CN113792471B - A Monte Carlo calculation method for multi-particle multi-collision micro-discharge threshold - Google Patents

Abstract

A method for calculating a multi-particle multi-collision micro-discharge threshold Monte Carlo belongs to the technical field of space microwaves. The invention provides a Monte Carlo method for efficiently and accurately calculating micro-discharge threshold values of a satellite-borne microwave component, which carries out randomization treatment on the emergent energy, angles and phases of a plurality of initial electrons, and the physical process of the occurrence of a micro-discharge effect is more objectively and accurately represented by the multi-particle-multi-collision process according to the number of actual secondary electrons generated by collision electrons and the corresponding energy participating in the micro-discharge process after the collision moment. The calculation result shows that the calculation accuracy of the proposed method is obviously improved compared with the existing Monte Carlo method by taking the commercial particle simulation software result as a reference, and the calculation efficiency of the proposed method is obviously improved compared with that of the particle simulation method.

Description

A Monte Carlo calculation method for multi-particle multi-collision micro-discharge threshold

Technical field

The invention relates to a multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method, belonging to the field of space microwave technology.

Background technique

The micro-discharge effect, also known as the secondary electron multiplication effect, refers to the resonant discharge phenomenon that occurs when the component is at a pressure of 1×10 ^-3 Pa or lower and is subjected to high power. High-power microwave components in spacecraft payloads such as output multiplexers, filters, switch matrices, antenna feeds, etc. are prone to micro-discharge effects. Once the micro-discharge effect occurs, it will cause serious consequences: the noise level will increase and the output power will decrease. ; The standing wave ratio of the microwave transmission system increases, the reflected power increases, and the channel is blocked; the surface of microwave components is damaged and the load life is shortened; the spacecraft load permanently fails, so micro-discharge is an effect that must be overcome during the development of high-power microwave components one.

Microdischarge risk assessment of spaceborne microwave components through microdischarge sensitive areas or analysis methods during the design stage is an effective means to reduce repeated designs and avoid long-term ground tests. At present, microdischarge analysis methods have been developed, including theoretical analysis methods including classical theory and statistical theory, as well as numerical simulation methods including Monte Carlo (MC) and particle simulation (Particle-in-Cell, PIC). Since the theoretical method requires an analytical solution of the electron motion trajectory, it is difficult to apply it to the calculation of the microdischarge threshold of microwave components with complex structures. The PIC method simulates the movement of particles under electromagnetic fields and the collision between particles and component surfaces. It makes few omissions and assumptions. It not only takes into account complete motion parameters such as the speed, direction, and phase of the electron exit surface, but also considers the interaction between electrons and electromagnetic fields. It can realize micro-discharge threshold simulation of complex microwave component structures such as impedance transformers, ridge waveguide filters, and coaxial cavity filters. However, the particle simulation method needs to update the particle state and the field distribution on the grid nodes within the divided grid, which requires a large computational hardware overhead and is time-consuming. Since the MC method does not consider the interaction between electrons and electromagnetic fields, it has an advantage over the PIC method in terms of time cost. However, there are three currently proposed methods: single particle-multiple collisions, multi-particles-single collisions, and pseudo-multiple particles-multiple collisions. The Monte Carlo microdischarge threshold calculation method still needs to be improved in terms of calculation accuracy due to problems in the algorithm itself.

Contents of the invention

The technical problem solved by this invention is to overcome the shortcomings of the existing technology and provide a multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method.

