# Патент USA US3061730

код для вставкиOct. 30, 1962 3,061,720. H. EWALD SPECTROGRAPH Filed Feb. 29, 1960 5 Sheets-Sheet 1_ 1x. 8 am 4%.w.8.m?”. my .M M u m W: B .w.m,3am 2 W Ydrwi INVENTOR -HE/NZ E WALD M ._ ATTORNEYS Oct. 30, 1962 H. EWALD‘ SPECTROGRAPH Filed Feb. 29, 1960 3,061,720 3 Sheets-Sheet 2 Q“0.31m. umEw..h . ‘s. u?mcuE Mmhv E m,‘mm Evian. Q53a/QEQ. *.“Q3ogvksw 0R\3QSkQg. xomtbku INVENTOR HE/NZ EWALD “W W ATTORNEYS Oct. 30, ‘1962 H. EWALD 3,061,720 SPECTROGRAPH Filed Feb. 29, 1960 3 Sheets-Sheet 3 \ I x l f 7 INVENTOR Fig. 7 HE/NZ EWALD BY ATTORNEY$ United States Patent O??ce 3,051,720 Patented Oct. 30, 1962 1 2 3,061,720 FIGURES 1 and 2 are schematic views of toroidal condensers for use in a spectrograph constructed accord SPECTROGRAPH Heinz Ewald, 36 Clemenssu-asse, Munich, Germany Filed Feb. 29, 1960, Ser. No. 11,604 5 Claims. (Cl. 250--41.9) ing to my invention; FIGURE 3 is a sectional view of a mass spectrograph according to my invention, with direction and velocity focusing which does not have intermediate radial images in and between the ?elds and for which the aberration The present invention relates to spectrographs. More in particular, the present invention relates to mass spec coe?icients are equal to zero; FIGURE 4 is a sectional view of a mass spectrograph trographs and energy spectrographs having condensers which are corrected for image errors. The term “spectrograph” as used in the present speci ?cation and claims is intended to comprehend spec 10 according to my invention, with a homogeneous ?eld and a toroidal condenser having plane entrance and exit front surfaces and for which the aberration coe?icient A33 is equal to Zero; FIGURE 5 is a schematic view of a spherical condenser trometers. It is known that spectrographs comprise condensers which are mostly of the toroidal-shaped type which is 15 for use in a spectrograph constructed according to my to be understood as comprising the spherical-type con densers, but which can also be cylinder-shaped. These condensers are electron- and ion-optical focusing invention; possible to provide condensers with a satisfactory correc tion of image errors. Although it has become known to provide condensers in spectrographs corrected to some extent for image errors with respect to the image error coefficient (hereinbelow designated as A33) of the half effective axial angle of divergence of the rays of par The electrodes of a toroidal condenser as shown in FIGURES 1 and 2 for example, have a common rota tional axis, e.g. in FIGURE 1 the z-axis of an r, 95, FIGURE 6 illustrates a single condenser plate used in the spectrograph shown in FIGURE 4, and systems with the help of which rays of charged particles, FIGURES 7, 8 and 9 illustrate sectional views of the such as electrons, elementary particles, or ions may be 20 condenser plate of FIGURE 6 and respectively taken at separated into an energy spectrum. Spherical and cylin lines 7, 8, and 9 therein. drical condensers are special cases of the more common The following considerations, with reference to FIG toroidal condensers. ' URES 1 and 2, will more fully explain the novel feature The known spectrographs are unsatisfactory because of of my invention and the considerable advance over the considerable image errors. Heretofo-re it has been im art. z-system of cylinder coordinates, and a common plane of symmetry, as in FIGURE 1 the plane z=0. Their radial and axial main radii of curvature in the points ticles passing through the spectrograph to the place of image, it has hitherto not been possible to provide special kinds of spectrographs with condensers wherein all image of the circle of intersection with the plane of symmetry =0 may be r,,, rb and R,,, Rb, respectively. The radial error coe?icients are corrected so as to become zero. plane of symmetry and vertical to it in planes going through the z-axis, respectively. The centers of these curvatures coincide with the origin of the‘coordinate and axial main circles of curvature are ‘falling in the Furthermore, the partial image correction of just one image error coe?icient according to the known art re quires a complicated and particular con?guration of the system or they are located in the plane z=0 on the circles front surfaces