Multi-turn time-of-flight mass spectrometers with electrostatic sectors

Abstract

The mass resolution of a time-of-flight (TOF) mass spectrometer is directly proportional to its total flight pathlength. Multi-turn or multi-passage ion optical geometries are necessary to obtain fight distances of sufficient length within reasonable size limitations. We have investigated ion optics for a multi-turn TOF mass spectrometer with electrostatic sectors. The concept of ‘perfect’ focusing conditions is introduced. Furthermore, a new type of multi-turn TOF mass spectrometer, the MULTUM Linear plus, was developed. It consists of four cylindrical electric sectors and 28 electric quadrupole lenses. It has a vacuum chamber 60 × 70 × 20 cm in size. Mass resolution is demonstrated to increase according to the number of ion cycles. A mass resolution of 350 000 (m/z = 28, FWHM) was achieved after 501.5 cycles. The MULTUM Linear plus analyzer is not simple, however; 28 electric quadrupole lenses are used. In order to reduce the number of ion optical parts, an improved multi-turn TOF mass spectrometer, the MULTUM II, consisting of only four toroidal electric sectors, was also developed. The possibility of tandem mass spectrometric applications using multi-turn TOF mass spectrometers is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.

INTRODUCTION

The time-of-flight (TOF) mass spectrometer has become an especially powerful and attractive instrument in the field of mass spectrometry (MS) since the introduction of pulsed laser ionization methods and the development of very fast electronics. In particular, the introduction of matrix-assisted laser desorption/ionization (MALDI) extended applications into the biochemical field.1 The merits of the TOF mass spectrometer are well recognized: (1) high ultimate mass range, (2) very high transmission and (3) ability to record the entire mass spectrum simultaneously. However, a major limitation of the TOF mass spectrometer, which has often been mentioned, is its relatively poor mass resolution. In order to improve mass resolution, the following methods were introduced. (1) In order to minimize the effects of spatial and velocity deviations on time resolution, two-stage acceleration and time-lag focusing methods were introduced by Wiley and McLaren.2 (2) For the same purpose, orthogonal acceleration ion sources were developed by Dawson and Guilhaus3 and Dodonov et al.4 (3) In an effort to achieve energy focusing, the ion mirror was devised by Alikanov and Mamyrin et al.5 Ions of the same m/z with different energies can be made to arrive at the detector at the same time. (4) In order to achieve isochronous focusing and space focusing, electric sectors were proposed by Poschenrieder.6 As an example of this method, a TOF mass spectrometer consisting of four toroidal electric sectors was constructed and tested by Sakurai et al.7 This instrument allows simultaneous triple isochronous and triple space focusing.

The mass resolution of a TOF mass spectrometer is directly proportional to its total flight pathlength. Therefore, a long flight path is essential to achieve high mass resolution. Ordinarily, the flight length of an instrument is finite and fixed, and the value is proportional to the size of the instrument. Accordingly, the maximum practical value is several meters. It is difficult to achieve higher mass resolution by extending the length. To overcome this problem, the following systems were proposed. (1) Electrostatic multi-pass mirror systems were proposed by Wollnik and Przewloka8 and constructed by Casares et al.9 and Wollnik and Casares.10 In this type of instrument, ions are reflected by two or more mirrors, and stored between these mirrors. In this way, ions fly the same path many times. (2) Multi-turn ion optical geometries using electric sectors were proposed by Poschenrieder.6 The optical geometry has a closed orbit. Ions are stored in the orbit and traverse the same orbit many times. Accordingly, the flight path length can be extended as much as desired. Poschenrieder described ion injection and ejection (for detection) as possibly causing some problems. The multi-turn TOF mass spectrometer had then not yet been constructed. Matsuo and co-workers found a solution which allowed ions to be injected and ejected through a hole in each of the outer sector electrodes11 and constructed multi-turn TOF mass spectrometers called the MULTUM Linear plus12, 13 and the MULTUM II14 as described in detail below. Sakurai et al.15 also found a solution in which ions were injected and ejected by additional deflecting electrodes and constructed the multi-passage TOF mass spectrometer termed OVAL.

We adopt a multi-turn geometry to improve mass resolution. If the ion beam is divergent, both mass resolution and ion transmission decrease with increasing number of cycles around the system. We studied the ion optics of a multi-turn TOF mass spectrometer consisting of electric sector fields.11, 16 By introducing symmetry in the arrangement of sectors, multiple time and space focusing can easily be achieved.16, 17 Using this principle, some ion optical systems for a multi-turn TOF mass spectrometer which achieve ‘nine-fold focusing’ were found. We refer to this focusing as ‘perfect space and time focusing’.16 One of these proposed TOF systems, the MULTUM Linear plus, was constructed as a laboratory model for the COSAC project of the ROSETTA space mission.12, 13 It consists of four cylindrical electrostatic sectors and 28 electric quadrupole lenses. In order to inject and eject ions, it was combined with a linear-type TOF mass spectrometer. Four electric quadrupole triplets were used to achieve perfect space focusing of the linear type TOF mass spectrometer. It was experimentally demonstrated that mass resolution increased according to the number of ion cycles through the ion optical system. A mass resolution of >350 000 was achieved after 500 cycles.18 The MULTUM Linear plus analyzer was not simple, however; 28 electric quadrupole lenses were used. Another multi-turn TOF mass spectrometer, the MULTUM II, was also developed in an effort to reduce the number of quadrupole lenses.14 The new instrument consists of only four toroidal sectors. We demonstrate that mass resolution increases according to the number of cycles.

In this paper, the theory of ion optics for multi-turn TOF mass spectrometers is described. Experimental results obtained with multi-turn TOF mass spectrometers, the MULTUM Linear plus and the MULTUM II, are also reported.

ION OPTICS FOR MULTI-TURN TIME-OF-FLIGHT MASS SPECTROMETERS

Transfer matrix method of expressing ion trajectories

Generally, the methods used to calculate ion trajectories in electromagnetic fields are classified as (1) the transfer matrix method and (2) the ray tracing method. Here the transfer matrix method is used.