The technical solution of the present invention is: a multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method, including the following steps:

S1, according to the probability distribution consistent with the initial electron energy, angle, and phase, N initial electrons are randomly generated. The N initial electron states are: position r _i , energy E _i , angle (θ _i , Ф _i ), phase t _i ;

S2, calculate the electromagnetic field inside the microwave component according to the input frequency f and input power W;

S3, update the state of the electron entering the electromagnetic field. The electronic state is: position r _in , energy E _in , angle (θ _in , Ф _in ), phase t _in . For the initial electron, the two states are the same;

S4, calculate the electron motion trajectory within the time step Δt;

S5, determine whether the position of the electron within the time step Δt has reached the component boundary. If it has not arrived, repeat S4~S5; otherwise, record the state of the electron collision at the boundary: position r _p , energy E _p , angle (θ _p ,Ф _p ), phase t _p ;

S6, use the electron energy E _p and angle (θ _p , Ф _p ) at the moment of collision, and calculate the secondary electron emission coefficient (δ _ts , δ _e , δ _r ) and the secondary electron emission coefficient according to the surface material properties of the microwave component. Each energy spectrum distribution (f _1,e , f _1,r , f _n,ts ) and the probability P _n of generating n electrons, and calculate the energy E _si and angle (θ _si , Ф _si ) of the ejected electron; i= 0,1,…,n;

S7, determine whether the set cut-off condition is reached. If it is reached, it is determined whether micro-discharge occurs and ends; if it is not reached, it returns to S3.

Further, the probability of generating n electrons is

in, They are respectively the probability of not generating intrinsic secondary electrons, the probability of generating 1 intrinsic secondary electron, and the probability of generating n intrinsic secondary electrons.

Further, the method for calculating the energy _Es of the ejected electron includes the following steps:

Generate a random number RAND ₁ between 0 and 1, compare RAND ₁ with the probability P _n of generating n electrons, and determine the actual number n of electrons generated;

If n=0, no secondary electrons are produced;

If n _{= 1} , calculate the energy E _{s1 of} the ejected electron according to the probability distribution _of Energy spectrum, f _1,r is the energy spectrum that produces one reflected electron, f _1,ts is the energy spectrum that produces one intrinsic secondary electron;

If n≥2, calculate the energy of the ejected electrons E _s1 , E _s2 ... _{E sn} according to the _probability distribution of .

Further, the exit angle (θ _si , Ф _si ) of the i-th emitted electron is calculated according to the following steps:

sinθ _si is a random number sampled between [-1,1], Ф _si is a random number sampled between [0,2π].

Further, the cut-off condition is reaching the maximum number of cycles, or calculation time, or number of electrons, or other artificially set conditions.

Further, the method for determining whether microdischarge occurs includes the following steps:

If the number of cycles collsion_num is used as the method to determine the micro-discharge threshold, then calculate δ _equl = (δ ₁ + δ ₂ +...+δ _{collsion_num} )/collsion_num; where δ ₁ , δ ₂ ,..., δ _{collsion_num} are the i-th collision respectively. _The average _secondary electron emission coefficient _of Discharge threshold voltage;

If the change trend of the number of electrons that evolves over time is used as the method to judge the microdischarge threshold, then the number of electrons decreases with time, then microdischarge does not occur under this calculation condition; if the number of electrons increases with time, then microdischarge occurs under this calculation condition. Discharge; if the number of electrons does not change over time, this voltage is the micro-discharge threshold.

Further, the secondary electron emission coefficient δ = δ _ts + δ _e + δ _r , δ _ts is the emission coefficient of intrinsic secondary electrons, δ _e is the emission coefficient of elastically scattered electrons, and δ _r is the emission of reflected electrons. coefficient.

Furthermore, the solution method for the trajectory of electrons in the electromagnetic field is:

In the rectangular coordinate system, the trajectory of the electron is given by Decide;

In the cylindrical coordinate system, the trajectory of the electron is given by Decide;

Among them, (x, y, z) is the position of the electron in the x, y, z direction in the electromagnetic field in the Cartesian coordinate system, is the radial, angular, and axial position of the electron in the electromagnetic field in the cylindrical coordinate system. Adding one point to the position of the electron represents the speed in that direction, and adding two points represents the acceleration in that direction. E and B respectively are the electric and magnetic fields in this direction, q is the unit charge of the electron, and m is the electron mass.

Further, after the electron collides with the boundary, the state of the electron entering the electromagnetic field is updated as follows: the electron position r _in is updated to the position of the electron collision, the energy E _in is updated to the energy of the emitted electron in step 6, and the angle (θ _in , Ф _in ) is updated. is the angle of the emitted electron in step 6, and the phase t _in is updated to the moment when the electron collides with the boundary.