on the entrance ‘or the exit side or on both sides of the condensers. The front surfaces must 40 have curvatures calculated in a determined manner. It is therefore an object of the present invention to provide a spectrograph with condensers which are more perfectly corrected for image errors than any of the r=r,,—-Ra and r=rb--Rb, respectively. The section of a circle r=ae(ra<ae<rb), z=0 located in the plane of symmetry between the electrodes together with its straight prolongations outside of the sector ?eld may be designated as mean orbit. Orbits of charged particles progressing in the neighborhood of this mean known spectrographs. orbit can be calculated with formulas generally known in the art. The potential surface between the two electrodes ex It is another object of the present invention to provide a spectrograph with condensers which are more perfectly corrected for image errors than any of the known spec trographs, which correction obtains even where double tending through the mean orbit has the radial radius focusing mass spectrographs having condensers with plane radius of curvature in these points is indicated by Re (see FIGURE 2). A neighboring surface of equipoten tial may have the axial radius of curvature R in the points of its circle of intersection with the symmetry plane 1:0. For points of the symmetry plane the derivative of curvature ae in the points of the mean orbit; its axial entrance and exit surfaces are used. It is still another object of the present invention to provide a spectrograph with condenser-s which are more perfectly corrected for image errors than any of the known spectrographs, and which do not have any inter mediate radial images in and ‘between the ?elds besides the ?nal images. Other objects and advantages of the present invention will become apparent as the description and explanation thereof proceeds. 60 indicates the amount of the change of the axial radius of curvature R of the surfaces of equipotential when proceeding from a point of the mean orbit in radial r-direction to a neighboring point Re and R’e can be calculated as functions of ra, ae, rb, Ra, Rb, and vice versa RE and Rh can be calculated as functions of r,,, ae, The objects are achieved by the invention which is based on my discovery that in the known spectrographs condensers, and particularly double curved toroidal con densers are characterized by the fact that the value R'e, rb, Re, R'e to be presently de?ned, is equal to one (R',,=1). Accord 65 This formula is given by Formulas 4, 2 and 3 in my ing to my invention the de?ciencies of the known art paper in “Zeitschrift fiir Naturforschung” (ZfN), vol. are overcome by providing condensers characterized by 14a, page 198, referred to below the fact that the value R’e is unequal to one, and may also become negative. The invention is illustrated in the accompanying draw ings, wherein: 3,061,720 4 wherein r may be either ra or rb for the calculation of either Ra or Rb. It will be understood from the ‘formulas given in the various papers referred to below, which formulas have been made part of this speci?cation, that this R’e is one of the variables to be selected in order to verify the equations for the error coefficients A11, A12, A22 and A33. As stated above this R’e is to be unequal to unity which is a condition found by me to render at least one of these coe?icients substantially zero in the types of apparatus discussed ‘below. This is independent of the particular meaning of R’,,. For explanatory reasons, however, it is believed to be readily apparent, that R'e=l has also the following geometrical meaning: As it can be seen from FIG. 1, the radial radii 11a and rb have a common in the ?elds and also of the values of R’e of the con densers. According to the present invention, the condensers are so constructed, that the values R’e are unequal to 1 and may also be negative. It is thus possible to construct mass spectrographs corrected for image errors with which do not have any intermediate radial images in and between the ?elds besides the ?nal images. It is further more possible to construct so-called double focusing mass spectrographs which are corrected for the radial angular aberration of axial origin (A33=O) and have plane en :- trance and exit surfaces of the condensers, while the coe?