CN115047259A - Particle charge-to-mass ratio measuring method based on frequency-adjustable two-dimensional linear ion trap - Google Patents
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- 239000002245 particle Substances 0.000 title claims abstract description 112
- 238000005040 ion trap Methods 0.000 title claims abstract description 52
- 238000000034 method Methods 0.000 title claims abstract description 29
- 238000006073 displacement reaction Methods 0.000 claims abstract description 7
- 238000013016 damping Methods 0.000 claims description 10
- 230000008569 process Effects 0.000 claims description 9
- 230000005484 gravity Effects 0.000 claims description 4
- 230000001133 acceleration Effects 0.000 claims description 3
- 230000001419 dependent effect Effects 0.000 claims description 3
- 238000002474 experimental method Methods 0.000 abstract description 14
- 238000012545 processing Methods 0.000 abstract description 4
- 229920002261 Corn starch Polymers 0.000 description 17
- 239000008120 corn starch Substances 0.000 description 17
- 239000002184 metal Substances 0.000 description 16
- 238000004812 paul trap Methods 0.000 description 14
- 239000008187 granular material Substances 0.000 description 13
- 238000013461 design Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 5
- 230000005684 electric field Effects 0.000 description 4
- 238000004364 calculation method Methods 0.000 description 3
- MWPLVEDNUUSJAV-UHFFFAOYSA-N anthracene Chemical compound C1=CC=CC2=CC3=CC=CC=C3C=C21 MWPLVEDNUUSJAV-UHFFFAOYSA-N 0.000 description 2
- 150000002500 ions Chemical class 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
- 239000000843 powder Substances 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
- 241000195947 Lycopodium Species 0.000 description 1
- 239000004809 Teflon Substances 0.000 description 1
- 229920006362 Teflon® Polymers 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
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- 230000000452 restraining effect Effects 0.000 description 1
- 230000000717 retained effect Effects 0.000 description 1
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- 239000000126 substance Substances 0.000 description 1
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- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R29/00—Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
- G01R29/24—Arrangements for measuring quantities of charge
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- G—PHYSICS
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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- H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
- H01J49/00—Particle spectrometers or separator tubes
- H01J49/0027—Methods for using particle spectrometers
- H01J49/0031—Step by step routines describing the use of the apparatus
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
- H01J49/00—Particle spectrometers or separator tubes
- H01J49/0027—Methods for using particle spectrometers
- H01J49/0036—Step by step routines describing the handling of the data generated during a measurement
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Abstract
The invention discloses a particle charge-to-mass ratio measuring method based on a frequency-adjustable two-dimensional linear ion trap, which comprises the following steps of: step 1, connecting an ion trap circuit, shaking charged particles into the ion trap, and binding the charged particles; step 2, adjusting the alternating voltage and the alternating frequency, and shooting particle pictures under different alternating frequencies; step 3, processing the particle photo image, and measuring the displacement of the selected particles; and 4, calculating the radius and the charge-mass ratio of the particles according to the frequency information and the position information of the particles obtained by processing the pictures to obtain a final result. The invention optimizes the traditional experiment method for binding particles by the ion trap, and has higher safety and good teaching experiment performance.
Description
Technical Field
The invention relates to the field of physical experiment methods, in particular to a particle charge-to-mass ratio measuring method based on a frequency-adjustable two-dimensional linear ion trap.
Background
The ion trap is a device for restraining charged particles by adopting an alternating electric field or a magnetic field, and has the advantages of simple construction, low manufacturing cost and high sensitivity. Therefore, the method is widely applied to the fields of precise spectrum, frequency standard, inspection basic physics, quantum computing, mass spectrometer, atomic molecule manufacturing new forms of substances, quantum physics and the like.
In these applications, the ion trap operates primarily in a vacuum, using radio frequency electric fields. In fact, the basic principle of the ion trap is explored, the working condition of the ion trap is not necessarily harsh, and the ion trap can also work at normal temperature and normal pressure and be used for demonstration experiments of science and technology museums or physical teaching.