The coordinate system (x, y, z) is defined with its origin on the optical axis, with the z direction along the optical axis as shown in Fig. 1. In principle, ion trajectories in electric or magnetic fields can be calculated by solving the equations of motion. The geometric trajectory of an arbitrary particle can be expressed by an ion optical position vector (x, α, y, β, γ, δ), where x, y and α, β denote the lateral and angular deviations of the ion under consideration from a reference ion at the object. The mass and energy deviations, γ and δ, are defined as

• (1)

where m, U and q are the mass, energy and charge, respectively, of an arbitrary ion and m₀, U₀ and q₀ are those of a reference ion. In order to describe flight time, the concept of the pathlength deviation, l,19 is added to the original ion optical position vector. The new position vector (x, α, y, β, γ, δ, l) at an arbitrary profile plane is related to the initial position vector (x₀, α₀, y₀, β₀, γ, δ, l₀) in a first-order approximation by a transfer matrix A in the following manner:

• (2)

Figure 1. Definitions of the coordinate system and of the elements of ion optical position vectors.

A transfer matrix of each optical component can be calculated numerically when its physical parameters are given. If the system consists of several ion optical components, such as electric sectors, quadrupole lenses and drift spaces, the total transfer matrix R can be simply obtained by multiplying the transfer matrix of the individual elements as

• (3)

Focusing conditions of an entire system will be discussed using the above overall transfer matrix elements R(i|j).

In the present research, only electric sectors and electric quadrupole lenses are used. Then, the conditions R(x|γ) = 0 and R(α|γ) = 0 are always fulfilled.

Ideal perfect space and time focusing conditions

In this section, we discuss the ion optical conditions for a multi-turn TOF mass spectrometer. The first involves the geometric conditions for multi-turn systems, namely the requirements for closing the ion optical orbit. Multi-turn TOF mass spectrometer geometries with such orbits have already been proposed.6, 11 They did not, however, satisfy the second condition, namely the ‘perfect focusing condition’.16 In this case, ion beam divergence and mass resolution decrease with increasing number of cycles around the system. To avoid this problem, ions should return to the point of origin in the system, in other words, the absolute value of the position and angle at the detector plane should be the same as those under the initial conditions in both the horizontal (x direction) and the vertical (y direction) planes. Such conditions can be expressed using the transfer matrix in the first-order approximation as

• (4)

It should be noted that the character 0 (zero underlined) indicates a matrix element which is set at zero. On the other hand, 0 (zero not underlined) means zero by definition. The condition R(x|α) = 0 (angular focusing), the condition R(x|δ) = 0 (energy focusing) and the condition R(x|x) = ±1 for lateral magnification are required to conserve the absolute value of the lateral deviation (|x| = |x₀|) in the horizontal direction. In the same way, the condition R(y|β) = 0 (angular focusing) and the condition R(y|y) = ±1 for lateral magnification are required to conserve the absolute value of the lateral deviation (|y| = |y₀|) in the vertical direction. Moreover, R(α|x) = R(α|δ) = 0 and R(α|α) = ±1 are required to conserve the absolute value of the angle (|α| = |α₀|) in the horizontal direction and R(β|y) = 0 and R(β|β) = ±1 are required to conserve the absolute value of the angle (|β| = |β₀|) in the vertical direction. In the case of a TOF mass spectrometer, triple time focusing R(l|x) = R(l|α) = R(l|δ) = 0 is also required. Accordingly, we require ‘nine-fold focusing’, i.e. the nine 0 elements should be zero to achieve perfect space and time focusing. The final goal is to find an ion optical system whose overall transfer matrix can be set to meet the above. Here, we call the system with a magnification of (+1) the normal image type (N-type) and the (−1) system the inverse image type (I-type).

In our experience, it is easy to find the solution of R(x|x) = ±1 and R(x|α) = 0, but it is very difficult to satisfy these parameters with R(α|x) = 0 simultaneously. In order to overcome this difficulty, symmetrical geometries are introduced.

Symmetrical geometry systems consisting of two units

By introducing symmetry in the arrangement of the ion optical components, multiple focusing conditions are easily achieved under some circumstances.16, 17 In this paper, we will treat only symmetrical systems consisting of electric fields.

Generally, a symmetrical system consists of two basic units (elements). A system consisting of four elements, for example, can be understood as a doubly symmetric system of two units. Detailed discussions about the characteristics of a symmetrical arrangement consisting of two units and four units are given in Refs17 and16, respectively. Here, we simply explain the characteristics of a symmetrical arrangement.

We define the transfer matrix A as a basic unit which is usually obtained by multiplication of the matrices of drift spaces, electric sectors or electric quadrupole lenses. We can derive the point-symmetric matrix A* of A and the plane-symmetric matrix A⁻ from the transfer matrix A based on the inverse matrix concept. Both are presented in detail the Appendix in Ref. 17. The total transfer matrix of a point symmetric system, A*A, and a plane symmetric system, A⁻A, can be obtained only by multiplying the transfer matrix. These total transfer matrices should satisfy the perfect focusing condition of Eqn (4).

The four cases in Table 1 are the only solutions fulfilling the perfect space and time focusing conditions for the symmetric system. It can be understood that these types of solutions correspond to the focusing status at the intermediate point, namely, whether ion beams are focused (A(x|α) = 0) or parallel (A(α|α) = 0). We express these differences by using the symbol ● for focusing and ˆ for parallel at the intermediate point. For example, the type termed a ‘point symmetry system with an intermediate image’ can be expressed as A* ● A and the type referred to as a ‘plane symmetry system without an intermediate image’ where the ion beams are parallel at the intermediate point can be expressed as A⁻○A.

Table 1. Four different solutions for perfect space focusing conditions in the horizontal plane. The symbols ● and ˆ indicate focusing status: ‘focusing’ and ‘parallel’ at the intermediate point, respectively

Type		Required conditions	Characteristics
Point Symmetry	PX1	A(x|x) = 0, A(α|α) = 0,	A*○A
		A(x|δ) = 0, A(l|δ) = 0	I-type
	PX2	A(x|α) = 0, A(α|x) = 0,	A*●A
		A(x|δ) = 0, A(l|δ) = 0	N-type
Plane Symmetry	LX1	A(x|x) = 0, A(α|α) = 0,	A^−○A
		A(α|δ) = 0, A(l|δ) = 0	I-type
	LX2	A(x|α) = 0, A(α|x) = 0,	A^−●A
		A(α|δ) = 0, A(l|δ) = 0	N-type

Similar requirements must be satisfied in the vertical direction, as shown in Table 2. Since there is no energy dispersion or time term in the first-order approximation in the vertical direction, the required conditions of a point symmetric system are identical with those of a plane symmetric system.

