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Mass-spectrometer with ion multiple passage of a magnetic field
Nuclear Instruments and Methods in Physics Research A329 (1993) 202-206 North-Holland
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SectionA
Mass-spectrometer with ion multiple passage of a magnetic field S .P. Karetskaya, V.M . Kel'man, A.G. Mit' and E.M. Yakushev
Nuclear Physics Institute, Academy of Sciences of Republic of Kazakhstan, Alma-Ata 480082, Kazakhstan
Received 27 March 1992 and in revised form 25 September 1992
The statical mass-spectrometer in which ions traverse three times the field created by the magnet, having poles shaped as regular hexagons, is constructed and tested . The mass dispersion equals 2820 mm with the radius of an ion trajectory in a magnetic field equal to 120 mm . In the mass-spectrometer the focusing in energy and in two angles of beam divergence is provided, all geometrical aberrations of the second order are corrected. The device ion-optical scheme is described, theoretical undergrounds for alike scheme construction are given, test results are presented. The resolving power of the order of 14000 at the level of 10% of a peak height is obtained for the widths of the input and output slits equal to 0.1 mm .
1. Introduction
2. Mass-spectrometer ion-optical system
One of the ways to increase the statical mass-spectrometer dispersion without substantial enlarging of magnet sizes is the application of the ion-optical schemes in which the field of the same magnet is passed many times. Then dispersion grows proportionally to the passage number and may become rather significant even for small magnets [1-5]. In this paper we are concerned with the mass-spectrometers based on such ion-optical schemes with the deflecting systems created on the base of two-dimensional, independent of one of the Cartesian coordinates, magnetic and electric fields . Advantage of such fields is their applicability to creation of deflecting devices with very small angular geometrical aberrations which possess, however, large angular dispersion [6-8]. Just the angular characteristics determine the resolving power of a device with such deflecting systems. One of possible ion-optical schemes of the massspectrometer with ion multiple passage of a magnetic field based on two-dimensional deflecting fields is proposed in ref. [4]. In the Nuclear Physics Institute of Academy of Sciences of Republic of Kazakhstan the mass-spectrometer has been constructed and tested for triple passage of a magnetic field by ions . The obtained results for one and two passages are given in ref. [9]. Herein, the more detailed description together with the test results for three ion deflections in a magnetic field are presented.
The ion-optical system for the built mass-spectrometer is shown schematically in fig. 1 . Its mediate plane (the figure plane) is the symmetry (antisymmetry) plane for an electrostatic (magnetic) field. We assume that the plane is located horizontally . The magnetic poles 1 have the form of regular hexagonals . For every passage ions enter a magnetic field in one side of the hexagon and leave it from another . So as the sides are parallel, the input and output edge fields, together with the central uniform field, may be considered as one two-dimensional field. For an appropriate field intensity and for some definite angle of an ion entrance such field represents a telescopic system - the magnetic prism which conserves incident spatial beam parallelism after a deflection too [6,8]. The distance between the opposite sides of a hexagon equals 188 mm . The interpolar gap is 6 mm . To provide such a small gap, the pole block mounted on a support flange made of a nonmagnetic substance is placed inside a vacuum chamber. The external part of the magnet yoke contains three columns; two along which a magnetic flux flows from one pole to another. The electrostatic systems of the mass-spectrometer, grouped into four blocks, are placed between the columns. To improve the two-dimensional nature of the edge magnetic fields around electromagnetic plates, six pairs of the rectangular plates 3 are situated parallel to the pole edges at the distance 6 mm . The plates
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2
Fig. 2. The electrostatic system, collimating and deflecting an ion beam .
