a point located at a distance u f om the median plane; Fig. 2b is a schematic sid view, in the vertical (x,z)-plane of the view shown in Fig. 2a, showing the "axial aperture angle" β of one trajectory of the ion beam originating at a point located at a distance s from the vertical plane.

In. a; system using magnetic prisms,' such as a., magnetic-sector type mass separator, the direction of propagation of the ion beam s defined as the x-axis (the '.. longitudinal direction), the direction of the magnetic lines of force, which is perpendicular to x, is defined as the '. '' z-axis (axial direction), the y or radial direction being the third orthogonal axis .and the origin.of. the coordinate . system is located in the . centre .of the virtual object.' The -^y and x-z. planes are' referred to as. the median and vertical planes-, respectively.- (See Figs 1,and 2). .

With a magnetic sector type mass separator the' aberration of the image' Ay in the y-axis is most decisive in the determination of the separating power, since -it causes :the blurring of the image in the. intervals between neighbouring images, which may cause their mutual overlapping.

This aberration is due to ions having' trajectories . which deviate slightly .from the principal trajectory. The deviating trajectories are defined by the- following variables:... u, a, s, β, which. are all shown in Figs. 2a and 2b of the accompanying drawings.- a and β are the radial and axial aperture angles, respectively, u and s are the horizontal and vertical distances, respectively of-the'point of origin of the' trajectory, from the 'Vertical and median planes, respectively." -"..'. ■ .··· ".

The radial aberration A can be expressed as a sum of terms -in various . powers of u, a, s. and β and combinations ■'of powers- of these variables. These terms -can be either/- homogeneous,- such as (a second order term), or non-: homogeneous, Buch as β β (a third order term). All terms have appropriate coefficients A^, which are complicated functions of the major geometrical parameters of the system, a nd of Other minor parameters related to the fringe field of the magnetic prism. She major parameters, most of which are shown in Fig. 1 of the accompanying drawings are: φ - the angle of the magnetic field sector. £*# g" - the angles of incidence and exit respectively, of the beam at the entry and exit boundaries of the magnetic field. %9 » V - distance of object sli and image* respectively, from the magnetic field entry and exit boundaries respectively. r» , r" - the radii of curvature of these boundaries at the points of Intersection of the principal trajectory. tV, t" - the third order coefficients defining the third order profile of these boundaries* As used in this specification the terms "entr boundary" and "exit boundary" of a magnetic field are the effective field boundaries of the magnetic prism* which have been determine taking into account the magnetic fringe fields and as contrasted with the physical boundaries of the magnetic prisms. The effective boundaries can be calculated, e.g. according to R. Herzog, Z. ifaturf, 10a, 887 (1955).

The geometrical parameters determining lengths are hereinafter expressed in pure numbers as ratios of the radius of deflection R, which is shown in Fig. 1, while angles are expressed i radians.

C e invention is not concerned with the variable u and since the width of the exit slit is very small compared to its e t m d th t = 0 n t co s ati n d exit slit in the median x*y plane oan be considered as a point source. On this assumption those aberration terms containing powers of u are neglected, hereinafter.

In order to achieve optimal image qualities in necessary particular system', it is ^t-*ee4-e««Ae to choose the major geometrical' parameters so that the sum of the aberration terms to the highest possible orde is minimalized.

In practice this may be done by formulating mathematical expressions for the coefficients of the aberratio terms up to the required order, involving the geometrica parameters mentioned above. 3?hese expressions are then equated to zero and a set of equations for the required parameters is thus obtained.

Mathematical expressions for the aberration term's up to the second order inclusive, in which the magnetic fringe fields have been taken into account, have been formulated by Wollnik, Nucl. Instr. and Meth. £!, 215 (1965).

A mathematical formulation of the aberration terms up to and including the third order terms has only been given without including the effects o f inge fields b Ludwig, Z. Haturf. 22a. 553 (1967). But evGn if such an expression we e available, which would take into consideration the fringe fiel effects, its complexity makes it doubtful whether actual solutions for the various parameters could be reached, affording the desired minlmalization of the aberration.