The charged particles are changed and moved due to the constraint of the ion trap, so that the ion trap has good ornamental and teaching significance, and people can use the ion trap for demonstration. For example, h.winter and h.w.ortjohann introduced their experiments in an article published in 1991: charged anthracene particles are stored under atmospheric pressure using a simplified design three-dimensional ion trap. Kenneth g.libbrecht and Eric d.black presented their experiments in a paper published in 2018, with three-dimensional ion traps of different designs simplifying the device to trap the lycopodium spore particles. However, in the teaching demonstration devices of these ion traps in the prior art, the commercial power output is directly connected to the transformer to form a stable power supply voltage, and there is no dimension with adjustable voltage and frequency, which is not only not safe enough, but also does not have dimension with adjustable frequency for experimenters to operate and experiment to verify the movement of particles in the ion traps.
As for the current physical experiments of colleges and secondary schools, the practical ability and thinking ability of students are very needed to be exercised. The ion trap is used as a teaching demonstration experiment, is vivid and interesting but has very high voltage and is very dangerous, so that how to design an ion trap experiment method which is adjustable and safe for students under the condition of ensuring that high voltage can bind charged particles is an urgent problem to be solved.
Disclosure of Invention
The invention aims to provide a particle charge-to-mass ratio measuring method based on a frequency-adjustable two-dimensional linear ion trap, and aims to solve the problems of poor safety and lack of adjusting dimensionality of the particle measuring method based on the ion trap in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the particle charge-to-mass ratio measuring method based on the frequency-adjustable two-dimensional linear ion trap comprises the following steps of:
step 4.1, firstly, calculating a motion equation, considering air damping and gravity, and describing the motion equation of the particles in the x direction and the y direction in the ion trap by using a corrected Marseh equation;
step 4.2, estimating the deviation center displacement of the particles, and adjusting the deviation center displacement according to the corrected Markov equation to obtain the corresponding frequency-offset position relation when the particles can be bound by the ion trap;
4.3, after the position offset of the particles under different frequencies is obtained, the square omega of the angular frequency is used 2 As an independent variable, the position offset u of the particle 0 As dependent variables, the following linear fit was performed:
u 0 ＝p(1)Ω 2 +p(2)，
wherein, p (1) and p (2) represent two undetermined fitting coefficients respectively, and the two undetermined fitting coefficients have the following relations:
the formula of the fitting coefficient to be determined can be used for obtaining:
where Ω 2 pi f is the angular frequency of the alternating voltage, η 1.8 × 10 -5 kg/(M · s) is the air damping coefficient, ρ is the particle density, R is the particle radius, Q is the particle charge, M is the particle mass, V ac Is the amplitude of the alternating voltage, r 0 Is the well center to electrode edge distance, g is the gravitational acceleration;
thus, the charge-to-mass ratio of the particles is calculated from the fitting coefficients p (1) and p (2) obtained by linear fitting
And an estimate of the radius R.
Further, the process of step 3 is as follows:
step 3.1, correcting the inclination angle of the particle photo;
step 3.2, carrying out pixel-distance ratio calibration on the particle picture after the inclination angle is corrected;
and 3.3, positioning the particle position in the calibrated particle picture to obtain particle position information.
Further, in step 3.1, the tilt angle of the particle image is corrected according to the geometry of the ion trap electrode in the particle image.
Further, in step 3.2, the particle photo pixel-distance ratio scaling is realized according to the pixel quantity and the actual distance between the ion trap electrodes in the particle photo.
The invention optimizes the traditional experiment method for binding particles by the ion trap, a new experiment method is formed by inputting alternating voltage and frequency to the ion trap and combining the collected pictures, and the charge-to-mass ratio and the radius of the particles can be measured by further calculation. The invention does not need to keep the ion trap at higher working voltage, thereby having higher safety, and by providing the adjustment dimensions of voltage and frequency, an experimenter can more fully understand the relationship between the movement of particles in the ion trap and the shape of the particles, thereby having good teaching experiment performance.
Drawings
Fig. 1 is a schematic diagram of a two-dimensional linear Paul trap structure employed in the present invention, in which: (a) is a two-dimensional linear Paul trap structure section diagram; (b) is an overall schematic diagram of a two-dimensional linear Paul trap structure.