Fig. 1. The ion-optical system of the mass-spectrometer with ion triple passage of a magnetic field . of every pair are parallel to each other and situated at the same distance from the mediate plane as the magnetic poles are. The scattering field outside the plates is terminated by the permaloy screens 4,12 . For this purpose they are provided by the permaloy crosspiece 9,16', the screens 4,12 serving as electrodes for an electrostatic systems. The plates of other electrodes are made of titanium . Every electrode of an electrostatic system is composed of two identic electrically closed parallel plates situated symmetrically and equidistantly, as the magnetic poles, with respect to the mediate plane. Thus, the internal surfaces of all electrode plates, of the plates 3 and of magnet poles lie in two parallel planes, and between the latters ions move . The ion beam, emitted from the source slit 11, is collimated and deflected by the input electrostatic block composed of five electrodes 4-8 . The electrodes 6-8 of the block (figs. 1, 2) form a transaxial lens, while the electrodes 4-6, separated by the straight parallel slits, represent a telescopic refracting system . In fig. 2 the lens major plane H, related to horizontal focusing, and the refraction effective plane A of the telescopic system are shown by dashed lines. The angle of ion entrance into the refracting system i * = 64°40',
and the exit angle j * = 31 °15' . The lens parameters are chosen in such a way that its focal planes of the horizontal and vertical focusing coincide in the object space. The output slit 11 of an ion source has been placed in this common focal plane, so the spatial divergent ion beam emitted by any point of the slit is transformed by the lens into a parallel one. The focus length in the lens object space fr o and f,o, characterizing horizontal and vertical focusing, are equal to 382 mm and 219 mm respectively . At the angles of ion entrance into a magnetic field and of ion exit a = 51° the beam keeps its parallelism in the vertical plane on its leaving the magnetic field. The radius of ion trajectory curvature in the homogeneous part of a magnet field is p = 120 mm . The ion return into a magnetic field is accomplished by an electrostatic telescopic system - the turning block with the electrodes 12-15, creating two two-dimensional fields in the region of ion motion, every of which reflects and refracts the beam (fig. 3) . When calculating, the potentials at the block electrodes and the widths of the electrodes 13,14 are chosen in such a way that the parallel input spatial beam conserves its parallelism after its transition from one two-dimensional field to another. In fig. 3 the dashed lines show the effective planes of refraction B and reflection C. The angles between
Fig. 3 . The electrostatic system returning ions into a magnetic field.
204
S.P. Karetskaya et al. / Mass-spectrometer
the effective planes referring to the first two-dimensional field and to the second one are )3 = 2j = 84°28' and i = 68°46' . Leaving the magnetic field after triple deflection (fig . 1) the ions are located in the output block of a mass-spectrometer, identical to the input one. The slit of the ion receiver 17 is located in the back focal plane of the transaxial lens . Herein the image of the source slit is formed . When passing the whole ion-optical system of the mass-spectrometer the beam is deflected from the primary direction at the angle rr - 0, & = 24°50' . The transversal sizes of the beam are limited by two mutually perpendicular regulated slits forming a diaphragm with a rectangular opening 10 . The partition 18 prevents ions from penetration into a receiver after one deflection . The sizes in the drawings are given in mm . The magnitudes of potentials V at the electrodes are: V = -1 .19U, V6 = 0.670, VS = 0.470, V1 3 = -0 .140, Vl4 = -0 .92U, V15= 0.64U. Indices correspond to numerical notations of the electrodes in the drawings, U is the accelerating voltage of the ion source . The rest electrodes have been grounded, and its potentials are assumed to be equal to zero . 3. Theoretical background Here we present theoretical reasoning for construction of the ion-optical schemes of the type considered. Now we discuss a general case of the magnetic prism in the shape of a regular 2n-gon with the field passed n times by ions . The electrostatic systems like the one shown in fig. 1 are placed around the prism. One of them, mounted at the input, collimates an ion beam, while another, being at the output, focusses it, and (n - 1) systems return ions into a magnetic field. Let us introduce the system of curvilinear orthogonal coordinates: s, x, y, with the s axis directed along the axial trajectory of the ion beams, the x axis along the main normal to it, and the y axis along the binormal . The directions of the s and x axes are seen in fig. 1, where the y axis is directed upwards, perpendicular to the drawing plane. For theoretical consideration an electrical potential cp is normalized in such a way that for the particle moving along the axial trajectory the equality mu g/2 = -ecp is valid (e, m and c are the particle charge, mass and speed, respectively) . The scatter of initial velocities is taken into account by the extra term £, the kinetic energy of an arbitrary particle mu g/2 = -e(ep +e). cp differs from the real potential V, equal to zero at the grounded electrodes, by the magnitude of the accelerating potential of the ion source, cp = V - U. Consider an arbitrary trajectory of the analysed beam . Specify its linear coordinates in the plane of the output slit of an ion source x = x0, y = yo, and its
angular coordinates in the object space dx/ds =x,,, dy/ds =yô . Determine the coordinates of the trajectory considered in the plane of the input slit of an ion detector x = x,, y = y 1 . The coordinate x, will be determined with the geometrical aberrations of the second order being taken into account, while the coordinate y l will be found in the paraxial approximation . After the collimator lens x' =x% = -x,/f,,, y' =y' _ - yo/fy l, where fxl and fyl are the focal lengths of the lens in the image space of the horizontal direction of focusing and the vertical one respectively . After the refracting telescopic system of the input electrostatic block x'= x, = Tlxk+A ;(~Pu/~*)EO+di, Y' = Yi = 'Ylykl
where Tl and yl are the horizontal and vertical angular magnifications of this system, u ; is its angular dispersion in energy, d', is the total angular aberration, s, = e/cp, lp * and cp, are the input and output potentials of the refracting system . They coincide with the potentials at the appropriate electrodes of this system 1P * = 1Ps1 1Go = (P4 . The potential to, is one of the object space of the entire ion-optical system, cp, = ~co . It is known [6] that FI =tan j */tani *, di =K,Yk2,
ai =(1/2)(1-cp * /cp,)tan j*,
Ki = (1/2)(Yî - 1) tan j*,
where i * and j * are the angles of incidence and refraction for the axial trajectory, counted from the normal to the straight slits. The aberration correction d', in two-dimensional deflecting fields contains only two terms of the second order of smallness, one of which being proportional to xk2, while another to yk2. In mass-spectrometry usually x0 << yo , and, hence, xk << yk, so here and further we may neglect the terms of the order of x k2. After the first passage of a magnetic field by ions x'=xM1 =x,'
+ AR,S,+J,,
= I'lxk+(Ai 1Po/1P * +AM)£o+Amso+d'l+dm , Y' = Ym1 = -Y1 = - 'Y1 Yk .