It is an object of the presen invention to provide a new and improved ion optical system which permits the formulation of definite mathematical expressions for the coefficients of the aberration terms up to and including the • - -third order, in which account is taken of the fringe field effects, and the practical solution of these equations, to determine the optimal geometrical parameters; of the system.

According to the present invention there is provided an: ion optical system used with a homogeneous magnetic prism having pole pieces spaced apart a distance "g" establishing a magnetic field in the "ZM direction of an orthogonal coordinate system having axes "X", ^Y n and "ZM comprising! an ion source for producing ions? means defining an, emission alit whose length S in the "Z" direction is large in comparison to its width in he "Y" direction for establishing the emitting area of the source? an extraction system for shaping ions emitted from the slit into a beam vrhose principal trajectory is in the X-direction and which has a radial divergence angle a in the radial "X-Y" plane; -means fo causin the. ion beam ÷p converge in the axial "X-Z" plane and tobe axially focused a distance from the slit into a line perpendicular to he principal trajectory of the beam and lying i the median radial "X-Y" plane, where is the distance between the slit and the effective entry boundary of the field of the magnetic prism? the ion source being cooperable with the extre.ction system for causing the maximum angular dispersion Δβπ1βχ in the axial "X-Z" plane to be much smaller than g/1* where Δβ is the deviation in the "X-Z" plane of the trajectories of ions emitted from any point on the area of the source from a line connecting such point to the focus; the parameters of the optical system being such that: (a) the angle of incidence € of the beam at the entry boundary of the magnetic field is zero for causing the principal trajectory of the beam to be normal to the entry - 6a * . : - - boundaries respectively, the angle 0 of the magnetic field sector/ nd the angle of exit β" of the b¾am at the exit boundary of the magnetic field all havin i values .which satisfy the main focusing .conditions,/ as defined herein (c) the quantities 1' and 1", 0 and G ff t and the radius of curvature r" of the, exit ' boundary, being such that the coefficient of the (S a) aberration term, as fined herein, is zero; nd (d) the quantities IV, 1", , , €" and rn being such that the coefficient of the (3Δβ) ' aberration term, as defined herein, is zero* In most ion sources used with such optical systems, every point of the object slit emits a narrow bundle of rays each deviating b > some value &β from the mean! direction β originating at this point .

As indicated above, the present invention relates onl to ion optical systems wherein this angular, dispersion-is; ·...'· relatively small, namely wherein: M. ί ^mx ' ; ' where g is the width of the gap of the magnetic prism and · is as hereinbefore defined. In systems having larger angular dispersions Δβ, the axial focusing of the; ion beam according to the invention is in practice unfeasible.

The variable Δβ iwhich will appear in certain terms of the expression for the aberration, by virtue of it being very small in the systems concerned, may be regarded as a deviation of second order. ' ' -.

In c onsequence of this axial ocussing of the ion beam, according to the invention, at the entry boundary of . the magnetic field, all ion trajectories, having differen radial aperture angles , cross the entry boundary substantially in the median plane, i.e. their z coordinate is 0 at the entry boundary. The contribution of the fringe field at the entry boundary to the aberration of the image is thus eliminated, and as a consequence, a large number of terms in the mathematical expressions for the Image aberration are cancelled. The resulting simplified equations, -wherein the terms up to the third order inclusive are made equal to 0, can now be actually solved to afford real values for the geometrical parameters* Moreover* by this axial focussing o the beam, the homogeneous second and third order aberration terms in a can be cancelled through the proper choice of the profile of the entry boundary as expressed by r' and t1, which parameters were not involved in the expressions for the other optica conditions and had no effect on the particular solutions obtained for the other parameters. Moreover, In order to correct for unavoidable discrepancies of the system as compared with the deducted theoretical values, these aberrations can still further be minimalized empirically by changing the profile of the entry boundary of the magne (by "shimming" )r without thereby upsetting the other characteristics of the optics, which have, previously been determined through computation.