Table 2. Two different solutions for perfect focusing conditions in the vertical plane. The superscript s indicates the symmetries, ‘*’ or ‘−’

Type	Required conditions	Characteristics
Y1	A(y|y) = 0, A(β|β) = 0	A^s○A I-type
Y2	A(y|β) = 0, A(β|y) = 0	A^s●A N-type

Symmetrical geometry systems consisting of four units

A symmetric system consisting of two basic units that satisfy the perfect focusing conditions has not yet been found. In the next step, we introduce ‘doubly symmetric geometry’, namely four units are combined in such a way that two units are multiplied by two units. The purposes are (1) to find a perfect focusing geometry consisting of four units, (2) to find a perfect focusing geometry in the vertical direction also and (3) to simplify achievement of a closed trajectory.

Generally, there are four types of combinations:

• (a)
  point symmetric system composed of point symmetric systems: (A*A)*(A*A);
• (b)
  plane symmetric system composed of point symmetric systems: (A*A)⁻ (A*A);
• (c)
  point symmetric system composed of plane symmetric systems: (A⁻A)*(A⁻A);
• (d)
  plane symmetric system composed of plane symmetric systems: (A⁻A)⁻(A⁻A).

The total transfer matrices of these symmetric systems are obtained by multiplying the transfer matrix and comparing it with the perfect focusing condition, Eqn (4), to obtain the required conditions. The required conditions for achieving perfect focus are described in detail in Ref. 16. In this paper, we explain the required conditions only for type (b), which is adopted for our multi-turn TOF mass spectrometers.

The required conditions for the horizontal directions are classified into the three cases presented in Table 3. The BX1 type is simply the system connecting the PX1 type in Table 1 with the point symmetric system of PX1. The BX2 type is similar to the system connecting the PX2 type with the plane symmetric system of PX2. However, the number of conditions required to achieve perfect focusing can be reduced from four to three. The type BX3 only appears in doubly symmetric geometry. Ion beams are parallel at the point after two basic units. The number of required conditions can be reduced from four to three. The final essential conditions for the vertical directions are also classified into the three cases presented in Table 4. In the vertical direction, as the symmetric system consists of two units, there is no difference between point and plane symmetry. Therefore, the same conditions are also required in the other three symmetric systems.

Table 3. The perfect focusing conditions of (A*A)⁻(A*A) geometry in the horizontal direction

Type	Required conditions	Characteristics
BX1	A(x|x) = 0, A(α|α) = 0,	(A*○A)^−● (A*○A)
	A(x|δ) = 0, A(l|δ) = 0	N-type
BX2	A(x|α) = 0, A(α|x) = 0,	(A*●A)^−●(A*●A)
	A(l|δ)−2A(x|δ)A(α|δ) = 0	N-type
BX3	2A(x|x)A(α|α)−1 = 0,	(A*A)^−○(A*A)
	A(x|δ) = 0, A(l|δ) = 0	I-type

Table 4. The perfect focusing conditions of a symmetric system consisting of four units in the vertical direction. The superscript s indicates the symmetries, ‘*’ or ‘−’

Type	Required conditions	Characteristics
QY1	A(y|y) = 0, A(β|β) = 0	(A^s○A)^s●(A^s○A)
		N-type
QY2	A(y|β) = 0, A(β|y) = 0	(A^s●A)^s●(A^s●A)
		N-type
QY3	2A(y|y)A(β|β) − 1 = 0	(A^sA)^s○(A^sA)
		I-type

Ion optical systems satisfying the perfect focusing condition

Several ion optical systems for multi-turn TOF mass spectrometry that satisfy the perfect focusing condition have been found by using the principles described in the previous section. In this section, the characteristics of three perfect focusing systems, MULTUM, MULTUM II and figure-of-eight type geometry, are discussed.

MULTUM geometry

MULTUM geometry consists of four cylindrical electrostatic sectors and eight electric quadrupole lenses. The ion trajectories simulated by TRIO-DRAW20 are shown in Fig. 2. The basic unit is comprised of four drift spaces, two electric quadrupole lenses and a cylindrical electrostatic sector. The ion optical parameters of the basic unit and the total transfer matrix elements of the basic unit and whole system are given in Table 5. This system consists of a BX1 type in the horizontal direction and a QY3 type in the vertical direction. In the horizontal direction, perfect focusing is achieved and the image type is inverse (I-type) after half a cycle (two units). Therefore, the image type at one cycle (four units) is normal (N-type). In the vertical direction, the perfect focusing condition is satisfied only after one complete cycle and the image is I-type.

Figure 2. Ion trajectories of the MULTUM geometry multi-turn TOF mass spectrometer simulated by TRIO-DRAW. (a) Top view; (b) x-direction; (c) y-direction; (d) pathlength deviation mode.

Table 5. Ion optical parameters of the basic unit and the total transfer matrix elements of the basic unit and whole system of the MULTUM geometry