Herein it has been implied that in a magnetic prism, conserving parallelism of a beam, the angular magnification is equal to + 1 in the mediate plane and to - 1 in the perpendicular direction. S, = Am/m, is a relative deviation of a particle mass from its main mass mo, Am is angular dispersion of a magnetic prism in mass and in energy, dm is total angular aberration of a magnetic field on one passage. It is known that ,a' = tan a,
dm = kmy'yk2 ,
k , = -tan a,
where a is the entrance angle counted from a normal to a magnetic pole edge for the axial trajectory in a magnetic field.
S.P. Karetskaya et al. / Mass-spectrometer
On the first returning of ions into a magnetic field by the electrostatic turning block, x' = Xnl =Xml
+ .q &0
+dn =F,x'
+ amso
+ (al~PO/~ * +am + an)e 0 +d j +d m+an,
Y' = Ym = Y~1
=
-YIYk,
where it has been assumed that, due to symmetry conditions, the angular magnifications of the turning block in the mediate plane and in the perpendicular direction equal 1. It is not difficult to determine the angular dispersion in energy a ;, and the aberration correction do for a turning block summing the actions of two telescopic two-dimensional fields for which these parameters are known . Thus, an = (1 - ~Po/~P) tan i, Kn =
(yn -
an = K,Y2Yk
2,
1) tan i,
where te ll = cp 12 , cP = cP 14 , i and j are the angles of entrance and exit for the first refracting system of the block, yn is the angular vertical magnification of its first half which consists of the refracting system and a mirror . To provide the beam entering a magnetic field once more at the same angle a, the sum of angles i and j must satisfy the following condition: I i I + I j I = a */2 + I a 1, where a * = rr(1 - 1/n) is the internal angle of 2n-angular magnetic prism. After the nth passage of the magnetic field by ions x'
=xm
= FI X,' + na .5, + (ailPnlw * + na .' + (n - 1)an)eo +,A', +ndn, + (n - 1)dn, Y = Ymn = ( - 1) n y1yk " After beam refraction in the telescopic refracting system of the output electrostatic block
XI=
X2=r2Xmn =xk+namF2 50
+aieo+("I +ndn+(n -1 )d n) r2+d2, n Y' = Y2 = Y2Ymn = ( -1 ) Yk, where r2 and Y2 are the angular magnifications of the refracting system of the output electrostatic block, 92 is its angular dispersion in energy, d2 is the aberration correction .
r2= 1/r1 = tan i */tan j*, A.2= -(1/2)(1~2=K2 12 Yk2 ,
In the back focal plane of the focusing lens of the output electrostatic block X=Xf=X2fxl = -XO+amSO+aefxle0+d~fxl~ Y = Yf = Y2'fy l = ( - I) n-1 Yo, where fx1 and fy1 are the focal lengths of an object space of the lens. Thus, the linear magnification of the entire ion-optical system of a mass-spectrometer in the mediate plane equals -1, while in the orthogonal direction The linear dispersion in mass is ,a m =nam1-2f x I =n tan a(tan i */tan j*)f,
= n tan a(cos j */cos i * )fx0,
where fxo is the focal length of the image space of the focusing lens which is equal to that of the object space of the collimating lens . The focusing in energy is reached if ar = (ai~Po/~P * +n4~ + (n - 1)an)r2 +a2 = 0, the geometrical aberrations of the second order are absent if d'= (di +ndn,+ (n- 1)dn)r2+d2=0 . Substituting the entering values into the latter two equalities, we transform these conditions to the form : (1pol~p * - 1) tan j * + n tan a
+(n - 1)(1 -cpol~o) tan i =0, (1/y ; - 1) tan j* +n tan a +(n-1)(1-y.;) tan i=0.