It is of further advantage to design the ion optical system according to the invention, so that the ion beam will ente the magnetic field perpendicularly to the effective entry linear boundary, so as t o achieve a maximiim coincidence ©f its/ xial The convergence and focussing of the ion be m can he effected in various ways. Thus, fo example, the ion source can he designed with appropriately curved source and extraction electrodes, their common centre of curvature coinciding with the desired focus, of the beam., Preferably and additionally it is arranged that the axis of the collimatin magnetic field in the souroe should be curved.

Alternatively, when a relatively short object slit is used in the system, it is sufficient that only the extraction electrode is curved (while the source electrode is planar and the axis of the collimating magnetic field is straight). In this case, however, the centre of curvature of the extraction electrode should not be located at the entry boundary of the magnetic prism, but will be intermediate to this boundary and ion source.

While specific reference is made throughout the specification to the use of the invention in a mass separator, the advantages of the new ion optioal system according to the invention are such as to render it equally applicable in other forms of equipment using magnetic prisms, e.g. in magnetic sector type ion collimators·<.

For a better understanding of the invention and to show how it can be carried out in practice, reference is made to the accompanying drawings in which: Pig. 3a is a schematic plan view of an ion optical system according to the invention, showing three ion trajectories, the intermediate one bein the principal trajectory I Flg,< 3b is a schematic side view of the vie shown in to the invention, which focus coincides with the magnetic field boundaryj Pig. 4a is a schematic horizontal cross sectional view of the ion source according to one embodiment of the invention! Fig. 4b is a vertical cross section of the ion source shown in Pig. 4a showing the curved electrodes and magnetic field employed for generating the axially converging ion beami Pig. 5a is a schematic side view Of an ion optical system of an ion beam collimator of the magnetic secto typei Fig. 5b is a* schematic top view of the ion beam collimator corresponding to Fig. 5a.

The axial focussing of the ion beam, according to the invention and as represented in Pig. 3b can be expressed as a definite correlation between β and s, namely» ø . :3s " 7. wherein J|/ is the distance between the exit slit and the effective boundary of the magnetic field (see Pig. 1).

Fig. 3b further shows the ion beam which is axially focussed, according to the invention, and a random poin at the object slit emitting a narrow bundle of rays deviating from β by the value Δβ, which is very small and may be regarded as a deviation Of second order.

As stated hereinbefore, bes results are obtained by the axial focussing of the ion beam according to the invention, when the optical system is designed so that the (l) · The equation concerning the elimination of the first term, namely making Xfs2a = 0 ,■ constitutes the requirement for a constant curvature of the image, independent of the radial aperture angle a. It has the form: where where define also (2) ·■ The. second term in εΔβ is ■ a third order term' (since Δβ 'is considered as a second order deviation) and concerns the aberration due to the axial- angular dispersion Δβ . The requirement for the elimination of this term is expressed by the equation: wherein K" and D are as defined in (l) above.

■ The equations in (l) and (2) above, when solved simultaneously together with the main focussing condition (c) a bove, will provide a two dimensional plurality of theoretical solutions ■ for the five geometrical parameters j^' , J^" , r" and £ " . (3) The requirement for second order radial foc.ussing, 2 · '■ ' ■ ' i.e. elimination of the . aberration term in α , can; now be easily satisfied by determining' rr (the radius: of curvature of the entry boundary) according to. the . Hintenberger equations' Z. Naturf. 12a, 377 (1957), in which any desired set of the geometrical parameters as previously obtained from (l) and (2) can be inserted. (4) - The remaining aberration term in a , . expressing the third order aperture aberration, relates .to the requirement for' a third order radial focussing. In an ion optical system according, to the invention, where the ion beam is focussed axially, this term can be eliminated,' without disturbing the other qualities of the optical system,' by giving the entry ■boundary, a third order profile, which can be done by computation. Alternatively or additionally, the. third order, aberrations due to the discrepancies .of the system as compared to the theoretical values, can be corrected empirically by "shimming"-, i.e. adding It was shown above that the equations in (1) and (2) together with the condition (c) provide a two dimensional plurality of solutions for the major geometrical parameters.