Ion optical parameters of the basic unit—
Drift space			DL = 0.0461
Electrostatic Q-lens entrance			QR = 0.0050, NQ1 = 2
Electrostatic Q-lens			QKE = −36.1600, QLE = 0.0100
Electrostatic Q-lens exit			QR = 0.0050, NQ2 = 2
Drift space			DL = 0.0218
Toroidal ESA entrance			RO1 = 0.0000, GAP = 0.0038, NE1 = 2
Toroidal ESA			AE = 0.0500, WE = 156.87, C17 = 0.0000 C2 = 0.0000
Toroidal ESA exit			RO2 = 0.0000, GAP = 0.0038, NE2 = 2
Drift space			DL = 0.0661
Electrostatic Q-lens entrance			QR = 0.0050, NQ1 = 2
Electrostatic Q-lens			QKE = −21.0220, QLE = 0.0100
Electrostatic Q-lens exit			QR = 0.0050, NQ2 = 2
Drift space			DL = 0.0300
Total transfer matrix of the basic unit—
	x	α	γ	δ	xx	xα	xγ	xδ	αα	αγ
x	−0.00005	−0.08619	0.00000	0.00000	0.10052	5.78695	0.00000	2.98495	0.44564	0.00000
α	11.60185	−0.00010	0.00000	−0.37245	389.78232	120.01601	0.00000	15.51453	7.18874	0.00000
t	0.00006	0.06433	0.16044	0.00000	−29.66154	−7.21246	0.00003	−0.99933	−0.34118	0.03216
	αδ	γγ	γδ	δδ	yy	yβ	ββ
x	0.11518	0.00000	0.00000	−0.02990	0.00017	−0.00001	0.00000
α	0.45282	0.00000	0.00000	−0.21624	60.60295	−3.30910	0.04517
t	0.03937	−0.04011	0.00000	0.10596	7.96619	−0.10649	0.07544
	y	β
y	−2.13396	0.12469
β	−4.00992	−0.23431
Total transfer matrix of the whole system—
	x	α	γ	δ	xx	xα	xγ	xδ	αα	αδ
x	0.99997	−0.00003	0.00000	0.00002	0.38379	41.32706	0.00000	−0.00425	0.00143	0.00000
α	0.00230	0.99996	0.00000	0.00005	−0.15294	−0.67270	0.00000	−138.66237	−20.65630	0.00000
t	0.00010	0.00000	0.64177	0.00000	−118.47670	0.02916	0.00005	4.91923	−0.03545	0.00000
	αδ	γγ	γδ	δδ	yy	yβ	ββ
y	0.15697	0.00000	0.00000	−0.00001	0.00001	−0.00001	0.00000
α	0.01475	0.00000	0.00000	1.38775	−0.00021	0.00000	−0.00003
t	−0.00070	−0.16044	0.00000	0.33455	60.12567	−0.00001	0.20528
	y	β
y	−0.99998	0.00000
β	0.00052	−0.99998

MULTUM II geometry

The MULTUM II geometry consists of only four toroidal electrostatic sectors. The ion trajectories simulated by TRIO-DRAW are shown in Fig. 3. The basic unit is comprised of two drift spaces and a toroidal electrostatic sector (the c-value = r0/R021 of a toroidal electric sector field is 0.033, where r0 is the radius of the main path and R0 is the axial radius of curvature of the middle equipotential surface). The ion optical parameters of the basic unit and the total transfer matrix elements of the basic unit and whole system are given in Table 6. This system consists of a BX3 type in the horizontal direction and a QY3 type in the vertical direction. The perfect focusing condition is satisfied after one cycle (four units) and the image is I-type in both the horizontal and vertical directions.

Figure 3. Ion trajectories of the MULTUM II geometry multi-turn TOF mass spectrometer. (a) Top view; (b) x-direction; (c) y-direction; (d) pathlength deviation mode.

Table 6. Ion optical parameters of the basic unit and the total transfer matrix elements of the basic unit and the whole MULTUM II

Ion optical parameters of the basic unit—
Drift space			DL = 0.0809
1			RO1 = 0.0000, GAP = 0.0050, NE1 = 2
Toroidal ESA			AE = 0.0500, WE = 157.10, C1 = 0.0337, C2 = −0.0023
Toroidal ESA exit			RO2 = 0.0000, GAP = 0.0050, NE2 = 2
Drift space			DL = 0.1089
Total transfer matrix of the basic unit—
	x	α	γ	δ	xx	xα	xγ	xδ	αα	αγ
x	0.96902	−0.03095	0.00000	0.00079	−44.35664	−2.86038	0.00000	2.02607	0.12107	0.00000
α	16.15310	0.51604	0.00000	−0.40421	−138.61584	8.49187	0.00000	5.11800	2.64651	0.00000
t	−0.81107	0.02430	0.16347	−0.00064	19.09068	−0.06778	−0.40554	−1.27885	−0.10135	0.01215
	αδ	γγ	γδ	δδ	yy	yβ	ββ
x	0.05325	0.00000	0.00000	−0.02290	−0.13674	0.10883	0.01871
α	−0.35358	0.00000	0.00000	−0.04836	1.65087	0.95341	0.53790
t	0.02120	−0.04087	−0.00032	0.11162	0.10071	−0.04908	−0.01342
	y	β
y	0.68304	0.28207
β	−1.77099	0.73270
Total transfer matrix of the whole system—
	x	α	γ	δ	xx	xα	xγ	xδ	αα	αγ
x	−0.99996	−0.00001	0.00000	−0.00160	92.86260	−0.00977	0.00000	0.14444	−0.25006	0.00000
α	0.00805	−0.99996	0.00000	−0.00033	−21.78542	−185.51624	−0.00001	92.10364	0.00610	0.00000
t	0.00000	−0.00321	0.65388	0.00005	−36.64230	−0.29793	0.00000	0.09965	−0.03730	−0.00160
	αδ	γγ	γδ	δδ	yy	yβ	ββ
x	−0.09410	0.00000	0.00000	0.05080	0.12135	−0.00015	−0.01109
α	−0.15257	0.00000	0.00000	0.07349	0.01627	7.02659	−0.00354
t	0.16428	−0.16347	0.00002	0.36842	−0.00145	0.01128	−0.00019
	y	β
y	−1.00000	0.00076
β	−0.00445	−1.00000

Figure-of-eight type geometry

‘Figure-of-eight type’ geometry consists of two cylindrical electrostatic sectors and eight electric quadrupole lenses. The ion trajectories simulated by TRIO-DRAW are shown in Fig. 4. The basic unit is comprised of six drift spaces, four electric quadrupole lenses and a cylindrical electrostatic sector. The ion optical parameters of the basic unit and the total transfer matrix elements of the basic unit and whole system are given in Table 7. This system consists of a AX1 type, described in Ref. 16, in the horizontal direction and a QY1 type in the vertical direction. The perfect focusing condition is satisfied after two cycles (four units) and the image is N-type in both the horizontal and vertical directions. The system must be operated for two cycles, at a minimum.

Figure 4. Ion trajectories of the figure-of-eight type geometry multi-turn TOF mass spectrometer. (a) Top view; (b) x-direction; (c) y-direction; (d) pathlength deviation mode.