y1 =
1/yl,
tan i*,
Kz =- (1/2)(y22 - I) tan i
(2)
If the load on achromatization of the scheme is distributed uniformly between the refracting systems of all electrostatic blocks, i.e ., if the equality (1 -
tan gy * = (cp11 /cp - 1) tan i = tap a
(3)
takes place, and, besides, if one requires that y1 = ±( w */ ,Po)1
+(a~tPol~P * +nam + (n - 1)an)r2e0
tos
/
2,
yn = ±40/w),
(4)
then both conditions (1) and (2) are to be satisfied . Thus, even in the complex scheme with multiple passage of a magnetic field by ions, in which deflecting telescopic systems based on two-dimensional electric and magnetic fields are used, geometrical aberrations of the second order are eliminated with ease, because one has to compensate only the nonzero kind of aberrations, whereas in sectorial fields one would minimize four kinds of aberrations. The geometrical aberrations of the third order of smallness are not large in the schemes in question . They are absent in the deflecting systems which are used here and are composed of but the aberrations of the collimating and focusing transaxial lenses which possess, as is known, small aberrations .
20 6
S.P. Karetskaya et al. / Mass-spectrometer
5. Conclusion
MC~O t
Fig. 4. The spectrogram of the doublet (14N2)+_(12C 160)+ . For the constructed mass-spectrometer, n = 3, the conditions (3) and (4) are satisfied. Mass dispersion is quite large, u m = 2820 mm, despite a small radius of ion trajectories in a magnetic field and, respectively, small size of the magnet . 4. Test results The received at the mass-spectrometer spectrogram of the doublet (14Nz)+-(12Ct°O)+ with the mass difference equal to 0.011 a.m .u . is shown in fig. 4. When recording, the slit widths of a source and a receiver were Sl = SZ = 0.1 mm, while the appropriate heights were, correspondingly, 1 .5 and 3 mm . The width of the diaphragm rectangular opening 10 (fig . 1) limiting the transverse cross-section of the ion beam was 0.6 mm, the height was 1 mm . The accelerating voltage of an ion source was U = 3 kV . It follows from spectrogram that the mass-spectrometer resolving power determined by the line widths at the level of 10% of a line height reaches 14000. It slightly differs from its theoretical meaning derived under the assumption that aberration influence may be neglected.
Theoretical study of the described scheme of a statical mass-spectrometer and test of the constructed model have shown that such mass-spectrometers may possess significant resolving power at small sizes and wide slits of a source and a receiver of ions . It is explained by the fact that in the scheme with multiple passage of a magnetic field by ions the telescopic systems based on two-dimensional (plane) electric and magnetic fields are used as refracting and reflecting elements . The systems are calculated in such a way that they, as a whole, may provide ion focusing in energy and bring in very small geometrical aberrations . The aberrations of the second order of smallness are eliminated while those of the third one are absent . The electrostatic transaxial lenses having also very small aberrations are used in the collimating and focusing parts of a mass-spectrometer . The schemes of the type considered are useful for the cases one needs a compact high-resolution mass-spectrometer with a wide slit of the ion source . References [1] M. Fortin and M. Baril, Rev. Sci. Instr. 43 (1972) 1140 . [2] P. Boulanger and M . Baril, Nucl . Instr. and Meth . A 298 (1990) 161 . [3] N.I . Tarantin, USSR authority certificate No. 1076983, Bul. iz . 1984 . No 8 (in Russian) . [4] A.A . Zernov et al ., USSR authority certificate No . 1101076, Bul. iz . 1984 . No . 24 (in Russian). [5] L.G. Beizina, S.P . Karetskaya and V.M . Kel'man, USSR Authority certificate No. 1525774, Bul. iz . 1989 . No . 44 (in Russian) . [6] V.M . Kel'man, S.P . Karetskaya, L.V . Fedulina and E.M Yakushev, Electron-optical elements of prism spectrometers for charged particles. Alma-Ata : Science of Kazakh SSR. (1979) 232 pages (in Russian) . [7] V.M . Kel'man, LV . Rodnikova and L.M . Sekunova, Statical mass-spectrometers, Alma-Ata : Science of Kazakh SSR. 1985 . 264 pages (in Russian) . [8] V.M . Kel'man, L.M . Nazarenko and E.M . Yakushev, Zh .T.F. 46(8) (1976) 170 (in Russian) . [9] C.P. Karetskaya, V.M . Kel'man, A.G . Mit' and E.M . Yakushev, Piz'ma v ZhTF 16(8) (1990) 69 (in Russian) .