In practice, however* several additional conditions, arising out of technical o economical considerations, will further limit the choice of alternative solutions. For example, it may be desired to give- the system a semi-symmetrical design, i.e. = or it may be desired to make the total path for a given mass dispersion value D length of the ions as small as possible/, in order to reduce the ion scattering by collision with molecules of the residual gases in the vacuum system.

By way of an example, the following values were calculated for the relevant parameters by the equations in (l)-(3) above, using the value I^" « 0.03 , and adding the limitation of JL' <9 =» 64° £· «. 0, M » 29°40» * JfcM « 2.66 l/r» .= 0.319, 1/r" - -0.179 (As stated above, the lengths are expressed as relative to R).

In another, embodiment of the invention, the principle of axial focussing. of the ion beam is applied to the ion optical system of a magentic prism ion collimator (see Figs. 5a, ,5b). The function of such an instrument is to provide a ■ beam of ions, which is parallel both in the axial (z) and the radial (y) direction.

Conventional ion beam collimators have usually employed magnetic and/or electrostatic lenses., and therefore were restricted to the use of small circular emission holes at the ion source. The present invention permits the use, in such a system, of a long emission slit, increasing considerably the intensity .of the. parallel beam thus obtained.

The calculation of the' main, parameters for an ion beam collimator is comparatively simple,, when the ion beam is. axially focussed at the effective entry boundary of the magnetic field, according to the invention. This results ih the same conditions as in the case of the mass separator described above, namely: (a) . β = ' -' s xT . ■ Here again it is advantageous to arrange for normal incidence of the beam in respect to the entry boundary, as. expressed by: . (b) ; g' == 0 · The requirement for a parallel ion beam, whose > focus may be assumed' at .infinity, imposes the further condition in the x,y and x,z planes. ' '·. .

Considering first the axial geometry (in the x-z plane) as represented in Fig. 5a, appropriate values for . the magnet parameters for parallelism in the x-z plane are calculated. For these calculations the focus point of the beam at the entry boundary is regarded as a virtual object, and the- following "axial condition" is obtained: .1 = tg£" - 1 +_2tgieji j . -† Cos €" . β ' It is then easy to derive an appropriate value of J' in order to obtain with the above parameters a beam · parallel also in the x-y plane, (Fig. 5b), b 'applying the usual formulae of radial geometry, which assume the form: Given the main. parameters of the system, the second and third order aberrations can now be minimaliz'ed . First the exit boundary curvature:! of 'the field is adjusted, if r" necessary, in order to obtain an optimal high order collimation in the axial geometry.' Then the curvature 1 of the entry r~ curvature is adjusted, in turn, for optimal high-order collimation in the radial geometry. Because of the, axial focussing of the beam, according to the invention; .the second; adjustment can be done without effecting the quality of the previously optimalized axial collimation.' The main parameters calculated by the method described above for an actual embodiment, using the value of Ip" = 0.03' are ( £ ' = 0 required) * = 75°; g"' = 40Ο40· ; ' j V = 1.48.

Curvatures of the entry and exit boundaries can be. easily Figs. 4a and 4b show schematic cross sectional views in the horizontal and vertical planes, respectively, of an ion source according to one embodiment of the invention.

The ion source consists, essentially, of a box 11 made of an mo.*t Q ici£il electrically conducting motel, one wall 12 of which is cylindrically curved and provided, at its center, with a exit slit or object slit 13 consisting of a narrow rectangular opening, its longitudinal axis being parallel to the axis of curvature of this wall 12 and to the z axis of the system.

A side wall of the box is provided with a small aperture 14, for the entry of the ionizing eleotron beam (or the arc)» originating at the cathode 15 which is located outside the box 11 and near the aperture 14. Outside the box 11 there are also provided means (not shown) for creating a curved magnetic field extending inside the source, whose curved axis 16 (Fig. 4b) lies .in the vertical x-zJ"plarie. ' ■■ . The purpose o this curved magnetic field is to curve the ionizing electron beam, so as to coincide with the axis 16 of the field. In addition this magnetic f eld has the usual effect o collimating the electron beam and "concentrating" it by decreasing its cross section.