Table 7. Ion optical parameters of the basic unit and the total transfer matrix elements of the basic unit and the whole figure-of-eight type geometry system

Ion optical parameters of the basic unit—
Drift space			DL = 0.0724
Electrostatic Q-lens entrance			QR = 0.0050, NQ1 = 2
Electrostatic Q-lens			QKE = 54.2980, QLE = 0.0100
Electrostatic Q-lens exit			QR = 0.0050, NQ2 = 2
Drift space			DL = 0.0100
Electrostatic Q-lens entrance			QR = 0.0050, NQ1 = 2
Electrostatic Q-lens			QKE = −57.0580, QLE = 0.0100
Electrostatic Q-lens exit			QR = 0.0050, NQ2 = 2
Drift space			DL = 0.0100
Toroidal ESA entrance			RO1 = 1.0000 GAP = 0.0004, NE1 = 2
Toroidal ESA			AE = 0.0500 WE = 227.95, C1 = 0.0000, C2 = 0.0000
Toroidal ESA exit			RO2 = 1.0000 GAP = 0.0004, NE2 = 2
Drift space			DL = 0.0100
Electrostatic Q-lens entrance			QR = 0.0050, NQ1 = 2
Electrostatic Q-lens			QKE = −57.0580, QLE = 0.0100
Electrostatic Q-lens exit			QR = 0.0050, NQ2 = 2
Drift space			DL = 0.0100
Electrostatic Q-lens entrance			QR = 0.0050, NQ1 = 2
Electrostatic Q-lens			QKE = 54.2980, QLE = 0.0100
Electrostatic Q-lens exit			QR = 0.0050, NQ2 = 2
Drift space			DL = 0.0724
Deflection is in reverse sense
Total transfer matrix of the basic unit—
	x	α	γ	δ	xx	xα	xγ	xδ	αα	αγ
x	0.00016	−0.13779	0.00000	0.02434	−2.78514	−0.85051	0.00000	−2.16933	−0.05861	0.00000
α	7.25553	0.00016	0.00000	0.17662	−22.38365	−6.17036	0.00000	−11.26428	−0.38386	0.00000
t	−0.35325	−0.04869	0.21191	0.00860	16.45989	2.25226	−0.17662	−0.36479	0.31060	−0.02434
	αδ	γγ	γδ	δδ	yy	yβ	ββ
x	−0.21408	0.00000	0.00000	−0.00113	−91.06010	−7.99276	−0.22139
α	−2.18396	0.00000	0.00000	0.10198	−509.28745	−57.98248	−2.08321
t	−0.07517	−0.05298	0.00430	0.11186	104.33482	8.51299	0.35222
	y	β
y	0.00039	−0.05613
β	17.81189	0.00039
Total transfer matrix of the whole system—
	x	α	γ	δ	xx	xα	xγ	xδ	αα	αγ
x	0.99953	0.00009	0.00000	−0.00002	−0.00211	−0.00040	0.00000	0.00683	0.00011	0.00000
α	−0.00454	0.99953	0.00000	0.00008	0.00948	0.00423	0.00000	67.31042	0.00020	0.00000
t	−0.00017	0.00003	0.84763	0.00000	69.75835	0.00105	−0.00008	0.00260	1.32465	0.00002
	αδ	γγ	γδ	δδ	yy	yβ	ββ
x	−1.27809	0.00000	0.00000	0.22581	−0.16463	−0.00383	0.00084
α	0.00668	0.00000	0.00000	−0.00142	0.31473	0.00966	0.00076
t	−0.91966	−0.21191	0.00000	0.61188	546.11859	0.00404	1.72042
	y	β
y	0.99953	0.00009
β	−0.02775	0.99952

THE MULTI-TURN TOF MASS SPECTROMETER MULTUM LINEAR PLUS

Analyzer

We designed and constructed a multi-turn TOF mass spectrometer using MULTUM geometry as a laboratory model for cometary exploration. The system consists of four discrete units, each comprised of an electric quadrupole lens, a cylindrical electrostatic sector and an electric quadrupole lens. The deflection radius of the cylindrical electric sector is 50 mm, the deflection angle is 156.87°, the gap between the electrodes is 7.5 mm and the applied voltage is ±225 V if the accelerating voltage of the ions is 1500 V. The quadrupole lens length is 10 mm and the radius of the inscribed circle of the electrodes is 5 mm. The voltage applied to four quadrupole lenses near the crossing point is ±16.57 V and that of the other lenses is ±49.04 V. The total pathlength of one cycle is 1.284 m.

In order to inject and eject ions, a linear-type TOF mass spectrometer was combined with MULTUM. This system is referred as the MULTUM Linear plus. The total path length of the linear system is 0.428 m. Four quadrupole triplets were used to achieve perfect space focusing. Ion trajectories simulated by TRIO-DRAW are shown in Fig. 5. A schematic drawing and a photograph of the MULTUM Linear plus are presented Figs 6 and 7, respectively. The length of the quadrupole lenses SQ1, SQ3, SQ4, SQ6, CQ1, CQ3, CQ4, CQ6, Q1, Q3, Q6, Q8, Q9, Q11, Q14 and Q16 is 5 mm and the radius of an inscribed circle is 10 mm. The voltage applied to SQ1, SQ3, SQ4, SQ6, CQ1, CQ3, CQ4 and CQ6 is ±242.5 V. The voltage applied to Q1, Q3, Q6, Q8, Q9, Q11, Q14 and Q16 is ±254.9 V when ions are injected and ejected. The dimensions of the quadrupole lenses SQ2, SQ5, CQ2, CQ5, Q2, Q7, Q10 and Q15 are the same as those of the quadrupole lenses used in MULTUM. The voltage applied to SQ2, SQ5, CQ2 and CQ5 is ±220.9 V. The quadrupole lenses Q2, Q7, Q10 and Q15 are shared with the quadrupole lenses used in MULTUM. The voltage applied to Q2, Q7, Q10 and Q15 is ±231.1 V in the injection and ejection modes.

Figure 5. Ion trajectories of the MULTUM Linear plus. (a) Top view; (b) x-direction; (c) y-direction.

Figure 6. Schematic drawing of the MULTUM Linear plus.

Figure 7. Photograph of the MULTUM Linear plus in the vacuum chamber.