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SectionA
Mass-spectrometer with ion multiple passage of a magnetic field S .P. Karetskaya, V.M . Kel'man, A.G. Mit' and E.M. Yakushev
Nuclear Physics Institute, Academy of Sciences of Republic of Kazakhstan, Alma-Ata 480082, Kazakhstan
Received 27 March 1992 and in revised form 25 September 1992
The statical mass-spectrometer in which ions traverse three times the field created by the magnet, having poles shaped as regular hexagons, is constructed and tested . The mass dispersion equals 2820 mm with the radius of an ion trajectory in a magnetic field equal to 120 mm . In the mass-spectrometer the focusing in energy and in two angles of beam divergence is provided, all geometrical aberrations of the second order are corrected. The device ion-optical scheme is described, theoretical undergrounds for alike scheme construction are given, test results are presented. The resolving power of the order of 14000 at the level of 10% of a peak height is obtained for the widths of the input and output slits equal to 0.1 mm .
1. Introduction
2. Mass-spectrometer ion-optical system
One of the ways to increase the statical mass-spectrometer dispersion without substantial enlarging of magnet sizes is the application of the ion-optical schemes in which the field of the same magnet is passed many times. Then dispersion grows proportionally to the passage number and may become rather significant even for small magnets [1-5]. In this paper we are concerned with the mass-spectrometers based on such ion-optical schemes with the deflecting systems created on the base of two-dimensional, independent of one of the Cartesian coordinates, magnetic and electric fields . Advantage of such fields is their applicability to creation of deflecting devices with very small angular geometrical aberrations which possess, however, large angular dispersion [6-8]. Just the angular characteristics determine the resolving power of a device with such deflecting systems. One of possible ion-optical schemes of the massspectrometer with ion multiple passage of a magnetic field based on two-dimensional deflecting fields is proposed in ref. [4]. In the Nuclear Physics Institute of Academy of Sciences of Republic of Kazakhstan the mass-spectrometer has been constructed and tested for triple passage of a magnetic field by ions . The obtained results for one and two passages are given in ref. [9]. Herein, the more detailed description together with the test results for three ion deflections in a magnetic field are presented.
The ion-optical system for the built mass-spectrometer is shown schematically in fig. 1 . Its mediate plane (the figure plane) is the symmetry (antisymmetry) plane for an electrostatic (magnetic) field. We assume that the plane is located horizontally . The magnetic poles 1 have the form of regular hexagonals . For every passage ions enter a magnetic field in one side of the hexagon and leave it from another . So as the sides are parallel, the input and output edge fields, together with the central uniform field, may be considered as one two-dimensional field. For an appropriate field intensity and for some definite angle of an ion entrance such field represents a telescopic system - the magnetic prism which conserves incident spatial beam parallelism after a deflection too [6,8]. The distance between the opposite sides of a hexagon equals 188 mm . The interpolar gap is 6 mm . To provide such a small gap, the pole block mounted on a support flange made of a nonmagnetic substance is placed inside a vacuum chamber. The external part of the magnet yoke contains three columns; two along which a magnetic flux flows from one pole to another. The electrostatic systems of the mass-spectrometer, grouped into four blocks, are placed between the columns. To improve the two-dimensional nature of the edge magnetic fields around electromagnetic plates, six pairs of the rectangular plates 3 are situated parallel to the pole edges at the distance 6 mm . The plates
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2
Fig. 2. The electrostatic system, collimating and deflecting an ion beam .
