US 3473018 A
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Oct. 14, 1969 w. M. BRUBAKER 3,473,018
AND COAXIAL ELECTRODES MASS ANALYZER USING TWO SPACED, TUBULAR,
Filed March 2, 1967 IL u UN V ENTOR. M4 504/ ///I 52/54/52 United States Patent US. Cl. 25041.9 Claims ABSTRACT OF THE DISCLOSURE A non-magnetic mass analyzer for separating charged particles according to their mass to charge ratio. The analyzer utilizes the effect of an AC electric field of predetermined amplitude and frequency combined with a DC electric field of predetermined amplitude and polarity created within a confined area to achieve mass separation. Two concentrically oriented electrically conductive cylinders are provided with the combined electric fields being created within the space between the two cylinders. Charged particles of a predetermined mass to charge ratio introduced at the entrance end of the analyzer are transmitted to a charged particle detector at the exit end. Particles of other than the predetermined ratio impinge on the cylinder walls and are discharged thereon.
BACKGROUND OF THE INVENTION This invention relates to mass analyzers and in particular to a non-magnetic instrument utilizing a specific type of electric field created between two coaxial cylinders to separate charged particles according to their mass to charge ratio.
Analyzers constructed and energized according to the present invention are similar to other non-magnetic analyzer instruments such as monopole or quadrupole mass filters in that mass separation is achieved by means of the effect of a combined AC and DC electric field created in the analyzing portion of the instrument. Because of its characteristics of operation it is contemplated that the present invention will have particular utility as a leak detector in which the apparatus is energized so as to render it sensitive to the presence of ions of helium or some similar tracer element.
In brief, operation of analyzer is accomplished by connecting sources of AC and DC potential to the cylinders of the analyzer to create an electric field in the space between them. Charged particles injected into the region between the two cylinders experience both a translational acceleration along the longitudinal axis of the analyzer and a radial acceleration toward the outer cylinder due to the AC field. It has been found that the magnitude of this radial acceleration is uniquely related to the mass to charge ratio of the charged particle. Transmission of such particles through the analyzer is achieved by balancing the radial acceleration imparted to the particle with an acceleration due to a DC field of proper polarity.
SUMMARY OF INVENTION The present invention provides a mass analyzer for separating charged particles of different mass comprising a first tube and a second tube located interiorly of the first tube, the second tube having a length which is substantially co-extensive with the length of the first tube. Means are provided for imposing a static electric field of a predetermined magnitude and polarity between the tubes and means are also provided for imposing an alternating electric field of a predetermined magnitude and frequency between the tubes. In addition, means for introducing charged particles into the space between the tubes are provided, together withv means for collectin or detecting the ice presence of particles emerging from the exit of the analyzer.
In the preferred embodiment of the analyzer of this invention, the cylinders of the analyzer are separated into segments insulated from one another to permit the connection of sources of AC and DC potential of various amplitudes to each of the individual sectors (segment pairs) to reduce the boundary effects at the entrance and exit ends of the analyzer as charged particles traverse the boundaries from the regions of zero field outside the analyzer to the region of strong electric field therewithin.
DESCRIPTION OF THE DRAWING These and other aspects of the invention will be better understood by reference to the following figures in which:
FIG. 1 is an end view of the analyzer of the present invention, including a schematic representation of an AC and DC source used to energize the analyzer;
FIG. 2 is a view taken along lines 22 of FIG. 1;
FIG. 3 is a section view taken along lines 3-3 of FIG. 1 indicating the average position of charged particles of various mass to charge ratios introduced into and passed through the analyzer; and
FIG. 4 is a view taken along line 33 of FIG. 1 illustrating the path of motion of charged particles of the selected mass to charge ratios introduced at an angle to the axis of the analyzer.
DESCRIPTION OF THE PREFERRED EMBODIMENTS A simplified representation of the analyzer of this invention is shown in the end and side views of FIGS. 1 and 2, respectively. As shown in these figures, the analyzer comprises a first tube 10 and a second tube 12 coaxially disposed within the first. Connected between the two cylinders is a source of AC potential 14 and a source of DC potential 16. The parameters of the amplitude and frequency of the signal from the AC source 14, and the amplitude of the signal from the DC source 16 will be discussed in more detail subsequently. The polarity of the DC source 16 with respect to inner cylinder 12 is determined by the charge of the particles to be analyzed. For positively charged particles, the positive pole of the battery 16 is connected to cylinder 10. If used with negatively charged particle, the negative pole of the DC source 16 is connected to the outer cylinder.