The entire system was fixed on a base plate of 40 × 40 cm. The base plate was fixed in the vacuum chamber, which is 60 × 70 × 20 cm in size. The vacuum chamber was evacuated with a turbomolecular pump (PT1500, Mitsubishi Heavy Industries, Hiroshima, Japan). The vacuum was maintained at about (2–7) × 10⁻⁵ Pa. This instrument has two main slits, two collector slits, two α slits and four β slits.

Ion source

A two-stage acceleration electron ionization (EI) ion source2 was used. This type of ion source can compensate for the flight time deviation caused by the distribution of the initial position of the ions. This focusing condition is satisfied in the linear part of the MULTUM Linear plus.

Detector and data acquisition system

Two micro-channel plates (MCPs) 14.5 mm in diameter (F4655-10, Hamamatsu Photonics, Shizuoka, Japan) were attached at the positions of detectors 1 and 2, as shown in Fig. 6. The output signals were accumulated with a digital oscilloscope (LC564A, LeCroy Japan, Osaka, Japan).

System operation

Figure 8 is a block diagram of the pulse control circuits. The oscillator provides a trigger pulse for a digital pattern generator (CompuGen T30, Gage Applied Sciences, Montreal, Canada). The digital pattern generator provides the timing signals for the ion source, the ion gate, the sector I or III and IV electrodes, the quadrupole triplets that form part of the linear TOF mass spectrometer and the digital oscilloscope. When ions were injected into the multi-turn parts, the voltage of sector IV was off and the voltages of quadrupole lenses Q14, Q15 and Q16 were the same as those of linear TOF mode. Before the ions complete a cycle and return to the starting point, the voltage of sector IV was turned on, the voltages of quadrupole lenses Q14 and Q16 were turned off and the voltage of quadrupole lens Q15 was switched to that for circulation. After the ions had undergone the desired number of cycles, the voltage of sector I or III was turned off and the voltages of quadrupole lenses Q1, Q2, Q3 or Q9, Q10, Q11 were switched to those for linear TOF to eject the ions from the multi-turn portion.

Figure 8. Timing chart of the pulse control circuits.

Generally, light ions catch up with and pass heavy ions in the multi-turn portion. If the ions are overtaken and there are many peaks, it is difficult to determine m/z from the flight time because one cannot decide the number of cycles of each peak. In order to avoid such complicating phenomena, only ions that can be observed in the same number of cycles are injected into the multi-turn orbit. An ion gate was introduced for this purpose. The mass range narrows when the number of cycles N becomes large. In the case of large N, the mass range is (m_max − m_min)/m_max ≈ 2/N, where m_max and m_min are the maximum and minimum m/z observed with the same number of cycles, respectively.

Experiments

The performance of the MULTUM Linear plus was evaluated using the CO and N₂ doublet. Generally, the mass resolution of a TOF mass spectrometer is directly proportional to its total flight pathlength. However, if the aberrations are too large, the mass resolution may decrease after many cycles. Hence we need to confirm the increase in mass resolution with the number of cycles experimentally.

The experimental conditions were as follows: (1) the electron energy was 70 eV; (2) the electron current was 200 µA; (3) the pulse voltage applied to the first stage electrode of the ion source was 420 V and the total acceleration voltage of ions was 1.5 kV; (4) the background pressure was 6.2 × 10⁻⁵ Pa and the pressure increased to 6.7 × 10⁻⁵ Pa when CO gas was introduced; (5) the voltage supplied to the micro-channel plate was −2.25 kV; (6) the sampling rate of the digital oscilloscope was 2 GS s⁻¹ and the TOF spectra were obtained by summing 5000 spectra on the digital oscilloscope; (7) the repetition frequency was 100 Hz; and (8) the ion gate was used to inject only ions of m/z 25–30 into the multi-turn section of the instrument.

The TOF spectra of the CO⁺–N₂⁺ doublet for 25.5, 101.5, 301.5 and 501.5 cycles are shown in Fig. 9. A mass resolution of 350 000 (at m/z = 28, FWHM) was achieved after 501.5 cycles. The flight times and also the differences in the arrival times between CO⁺ and N₂⁺ increased linearly with the number of cycles. Meanwhile, the peak widths remained almost the same. The relationship between the number of cycles and mass resolution is shown in Fig. 10. The mass resolution is measured as t/2Δt at the N₂⁺ peak, where t is the time of flight and Δt is the full width of the peak at half-maximum height (FWHM). The mass resolution increases linearly with the number of cycles from 0 to 300. After 300 cycles, the mass resolution increases but not linearly, because the influence of higher order aberration appears.

Figure 9. TOF spectra of CO⁺–N₂⁺ doublet for 25.5, 101.5, 301.5 and 501.5 cycles by the MULTUM Linear plus.

Figure 10. Relationship between the number of cycles and the mass resolution by the MULTUM Linear plus.

Transmission through the MULTUM Linear plus was recorded for the number of cycles. The result is illustrated in Fig. 11. The ordinate is the intensity (the sum of the areas of the CO⁺ and the N₂⁺ peaks) and is normalized such that the intensity after completion of a half cycle is 1 unit. The ion signal intensity after 100 cycles was 20–30% of that after a half cycle. The ion signal intensity decreased rapidly during the first 10 cycles, then did so more gradually. The major reason for the decrease in ion signal intensity in the first 10 cycles was that ions having large initial deviations escaped by hitting the electrodes. After 10 cycles, small-angle scattering caused by collisions with neutral particles became the major reason. The solid line in Fig. 11 was obtained by fitting the following function to the data from 10 to 500 cycles;

• 

where I is the ion signal intensity, l is the flight length and λ is the mean free path. The derived value of λ was 150 m. This is consistent with our experimental condition (6.7 × 10⁻⁵ Pa). Ion transmission exceeded 99% per cycle. Consequently, we can conclude that this new TOF mass spectrometer has a stable multi-turn orbit.

Figure 11. Variation in ion transmission with the number of cycles and resolution by the MULTUM Linear plus. The ordinate is the intensity, i.e. the area of both the CO⁺ and N₂⁺ peaks, and is normalized such that the intensity after half a cycle is 1 unit.