Fig. 1. The ion-optical system of the mass-spectrometer with ion triple passage of a magnetic field . of every pair are parallel to each other and situated at the same distance from the mediate plane as the magnetic poles are. The scattering field outside the plates is terminated by the permaloy screens 4,12 . For this purpose they are provided by the permaloy crosspiece 9,16', the screens 4,12 serving as electrodes for an electrostatic systems. The plates of other electrodes are made of titanium . Every electrode of an electrostatic system is composed of two identic electrically closed parallel plates situated symmetrically and equidistantly, as the magnetic poles, with respect to the mediate plane. Thus, the internal surfaces of all electrode plates, of the plates 3 and of magnet poles lie in two parallel planes, and between the latters ions move . The ion beam, emitted from the source slit 11, is collimated and deflected by the input electrostatic block composed of five electrodes 4-8 . The electrodes 6-8 of the block (figs. 1, 2) form a transaxial lens, while the electrodes 4-6, separated by the straight parallel slits, represent a telescopic refracting system . In fig. 2 the lens major plane H, related to horizontal focusing, and the refraction effective plane A of the telescopic system are shown by dashed lines. The angle of ion entrance into the refracting system i * = 64°40',
and the exit angle j * = 31 °15' . The lens parameters are chosen in such a way that its focal planes of the horizontal and vertical focusing coincide in the object space. The output slit 11 of an ion source has been placed in this common focal plane, so the spatial divergent ion beam emitted by any point of the slit is transformed by the lens into a parallel one. The focus length in the lens object space fr o and f,o, characterizing horizontal and vertical focusing, are equal to 382 mm and 219 mm respectively . At the angles of ion entrance into a magnetic field and of ion exit a = 51° the beam keeps its parallelism in the vertical plane on its leaving the magnetic field. The radius of ion trajectory curvature in the homogeneous part of a magnet field is p = 120 mm . The ion return into a magnetic field is accomplished by an electrostatic telescopic system - the turning block with the electrodes 12-15, creating two two-dimensional fields in the region of ion motion, every of which reflects and refracts the beam (fig. 3) . When calculating, the potentials at the block electrodes and the widths of the electrodes 13,14 are chosen in such a way that the parallel input spatial beam conserves its parallelism after its transition from one two-dimensional field to another. In fig. 3 the dashed lines show the effective planes of refraction B and reflection C. The angles between
Fig. 3 . The electrostatic system returning ions into a magnetic field.
204
S.P. Karetskaya et al. / Mass-spectrometer
the effective planes referring to the first two-dimensional field and to the second one are )3 = 2j = 84°28' and i = 68°46' . Leaving the magnetic field after triple deflection (fig . 1) the ions are located in the output block of a mass-spectrometer, identical to the input one. The slit of the ion receiver 17 is located in the back focal plane of the transaxial lens . Herein the image of the source slit is formed . When passing the whole ion-optical system of the mass-spectrometer the beam is deflected from the primary direction at the angle rr - 0, & = 24°50' . The transversal sizes of the beam are limited by two mutually perpendicular regulated slits forming a diaphragm with a rectangular opening 10 . The partition 18 prevents ions from penetration into a receiver after one deflection . The sizes in the drawings are given in mm . The magnitudes of potentials V at the electrodes are: V = -1 .19U, V6 = 0.670, VS = 0.470, V1 3 = -0 .140, Vl4 = -0 .92U, V15= 0.64U. Indices correspond to numerical notations of the electrodes in the drawings, U is the accelerating voltage of the ion source . The rest electrodes have been grounded, and its potentials are assumed to be equal to zero . 3. Theoretical background Here we present theoretical reasoning for construction of the ion-optical schemes of the type considered. Now we discuss a general case of the magnetic prism in the shape of a regular 2n-gon with the field passed n times by ions . The electrostatic systems like the one shown in fig. 1 are placed around the prism. One of them, mounted at the input, collimates an ion beam, while another, being at the output, focusses it, and (n - 1) systems return ions into a magnetic field. Let us introduce the system of curvilinear orthogonal coordinates: s, x, y, with the s axis directed along the axial trajectory of the ion beams, the x axis along the main normal to it, and the y axis along the binormal . The directions of the s and x axes are seen in fig. 1, where the y axis is directed upwards, perpendicular to the drawing plane. For theoretical consideration an electrical potential cp is normalized in such a way that for the particle moving along the axial trajectory the equality mu g/2 = -ecp is valid (e, m and c are the particle charge, mass and speed, respectively) . The scatter of initial velocities is taken into account by the extra term £, the kinetic energy of an arbitrary particle mu g/2 = -e(ep +e). cp differs from the real potential V, equal to zero at the grounded electrodes, by the magnitude of the accelerating potential of the ion source, cp = V - U. Consider an arbitrary trajectory of the analysed beam . Specify its linear coordinates in the plane of the output slit of an ion source x = x0, y = yo, and its
angular coordinates in the object space dx/ds =x,,, dy/ds =yô . Determine the coordinates of the trajectory considered in the plane of the input slit of an ion detector x = x,, y = y 1 . The coordinate x, will be determined with the geometrical aberrations of the second order being taken into account, while the coordinate y l will be found in the paraxial approximation . After the collimator lens x' =x% = -x,/f,,, y' =y' _ - yo/fy l, where fxl and fyl are the focal lengths of the lens in the image space of the horizontal direction of focusing and the vertical one respectively . After the refracting telescopic system of the input electrostatic block x'= x, = Tlxk+A ;(~Pu/~*)EO+di, Y' = Yi = 'Ylykl
where Tl and yl are the horizontal and vertical angular magnifications of this system, u ; is its angular dispersion in energy, d', is the total angular aberration, s, = e/cp, lp * and cp, are the input and output potentials of the refracting system . They coincide with the potentials at the appropriate electrodes of this system 1P * = 1Ps1 1Go = (P4 . The potential to, is one of the object space of the entire ion-optical system, cp, = ~co . It is known [6] that FI =tan j */tani *, di =K,Yk2,
ai =(1/2)(1-cp * /cp,)tan j*,
Ki = (1/2)(Yî - 1) tan j*,
where i * and j * are the angles of incidence and refraction for the axial trajectory, counted from the normal to the straight slits. The aberration correction d', in two-dimensional deflecting fields contains only two terms of the second order of smallness, one of which being proportional to xk2, while another to yk2. In mass-spectrometry usually x0 << yo , and, hence, xk << yk, so here and further we may neglect the terms of the order of x k2. After the first passage of a magnetic field by ions x'=xM1 =x,'
+ AR,S,+J,,
= I'lxk+(Ai 1Po/1P * +AM)£o+Amso+d'l+dm , Y' = Ym1 = -Y1 = - 'Y1 Yk .