FIG. 2 is a schematic diagram of the simulation of the charged particle motion trajectory in the two-dimensional linear Paul trap of the present invention.
FIG. 3 shows the differential q and linear damping obtained by the present invention
And taking the motion track of the particles.
Figure 4 is an experimental image and data processing interface for an ion trap according to the present invention.
Fig. 5 is a graph of a linear fit of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and based on the embodiments of the present invention, all other embodiments obtained by a person skilled in the art without creative efforts belong to the protection scope of the present invention.
An ion trap is a device that uses a magnetic or alternating electric field to confine particles in a confined space. When an ion can be bound by the ion trap, its kinematic parameters are in the stable region. By changing parameters (such as alternating voltage and frequency) of the electromagnetic field, kinematic parameters of ions in the trap can enter the unstable region and then leave the ion trap.
The ion trap adopted by the method is a two-dimensional linear Paul trap, the structure of the ion trap is shown in figures 1(a) and (b), the ion trap is provided with four parallel metal rod electrodes 1, the symmetrical centers of the four metal rod electrodes 1 are the trap center 2, therefore, the four metal rod electrodes 1 are uniformly surrounded around the trap center 2, the diagonal metal rod electrodes are used as one group, and the two groups are respectively connected with a frequency-adjustable Paul trapThe amplitude of the alternating voltage is set as V ac 。
The specific process of the invention is as follows:
And 2, adjusting and changing alternating voltage and alternating frequency output by the two-dimensional linear Paul trap power supply circuit, turning on a power supply, shooting and collecting corn starch particle photos under different alternating frequencies through a CCD (charge coupled device) camera, and collecting at least five groups during collection. The binding of the corn starch granules can be observed by a picture of a CCD camera. The amplitude and frequency of the output voltage are adjusted to observe the change of the binding condition.
Wherein, the specific data of the voltage and alternating frequency regulated by the invention, the position of the corn starch granules and the like are shown in the table 1:
TABLE 1 data sheet
| Angular frequency omega/Hz | Output voltage/V | Pixel position | Distance d/mm from center |
| 50 | 3187.8 | 772 | 1.21254 |
| 70 | 3187.8 | 786 | 1.50523 |
| 80 | 3187.8 | 799 | 1.77700 |
| 90 | 3187.8 | 816 | 2.13240 |
| 100 | 3187.8 | 830 | 2.42509 |
In the invention, six groups of voltages and angular frequencies are output by a signal source, corresponding pixel position data are collected, and the charge-to-mass ratio of the corn starch granules is calculated based on the data.
step 3.1, correcting the inclination angle of the picture of the corn starch granules;
since the picture taken by the CCD camera may be tilted (as shown in the lower left corner of fig. 4), resulting in a two-dimensional linear Paul trap where the metal rod electrode is not horizontal in the picture, a modification of the tilt angle of the picture is required.
Firstly, selecting a first point of the upper edge of an upper metal rod electrode in a two-dimensional linear Paul trap; then, a second point is selected on the upper edge of the metal rod electrode at a distance, and after the selection is completed, the picture is corrected to the horizontal direction according to the positions of the two points and the angle of the connecting line, so that the metal rod electrode is displayed horizontally, and thus the tilted picture can be corrected.
Step 3.2, calibrating the position of the particles;
because the conditions of the CCD camera are different during shooting, the pixel-to-distance ratio in the shot pictures is different, and therefore the pixel-to-distance ratio needs to be calibrated for each picture.
After the photo is corrected to be horizontal, four points of the upper edge and the lower edge of the upper metal rod electrode and the lower metal rod electrode in the two-dimensional linear Paul trap are sequentially selected (namely, one point is sequentially selected on the upper edge of the upper metal rod electrode, one point is sequentially selected on the lower edge of the upper metal rod electrode, one point is selected on the upper edge of the lower metal rod electrode, and one point is sequentially selected on the lower edge of the lower metal rod electrode); the distance between the two rods is thus determined and the pixel-to-distance ratio of the picture is scaled according to the actual separation of the two rods (e.g., preferably 15mm) in the two-dimensional linear Paul trap design parameters.
