CN111797561A - Method for solving moving circle center of moving charged particle based on Lorentz component formula - Google Patents
Method for solving moving circle center of moving charged particle based on Lorentz component formula Download PDFInfo
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Abstract
The invention belongs to the technical field of physical electromagnetism and charged particle motion, and particularly relates to a method for solving the motion circle center of a moving charged particle based on a Lorentz component formula. The method comprises the following steps: collecting information through a sensor; setting two-dimensional coordinate parameters by using the obtained information; after setting parameters, carrying out orthogonal decomposition on the charged particle speed along the direction of a two-dimensional coordinate axis; calculating the bisection speed by applying a Lorentz component principle and solving a corresponding circular center line; the two circle center lines are converged to carry out circle center positioning. The method greatly simplifies the expression mode of the circle center position when the charged particles do uniform circular motion in the magnetic field by utilizing the characteristics of the two-dimensional model, coordinates and concretes the circle center position, makes the original abstract expression mode of the circle center position more concrete and objective, and is convenient for realizing the later computer programming analysis of the motion process of the charged particles in the magnetic field.
Description
Technical Field
The invention belongs to the technical field of physical electromagnetism and charged particle motion, and particularly relates to a method for solving the motion circle center of a moving charged particle based on a Lorentz component formula.
Background
When the moving charged particles enter a magnetic field, the moving charged particles can perform uniform-speed circular motion due to Lorentz force under the condition of no external force interference, scientists design various instruments such as a speed selector, a cyclotron and the like according to the principle for decades, and great promotion is made for scientific development.
The traditional calculation method can obtain the motion radius and the circle center position of the circular motion of the moving charged particles in the magnetic field according to the charge quantity q of the charges at the motion points, the self mass m, the motion speed v and the magnetic induction intensity B of the magnetic field, but it is relatively difficult and complicated to calculate the motion radius by using a Lorentz formula and then determine the expression of the circle center position in a two-dimensional coordinate system by using a left-hand rule, and the relatively abstract expression mode also brings much inconvenience to a computer when a program software analyzes the motion process of the charged particles and makes the computer difficult to realize.
At present, research on Lorentz force algorithms is relatively less, and through literature search, documents related to the Lorentz force research are long in age, and related algorithms are much less and less. Therefore, in order to meet the needs of scientific and technological development, fully apply the lorentz force and realize the feasibility of computer programming, it is very important to research the relevant algorithms.
Disclosure of Invention
The invention provides a method for solving the moving circle center of a moving charged particle based on a Lorentz component formula, which solves the circle center of the uniform-speed circular motion of the charged particle in a magnetic field by utilizing the Lorentz component, obtains a position coordinate with an accurate circle center by orthogonally decomposing the speed of the charged particle in the magnetic field according to a coordinate axis direction and combining a Lorentz formula and a left-hand rule, greatly simplifies the expression of the circle center position in a two-dimensional coordinate system, and makes the assumption of analyzing the point charge moving process by applying a computer program in the future easier to realize.
The technical scheme of the invention is as follows:
a method for solving the moving circle center of a moving charged particle based on a Lorentz component formula comprises the following steps of firstly, collecting data of magnetic field information and the moving speed of the charged particle in a magnetic field through a sensor; then, two-dimensional modeling is carried out according to the collected data information of the magnetic field direction, the magnetic field size, the motion speed of the charged particles, the speed direction of the charged particles, the mass of the charged particles and the charge quantity of the charged particles; the velocity of the moving charged particles in the magnetic field is then measured in two dimensionsOrthogonal decomposition is carried out in the coordinate axis direction to obtain the component velocity v of the charged particles in two directionsxAnd vy(ii) a Then, two component forces f of the Lorentz force along the coordinate axis direction are determined by utilizing the Lorentz component formula principle, the Lorentz formula and the left-hand rulexAnd fySolving the acceleration generated in the corresponding direction of the Lorentz force component by using a formula, and solving the sizes of different motion radiuses generated in the corresponding directions of different Lorentz force components by using the acceleration; finally, according to the obtained different Lorentz component forces, making two circle center lines parallel to the coordinate axes according to the different movement radiuses generated in the corresponding directions, and determining the specific position of the movement circle center of the charged particle according to the intersection point of the circle center lines;
