Ion mobility tube for improving peak separation degree of ion mobility spectrum

Abstract

The application discloses an ion migration tube for improving peak separation degree of ion mobility spectrum. Two first and second ion gates are arranged in the ion migration tube, and the ion migration tube is divided into ionization area, migration area and compression area which are sequentially adjacent. A constant axial uniform direct current electric field is formed in the migration area, and ion clusters injected through the first ion gate are separated into multiple sheet-shaped ion clusters with different ion mobility K and transmitted to the second ion gate. The second ion gate is opened for a short time with multiple delays relative to the first ion gate, sheet-shaped ion clusters with different ion mobility K in the migration area are sequentially selected and injected into the compression area for compression correction of ion cluster time domain width, and then rapidly transmitted to an ion receiving electrode for detection. The ion migration tube disclosed by the application can improve the resolution of the ion migration tube and effectively improve the peak separation degree of the ion mobility spectrum.

Description

Technical Field

[0001] This invention relates to the ion migration tube, a core component of ion mobility spectrometers, and more specifically, to an ion migration tube for improving the peak-to-peak resolution of ion mobility spectra. Background Technology

[0002] Ion mobility spectrometry (IMS) is a pulsed ion cluster separation and detection technique similar to time-of-flight mass spectrometry (TOF-MS). Pulsed ion clusters are primarily formed through ion-gated implantation. Ion clusters implanted into the IMS migration region via ion gating undergo transport and separation within a uniform axial DC electric field. The initial implantation time-domain width w of the ion cluster... inj The time-domain width of ion clusters is broadened due to factors such as ion thermal motion diffusion and Coulomb repulsion. diff w coul Together, they determine the resolving power and peak separation of the ion mobility spectrum, i.e., R = t d / (w inj 2 +w diff 2 +w coul 2 ) 1 / 2 R p-p =0.59(1 / α-1)R.

[0003] Conventional IMS typically employs a single ion gate, with the initial implantation time domain width w of the ion cluster during ion-gated implantation. inj Compression is employed to improve the resolution of ion mobility spectra. For example, Chen et al. (CN100491765B) disclosed a control method for a Bradbury-Nielsen type ion gate (BNG) in 2018. When the BNG is closed, the voltage of both sets of wires is simultaneously increased, forming a time-domain enhanced electric field in the region of the migration region adjacent to the ion gate, thereby increasing the initial injection time-domain width w of the ion clusters injected into the migration region. inj Compression is performed to improve IMS resolution. Chen Hong et al. (CN111199865B) disclosed a three-parallel gate ion gate and control method in 2018, which controls the initial implantation time domain width w of the ion cluster during ion cluster implantation. inj Two-stage compression improves IMS resolution. However, neither of these patents reports whether peak-to-peak separation is improved. Furthermore, this method of compressing the initial implantation time-domain width of ion clusters only significantly improves resolution for IMS with short ion migration region lengths (L). When the ion migration region length (L) is large, the time-domain broadening of ion clusters caused by factors such as ion thermal diffusion and Coulomb repulsion becomes more pronounced. diff wcoul IMS resolution R and peak-to-peak separation R p-p The influence of [w] intensifies and plays a dominant role. Therefore, how to [address] w diff and w coul Compression correction is key to improving both resolution and peak-to-peak separation in IMS with a large migration region length L. Summary of the Invention

[0004] This invention provides an ion migration tube for improving peak-to-peak resolution in ion mobility spectra. The ion migration tube has two parallel, spaced-apart first and second ion gates, dividing the tube's interior into three sequentially adjacent regions: an ionization region, a migration region, and a compression region. A constant, axially uniform DC electric field is formed within the migration region, while a time-domain enhanced DC electric field, synchronized with the opening and closing of the ion gates, is formed within the compression region. The first ion gate, combined with the migration region, enables pulsed injection of initial ion clusters and separation of ion mobility K. The second ion gate, combined with the compression region, enables gated injection of ion clusters with different ion mobilities K within the migration region and compression of the time-domain width. This improves both the resolution of the ion migration tube and the peak-to-peak resolution in the ion mobility spectrum.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] An ion migration tube for improving the peak-to-peak separation of ion migration spectrum, wherein the ion migration tube is a cylindrical hollow cavity formed by three or more annular electrodes and two or more annular insulators coaxially and alternately stacked from left to right, with an ion source provided at the left end of the cavity and an ion receiving electrode provided at the right end.