A computer-readable storage medium. The computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the steps of the multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method are implemented. .

The advantages of the present invention compared with the prior art are:

(1) The present invention overcomes the problem of the existing Monte Carlo method that during the calculation process, no matter what the secondary electron emission coefficient of the colliding electron is, only one electron is regenerated to participate in the next collision. According to the actual secondary electron emission process, the present invention may emit an actual number of secondary electrons, and the number of emitted electrons conforms to a certain probability distribution. However, the statistical value of the number of electrons generated by the collision of multiple electrons in the same state must be equal to the secondary electron emission coefficient, thereby improving the accuracy of the calculation results;

(2) The present invention uses the random state of multiple initial electrons as the starting state, and the calculation also includes electrons with all energies during the secondary electron emission process after the electrons collide with the surface of the component, significantly improving the accuracy of the calculation results;

(3) In the process of advancing the trajectory of electrons in the electromagnetic field, the present invention does not need to update the particle state in the grid and the field distribution on the grid nodes according to the time step according to the particle simulation method, thus avoiding the need for computing hardware. Problems such as high cost and time consuming. ;

Description of the drawings

Figure 1 is a schematic flow chart of the method of the present invention;

Figure 2 is a comparison result of micro-discharge threshold calculation and other calculation methods according to the embodiment of the present invention.

Detailed ways

In order to better understand the above technical solution, the technical solution of the present application is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present application and the specific features in the embodiments are a detailed description of the technical solution of the present application, and This is not intended to limit the technical solution of the present application. If there is no conflict, the embodiments of the present application and the technical features in the embodiments can be combined with each other.

The multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method provided by the embodiment of the present application will be further described in detail below in conjunction with the accompanying drawings of the description. The specific implementation method may include (as shown in Figures 1 to 2):

(1) According to the probability distribution consistent with the initial electron energy, angle, and phase, N initial electrons are randomly generated. The N initial electron states are: position r _i , energy E _i , angle (θ _i , Ф _i ), phase t _i ;

(2) Calculate the electromagnetic field inside the microwave component according to the input frequency f and input power W;

(3) Update the state of the electron entering the electromagnetic field. The electronic state is: position r _in , energy E _in , angle (θ _in , Ф _in ), phase t _in . For the initial electron, the two states are the same;

(4) Use the fourth-order Runge-Kutta method to calculate the electron trajectory within the time step Δt;

(5) Determine whether the position of the electron within the time step Δt reaches the component boundary. If it does not arrive, continue to advance according to (4). If it reaches the boundary, record the state of the electron collision at the boundary: position r _p , energy E _p , angle (θ _p ,Ф _p ), phase t _p ;

(6) Using the electron energy E _p and angle (θ _p , Ф _p ) at the moment of collision, and based on the surface material characteristics of the microwave component, calculate the secondary electron emission coefficient (δ ts , δ e , δ r ), and the secondary electron emission coefficient (δ _ts , δ _e , δ _r ) and the Furman model based on the surface material characteristics of the microwave component. Each energy spectrum distribution of subelectronic electrons (f _1,e , f _1,r , f _n,ts ) and the probability of generating n electrons

(6a) Generate a random number RAND ₁ within the range of 0 to 1, compare RND ₁ and P _n , and determine the actual number of electrons generated n;

(6b) If n=0, no secondary electrons are produced;

_{( 7} ) If n _{=1, calculate the energy E s1 of the} ejected electron according to the probability distribution of The energy spectrum of scattered electrons, f _1,r is the energy spectrum that produces one reflected electron, f _1,ts is the energy spectrum that produces one intrinsic secondary electron;;

If n≥2, calculate the energy of the ejected electron E _s1 , E _s2 ...E _sn according to the probability distribution of X(n)=f _n,ts ;

(8) Determine whether the set cut-off condition is reached. If it is reached, determine whether micro-discharge occurs. If it is not reached, return to step (3).