‘icients A11, A12, A22 may be unequal to zero. And it is also possible to construct energy spectrographs which are corrected for angular aberration with A11=A33=0. in this'case the R of an eqnipotential surface would vary It is, of course, also possible to bring the coefficient as does r taken in the direction of r; thus dR/dr=\1 would necessarily follow therefrom. Accordingly, the 20 A33 to zero in a known manner, speci?cally by providing origin. If the axial radii R9, and Rh had also common origin, then dR/dr would necessarily be ‘unity, because the front surfaces on the entrance or the exit side or discovery is that dR/dr%l as a condition to render the error coe?icients zero, is equivalent to the condition that on both sides of the condensers with curvatures which are symmetrical to the plane z=O the needed radii of the origin of Ra be unequal to the origin of Rb in case ra and rb have a common origin. curvature q of which can be calculated in a manner known . in the art. The first order focusing properties (radial and axial focus lengths and image distances of the usually astig matic focusing) of an energy spectrograph consisting of On the basis of the foregoing explanation the invention will next be described with reference to two examples of spectrographs with condensers according to the invention illustrated in FIGURES 3 and 4 of the accompanying one or several toroidal condensers, as well as such prop erties of combinations of such condensers with magnetic ?elds to mass spectrographs are mainly dependent of the 30 drawings. The ?rst example illustrated in FIGURE 3 relates to values of a6 and Re and of the mean angle or angles of a mass spectrograph with direction and velocity focusing deflection ¢e in the condenser or in the condensers, re which does not have intermediate radial images in and spectively. They are not dependent of the value or the between the ?elds and for which the aberration coeffi values, respectively, of R'e; but the second order focusing cients A11, A12, A22, A33 are equal to zero. FIGS. 6 to 35 properties, especially the image errors at the points of 9 illustrate a toroidal condenser plate used for this ex the images are also dependent of the value or the values, ample de?ning a straight entrance but a curved (curvature respectively, of R’,,. q)-exit. When imaging an object point located on the mean A schematic section through the apparatus within the orbit on the object side, e.-g. a point of the entrance slit 40 symmetry plane 1:0 is shown in FIGURE 3. In this of the spectrograph, into a radial focusing line located ?gure the values ¢m=90° and ae/Re=1.36 are given on the mean orbit on the image side (or, in the case of arbitrarily and vertical entrance of the mean orbit into the so-called stigmatic ‘focusing into an image point lo cated on the mean orbit) by using particle rays progressing in the neighborhood of the mean orbit, the radial image the magnetic ?eld (e'=[)) and the attainment of stigmatic focusing (equal radial and axial image distances of the ?eld combination) are assumed. The distance l’e of the errors are determined by the general formula entrance slit from the entrance limit of the electrical ?eld shall be equal to the focal distance In this formula on and a, are the half effective radial and axial angles of divergence of the rays passing through the spectrograph to the place of the image; 17 represents H. the half maximum relative difference of the kinetic en of the electrical ?eld. From the knowledge of gbm, ergies of the rays passing through the spectrograph to the place of the image. a, dz, 1; are small compared to 1. There is another way of writing the image coe?i cients, which is given in ZfN, vol. 12a, page 538, par as K ticularly on page 539, lFormula 8, thereof l'.e‘=ge and from the Well-known ?rst order double focus wherein a’, and a'z are the same as a and 0:2 given above but wherein B is half the maximum relative difference of the velocities ‘of rays passing through the spectrograph at the place of the image (see L.c., page 538 supra). It is apparent, that ,8 and 17 are interrelated by constant factors. It is further apparent, the 111:0 then, of course, is also