[0007] The cavity is located between the ion source and the ion receiver. From left to right, a first ion gate and a second ion gate are sequentially arranged, dividing the cavity into three regions. The region between the ion source and the first ion gate constitutes the ionization region, and the region between the first and second ion gates forms an axial length region of L. d migration area, L d The length is between 100 and 200 mm, preferably between 110 and 140 mm, and the axial length between the second ion gate and the ion receiving electrode is L. c The compressed area, L c The thickness is between 1 and 15 mm, preferably between 5 and 10 mm;

[0008] The first ion gate consists of a first gate electrode and a second gate electrode arranged insulated from left to right and parallel to each other. The second ion gate consists of a third gate electrode and a fourth gate electrode arranged insulated from left to right and parallel to each other. The voltage applied to the second gate electrode and the third gate electrode is constant, forming a constant axially uniform DC electric field E in the migration region. dThe voltage of the first gate electrode is modulated to be higher or lower than the voltage of the second gate electrode to control the opening or closing of the first ion gate. The voltage of the fourth gate electrode is modulated to be higher or lower than the voltage of the third gate electrode to control the opening or closing of the second ion gate. When the second ion gate is open, the same axially uniform DC electric field E is formed in the compression region as in the migration region. d E d Between 15 and 30 V / mm, preferably 20 to 25 V / mm, when the second ion gate is closed, a time-domain enhanced axially uniform DC electric field E is formed in the compression region. c E c The voltage is between 100 and 150 V / mm, preferably between 110 and 130 V / mm;

[0009] L d Greater than L c E c Strength greater than E d The intensity and ion mobility K of an ion take much longer to migrate through the migration region than the ion takes to migrate through the compression region.

[0010] When the ion migration tube is working, neutral sample molecules entering the ionization region are ionized by the ion source to form product ions. The first ion gate is briefly opened at the zero point of the ion migration tube's working cycle, T=0. Product ions in the ionization region are injected into the migration region in the form of pulsed ion clusters. Product ions with different ion mobilities K are affected by the DC electric field E in the migration region. d Driven by the ion, they are separated into N thin-film ion clusters and migrate toward the second ion gate, where N is a positive integer greater than or equal to 3;

[0011] The second ion gate occurs at time T = t. delay-1 T = t delay-2 ..., T = t delay-N The system is briefly turned on and off sequentially, which affects the ion mobility K1 = L in the migration region. d / (E d ×t delay-1 K2 = L d / (E d ×t delay-2 ), ..., K N =L d / (E d ×t delay-N Thin sheet-like ion clusters are sequentially gated and injected into the compression region. The time domain width of the thin sheet-like ion clusters is compressed, and they are rapidly transported to the ion receiving electrode for detection. At the end of the ion migration tube's working cycle, T = t period At that time, the ion migration tube outputs a complete ion migration spectrum with effectively improved peak-to-peak resolution;

[0012] Delay time t delay-1 tdelay-2 、…、t delay-N t period All are positive numbers greater than 0, and t delay-1 <t delay-2 <...<t delay-N <t period ion migration tube working cycle t period The value is 15-25ms;

[0013] Ion mobility K1=L d / (E d ×t delay-1 K2 = L d / (E d ×t delay-2 ), ..., K N =L d / (E d ×t delay-N All numbers are positive, and K1 > K2 > ... > K N .

[0014] The ion migration tube disclosed in this invention divides the interior of the ion migration tube into three sequentially adjacent regions: an ionization region, a migration region, and a compression region, by setting two mutually spaced and parallel ion gates within the same ion migration tube. A constant axially uniform DC electric field is formed in the migration region, which separates the ion clusters injected through the first ion gate into multiple thin-plate-like ion clusters with different ion mobilities K, and then transmits them to the second ion gate. The second ion gate opens briefly and repeatedly with delay relative to the first ion gate, sequentially selecting and injecting the thin-plate-like ion clusters with different ion mobilities K in the migration region into the compression region for compression correction of the ion cluster time-domain width, and then rapidly transmitting them to the ion receiving electrode for detection, ultimately obtaining an ion migration spectrum with effectively improved peak-to-peak separation.