Specifically, the solution provided in the embodiment of this application includes the following steps: parallel flat plates, 1 mm gap, and Furman-Ag material on the surface

(1) Generate N = 1000 initial electrons, and the energy E ₀ of 1000 initial electrons satisfies the distribution σ=3eV, μ=5eV; the initial electron angle satisfies the distribution f(θ ₀ )-sin2θ ₀ ; the initial electron azimuth angle/> Randomly distributed in [0, 2π], the initial electron phase t ₀ is randomly distributed in [0, T _wave ], then the exit electron speed is

(2) Calculate the electromagnetic field of parallel plates with a gap of x=1mm. The frequencies are set to f=1.06GHz, 2.14GHz, 3.71GHz, 5.33GHz, and 7.97GHz. The internal electromagnetic field is determined by the following formula E=[-Vsin(ωt- βz),0,0]

(3) The state of electrons entering the electromagnetic field Initial time/>

(4) The advancement of electron motion trajectories in the electromagnetic field is solved by the fourth-order Runge-Kutta method,

Set the time step Δt = T _wave /50, and solve the electron trajectory according to the above formula within the dt range. When solving for the first time, [v _x v _y v _z ] is the initial electron velocity solved in step (1);

(5) Every time the electron trajectory is solved within the Δt time step, it is judged whether the x-direction trajectory of the electron satisfies x>1mm or x<0mm. If not, go to step (4). [v _x v _y v _z ] Let It is determined as the last solution result of step (4);

(6) The electron collides with the device surface at this time, the collision position x _p , the collision time t _p , the number of collisions collsion_num=1 (for each subsequent collision, collsion_num+1), the collision speed is obtained from the result of step (4) [ v _px v _py v _pz ], then relative to the incident electron energy on the material surface Incident electron angle/> Calculate the number of emitted electrons, secondary electron emission coefficient δ ₁ and energy according to the Furman model. Assume that 2 electrons are emitted, and the corresponding energy is [E _s1 , E _s2 ], angle/>

(7) Determine collsion_num<10000, if not, return to step (3), and the electron enters the electromagnetic field state respectively/> and/>

The method to determine whether micro-discharge has occurred includes the following steps:

If the number of cycles collsion_num is used as the method to determine the micro-discharge threshold, then when collsion_num>10000, calculate δ _equl = (δ ₁ + δ ₂ +...+δ _{collsion_num} )/collsion_num; where, δ ₁ , δ ₂ ,..., δ _{collsion_num} are respectively the average value of the secondary electron emission coefficient of the i-th collision; if δ _equl >1, then micro-discharge occurs under this calculation condition; if δ _equl <1, then micro-discharge does not occur under this calculation condition; if δ _equl =1, this voltage is the micro-discharge threshold voltage.

Further, the secondary electron emission coefficient δ = δ _ts + δ _e + δ _r , δ _ts is the emission coefficient of intrinsic secondary electrons, δ _e is the emission coefficient of elastically scattered electrons, and δ _r is the emission coefficient of reflected electrons.

If the change trend of the number of electrons that evolves over time is used as the method to judge the microdischarge threshold, then the number of electrons decreases with time, then microdischarge does not occur under this calculation condition; if the number of electrons increases with time, then microdischarge occurs under this calculation condition. Discharge; if the number of electrons does not change over time, this voltage is the micro-discharge threshold.

Furthermore, the solution method for the trajectory of electrons in the electromagnetic field is:

In the rectangular coordinate system, the trajectory of the electron is given by Decide;

In the cylindrical coordinate system, the trajectory of the electron is given by Decide;

Among them, (x, y, z) is the position of the electron in the x, y, z direction in the electromagnetic field in the Cartesian coordinate system, is the radial, angular, and axial position of the electron in the electromagnetic field in the cylindrical coordinate system. Adding one point to the position of the electron represents the speed in that direction, and adding two points represents the acceleration in that direction. E and B respectively are the electric and magnetic fields in this direction, q is the unit charge of the electron, and m is the electron mass.