And 3.3, after the grain photo is calibrated, obtaining the offset of the corn starch grains to the central position at the position of the shot corn starch grains in the image, namely obtaining the position information of the corn starch grains.
When the pixel and the actual position are specifically calibrated, the pixel point positions of the central point and the corn starch granules are determined, then the pixel corresponding to 6mm is determined by using the shot ruler picture, and further the length of the granules corresponding to the central point in the actual process is determined, so that the position information data of the corn starch granules are obtained.
the horizontal direction of the two-dimensional linear Paul trap is set as the x direction, the vertical direction is set as the y direction, the symmetric center of the four metal rod electrodes is set as the trap center, and the distance from each metal rod electrode to the trap center is r 0 Diagonal goldThe rod electrodes are in one group, and an alternating voltage V is connected between the two groups 0 cos(Ωt)；V 0 Is the voltage peak, Ω is the angular frequency, t is the time;
the potential near the well center (0,0) (x, y) from the boundary conditions can be:
wherein phi is 0 A potential at the center of the well;
the corresponding electric fields are:
wherein,
are unit vectors in the x, y directions, respectively.
The equation of motion for a particle in the x-direction can be written as:
where M is the particle mass and Q is the particle charge amount.
Let τ be Ω t/2,
the equation of motion of a particle can be written in a simple form (a) x ＝0)：
This is called the Mathieu equation in mathematics, where q is x And a x Is a key parameter in the Mathieu equation, and determines whether x tends to infinity τ → ∞, i.e., whether the particles can be stably bound in the trap. Wherein q is x And a x Are variables that are transformed for form simplification.
According to a numerical method, a x When the stable solution area of the Mathieu equation is 0, q is x <0.908. Once q of the particle x Beyond this range, the ion trap will be out of the constraint, as shown in fig. 2, which is a simulation diagram of the motion trajectory of charged particles in the ion trap.
The motion trajectory of the particle is calculated as follows, and an approximate solution can be obtained from the equation of motion (4) of the particle
Similarly, the calculation in the y direction is the same as the calculation in the x direction.
Different q and linear damping as shown in FIG. 3
Taking the motion track of the particles; in practical experiments, the influence of gravity and air resistance should be considered, and an external force term and a linear damping term are added to a corresponding motion equation
And even a non-linear damping term. These additional terms affect the motion parameter stability range of the particles and the motion trajectory of the particles.
According to the embodiment of the invention, the voltage frequency can be adjusted through an experimental device, and then particle information, such as charge-to-mass ratio data, is calculated through a frequency-displacement relation; the specific process is as follows:
considering air damping and gravity, the equations of motion for the particles in both the x and y directions (collectively expressed as u) can be described by the modified Marsey equation:
here, the
Where Ω 2 pi f is the angular frequency of the alternating voltage, η 1.8 × 10 -5 kg/(M · s) is the air damping coefficient, ρ is the particle density, R is the particle radius, Q is the particle charge, M is the particle mass, V ac Is the amplitude of the alternating voltage, r 0 Is the well center to electrode edge distance, g is the gravitational acceleration, and qx is the qx parameter of the Mathieu equation mentioned earlier, qy for the same reason.
The off-center displacement is further estimated as follows:
when the equation has a stable solution (corresponding to the particle being bound by the ion trap), the stable solution of this equation can be developed under a trigonometric function:
since the same is true for the x, y directions, u is used to refer to x, y collectively. An, Bn are coefficients that are expanded by trigonometric functions at different frequencies. u. u 0 The constant term represents the position offset of the particle, and can be regarded as micro-vibration combined by different frequencies of the particle around the position u 0.
Substituting equation (7) for equation (6), comparing the constant term, cos (2 τ) and sin (2 τ) coefficients, and ignoring the high frequency term A k ，B k K is 2, only the term n-1 is retained, and for the sake of simplicity, the expression A-A is used 1 ，B＝B 1
B, q, K F Substituting the expression into the above formula to obtain
From this it can be seen that u 0 And Ω 2 And has a linear relationship. In the present invention, the amount of positional deviation at different frequencies is measured in Ω 2 As independent variable, the position offset u of the particle 0 As a dependent variable, a linear fit u is made in the form 0 ＝p(1)Ω 2 + p (2), the coefficients have approximately the following relationship:
where u0 is the position offset of the particle, and p (1) and p (2) represent two fitting coefficients to be determined, like k and b in y ═ kx + b, respectively.