[0015] The advantages of this invention are:

[0016] The ion migration tube disclosed in this invention combines the ion gating function of dual ion gates with the ion cluster time-domain width compression function of the time-domain enhanced electric field induced by dual parallel gate ion gates, thereby improving the resolution of the ion migration tube and effectively enhancing the peak-to-peak separation in the ion migration spectrum.

[0017] The present invention will now be described in further detail with reference to the accompanying drawings: Attached Figure Description

[0018] Figure 1The structural diagram of the ion migration tube for improving peak-to-peak resolution of ion migration spectra disclosed in this invention is shown below. Wherein: 1, ultraviolet ion source; 2, ion receiving electrode; 3, first ion gate; 31, first grid electrode; 32, second grid electrode; 4, second ion gate; 41, third grid electrode; 42, fourth grid electrode; 5, ionization region; 6, migration region; 7, compression region; 8, drift gas inlet; 9, sample gas inlet; 10, gas outlet.

[0019] Figure 2 The operating mode of the ion migration tube disclosed in this invention is as follows: Fixed voltages V2 and V5 are applied to the second grid electrode 32 and the third grid electrode 41, respectively; the first grid electrode 31 controls the first ion gate 3 to open and close briefly by varying the voltage between V1 and V3; the fourth grid electrode 42 controls the second ion gate 4 to open and close briefly with multiple delays relative to the first ion gate 3 by varying the voltage between V4 and V6.

[0020] Figure 3 This invention discloses a special example of the operating mode of the ion migration tube. Fixed voltages V2 = -2610V and V5 = -180V are applied to the second grid electrode 32 and the third grid electrode 41, respectively. The first grid electrode 31 controls the first ion gate 3 to briefly open for 80μs and then close by varying the voltages V1 = -2660V and V3 = -2560V. The fourth grid electrode 42 controls the second ion gate 4 to briefly open and close twice with a delay of 100μs relative to the first ion gate 3, with the first delay time being t. delay-1 = 13.75ms, the second delay time is t delay-2 =14.5ms.

[0021] Figure 4 Example 2 of the operating mode of the ion migration tube disclosed in this invention. In this example, fixed voltages V2 = -2610V and V5 = -180V are applied to the second grid electrode 32 and the third grid electrode 41, respectively; the first grid electrode 31 controls the first ion gate 3 to briefly open for 80μs and then close by varying the voltages V1 = -2660V and V3 = -2560V; the fourth grid electrode 42 controls the second ion gate 4 to open and close with a single delay relative to the first ion gate 3 by varying the voltages V4 = -780V and V6 = -130V, for a delay time t. delay-1 =13.75ms, the ion gate opening time is t delay-2 +100μs-t delay-1 =850μs.

[0022] Figure 5Example 3 of the operating mode of the ion migration tube disclosed in this invention. In this mode, fixed voltages V2 = -2610V and V5 = -180V are applied to the second grid electrode 32 and the third grid electrode 41, respectively; the first grid electrode 31 controls the first ion gate 3 to be briefly opened for 80μs and then closed by varying the voltage between V1 = -2660V and V3 = -2560V; a fixed voltage V6 = -130V is applied to the fourth grid electrode 42 to control the second ion gate 4 to be normally open.

[0023] Figure 6 (a) Use Figure 3 (a) Using the ion migration tube in special working mode 1, the ion migration spectrum of the reagent ions in negative ion mode is obtained; (b) using Figure 4 The second example of the ion migration tube's operating mode shows the ion migration spectrum of the reagent ions in negative ion mode; (c) using Figure 5 The third example of the ion migration tube's operating mode shows the ion migration spectrum of the reagent ions in negative ion mode. Detailed Implementation

[0024] Example 1

[0025] The ion migration tube disclosed in this invention for improving peak-to-peak resolution in ion migration spectra is as follows: Figure 1 As shown in the image.