Ions directed into the space between the two cylinders encounter the effect of the combined AC and DC field created therein and assume certain characteristic paths of motion dependent upon their mass to charge ratio. FIG. 3 illustrates the average position of ions of three different masses m m and m with the parameters of energization being chosen such that particles of mass m are transmitted by the analyzer. Ions of mass m oscillate about a radius r known as the equilibrium radius for masses m with an amplitude insufficient to 'bring particles of this mass in contact with either of the two cylinders 10, 12 and hence this ion is transmitted to a collector 18. Ions of mass m and m have different equilibrium radii due to their different masses and when subjected to the influence of the combined fields within the analyzer are deflected toward and discharged upon the exterior and interior cylinders respectively. Suitable adjustment of the amplitudes of the excitation voltages and/or the frequency of the alternating voltage results in thetransmission of masses other than m through the: filter producing a signal at the collector 18 and a resultant spectrum 20 such as that shown on recorder 22.
The principle of operation of the analyzer of this invention is based on the balancing of the acceleration of a charged particle in an AC field by the acceleration in a DC field. The equation of motion for such a particle in a uniform alternating electric field is .1 mz=eEac sin wt 2 (eEac/mw sin wt If the field is slightly non-uniform in space, the motion of the particle will still be essentially sinusoidal, as expressed by Equation 2. However, since the force on the particle is 180 out of phase with the displacement, the impulse given to a particle during any AC cycle is finite and not zero. The effect of such cyclically imposed impulses is to give the charged particle a net acceleration toward the region of weaker field. In the present analyzer this is in the radial direction outward toward exterior cylinder 10. By balancing this acceleration with an equal but oppositely directed acceleration due to a DC field, the impulse will be balanced and the charged particle will oscillate without radial translation in the applied fields.
For purposes of discussion throughout, the fields and parameters considered will be those existing between two coaxial cylinders. In such a situation the field strength at any point between the two cylinders will be designated E U) or E (r) to designate the field strength at any particular radius measured from the center of the coaxial cylinders. If the approximation is made that the field is equal to the impressed voltage divided by the cylinder separation R R (R and R being the radii of the internal and external cylinders respectively), the error is considerably less than 1% if (R RQ/R is 0.1. Such an assumption will be made for purposes of this entire discussion.
In a non-uniform AC field such as that created in the space between two coaxial cylinders having an AC source connected between them, the force on a charged particle situated in such a space is somewhat different from that in a uniform field. If a particle in such a field has an average radial position of where r is the radius at a point midway between the cylinders and 18 is the fractional displacement of the particle from its equilibrium radius and under the influence of a nonuniform AC field the particle is executing pseudosinusoidal oscillations about this radial position, then at any instant of time its position is given by z sin of where 2 Solving and integrating the preceding expression, the average acceleration which the particle experiences as a result of its motion in the non-uniform alternating field becomes mr=eEac(r) sin at The preceding equation expresses the effective acceleration experienced by a charged particle as it moves in response to a non-uniform AC field. If this acceleration is balanced by an equal but oppositely directed acceleration in a DC field, the charged particle will experience no net acceleration in the radial direction. As shown above, the acceleration due to an AC field is outwardly directed for a charged particle of either polarity. The direction or polarity of a balancing DC field is dependent upon the sign of the charge of the particle. For positively charged particles the DC field is directed inwardly (positive pole of DC source is connected to outer cylinder) and vice versa for negatively charged particles.
The following analysis of the motion of charged particles in a combined AC and DC field assumes that the charge on the particle is positive. The acceleration in the DC field is given by the expression equating this expression to the acceleration resulting from motion in an AC field as given by equation (6):
o 0) ac( 0) +B) Simplifying the preceding equation, it becomes dc( 0) ac( o)=( 0 o) +B) From this equation it is noted that for a given analyzer geometry pattern and excitation conditions, the conditions of equal acceleration in the AC and DC fields require that m r (l+/9) =c (a constant) and m r =c =m r Thus it can be seen that if ions of mass m have stable equilibrium orbits at radius r ions of mass m have stable equilibrium orbits at radius r where To first order, ions injected into a coaxial analyzer at a radius other than their equilibrium radius (i.e., at a point where the AC and DC accelerations are not balanced) will oscillate about their equilibrium radius with an angular frequency 7.
The value of 'y is calculated as follows: A charged particle injected into the space between the cylinder of a coaxial analyzer at a point other than along its equilibrium radius will experience a net acceleration due to the fact that the acceleration due to the AC field and the acceleration due to the counterbalancing DC field are not equal in magnitude and opposite in direction. In such a case, the particle will respond to the difference or net acceleration between the two accelerations due to the two types of fields created within the analyzer ac' dc) From Equation 6 the acceleration due to the AC field at the equilibrium radius r is ac=( )(zo 0) 0)/( +fi) The acceleration due to the DC field (Equation 7) is do dc( 0) +5) From Equation 9 dc( 0) ae("0) 0 o) +fi) Combining the preceding three expressions and subtracting the acceleration due to the DC field from the AC field, the net acceleration experienced by a particle is expressed by where a =the balance a and a at r 1 6/ Fm) +B) The preceding expression demonstrates that Where an ion is displaced from the equilibrium radius r the forces on the particle are no longer balanced. From Equation 3, B is defined to be the fractional displacement of the particle from its equilibrium radius, i.e., (Ar) /r,,, and is normally less than 0.1 for typical operating conditions for the analyzer of this invention. Equation 14 further shows that the acceleration experienced by the particle is directed oppositely to this displacement and is proportional to it.