the method comprises the following steps:
first, information collection by sensors
The method comprises the following steps of monitoring and collecting information data such as magnetic field direction, magnetic field size, charged particle motion speed size, charged particle speed direction, charged particle mass, charged particle charge quantity and the like in real time through a sensor;
secondly, setting two-dimensional coordinate parameters by using the information data obtained in the first step
Setting parameters, wherein the charge quantity of the moving charged particles is q, the mass is m, the moving speed is v, the position is (x, y), and the magnetic induction intensity of the magnetic field is B;
thirdly, carrying out orthogonal decomposition on the speed of the charged particles along the direction of a two-dimensional coordinate axis
The velocity of the charged particles is subjected to orthogonal decomposition along a coordinate axis to obtain vxAnd vy；
Fourthly, utilizing Lorentz component formula to carry out stress analysis
For the partial velocity v of charged particlesxAnd vyUsing the principle of Lorentz component type fx＝qvyB、fy＝qvxB, Lorentz formula and left-hand rule determine two component forces f of Lorentz force along coordinate axis directionxAnd fy；
Step five, solving the circle center line
F is obtained by the fourth stepxAnd fyRespectively determining the distance between the circle center and the charged particle in the x and y directions, wherein the algorithm is as follows:
simultaneous:
the distance between the center of the circle and the x direction of the charged particles is obtained
Judging the circle center direction according to the left-hand rule and making a circle center line
Its + or-sign depends on the magnetic field direction; doing another circle center line in the same way
Sixthly, positioning the center of a circle
The fifth step obtains the intersection point of the two circle center lines
I.e. the centre of the circle of the charged particles making circular motion in the magnetic field.
The invention has the beneficial effects that:
(1) the invention utilizes the characteristics of the two-dimensional model, greatly simplifies the expression mode of the circle center position when the charged particles do uniform circular motion in the magnetic field, and coordinates and concreties the circle center position.
(2) The invention makes the original abstract circle center position expression mode more concrete and objective, and is convenient for realizing the future computer programming analysis of the motion process of the charged particles in the magnetic field.
(3) The invention can facilitate the cyclotron to monitor the motion condition of the charged particles in real time and adjust the abnormal motion by coordinating the circle center of the circular motion of the charged particles, and can greatly reduce the occurrence of acceleration failure.
(4) The invention can realize the function of more accurately controlling the motion trail of the charged particles and solve the problem of function failure caused by uneven charge distribution in partial Hall elements.
Drawings
Fig. 1 is a flow chart of an algorithm for solving the moving circle center of a moving charged particle based on a lorentz component equation.
Fig. 2 is a schematic diagram of an algorithm principle for solving a moving circle center of a moving charged particle based on a lorentz component equation.
Fig. 3 is a schematic view of a circle center line along the y-axis direction of an algorithm for solving the motion circle center of a moving charged particle based on a lorentz component equation.
Fig. 4 is a schematic diagram of a circle center line along the x-axis direction of an algorithm for solving the motion circle center of a moving charged particle based on a lorentz component equation.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in detail below with reference to the accompanying drawings.
The complete flow chart of the method for solving the moving circle center of the moving charged particle based on the Lorentz component formula is shown in figure 1.
The angle between the x axis and the alpha particle is taken as
Direction is as v ═ 3.2X 106The embodiment of the present invention will be described in detail by taking as an example the case of a motion at a speed of m/s in a uniform magnetic field having a magnetic field strength B of 0.0166T.
First, information collection by sensors
And information data such as the direction of the magnetic field, the magnitude of the magnetic field, the motion speed of the charged particles, the speed direction of the charged particles, the mass of the charged particles, the charge quantity of the charged particles and the like are monitored and collected in real time through the sensor.
Second, using the obtained information to set two-dimensional coordinate parameters
Parameters are set in which the charge amount of α particles is about +3.2 × 10-19C. Self-mass of about m-6.64 x 10-27kg. The moving speed v is 3.2 multiplied by 106m/s at the position of (x, y) ═ 5,4, where x and y are in metersThe magnetic induction intensity of the magnetic field is B0.0166T, and the vector directions are shown in fig. 2.
Thirdly, carrying out orthogonal decomposition on the speed of the charged particles along the direction of a two-dimensional coordinate axis
The velocity of the charged particles is subjected to orthogonal decomposition along a coordinate axis to obtain vxAnd vyWherein:
fourthly, utilizing Lorentz component formula to carry out stress analysis
For the partial velocity v of charged particlesxAnd vyUsing the principle of Lorentz component type fx＝qvsinθB、fyDetermining two component forces f of Lorentz force along coordinate axis direction by qvcos theta B, Lorentz formula and left-hand rulexAnd fyThe size and direction of (d).