[0026] The ion source 1 of the ion migration tube is a 10.6 eV ultraviolet ion source, and the ion receiving electrode 2 is a Faraday disk with a diameter of 6 mm, which is insulated and sealed on a metal shielding cylinder with an outer diameter of 30 mm. The first ion gate 3 and the second ion gate 4 are both double parallel grid ion gates (Tyndall-Powell type ion gates). The first ion gate 3 consists of a first grid electrode 31, a PTFE insulating ring, and a second grid electrode 32. The second ion gate 4 consists of a third grid electrode 41, a PTFE insulating ring, and a fourth grid electrode 42. The first grid electrode 31... The second grid electrode 32, the third grid electrode 41, and the fourth grid electrode 42 are all metal grids with a thickness of 0.05 mm and an outer diameter of 30 mm. The PTFE insulating ring has a thickness of 0.5 mm, an outer diameter of 30 mm, and an inner diameter of 20 mm. The ionization region 5, the migration region 6, and the compression region 7 are all coaxially and alternately stacked with annular electrodes with an axial length of 3.5 mm, an outer diameter of 30 mm, and an inner diameter of 20 mm, and annular insulators with an axial length of 1.5 mm, an outer diameter of 30 mm, and an inner diameter of 20 mm. The axial length of the ionization region 5 is 31.5 mm, and the axial length of the migration region 6 is L. d The axial length L of the compression zone 7 is 121.5mm. c It is 6.5mm;

[0027] An outlet 10 is provided on the side wall of the cavity adjacent to the photoionization source 1 in the ionization region 5, and a sample gas inlet 9 is provided on the side wall adjacent to the first ion gate 3. A drift gas inlet 8 is provided on the side wall of the cavity adjacent to the ion receiver electrode 2 in the compression region. A drift gas of 500 mL / min enters the ion migration tube through the drift gas inlet 8, flows into the ionization region 5 through the second ion gate 4 and the first ion gate 3, mixes with the sample gas of 100 mL / min entering the ionization region 5 through the sample gas inlet 9, and then flows out of the ion migration tube through the outlet. The drift gas is purified by activated carbon and 13X.

[0028] The clean air is filtered sequentially by molecular sieves, and the sample gas is clean air containing a specific concentration of the target analyte.

[0029] like Figure 2 As shown, fixed voltages V2 and V5 are applied to the second grid electrode 32 and the third grid electrode 41, respectively, forming a constant axially uniform DC electric field E within the migration region 6. d The first grid electrode 31 controls the first ion gate 3 to open and close briefly by varying voltages between V1 and V3; the first ion gate 3 is open when the voltage is V1 and closed when the voltage is V3. The fourth grid electrode 42 varies voltages between V4 and V6; the second ion gate 4 is open when the voltage is V6, forming an axially uniform DC electric field E within the compression region 7. d When the voltage is V4, the second ion gate 4 is closed, and an axially uniform DC electric field E is formed in the compression region 7. c E c For E d More than 5 times;

[0030] When the ion migration tube is working, neutral molecules of the sample gas entering ionization region 5 are ionized by the ultraviolet ion source to form product ions. At the zero point of the ion migration tube's working cycle, T = 0, the first ion gate 3 is briefly opened, injecting the product ions from ionization region 5 into migration region 6 in the form of pulsed ion clusters. Product ions with different ion mobilities K are in migration region 6 under a DC electric field E. d Driven by [something], they are separated into N thin-film ion clusters and migrate toward the second ion gate 4, where N is a positive integer greater than or equal to 3. The second ion gate 4 is located at time T = t [something]. delay-1 T = t delay-2 ..., T = t delay-N The system is briefly turned on and off sequentially, which affects the ion mobility K1 = L in migration region 6. d / (E d ×t delay-1 K2 = L d / (E d ×t delay-2 ), ..., K N =L d / (E d×t delay-N Thin sheet-like ion clusters are sequentially gated and injected into compression region 7. The time domain width of the thin sheet-like ion clusters is compressed, and they are transported to the ion receiving electrode 5 for detection. The time ends at the end of the ion migration tube's working cycle, T = t. period At that time, the ion migration tube outputs a complete ion migration spectrum.

[0031] Example 2

[0032] Clean air filtered sequentially through activated carbon and 13X molecular sieves was used as the bleaching gas at a flow rate of 500 mL / min, and clean air containing 1 ppm acetone was used as the sample gas at a flow rate of 100 mL / min. When the ion migration tube disclosed in Example 1 was operating... Figure 3 In the special case of the operating mode shown, with voltages V1 = -2660V, V2 = -2610V, V3 = -2560V, V4 = -780V, V5 = -180V, and V6 = -130V, a constant axially uniform DC electric field E is formed within the migration region 6. d =20V / mm, when the second ion gate 4 is opened, an axially uniform DC electric field E is formed in the compression region 7. d =20V / mm, when the second ion gate 4 is closed, an axially uniform DC electric field E is formed in the compression region 7. c =120V / mm; the duty cycle of the ion migration tube is 20ms, the opening time of the first ion gate 3 is 80μs, and the delay opening time t of the second ion gate 4 relative to the first ion gate 3 is... delay-1 =13.75ms, t delay-2 =14.5ms, the opening time of the second ion gate 4 is 100μs for both times.