Optionally, in a possible way, after the electron collides with the boundary, the state of the electron entering the electromagnetic field is updated as follows: the electron position r _in is updated to the position of the electron collision, and the energy E _in is updated to the energy of the ejected electron in step 6. , the angle (θ _in , Ф _in ) is updated to the angle of the emitted electron in step 6, and the phase t _in is updated to the moment when the electron collides with the boundary.

The calculation results of traditional MC, single particle-multiple collision (MC1), multi-particle-single collision (MC2), and multi-particle-multiple collision (MC3) based on the Monte Carlo method are from the literature (Lin Shu, Yan Yangjiao, Li Yongdong, Liu Chunliang 2014 Acta Physica Sinica 63147902), the calculation results of CST software are from the literature (Wang Hongguang, Zhai Yonggui, Li Jixiao, Li Yun, Wang Rui, Wang Xinbo, Cui Wanzhao, Li Yongdong 2016 Acta Physica Sinica 65 237901), the calculation results of this method are shown in Figure 2 , the calculation efficiency is shown in Table 1.

Table 1 Comparison of calculation efficiency of micro-discharge threshold of flat plate transmission lines

The present application provides a computer-readable storage medium. The computer-readable storage medium stores computer instructions. When the computer instructions are run on a computer, they cause the computer to execute the method described in Figure 1 .

Those skilled in the art will understand that embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment that combines software and hardware aspects. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, magnetic disk storage and optical storage, etc.) embodying computer-usable program code therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each process and/or block in the flowchart illustrations and/or block diagrams, and combinations of processes and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions executed by the processor of the computer or other programmable data processing device produce a use A device for realizing the functions specified in one process or multiple processes of the flowchart and/or one block or multiple blocks of the block diagram.

These computer program instructions may also be stored in a computer-readable memory that causes a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including the instruction means, the instructions The device implements the functions specified in a process or processes of the flowchart and/or a block or blocks of the block diagram.

These computer program instructions may also be loaded onto a computer or other programmable data processing device, causing a series of operating steps to be performed on the computer or other programmable device to produce computer-implemented processing, thereby executing on the computer or other programmable device. Instructions provide steps for implementing the functions specified in a process or processes of a flowchart diagram and/or a block or blocks of a block diagram.

Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. In this way, if these modifications and variations of the present application fall within the scope of the claims of the present application and equivalent technologies, the present application is also intended to include these modifications and variations.

Contents not described in detail in the specification of the present invention are well-known technologies to those skilled in the art.

Claims (9)