THE MULTI-TURN TOF MASS SPECTROMETER MULTUM II

We have already demonstrated that the multi-turn TOF mass spectrometer MULTUM Linear plus achieved a mass resolution of >350 000 after 501.5 cycles (flight length 644 m) at m/z = 28. The MULTUM Linear plus analyzer was not simple, however; 28 electric quadrupole lenses were used. Therefore, it was necessary to reduce the number of ion optical components. In order to reduce the number of these parts, we have designed and constructed a new multi-turn TOF mass spectrometer, using the MULTUM II geometry, consisting of only four toroidal electric sectors and no quadrupole lenses. A schematic drawing and photograph of MULTUM II are presented in Figs 12 and Fig. 13, respectively. The instrument has three housings: the ion source housing, the analyzer housing and the detector housing.

Figure 12. Schematic drawing of the MULTUM II.

Figure 13. Photograph of the MULTUM II.

Ion source

The ion source is the most important component of any type of mass spectrometer, and the development of MS can be seen as a function of ion source development. In the MULTUM Linear plus, only an EI ion source can be attached. The ion source and the analyzer are installed in the same vacuum chamber. As a result, the background pressure in a whole chamber rises when a gaseous sample is introduced through a needle valve. However, high vacuum is required to obtain good ion transmission, because the collision probability of ions with residual gas increases. Therefore, a differential ion source vacuum system is necessary. The MULTUM II ion source housing was separated from the analyzer housing and a differential vacuum pumping system was introduced. A turbomolecular pump (Turbo-250, Varian, Italy) was attached to the ion source housing. Various ion sources (EI, fast atom bombardment (FAB), matrix-assisted laser desorption/ionization (MALDI), electrospray ionization (ESI), inductively coupled plasma (ICP)) can also be attached to the ion source housing. We have already tested EI, FAB and MALDI sources.

An ion trap housing is located between the ion source housing and the analyzer housing. This configuration allows us to do a wide variety of experiments, e.g. ion–molecule reactions and MS/MS applications in the ion trap. The ion trap housing can be removed and the ion source housing can be attached directly to the analyzer housing when the ion trap is not necessary.

A Q-lens doublet was introduced between the ion source housing and the analyzer housing to improve ion transmission.

Analyzer

The multi-turn part consists of only four toroidal electric sector fields. It is difficult to make toroidal electric sector electrodes because of the small c-value21 of 0.033. Therefore, the four toroidal electric sector fields were produced using cylindrical electric sectors and Matsuda plates.22 The mean radius of the cylindrical electric sector is 50 mm, the deflection angle 157.1°, the gap between the electrodes 10 mm and the height of the electrodes 40 mm. The voltage applied to the cylindrical electrodes was ±299 V and that applied to the Matsuda plates was +170 V, with an accelerating voltage of 1500 V. The total pass length of one cycle was 1.308 m. All elements were hung on the top plate of the analyzer housing. A turbomolecular pump (PT500, Mitsubishi Heavy Industries) was attached to the multi-turn housing. Ions were injected and ejected through a hole in the outer sector electrodes similar to the MULTUM Linear plus.

Detector

In the detector housing, there were two detectors and an ion mirror. When the ion mirror was off, the ions ejected from the multi-turn housing flew towards an MCP 14.5 mm in diameter (F4655-13, Hamamatsu Photonics) attached at the position of detector 1 in Fig. 12. When the ion mirror was used, ions were detected using an MCP 27 mm in diameter with a center hole (F4294-09, Hamamatsu Photonics) attached at the position of detector 2 in Fig. 12.

The ion mirror was used to achieve energy focusing in the linear part. It consisted of 11 ring electrodes. Transmission meshes (85%) were attached to the first, fourth and last electrodes. The output signals from the MCPs were accumulated with a digital oscilloscope (LC564DL, LeCroy Japan).

System operation

The method by which the MULTUM II is operated is similar to that of the MULTUM Linear plus. While ions are injected into the multi-turn portions, the voltage of sector IV is off, but it is turned on before the ions return. After the ions have undergone the desired number of cycles, the voltage of sector I is turned off to eject the ions from the multi-turn portion.

A digital pulse/delay generator (Model 555-3, Berkeley Nucleonics, Richmond, CA, USA) was used to generate the timing signals as a substitute of the oscillator and digital pattern generator (CompuGen T30), because the number of timing signals necessary was decreased compared with MULTUM Linear plus. This generator provides timing signals of eight channels with 1 ns resolution.

Experiments

A two-stage acceleration EI ion source used in the MULTUM Linear plus was installed. Some preliminary test experiments were executed using the N₂–CO doublet. The experimental conditions were as follows: (1) the electron energy was 74 eV; (2) the electron current was 80 µA; (3) the pulse voltage applied to the first stage electrode of the ion source was 150 V and the total acceleration voltage of the ions was 1.5 kV; (4) the background pressure was 1.5 × 10⁻⁵ Pa in the ion source housing and 2.1 × 10⁻⁵ Pa in the analyzer housing, and the pressure in the ion source housing increased to 1.6 × 10⁻⁵ Pa when CO gas was introduced; (5) the voltage applied to the MCP was 1.7 kV; (6) the sampling rate of the digital oscilloscope was 4 GS s⁻¹ and the TOF spectra shown below were obtained by summing 25 000 spectra on the digital oscilloscope; (7) the repetition frequency of the digital pulse/delay generator was 100 Hz; (8) the ion gate was used to inject only ions at m/z 25–30 into the multi-turn portion; and (9) the ion mirror was not used in this experiment.

The TOF spectra of the N₂–CO doublet acquired using different flight pathlengths (20, 60, 80 and 100 cycles) are shown in Fig. 14. The relation between the number of cycles and the mass resolution of N₂⁺ from 0 to 100 cycles is shown in Fig. 15(a). It is clear that the mass resolution increased in proportion to the number of cycles. A mass resolution of 24 000 was achieved after 150 cycles. The peak width was almost constant at 26–31 ns. This was greater than that of MULTUM Linear plus, probably owing to the effect of the turnaround time, which depends on the focal length. The first gap field of the two-stage acceleration ion source weakens when the focal length is extended. Accordingly, the turnaround time is prolonged. The pathlength of linear portion of the MULTUM II is 80 cm and that of the MULTUM Linear plus is 40 cm. The focal length of the MULTUM II should be less. The focal length of an ion source can be reduced when a two-stage ion mirror is combined with a two-stage acceleration ion source.

Figure 14. TOF spectra of the N₂–CO doublet acquired using different flight pathlengths (20, 60, 80 and 100 cycles) by the MULTUM II.