A11=0 etc. and vice versa. The coe?icients A11 to A33 are ‘functions of the geometrical data of the ?elds and their combinations, i.e. of the radii of curvature of the mean orbits, of the surfaces of the electrodes, of the ?eld boundaries, of the directions of the ?eld bound (35 ing condition follow the values ¢e=29.5°, ge=2.86ae. By making zero simultaneously the expressions for A11, A12, A22 given in “Zeitschrift fiir Naturforschung” 12a, 539 (1957) (H. Liebl and H. Ewald, The Image Errors of Double Focusing Mass Spectrographs, Equations 9, 10, 11), the values ae=2.S6am, d=5.37am, k’=O.745am, R’e=-2.43 "are obtained. The three equations ‘for A11, A12 and A22 are: O aries, the relative arrangements and distances of the ?elds and the entrance slits, of the mean angles of de?ection 75 3,061,720 aside of the known, i.e. arbitrarily selected ¢m and c=ae/Re, the equations include the ‘following abbrevia tions: calculated value of R’e will be explained in the follow ing example. 'w' r‘ l neghblbly smal L2=I% sin H¢e+-2_2%(c0s (¢e.H) _1) H f __l’e “ l Z’e Mass spectrographs with A11=A12=A22=0 and 30 l'e=ge in which intermediate radial images in or between . the ?elds are allowed would require much larger angles of I€1_Zl; 00:’ H¢e+H <1_T) Sm H4)“ de?ection in one or in both of the ?elds. 2 K2=E(1——cos H(be) A further example illustrated in FIGURE 4 relates to a mass spectrograph with direction and velocity focus~ a A: 36 _3_£ 1 35 ing having a homogeneous magnetic ?eld and a toroidal 1e condenser having plane entrance and exit front surfaces, 2( +R ) and for which A33=O. A schematic section through this apparatus located within the symmetry plane is given in FIGURE 4. In 40 this case the values 6 =91 e=29.7" m:875" Re ae=12 cm. Re=9.6 cm. am=15 cm. These are given by the paper referred to in the last are given arbitrarily and vertical entrance of the mean mentioned Paper (Ewald and Liebl Z. Naturforsch, vol. 45 orblt into the magnetlc ?eld 15* assumed (6'=0)- More‘ 12a, page 128, et seq., 1957). Over, Furthermore, it appears that these equations for An, 1, :0 : A12 and A22 include: the angle 6' which is the angle between the straight mean orbit of the particles entering 8 °° ac ct Wat Vm g Re 6 is assumed As follows from “Zeitschri? fur Natup the magnetic ?eldaand the normal to theentrance bound- 50 forschung” 12a’ 539 (1957) (H. Li?bl and H_ Ewald, The my of the magmfuc ?eld m the entranfe pomt' (See Page Image Errors of Double Focusing Mass Spectrographs), 538 1-°-)’ 31‘? Iatlos ‘Te/“m, d/“w, (‘m/k , and R e‘ The Waning of d’ as’ am and k_ can be taken from FIG' and 12a, 32 (1957) (H. Ewald and H. Liebl, The Image Errors of the Toroidal Condenser), there is for each ?eld 3' d 1_S the d1S_tance of the, exlt ,Of the condenser,and 5 combination of this kind a linear dependence between R’e magnet‘? de?ectlqn System’ m_ which ‘the Fnean 0T1?“ of 5 and fag, which for the special values given above has the the particles therein have a radius am. k’ 18 the radius of the curved entrance boundary of the magnetic de?ection form 0 2841 system. If one selects a’ arbitrarily, the three equations for R'e=_ ' 2 ' amaz I _ a A11’ A12 and A33 are linear in R'e_ If one also Selects 60 In my example R e=—0.229l 1s chosen for WhlCh value one of the four yet unknowns arbitrarily, the other three 7633 and also A33 are equal to Zero can be calculated in simply solving these three equations In the ?rst one of these Papers referred to abmfe now having three unknowns. The above mentioned ?gures for as, a’, k’, and R’e have thus been obtained. By (_ZfN’ VOL 12a, Page 539 (1957)’ the formula ‘for A33 15 gwen by making zero the expression of A33 given in “Zeitschrift 65 ?ir Naturforschung” 12a, p. 544, Equation 17 (1957) A33=i(L33_|_1/2L2p2) . , . . . . (H. Liebl and H. Ewald, Stigmatically Focusing Mass usmg me abbrevlatlons glven m the other paper‘ Spectrographs With Double Focusing Practically of SecL __ E B (30-2) _& _l B . H ond Order), the value q=—0.642ae was obtained, q be- 70 33- ae2 2H(5c——2) H H+H“*(5c_2> sin ¢,, ing the radius of a cylindrical curvature of the exit surB I, face of the condenser the axis of which is located within the symmetry plane and is vertical to the direction of the mean orbit between