Thereby, it is possible to obtain:
therefore, the charge-to-mass ratio of the particle can be calculated from the coefficients p (1) and p (2) obtained by linear fitting
And an estimate of the radius R.
Based on the parameters set in table 1, the particle radius of the corn starch granules can be calculated by the above method of the present invention: 11.32 μm, charge-to-mass ratio: 0.001698C/kg, the number of electrons carried by the particle, except for electroneutrality: 96616, wherein the linear fit graph is shown in figure 5.
The described embodiments of the present invention are only for describing the preferred embodiments of the present invention, and do not limit the concept and scope of the present invention, and the technical solutions of the present invention should be modified and improved by those skilled in the art without departing from the design concept of the present invention, and the technical contents of the present invention which are claimed are all described in the claims.
Claims (4)
1. The particle charge-to-mass ratio measuring method based on the frequency-adjustable two-dimensional linear ion trap is characterized by comprising the following steps of:
step 1, providing frequency-adjustable alternating voltage to a two-dimensional linear ion trap, and enabling charged particles to be measured to fall into the ion trap;
step 2, changing the magnitude of the alternating voltage and the alternating frequency thereof, and collecting particle photos under different alternating frequencies;
step 3, obtaining position information corresponding to the particles based on the particle pictures collected in the step 2;
step 4, calculating the radius and the charge-to-mass ratio of the particles according to the alternating frequency information and the position information of the particles, wherein the process is as follows:
step 4.1, firstly, calculating a motion equation, considering air damping and gravity, and describing the motion equation of the particles in the x direction and the y direction in the ion trap by using a corrected Marseh equation;
step 4.2, estimating the deviation center displacement of the particles, and adjusting the deviation center displacement according to the corrected Markov equation to obtain the corresponding frequency-offset position relation when the particles can be bound by the ion trap;
4.3, after the position offset of the particles under different frequencies is obtained, the square omega of the angular frequency is used 2 As an independent variable, the position offset u of the particle 0 As dependent variables, the following linear fit was performed:
u 0 ＝p(1)Ω 2 +p(2)，
wherein, p (1) and p (2) represent two undetermined fitting coefficients respectively, and the two undetermined fitting coefficients have the following relations:
the formula of the fitting coefficient to be determined can be used for obtaining:
where Ω 2 pi f is the angular frequency of the alternating voltage, η 1.8 × 10 -5 kg/(M · s) is the air damping coefficient, ρ is the particle density, R is the particle radius, Q is the particle charge, M is the particle mass, V ac Is the amplitude of the alternating voltage, r 0 Is the well center to electrode edge distance, g is the gravitational acceleration;
thus, the charge-to-mass ratio of the particles is calculated from the fitting coefficients p (1) and p (2) obtained by linear fitting
And an estimate of the radius R.
2. The method for measuring the charge-to-mass ratio of the particles based on the frequency-tunable two-dimensional linear ion trap as claimed in claim 1, wherein the process of step 3 is as follows:
step 3.1, correcting the inclination angle of the particle photo;
step 3.2, carrying out pixel-distance ratio calibration on the particle picture after the inclination angle is corrected;
and 3.3, positioning the particle position in the calibrated particle photo to obtain particle position information.
3. The method according to claim 2, wherein in step 3.1, the tilt angle of the particle picture is corrected according to the geometry of the ion trap electrodes in the particle picture.
4. The method according to claim 2, wherein in step 3.2, particle photo pixel-to-distance ratio scaling is performed according to the pixel quantity and the actual distance between the ion trap electrodes in the particle photo.
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| CN116598040A (en) * | 2023-05-26 | 2023-08-15 | 华南理工大学 | Ion trap ion control experiment system |
| CN116598040B (en) * | 2023-05-26 | 2024-02-09 | 华南理工大学 | Ion trap ion control experiment system |
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