Figure 15. Relation between the number of cycles and the mass resolution of N₂⁺ (a) without an ion mirror and (b) with a mirror by the MULTUM II.

The TOF spectra of the N₂–CO doublet acquired with the ion mirror and the relation between the number of cycles and the mass resolution of N₂⁺ from 0 to 100 cycles is shown in Fig. 15(b). The peak width was almost the same, 11–14 ns, and a mass resolution of 47 000 was achieved after 100 cycles. The experimental conditions were as follows: (1) the pulse voltage applied to the first stage electrode of the ion source was 220 V and the total acceleration voltage of the ions was 1.5 kV, the focal length of an ion source being 40 cm under these conditions; (2) the voltage supplied to the MCP was 1.7 kV; and (3) the voltage supplied to the fourth electrode of the ion mirror was 588 V and that to the last electrode was 1560 V. Other conditions were the same as those used in the non-ion-mirror mode.

The intensity variation (the sum of N₂–CO doublets) with the number of cycles is shown in Fig. 16. The ordinate was normalized such that the intensity after 10 cycles was 1 unit. It is clear from Fig. 16 that the ion transmittance through the system exceeds 99% after one cycle. This shows that a ‘perfect focusing’ condition was achieved, similar to that of the MULTUM Linear plus.

Figure 16. The intensity variation (the sum of N₂–CO doublet) with the number of cycles with an ion mirror by the MULTUM II. The ordinate was normalized such that the intensity after 10 cycles was 1 unit.

FUTURE DIRECTIONS

Small mass spectrometer for planetary exploration

High mass resolution can be achieved, despite the multi-turn TOF mass spectrometer MULTUM II being a small instrument, and this instrument is suitable for planetary exploration. However, it is rather large and heavy for loading on a spacecraft. Miniaturization can be achieved by putting both an ion source and an ion mirror on the multi-turn orbit. Figure 17 is a schematic drawing of a proposed instrument. An orthogonal acceleration ion source3, 4 is suggested for ion injection into the multi-turn orbit. Ions go into the first stage of the two-stage acceleration ion source and are pushed out by applying the voltage to the push grid of the ion source. At this time, ions travel along the multi-turn orbit if the voltages are adjusted properly. After the ions have undergone the desired number of cycles, the voltage applied to ion mirror should be turned on, allowing the ions to be reflected towards the ion detector. The instrument can be made more compact and simplified by removing the linear portion.

Figure 17. Schematic drawing of the proposed small mass spectrometer for planetary exploration.

Tandem multi-turn time-of-flight mass spectrometer

It is possible to devise a high-performance tandem TOF mass spectrometer23 by introducing the technology of multi-turn TOF mass spectrometers. The TOF/TOF mass spectrometer has numerous merits: (1) it can achieve high energy collision-induced dissociation (CID) spectra; (2) there is no mass range limitation; and (3) high mass accuracy is achieved comparatively easily. Problems associated with the current TOF/TOF instruments include, however, the low mass-resolving power of the first mass analyzer. Using a multi-turn TOF mass spectrometer, adequate mass resolution can easily be achieved. There is another advantage to introducing a multi-turn TOF mass spectrometer as the first analyzer of a TOF/TOF instrument. Only the desired ions are picked up from the multi-turn orbit while other ions continue to be stored in the multi-turn orbit. Consequently, the stored ions, which are wasted in a conventional instrument, can also be picked as precursor ions. Multiple MS/MS experiments can be carried out without loss of ions.

Three types of TOF/TOF mass spectrometers, based on multi-turn TOF mass spectrometers, are proposed and schematic drawings are presented in Fig. 18. Type (a) combines a multi-turn TOF mass spectrometer with a reflectron TOF mass spectrometer. This type is a conventional TOF/TOF mass spectrometer, but the mass-resolving power of the first analyzer can be very high. The product ions are analyzed by differences in ion energy. The mass resolution of the second analyzer is low and the mass range measured simultaneously is limited. In the case of types (b) and (c), on the other hand, the mass resolution of the second analyzer is also very high. These instruments consist of two multi-turn TOF mass spectrometers and an ion trap (type (b)) or a multi-turn TOF mass spectrometer and an ion trap (type (c)). The product ions selected by the first analyzer are injected into the ion trap and stored. The ions dissociate in the ion trap by CID, photoinduced dissociation (PID), electron capture dissociation (ECD), and so on. The product ions are analyzed with another multi-turn TOF mass spectrometer (type (b)) or as in the first analyzer (type (c)). In case (c), MS/MS analysis is possible in only one multi-turn TOF mass spectrometer by injecting the product ions into the multi-turn orbit inversely. A combination of type (c) and surface-induced dissociation (SID)23 is expected to be optimal, because the product ions will be emitted in the opposite direction.

Figure 18. Schematic drawing of tandem TOF mass spectrometers, based on multi-turn TOF mass spectrometers.

Acknowledgements

The authors acknowledge to the encouragement and suggestions of the late Dr Takekiyo Matsuo of Osaka University. We also acknowledge the late Dr Toru Sakurai of the Japan Advanced Institute of Science and Technology for use of the calculation code Unify and for helpful discussions on ion optics. We are also greatly indebted to Mr Shin-ichi Yamaguchi of Shimadzu Corporation for the development of the ion sources and for helpful discussions. We thank Mr Toshio Ichihara of Osaka University for technical support. We express our thanks to Dr Helmut Rosenbauer and Dr Reinhard Roll of the Max Planck Institute for Aeronomy and Dr Arthur Ghielmetti of Lockheed Martin Advanced Research Center for construction of the MULTUM Linear plus as a laboratory model for the ROSETTA mission. We also thank Professor Masahiro Kimura of Kochi University of Technology, Professor Ryuichi Arakawa of Kansai University and Dr Yoshinao Wada of Osaka Medical Center and Research Institute for Maternal and Child Health for helpful discussions. The staff of the MS group of JEOL are thanked for technical support.

This work was supported by a Grant-in-Aid for Scientific Research (B) (09559012, 10044085, 11559012, 13559005) from the Ministry of Education, Science, Sports and Culture. The financial support of the Institute of Space and Astronautical Science and the Yamada Science Foundation is much appreciated.