The net acceleration which causes a particle to oscillate slowly about its equilibrium radius r is found by permitting to be a variable. Mathematically expressed, the second derivative of [3 is 1 for B 1 l! For 1 (5) equal to unity Thus it can be seen that ions introduced into the analyzer at some point other than their equilibrium radius or having an incrementof radial velocity when introduced at their equilibrium radius will oscillate about this radius in a sinusoidal manner with an angular frequency 7. The preceding analysis of motion can be illustrated in conjunction with FIG. 3. In that figure the equilibrium radius of ions of mass m is r Ions of masses m and m have different equilibrium radii of r and r respectively. Ions of mass m introduced at radius r parallel to the axis will oscillate about r with an amplitude r r and pass through the analyzer without impinging on either cylinder. FIG. 3 also depicts the trajectory envelopes for masses m and m injected into the analyzer along an axis other than their equilibrium radii. In both instances particles of such masses begin oscillation about their equilibrium radii and impinge on one of the two tubes of the analyzer.
It has been found that effective separation of charged particles of different masses is achieved when the separation between the cylinders is large enough to transmit particles of mass m under practical entrance conditions of position and direction, yet close enough that ions of mass m and m have high probability of striking either of the two cylinders and being discharged thereon.
The pertinent design equations relating excitation voltage and frequency, the ratio of DC to AC voltage and the geometrical configuration of the analyzer are derived from the. preceding analysis. From Equation '2 the amplitude of oscillations in response to an AC field is For normal dimensions of the analyzer, the potential gradient may be expressed by the ratio of the voltage impressed between the cylinders divided by the distance between them. That is 0)= ac 2" 1) Combining the two preceding expressions Where the geometry of the analyzer is given and hence the magnitude of 2 is determined (Z0 is some chosen fraction of R R the preceding equation relates the mass, frequency of excitation and excitation voltage. Applying the potential gradient as expressed in Equation 19 and combining Equation 9 with Equation 20 yields which provides the design equation relating the AC voltage to the DC voltage.
For a practical working analyzer, the final design consideration is that the ratio of the frequency of oscillation of the charged particle ('y) about its equilibrium axis to the excitation frequency (to) must be small. Combining Equations 10, 18, and the definition of z the ratio is 0/ o) Equations 20, 21, and 22 provide the necessary design equations for the analyzer.
Assuming the analyzer of the preceding description is used as a helium mass spectrometer and using the mks system of units, actual values in the preceding equations can be calculated. In addition to choosing helium for the transmitted mass, the dimensions of the cylindrical analyzer are chosen with R equal to 9' cm. and R to 11 cm. In this instance r will be 10 cm. and Z is chosen as 5 mm. Our design equations now become V =4 10- 1 V /V 1/20 v/ =x E After determining the preceding three values, the steps remaining are to choose operating voltages and frequency. Choosing the peak AC as 400 volts and w as 10 radians/ sec., the frequency becomes 1.6 megacycles. For one period of oscillation, i.e., the time in which a transmitted ion returns to its position relative to the equilibrium radius that it possessed upon entry, the transit time of the ion becomes 4.4 microseconds for the operating values chosen. The energy of helium ions which will traverse a filter L centimeters in length in 4.4 microseconds is demonstrating that the focusing forces are strong and the transit time for a given mass is short.
Entrance and exit conditions alfect the transmission efiiciency of an analyzer of the present invention. Since charged particles introduced into the analyzer move from an area of essentially zero electric field into an area of strong electric field such particles receive an impulse which is phase dependent as they enter the strong field. For a filter or analyzer consisting of cylinders of one continuous length, the impulse imparted to a charged particle must be limited, i.e., the phase angle for acceptance of charged particles in order to obtain transmission of a detectable number of ions through the analyzer is restricted to a certain width whose magnitude can be calculated and is dependent upon (a) the maximum radial component of velocity which the charged particle can have as it crosses its equilibrium radius and still be transmitted without striking the electrodes and (b) the phase angle of the AC field as the charged particle enters the filter.