An extraction electrode 17 is located a small distance from the curved "front" wall 12 of box 11 which is provided, with the slit 13. Φηΐβ electrode is provided with a slit 18 which corresponds in shape to the object slit 13 and/^is cylindrically curved to correspond with the curvature of the "front" wall 12 of box 11. The three centers of curvature in the (x,z)-plane of the axis 16 of the magnetic field of the ion source, of the front wall 12 provided with the exit slit 13 and located at the effective entry boundary of the magnetic sector, which is also the desired focus of the Ion beam in the axial (z) direction.

A high potential difference is maintained between the extraction electrode 17 and the ion source 11, the extraction electrode 17 being negative in respect with the ion source 11. The order of magnitude of this "acceleration 4 5 potential", as Used in mass separators is about 10 to 10 olts.; The ions of the isotopes to be separated are generated b electron Impact along the narrow region of the arc, whose center coincides with the axis 16 of the magnetic field of the ion source. The ions emerge out of the box 11 through the object slit 13, whereupon they are immediately subjected to the accelerating voltage, are propagated towards the extraction electrode 17 and by their acquired momentum pass through the slit 18 of this electrode in the direction of the focal point P oh the entry boundary of the magnetic sector field.

Claims (3)

1. CLAIMS 1# An ion optical system used with a homogeneous magnetic prism having pole pieces spaced apar a distance g" establishing a magnetic field in the "Z" direction of an orthogonal, coordinate system having axes "X" , "Υ.?· and "Z" comprising: an ion source for producing ions; means defining an emission slit whose length S in the "Z" direc-tion is large in comparison to its width in the "Y" direction for establishing the emitting area of the source; an extraction system for shaping ions emitted from the slit into a beam whose principal trajectory is in the X-direction and which has a radial divergence angle a in the radial "X-Y" plane? means for causing the ion beam to converge in the axial "X-Z" plane and to be axially focused a distance 1' from the slit into a line perpendicular to the principal trajectory of the beam and lying in the media radial "X-Y" plane, where 1· is the distance between the slit and the effective entry boundary of the field o the magnetic prism; the ion source being cooperable with the extraction system for causing the maximum angular dispersion Apmax in the axial "X-Z" plane to bo muc smaller than g/1* where Δβ is the deviation in the "X-Z" plane of the trajectories of ions emitted from any point on the area of the source from a line connecting such point to the focus; the parameters of the optical system being- 3uch that: (a) the angle of -incidence <£' of the beam at the entry boundary of the magnetic field is zero for causing the principal trajectory of the beam to be normal to the entry boundary; (b) the distance 1· and 1" of the object slit and 30030/2 sector, and the angle of exit £ w of the beam at the ',; exit boundary of the magnetic field all having values which satisfy the main focusing conditions, as defined herein; (c) the quantities 1· and 1", 0 and 6", and the radius of curvature r" of the exit boundary being such 2 that the coefficient of the a) aberration term, as defined herein, is zero; and (d) the quantities 1·, 1", 0,6" a d r" being such that the coefficient of the (SA£) aberration term, as defined herein, is zero.
2. 2. An ion optical system according to Claim 1, wherein the parameters of the optical system defining the entry boundary profile, namely the radius of curvature r' of the 2 entry boundary being such that the coefficient of the a aberration term is zero.
3. 3, An ion optical system according to either of Claims 1 or 2, wherein t', the coefficient of the third order term defining the third order profile of the entry boundary, has a value such that the coefficients of the a aberration term is zero* 4· An ion optical system according to Claim 1, wherein the parameter 1" has the value of infinity in both the "X-Y" and the WX-Z" planes Thereby a colllmated ion beam exits from the prism. 5· An ion optical system substantially as defined above by way of example and with reference to the accompanying drawings* For the Applicants DR. REINHOLD COOT AND PARTNERS