the two ?elds. The computation of the needed values of the axial radii of curvature RE and Rh of the electrodes ‘from the 75 +5___2 1- (cos 11458-0052 ?qbe) c a“ v- ,2 sin 2‘I/FQSa 2(5c——2) at,2 B=c+c2(1+R'e) c 3,081,720 8 curves of intersection of the electrode surfaces with V meridian planes extending through the rotational z-axis are symmetrical to the plane z=0. Mass and energy spectrometers and spectrographs cor rected for image errors according to my invention enable the realization of higher intensities and accuracies in measuring ion abundances, masses and energies. They will be used with great advantage for physical, chemical, medical, geological, and other problems. It will be understood that this invention is susceptible 1O This equation for A33 can be made zero, for example, with the set of values given in column 6, lines 42 and 43. to modi?cation in order to adapt it to different usages This equation is linear in R’e as it can be seen from hend such modifications within this invention as may fall and conditions, and, accordingly, it is desired to compre within the scope of the appended claims. the appearance of R’e as factor in B, appearing as factor in L33. 15 The manner of determining the needed axial radii of curvature of the condenser electrodes, with R’e and with the radial radii of curvature ra and rb of the electrodes What I claim is: 1. A mass spectrograph having direction and velocity focusing means, comprising; a toroidal condenser defining a mean angle of deflection ¢e, a magnetic de?ection sys tem disposed in the path of particles leaving said con schung" 11a, 156 (1956) (R. Albrecht, The Potential in 20 denser, said condenser and said de?ection system causing an image error de?ned by the sum of Doubly Curved Condensers), and'is described more ex being given, is described in “Zeitschrift fiir Naturfor plicitly in “Zeitschrift fiir Naturforschung” 14a, 198 (1959) (H. Ewald, Concerning the Image Error Correc tion of Doubly Focusing Mass Spectrographs). This formula has been given above in column 2. From r,,: 11.6 25 with a’, and 0/2 being radial and axial angles, respec tively, of a particle path with respect to said mean orbit cm. and rb=l2.4 cm. and the values given above follows and said 19 being half the maximum relative difference of the velocities of rays passing through said spectrograph at the place of the image thereof, wherein A11, A12, and trograph, A11=A33=0. The spectrograph has a toroidal condenser with the values ¢e=30°, ae=Re, ra=0.95ae, 30 A22 are determined by the following variable dimensions: ¢m, being the mean angle of de?ection in said magnetic rb=1.05ae, l’e=l",,=3.73»ae (object distance=image dis de?ection system; c’, being the angle between the straight tance), R’e=—1.046, Ra=1.()62ae, Rb=0.9S5ae, which for this example Ra=9.70 cm. and Rb=9.52 cm. According to still a further example of an energy spec mean orbit behind said condenser and the normal to the entrance boundary; am, being the radius of the mean orbit has a plane entrance front surface and a cylindrically curved exit front surface of the radius of curvature q=—1.67aB (outwardly convex-shaped). Due to the 35 of particles in said magnetic de?ection system; ae, being the radial radius of the mean orbit of particles in said equality of tie and Re the mean surface of equipotential condenser; Re, being the axial radius of equipotential sur between the electrodes is a spherical surface but the elec face through said mean orbit in said condenser; a’, being trodes have toroidal surfaces each having unequal main the distance between said condenser and said magnetic axial and radial radii of curvature. R’e and from this Re, and Rb and also q may be calculated from the rela 40 de?ection system; l'e, being equal to the focal distance of said condenser; It’, being the radius of the entrance tions Au=0 and A33=0. The formulas for All and A33 boundary of the magnetic field of said magnetic system; are described in “Zeitschrift fiir Naturforschung” 12a, 33 R’e, being the derivative of axial radius of the equipoten~ (1957) (H. Ewald and H. Liebl, The Image Errors of tial planes by radial direction in the plane of the mean the Toroidal Condenser), where, however, instead of A11 orbit in said