The impulse imparted to particles admitted to the filter can be limited by a filter according to the dotted configuration shown in FIG. 2. In that figure the outer cylinder 10 and the inner cylinder 12 are separated into segments 24, 26, and 28 corresponding, respectively, to the entrance, analyzing and exit portions of the filter. Separating each segment is an angular ring, 30 and 32, respectively, of a high dielectric material to insulate adjacent cylinder segments. In such an embodiment means for controlling the electrical voltage delivered to each segment from sources 14 and 16 must be provided. Suitable impedance and circuit connections from the two sources to each segment can be provided to apply appropriate potentials to the segments of each sector. Alternatively, three separate sources of AC and DC excitation, each having the desired output signal, can be connected respectively to each of the three segments of the filter. To reduce the impulse imparted to particles entering the analyzer the energization delivered to segment 24 is limited to a relatively small fraction of the electrical voltage provided in the analyzing sector 26. In this manner, charged particles entering the filter experience a more gradual transfer from a region of zero field to the region of relatively high electric field in the analyzing section of the filter or analyzer. Similarly, the voltage delivered to the exit sector 28 of the filter has a magnitude which is a fraction of that applied to the analyzing sector to reduce the kick or impulse as the sorted particles leave the filter.
In addition to the parameters chosen in the illustrative example, other sets of operating parameters can also be chosen, particularly other voltages and frequencies. The values chosen in the illustrative example emphasize the large strength of forces which act on charged particles introduced into the fields within the analyzer. These strong focusing forces cause the particles to return quickly to their equilibrium radii and permit the transmission of charged particles which are injected into the filter with sizeable components of radial velocity.
In normal circumstances large entrance apertures to the analyzer are to be used. Since the sensitivity of the instrument to variations in entrance velocity is small, ions introduced into the analyzer are normally subjected to strong accelerating electric fields prior to entrance into the filter. This enables the use of ion sources of high sensitivity. The end result of these factors is the ability to readily achieve large transport currents.
What is claimed is:
1. A mass analyzer for separating charged particles of diiferent masses comprising:
a first elongated, hollow, tubular electrode having a longitudinal axis;
a second elongated, tubular electrode located interiorly and coaxially of the first electrode, the two electrodes defining an annular, cylindrically shaped mass analyzing region between adjacent surfaces of the electrodes;
means for imposing a static electric field of a predetermined magnitude and polarity between the electrodes;
means for imposing an alternating electric field of a predetermined magnitude and frequency between the electrodes; the ratio of the static electric field and the alternating electric field being chosen with respect to the dimensions of said electrodes such that charged particles of a specific mass are transmitted through the analyzer;
means for introducing charged particles into the analyzing region in a direction generally parallel to the longitudinal axis of the first electrode at one end of the analyzer; and
means for collecting charged particles of said specific mass located at the end of the analyzing region opposite the charged particle introducing means.
2. An analyzer according to claim 1 wherein the tubular electrodes are cylinders.
3. A mass analyzer according to claim 2 wherein each of the cylinders is segmented into a plurality of coaxial sectors, each of said sectors being separate from adjacent sectors by a dielectric medium.
4. A mass analyzer according to claim 3 including means for creating a static electric field of a predetermined magnitude and polarity between each corresponding inner and outer cylinder sectors of the analyzer and means for creating an alternating electric field of predetermined magnitude and' frequency between each corresponding inner and outer cylinder sectors of the analyzer.
5. A mass analyzer for separating charged particles of diiferent masses comprising:
a first hollow cylinder;
a second cylinder located interiorly of the first cylinder and coaxially therewith;
means for imposing a static electric field of a predetermined magnitude and polarity between the cylinders;
means for imposing an alternating electric field of a predetermined magnitude and frequency between the cylinders;
means for introducing charged particles into the space between the cylinders in a direction generally parallel to the longitudial axis of the cylinders at one end of the analyzer; and
means for collecting charged particles of a predetermined mass located at the endof the analyzer opposite the charged particle introducing means wherein the analyzer is operated substantially according to the relationships:
where V is the peak alternating voltage, V is the peak static voltage, R is the radius of the first cylinder, R is the radius of the coaxial cylinder located interiorly of the first cylinder, r is the distance between the outer and inner cylinder corresponding to the equilibrium radius of the charged particle of predetermined mass, Z0 is the amplitude of oscillation of the charged particle at r m is the mass of the charged particles to be transmitted, e is the electric charge on an electron, ,3 is the fractional displacement of the particle from r 7 is the angular frequency of oscillation of the particle about its equilibrium radius when injected into the analyzer at a point other than its equilibrium radius and w is the angular frequency of the alternating electric field.
References Cited UNITED STATES PATENTS 3,143,647 8/1964 Gunther et al. 250-419 3,239,662 3/1966 Noller 25041.9 3,244,969 4/1966 Herb et a1 324-33 3,280,326 10/1966 Gunther 2504l.9
WILLIAM F. LINDQUIST, Primary Examiner