1. A multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method, which is characterized by including the following steps: S1, according to the probability distribution consistent with the initial electron energy, angle, and phase, N initial electrons are randomly generated. The N initial electron states are: position r _i , energy E _i , angle (θ _i , Ф _i ), phase t _i ; S2, calculate the electromagnetic field inside the microwave component according to the input frequency f and input power W; S3, update the state of the electron entering the electromagnetic field. The electronic state is: position r _in , energy E _in , angle (θ _in , Ф _in ), phase t _in . For the initial electron, the two states are the same; S4, calculate the electron motion trajectory within the time step Δt; S5, determine whether the position of the electron within the time step Δt has reached the component boundary. If it has not arrived, repeat S4~S5; otherwise, record the state of the electron collision at the boundary: position r _p , energy E _p , angle (θ _p ,Ф _p ), phase t _p ; S6, use the electron energy E _p and angle (θ _p , Ф _p ) at the moment of collision, and calculate the secondary electron emission coefficient (δ _ts , δ e , δ r ), and the secondary electron emission coefficients (δ ts , δ _e , δ _r ) and the secondary electron emission coefficients according to the surface material characteristics of the microwave component. Energy spectrum distribution (f _1,e , f _1,r , f _n,ts ) and the probability of generating n electrons P _n , and calculate the energy E _si and angle (θ _si , Ф _si ) of the ejected electron; i=0 ,1,…,n; S7, determine whether the set cut-off condition is reached. If it is reached, determine whether micro-discharge occurs and end; if it is not reached, return to S3; The method for determining whether microdischarge occurs includes the following steps: If the number of cycles collsion_num is used as the method to determine the micro-discharge threshold, then calculate δ _equl = (δ ₁ + δ ₂ +...+δ _{collsion_num} )/collsion_num; where δ ₁ , δ ₂ ,..., δ _{collsion_num} are the i-th collision respectively. _The average value of the secondary electron emission _{coefficient of} Micro-discharge threshold voltage; If the change trend of the number of electrons that evolves over time is used as the method to judge the microdischarge threshold, then the number of electrons decreases with time, then microdischarge does not occur under this calculation condition; if the number of electrons increases with time, then microdischarge occurs under this calculation condition. Discharge; if the number of electrons does not change over time, this voltage is the micro-discharge threshold. 2. A multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method according to claim 1, characterized in that: the probability of generating n electrons is in, They are respectively the probability of not generating intrinsic secondary electrons, the probability of generating 1 intrinsic secondary electron, and the probability of generating n intrinsic secondary electrons. 3. A kind of multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method according to claim 1, characterized in that the method for calculating the energy _Es of ejected electrons includes the following steps: Generate a random number RAND ₁ between 0 and 1, compare RAND ₁ with the probability P _n of generating n electrons, and determine the actual number n of electrons generated; If n=0, no secondary electrons are produced; If n _{= 1} , calculate the energy E _{s1 of} the ejected electron according to the probability distribution _of Energy spectrum, f _1,r is the energy spectrum that produces one reflected electron, f _1,ts is the energy spectrum that produces one intrinsic secondary electron; If n≥2, calculate the energy E _{s1 ,} E _s2 ... _{E sn} of the emitted electrons under different numbers of electrons according to the probability distribution of Energy spectrum of secondary electrons. 4. A multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method according to claim 1, characterized in that the emission angle (θ _si , Ф _si ) of the i-th emitted electron is calculated according to the following steps: sinθ _si is a random number sampled between [-1,1], Ф _si is a random number sampled between [0,2π]. 5. The Monte Carlo calculation method for multi-particle multi-collision micro-discharge threshold according to claim 1, characterized in that: the cutoff condition is reaching the maximum number of cycles, or the calculation time, or the number of electrons, or other conditions set artificially. 6. A multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method according to claim 1, characterized in that: the secondary electron emission coefficient δ = δ _ts + δ _e + δ _r , δ _ts is the basis represents the emission coefficient of secondary electrons, δ _e is the emission coefficient of elastically scattered electrons, and δ _r is the emission coefficient of reflected electrons. 7. A multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method according to claim 1, characterized in that: the method for solving the trajectory of electrons in the electromagnetic field is: In the rectangular coordinate system, the trajectory of the electron is given by Decide; In the cylindrical coordinate system, the trajectory of the electron is given by Decide; Among them, (x, y, z) is the position of the electron in the x, y, z direction in the electromagnetic field in the Cartesian coordinate system, is the radial, angular, and axial position of the electron in the electromagnetic field in the cylindrical coordinate system. Add one point to the symbol of the electron's position to represent the velocity in the direction represented by the original symbol, and add two points to represent the acceleration in the direction represented by the original symbol. E and B are the electric and magnetic fields whose sign subscripts indicate the direction respectively, q is the unit charge of the electron, and m is the electron mass. 8. A multi-particle multi-collision micro-discharge threshold Monte Carlo calculation method according to claim 1, characterized in that after the electron collides with the boundary, the state of the electron entering the electromagnetic field is updated as: the electron position r _in is updated as the electron collision The position and energy E _in are updated to the energy of the emitted electron in step 6, the angle (θ _in , Ф _in ) is updated to the angle of the emitted electron in step 6, and the phase t _in is updated to the moment when the electron collides with the boundary. 9. A computer-readable storage medium, the computer-readable storage medium stores a computer program, characterized in that, when the computer program is executed by a processor, the computer program implements any one of claims 1 to 8. Method steps.