[0033] Under the above conditions, the negative ion migration spectrum was obtained as follows: Figure 6 As shown in Figure a, the resolution of ion peak 1 (K1) is R1 = 165, the resolution of ion peak 2 (K2) is R2 = 168, and the peak-to-peak separation between ion peak 1 (K1) and ion peak 2 (K2) is R. p-p =7.71.

[0034] Example 3

[0035] Clean air filtered sequentially through activated carbon and 13X molecular sieves was used as the bleaching gas at a flow rate of 500 mL / min, and clean air containing 1 ppm acetone was used as the sample gas at a flow rate of 100 mL / min. When the ion migration tube disclosed in Example 1 was operating... Figure 4 In the second special case of the operating mode shown, the voltages V1 = -2660V, V2 = -2610V, V3 = -2560V, V4 = -780V, V5 = -180V, and V6 = -130V, and a constant axially uniform DC electric field E is formed within the migration region 6.d =20V / mm, when the second ion gate 4 is opened, an axially uniform DC electric field E is formed in the compression region 7. d =20V / mm, when the second ion gate 4 is closed, an axially uniform DC electric field E is formed in the compression region 7. c =120V / mm; the duty cycle of the ion migration tube is 20ms; the opening time of the first ion gate 3 is 80μs; ​​the single-time delay opening time t of the second ion gate 4 relative to the first ion gate 3 is... delay-1 =13.75ms, the opening time of the second ion gate 4 is t delay-2 +100μs-t delay-1 =850μs.

[0036] Under the above conditions, the negative ion migration spectrum was obtained as follows: Figure 6 As shown in b, the resolution of ion peak 1 (K1) is R1 = 110, the resolution of ion peak 2 (K2) is R2 = 148, and the peak-to-peak separation between ion peak 1 (K1) and ion peak 2 (K2) is R p-p =6.18.

[0037] Example 4

[0038] Clean air filtered sequentially through activated carbon and 13X molecular sieves was used as the bleaching gas at a flow rate of 500 mL / min, and clean air containing 1 ppm acetone was used as the sample gas at a flow rate of 100 mL / min. When the ion migration tube disclosed in Example 1 was operating... Figure 5 In the special case of the operating mode shown, with voltages V1 = -2660V, V2 = -2610V, V3 = -2560V, V4 = -780V, V5 = -180V, and V6 = -130V, a constant axially uniform DC electric field E is formed within the migration region 6. d =20V / mm, the second ion gate 4 remains open, and an axially uniform DC electric field E is formed in the compression region 7. d =20V / mm; the duty cycle of the ion migration tube is 20ms, and the opening time of the first ion gate 3 is 80μs.

[0039] Under the above conditions, the negative ion migration spectrum was obtained as follows: Figure 6 As shown in Figure c, the resolution of ion peak 1 (K1) is R1 = 70, the resolution of ion peak 2 (K2) is R2 = 95, and the peak-to-peak separation between ion peak 1 (K1) and ion peak 2 (K2) is R... p-p =4.22.

[0040] Comparative Example 5

[0041] contrast Figure 6Spectra b and c show that when the second ion gate 4 is opened with a single delay relative to the first ion gate 3, simultaneously selecting ion peak 1 (K1) and ion peak 2 (K2) into the compression region 7, the resolution of ion peak 1 (K1) and ion peak 2 (K2) is improved, and the peak-to-peak separation between ion peak 1 (K1) and ion peak 2 (K2) is also enhanced. This indicates that combining the gating function of the second ion gate 4 with the ion cluster time-domain width compression function of the time-domain enhanced electric field within the compression region 7 can effectively improve both the resolution of the ion migration spectrum and the peak-to-peak separation.