Step five, solving the circle center line
Through fxAnd fyThe distance between the center of a circle and the x and y directions of the charged particles can be respectively determined, and the algorithm is as follows:
simultaneous:
the distance between the center of the circle and the x direction of the charged particles is obtained
The direction of the circle center is determined according to the left-hand rule and the circle center line parallel to the y axis is made as shown in fig. 3 and 4
The input value is the circle center line
Doing another circle center line parallel to the x axis in the same way
The input value is the circle center line
Sixthly, positioning the center of a circle
Intersection point of two circle center lines
That is, (2.1715,6.8284) is the position coordinate of the center of the circle of the charged particles in the magnetic field.
Claims (1)
1. A method for solving the moving circle center of a moving charged particle based on a Lorentz component formula is characterized by comprising the following steps:
first, information collection by sensors
Monitoring and collecting information data of the magnetic field direction, the magnetic field size, the moving speed of the charged particles, the speed direction of the charged particles, the mass of the charged particles and the charge quantity of the charged particles in real time through a sensor;
secondly, setting two-dimensional coordinate parameters by using the information data obtained in the first step
Setting parameters, wherein the charge quantity of the moving charged particles is q, the mass is m, the moving speed is v, the position is (x, y), and the magnetic induction intensity of the magnetic field is B;
thirdly, carrying out orthogonal decomposition on the speed of the charged particles along the direction of a two-dimensional coordinate axis
The velocity of the charged particles is subjected to orthogonal decomposition along a coordinate axis to obtain vxAnd vy；
Fourthly, utilizing Lorentz component formula to carry out stress analysis
For the partial velocity v of charged particlesxAnd vyUsing the principle of Lorentz component type fx＝qvyB、fy＝qvxB, Lorentz formula and left-hand rule determine two component forces f of Lorentz force along coordinate axis directionxAnd fy；
Step five, solving the circle center line
F is obtained by the fourth stepxAnd fyRespectively determining the center of a circle and the charged particle x anddistance in y direction, the algorithm is as follows:
simultaneous:
the distance between the center of the circle and the x direction of the charged particles is obtained
Judging the circle center direction according to the left-hand rule and making a circle center line
Its + or-sign depends on the magnetic field direction; doing another circle center line in the same way
Sixthly, positioning the center of a circle
The fifth step obtains the intersection point of the two circle center lines
I.e. the centre of the circle of the charged particles making circular motion in the magnetic field.
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|---|---|---|---|---|
| US20090033249A1 (en) * | 2007-07-31 | 2009-02-05 | Macdonald-Bradley Christopher James | Method and apparatus for the acceleration and manipulation of charged particles |
| JP2019003457A (en) * | 2017-06-16 | 2019-01-10 | 国立大学法人名古屋大学 | Method of analyzing charged particle kinetics by lorentz force of magnetic field |
| CN110925157A (en) * | 2019-12-11 | 2020-03-27 | 大连理工大学 | Electrostatic plasma thruster |
| US20210053275A1 (en) * | 2018-03-19 | 2021-02-25 | Digital Alloys Incorporated | Apparatuses, methods and systems for printing three-dimensional objects |
-
2020
- 2020-07-17 CN CN202010693956.XA patent/CN111797561A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20090033249A1 (en) * | 2007-07-31 | 2009-02-05 | Macdonald-Bradley Christopher James | Method and apparatus for the acceleration and manipulation of charged particles |
| JP2019003457A (en) * | 2017-06-16 | 2019-01-10 | 国立大学法人名古屋大学 | Method of analyzing charged particle kinetics by lorentz force of magnetic field |
| US20210053275A1 (en) * | 2018-03-19 | 2021-02-25 | Digital Alloys Incorporated | Apparatuses, methods and systems for printing three-dimensional objects |
| CN110925157A (en) * | 2019-12-11 | 2020-03-27 | 大连理工大学 | Electrostatic plasma thruster |
Non-Patent Citations (3)
| Title |
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| 何佳晋;: "匀强电磁场中带电粒子的运动规律", 科技风, no. 36, 21 December 2018 (2018-12-21), pages 209 - 211 * |
| 侯璐景;姜克;王友年;: "带电粒子与二维强耦合尘埃等离子体的相互作用", 物理, no. 03, 12 March 2007 (2007-03-12), pages 30 - 33 * |
| 华东师范大学，第一附中物理教研组编: "《中学物理解题途径》", 31 August 1984, 华东师范大学出版社 , , pages: 249 - 250 * |
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