Herein it has been implied that in a magnetic prism, conserving parallelism of a beam, the angular magnification is equal to + 1 in the mediate plane and to - 1 in the perpendicular direction. S, = Am/m, is a relative deviation of a particle mass from its main mass mo, Am is angular dispersion of a magnetic prism in mass and in energy, dm is total angular aberration of a magnetic field on one passage. It is known that ,a' = tan a,
dm = kmy'yk2 ,
k , = -tan a,
where a is the entrance angle counted from a normal to a magnetic pole edge for the axial trajectory in a magnetic field.
S.P. Karetskaya et al. / Mass-spectrometer
On the first returning of ions into a magnetic field by the electrostatic turning block, x' = Xnl =Xml
+ .q &0
+dn =F,x'
+ amso
+ (al~PO/~ * +am + an)e 0 +d j +d m+an,
Y' = Ym = Y~1
=
-YIYk,
where it has been assumed that, due to symmetry conditions, the angular magnifications of the turning block in the mediate plane and in the perpendicular direction equal 1. It is not difficult to determine the angular dispersion in energy a ;, and the aberration correction do for a turning block summing the actions of two telescopic two-dimensional fields for which these parameters are known . Thus, an = (1 - ~Po/~P) tan i, Kn =
(yn -
an = K,Y2Yk
2,
1) tan i,
where te ll = cp 12 , cP = cP 14 , i and j are the angles of entrance and exit for the first refracting system of the block, yn is the angular vertical magnification of its first half which consists of the refracting system and a mirror . To provide the beam entering a magnetic field once more at the same angle a, the sum of angles i and j must satisfy the following condition: I i I + I j I = a */2 + I a 1, where a * = rr(1 - 1/n) is the internal angle of 2n-angular magnetic prism. After the nth passage of the magnetic field by ions x'
=xm
= FI X,' + na .5, + (ailPnlw * + na .' + (n - 1)an)eo +,A', +ndn, + (n - 1)dn, Y = Ymn = ( - 1) n y1yk " After beam refraction in the telescopic refracting system of the output electrostatic block
XI=
X2=r2Xmn =xk+namF2 50
+aieo+("I +ndn+(n -1 )d n) r2+d2, n Y' = Y2 = Y2Ymn = ( -1 ) Yk, where r2 and Y2 are the angular magnifications of the refracting system of the output electrostatic block, 92 is its angular dispersion in energy, d2 is the aberration correction .
r2= 1/r1 = tan i */tan j*, A.2= -(1/2)(1~2=K2 12 Yk2 ,
In the back focal plane of the focusing lens of the output electrostatic block X=Xf=X2fxl = -XO+amSO+aefxle0+d~fxl~ Y = Yf = Y2'fy l = ( - I) n-1 Yo, where fx1 and fy1 are the focal lengths of an object space of the lens. Thus, the linear magnification of the entire ion-optical system of a mass-spectrometer in the mediate plane equals -1, while in the orthogonal direction The linear dispersion in mass is ,a m =nam1-2f x I =n tan a(tan i */tan j*)f,
= n tan a(cos j */cos i * )fx0,
where fxo is the focal length of the image space of the focusing lens which is equal to that of the object space of the collimating lens . The focusing in energy is reached if ar = (ai~Po/~P * +n4~ + (n - 1)an)r2 +a2 = 0, the geometrical aberrations of the second order are absent if d'= (di +ndn,+ (n- 1)dn)r2+d2=0 . Substituting the entering values into the latter two equalities, we transform these conditions to the form : (1pol~p * - 1) tan j * + n tan a
+(n - 1)(1 -cpol~o) tan i =0, (1/y ; - 1) tan j* +n tan a +(n-1)(1-y.;) tan i=0.