[0042] Furthermore, in comparison Figure 6 Spectra a and b show that when the second ion gate 4 is opened twice with a delay relative to the first ion gate 3, allowing ion peak 1 (K1) and ion peak 2 (K2) to be sequentially selected into the compression region 7, the resolution of ion peak 1 (K1) and ion peak 2 (K2) is further improved, and the peak-to-peak separation between ion peak 1 (K1) and ion peak 2 (K2) is also further enhanced. This is because when ion groups with different ion mobilities K are sequentially injected into the compression region 7, it can be ensured that different ion groups experience the same time-domain width compression effect, thus achieving a further improvement in resolution and peak-to-peak separation.

Claims

1. An ion mobility tube for improving the peak separation of ion mobility spectrometry, the ion mobility tube is a cylindrical hollow cavity composed of 3 or more annular electrodes and 2 or more annular insulators alternately stacked coaxially from left to right, an ion source (1) is arranged at the left end of the cavity, and an ion receiving electrode (2) is arranged at the right end, characterized in that: The cavity is located between the ion source (1) and the ion receiver (2). From left to right, a first ion gate (3) and a second ion gate (4) are arranged to divide the cavity into three regions. The ion source (1) and the first ion gate (3) form an ionization region (5), and the first ion gate (3) and the second ion gate (4) form an axial length region of L. d The migration region (6), L d The length is between 100 and 200 mm, preferably between 110 and 140 mm, and the axial length between the second ion gate (4) and the ion receiving electrode (2) is L. c The compression zone (7), L c The thickness is between 1 and 15 mm, preferably between 5 and 10 mm; The first ion gate (3) is composed of the first grid electrode (31) and the second grid electrode (32) which are arranged in parallel and insulated from each other, and the second ion gate (4) is composed of the third grid electrode (41) and the fourth grid electrode (42) which are arranged in parallel and insulated from each other, the voltage applied to the second grid electrode (32) and the third grid electrode (41) is constant, and a constant axial uniform DC electric field E is formed in the migration zone (6) d The voltage of the first grid electrode (31) is modulated to be higher or lower than that of the second grid electrode (32) to control the opening or closing of the first ion gate (3), and the voltage of the fourth grid electrode (41) is modulated to be higher or lower than that of the third grid electrode (41) to control the opening or closing of the second ion gate (4), when the second ion gate (4) is opened, the same axial uniform DC electric field E as that in the migration zone (6) is formed in the compression zone (7) d , E d is between 15-30 V / mm, preferably 20-25 V / mm, when the second ion gate (4) is closed, a time-domain enhanced axial uniform DC electric field E c , E c is between 100-150 V / mm, preferably 110-130 V / mm; L d greater than L c , E c greater than E d , ions having an ion mobility of K have a transit time through the transit region (6) that is much greater than the transit time through the compression region (7).

2. The ion mobility tube according to claim 1, characterized in that: When the ion mobility tube works, the neutral sample molecules entering the ionization zone (5) are ionized by the ion source (1) to form product ions, the first ion gate (3) is opened at the timing zero point T=0 of the working cycle of the ion mobility tube, and the product ions in the ionization zone (5) are injected into the migration zone (6) in the form of a pulse ion group, and the product ions with different ion mobilities K are separated into N thin ion groups in the migration zone (6) under the driving of the direct current electric field E d , and migrate towards the second ion gate (4), N is a positive integer greater than or equal to 3. The second ion gate (4) is opened and closed momentarily at the timing T=t delay-1 , T=t delay-2 , …, T=t delay-N , and the ion flux with ion mobility K1=L d / (E d ×t delay-1 ), K2=L d / (E d ×t delay-2 ), …, K N =L d / (E d ×t delay-N ) in the migration region (6) is sequentially selected and injected into the compression region (7). The time-domain width of the ion flux is compressed and rapidly transmitted to the ion receiving electrode (2) for detection. At the timing T=t period , the ion mobility spectrometer outputs a complete ion mobility spectrum with improved peak-to-peak separation.

3. The ion mobility tube according to claim 2, characterized in that: Delay time t delay-1 , t delay-2 , …, t delay-N , t period are positive numbers greater than 0, and t delay-1 < t delay-2 < … < t delay-N < t period The value of the ion transfer tube operating period t period is 15-25 ms; Ion mobility K1=L d / (E d ×t delay-1 K2 = L d / (E d ×t delay-2 ), ..., K N =L d / (E d ×t delay-N All numbers are positive, and K1 > K2 > ... > K N .

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