condenser; said variables being selected under and A33 the designations F11/a2 and F33/OlZ2, respectively, simultaneous condition of A11, A12, A22 being substan are employed. tially zero, with R’e being unequal to unity, and wherein There is stated that the axial radii Ra, Rb for said condenser are determined F11=(aeK11-l-l"e'L11) 'd'rz thus, in this case by the equation 50 Re2 A11=aeK11+l"e‘L11=0 _ We use l"e instead of l"re for the sake of clarity, but 1t is understood that l"e in this speci?cation is identical with l"re in the paper just referred to. This l"re=l”e wherein r may be any of the r,,, rb, for determination of can be calculated. Formula 36 in ZfN, vol. 12a, page 33. 55 RB and Rb, respectively. The abbreviations are given in the same paper A 2. Energy spectrograph comprising; a particle entrance L11, c, H, and A are the same abbreviations as given slit; a toroidal condenser having an entrance front sur explicitly above. Using ae=Re and l'ezl",a we obtain for R’,, the relation face and an exit, said entrance front surface being dis 65 posed at a distance l’e from said particle entrance slit; and from this with ¢e=30‘°, R’e=—1.046. However, in the expression for F33 We have to insert Lari-I33 from “Zeitschrift fiir Naturforschung" 12a, 544 (1957) (H. Liebl. and H. Ewald, Mass Spectrographs Practically With Second Order Double Focusing). Using R'e=——l.046, q is calculated from the condition F33=0. It will be noted that instead of toroidal condensers toms-like condensers may be used provided that the axial 75 said condenser focusing said particles at a distance 1",, from said exit; said condenser having a radial angle of (p, of de?ection, radial radii of the condenser plates ra and rb, axial radii thereof, Ra and Rb, and de?ning a mean particle orbit of radial radius (18 along the equi potential surface having axial radius Re, the ratio ae/Re being designated 0, said condenser being defined by the equations: 3,061,720 9 10 _ a6 H=’\/ ___£%a=‘/2_c H-V2—c_ —Re 20 under conditions of R’e unequal to unity. with R',, being unequal to unity. ‘n’ 4. In a spectrograph, a toroidal condenser including 3. Mass spectrograph comprising; a particle entrance slit; a magnetic de?ection system de?ning a mean angle two toroidally shaped condenser plates in which ra and rb are respectively predetermined radial radii of the said plates, ae and Re are the radial radius and the axial radius, boundary of radius k’ whereby an angle 6' is de?ned be- 25 respectively, of the mean particle orbit along an equipo tween the mean particle orbit and the normal to said en tential surface between said plates, axial radii RI, and Rb of trance boundary at the place of entrance; a de?ecting said plates being determined by the equations: condenser having planar entrance and exit surfaces and being interposed between said particle entrance slit at a distance l'e therefrom and said magnetic de?ection sys- 30 tern at a distance d therefrom; l’,a and d being taken from said entrance and said exit surface, respectively, said de of de?ection pm of radius am, having a curved entrance R, +(1_R/ R,2 )2 Rb=§1 Tb—ae+1_R, ?eeting condenser having a radial angle <1),, of de?ection, radial radii of the condenser plates ra and rb, axial radii thereof, Ra and Rb, and de?ning a mean particle orbit 35 of radial radius 06 along the equipotential surface having axial radius Re, the ratio a,,/Re being designated c, said condenser being de?ned by the equations: A33: _L33 _1L2P»=0 2 1': i l—2R’,,R rb_ae+-_-1_ 52, e 5. In a spectrograph, a toroidal condenser including two toroidally shaped condenser plates in which ra and rb are respectively predetermined radial radii of the said 40 plates, ae and Re are the radial radius and the axial radius, respectively, of the mean particle orbit along an equipo tential surface between said plates, axial radii Ra and Rh of said plates being determined by the equations: wherein R',, is unequal to +1. _ 2 ‘r +2(5c—2) 531)“ “be B=c+c2(1+ R18) ‘’ wherein R’e is smaller than +1. +%2 %(cos H¢,—— nos2 42%) BM? ‘’ References Cited in the ?le of this patent 55 Ewald, Liebl and Sauermann article in pages 129-137 of Zeitschrift fiir Naturforschung, vol. 14A, 1959.

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