y1 =
1/yl,
tan i*,
Kz =- (1/2)(y22 - I) tan i
(2)
If the load on achromatization of the scheme is distributed uniformly between the refracting systems of all electrostatic blocks, i.e ., if the equality (1 -
tan gy * = (cp11 /cp - 1) tan i = tap a
(3)
takes place, and, besides, if one requires that y1 = ±( w */ ,Po)1
+(a~tPol~P * +nam + (n - 1)an)r2e0
tos
/
2,
yn = ±40/w),
(4)
then both conditions (1) and (2) are to be satisfied . Thus, even in the complex scheme with multiple passage of a magnetic field by ions, in which deflecting telescopic systems based on two-dimensional electric and magnetic fields are used, geometrical aberrations of the second order are eliminated with ease, because one has to compensate only the nonzero kind of aberrations, whereas in sectorial fields one would minimize four kinds of aberrations. The geometrical aberrations of the third order of smallness are not large in the schemes in question . They are absent in the deflecting systems which are used here and are composed of but the aberrations of the collimating and focusing transaxial lenses which possess, as is known, small aberrations .
20 6
S.P. Karetskaya et al. / Mass-spectrometer
5. Conclusion
MC~O t
Fig. 4. The spectrogram of the doublet (14N2)+_(12C 160)+ . For the constructed mass-spectrometer, n = 3, the conditions (3) and (4) are satisfied. Mass dispersion is quite large, u m = 2820 mm, despite a small radius of ion trajectories in a magnetic field and, respectively, small size of the magnet . 4. Test results The received at the mass-spectrometer spectrogram of the doublet (14Nz)+-(12Ct°O)+ with the mass difference equal to 0.011 a.m .u . is shown in fig. 4. When recording, the slit widths of a source and a receiver were Sl = SZ = 0.1 mm, while the appropriate heights were, correspondingly, 1 .5 and 3 mm . The width of the diaphragm rectangular opening 10 (fig . 1) limiting the transverse cross-section of the ion beam was 0.6 mm, the height was 1 mm . The accelerating voltage of an ion source was U = 3 kV . It follows from spectrogram that the mass-spectrometer resolving power determined by the line widths at the level of 10% of a line height reaches 14000. It slightly differs from its theoretical meaning derived under the assumption that aberration influence may be neglected.
Theoretical study of the described scheme of a statical mass-spectrometer and test of the constructed model have shown that such mass-spectrometers may possess significant resolving power at small sizes and wide slits of a source and a receiver of ions . It is explained by the fact that in the scheme with multiple passage of a magnetic field by ions the telescopic systems based on two-dimensional (plane) electric and magnetic fields are used as refracting and reflecting elements . The systems are calculated in such a way that they, as a whole, may provide ion focusing in energy and bring in very small geometrical aberrations . The aberrations of the second order of smallness are eliminated while those of the third one are absent . The electrostatic transaxial lenses having also very small aberrations are used in the collimating and focusing parts of a mass-spectrometer . The schemes of the type considered are useful for the cases one needs a compact high-resolution mass-spectrometer with a wide slit of the ion source . References [1] M. Fortin and M. Baril, Rev. Sci. Instr. 43 (1972) 1140 . [2] P. Boulanger and M . Baril, Nucl . Instr. and Meth . A 298 (1990) 161 . [3] N.I . Tarantin, USSR authority certificate No. 1076983, Bul. iz . 1984 . No 8 (in Russian) . [4] A.A . Zernov et al ., USSR authority certificate No . 1101076, Bul. iz . 1984 . No . 24 (in Russian). [5] L.G. Beizina, S.P . Karetskaya and V.M . Kel'man, USSR Authority certificate No. 1525774, Bul. iz . 1989 . No . 44 (in Russian) . [6] V.M . Kel'man, S.P . Karetskaya, L.V . Fedulina and E.M Yakushev, Electron-optical elements of prism spectrometers for charged particles. Alma-Ata : Science of Kazakh SSR. (1979) 232 pages (in Russian) . [7] V.M . Kel'man, LV . Rodnikova and L.M . Sekunova, Statical mass-spectrometers, Alma-Ata : Science of Kazakh SSR. 1985 . 264 pages (in Russian) . [8] V.M . Kel'man, L.M . Nazarenko and E.M . Yakushev, Zh .T.F. 46(8) (1976) 170 (in Russian) . [9] C.P. Karetskaya, V.M . Kel'man, A.G . Mit' and E.M . Yakushev, Piz'ma v ZhTF 16(8) (1990) 69 (in Russian) .