CN113139292A - Simulation method for predicting negative hydrogen ion density - Google Patents

Simulation method for predicting negative hydrogen ion density Download PDF

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CN113139292A
CN113139292A CN202110454195.7A CN202110454195A CN113139292A CN 113139292 A CN113139292 A CN 113139292A CN 202110454195 A CN202110454195 A CN 202110454195A CN 113139292 A CN113139292 A CN 113139292A
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reaction
density
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CN113139292B (en
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张钰如
高飞
王友年
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Dalian University of Technology
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Dalian University of Technology
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Abstract

The invention belongs to the technical field of nuclear fusion, and provides a simulation method for predicting negative hydrogen ion density. The simulation method provided by the invention is to excite the vibration excited state H of 14 hydrogen molecules2(v 1-14), i.e. several adjacent excited states are treated as one particle. By doing so, not only can the number of particles contained in the model (i.e., the number of particle number conservation equations) be reduced, but the reactions between the particles in the group can be ignored (i.e., the number of chemical reactions contained in the model also drops significantly). The negative hydrogen ion density calculated by adopting a grouping model has a difference of less than 6% with the original model, and particularly has a difference of less than 1% when the air pressure is higher. In addition, relative differences are kept at a low level for other positive ion densities, H atom densities and electron temperatures, which fully indicates that the simulation method provided by the invention has high precision.

Description

Simulation method for predicting negative hydrogen ion density
Technical Field
The invention relates to the technical field of nuclear fusion, in particular to a simulation method for predicting negative hydrogen ion density.
Background
It is well known that controlled magnetic confinement nuclear fusion is one of the best ways to address the human energy crisis. Despite the fact that controlled magnetic confinement fusion plasmas have been studied for over half a century, many challenges remain. For example, in order to maintain the magnetic confinement fusion plasma at an extreme temperature of about 1.5 hundred million degrees celsius for a long time, it is not possible to use ohmic heating alone, and it is necessary to use a secondary auxiliary heating means. The neutral beam heating technology is the most important auxiliary heating mode in the magnetic confinement fusion device. Compared with the traditional positive ion beam source, the high-power radio-frequency negative hydrogen ion source can generate a high-density negative hydrogen ion beam, and the neutralization efficiency of the ion beam is greatly improved. Therefore, the negative hydrogen ion source becomes an important component of the neutral beam injection system in the nuclear fusion device.
In the radio frequency negative hydrogen ion source, there are two generation routes of negative hydrogen ions, namely a bulk generation process and a surface generation process. Wherein, in order to enhance the surface generation process, the wall of the chamber needs to be coated with a layer of cesium metal. However, cesium can react violently with air and can potentially initiate some complex and difficult to control process in the fusion reactor, so the bulk generation process is critical. In the process of generating the body, low-energy electrons and hydrogen molecules in a vibration excitation state generate dissociation adsorption reaction to generate negative hydrogen ions, namely e + H2(v)→H+H-。
Generally, in the simulation process of the rf negative hydrogen ion source, 23 kinds of particles need to be considered, including charged particles: electron e, positive ion H3 +Cationic H2 +Cationic H+And negative ion H-(ii) a Neutral particles: ground state H2Vibrational excited state H of molecule, ground state H atom, 14 hydrogen molecules2(v ═ 1 to 14) and excited state H of 2 hydrogen atoms (n ═ 2, 3). The various particles collide with each other, and chemical reactions are involved, such as more than one thousand, two and hundred. Furthermore, for each particle, a separate conservation of particle number equation is required to determine its density. Due to the large computational complexity, the above chemical reactions are only applicable to global models (zero-dimensional models, i.e. spatial distributions of individual physical quantities are neglected in the simulation).
However, the actual rf negative hydrogen ion source consists of a cylindrical source region and a rectangular diffusion chamber. Therefore, if the characteristics of the radio frequency negative hydrogen ion source are to be simulated accurately, a two-dimensional or even three-dimensional model is necessary. However, the complete chemical reaction cannot be included in the two-dimensional and three-dimensional models due to the limitation of computational efficiency.
Disclosure of Invention
In view of the above, the present invention provides a simulation method for estimating negative hydrogen ion density. The simulation method provided by the invention has the advantages of less quantity of equations to be solved and high accuracy of simulation results.
The invention provides a simulation method for predicting negative hydrogen ion density, which comprises the following steps:
setting a discharge condition: the power is 1 kW-30 kW, the pressure is 1-30 Pa, 14 vibration excited states of the hydrogen molecules are grouped according to the slope of the vibration distribution function of the hydrogen molecules under the set discharge condition, and the group is named as a vibration combination state giWherein i is 1, 2, 3 … … i;
based on the generation and loss reaction of the negative hydrogen ions, the particle number conservation equation of the negative hydrogen ions shown in the formula I is utilized to obtain the density of the negative hydrogen ions:
Figure BDA0003039982130000021
in the formula I, the compound is shown in the specification,
Figure BDA0003039982130000022
a source term representing the negative hydrogen ion generation and loss reaction j inside the chamber,
Figure BDA0003039982130000023
obtained using formula II:
Figure BDA0003039982130000024
in the formula II, kjThe reaction coefficients are: k is a radical ofjThe obtaining method comprises the following steps:
(i) when the generation and loss reaction of negative hydrogen ions is in the vibration combination statejIs a complex reaction coefficient kgi(ii) a The complex reaction coefficient kgiObtained using formula III:
Figure BDA0003039982130000025
in the formula III, kgiIs a complex reaction coefficient, kvIs in a vibrating combined state giIncluding vibrational excited states H2(v) The coefficient of reaction of, said kvThe function or constant of the electronic temperature is adopted, when the electronic temperature is used for the first time, the electronic temperature adopts a set initial value, and when the electronic temperature is not used for the first time, the latest electronic temperature obtained by calculation is adopted;
in the formula (III), the reaction solution is prepared,
Figure BDA0003039982130000026
obtained by the formula IV:
Figure BDA0003039982130000027
in the formula IV, EvIs a vibrational excited state H2(v) Energy of kBIs the boltzmann constant, and is,
Figure BDA0003039982130000031
is in a vibrating combined state giOf said temperature of
Figure BDA0003039982130000032
Obtaining the slope of the vibration distribution function;
(ii) when the negative hydrogen ion generation and loss reaction has no vibrational combination but has electrons involved, kjThe method comprises the following steps that the function of the electronic temperature is adopted, when the electronic temperature is used for the first time, the electronic temperature adopts a set initial value, and when the electronic temperature is not used for the first time, the latest electronic temperature obtained through calculation is adopted;
(iii) when the generation and loss reaction of negative hydrogen ions has neither vibrational combination nor participation of electrons, kjIs a constant;
in formula II: n isaAnd nbRespectively, the density of the reactants, said naAnd nbThe obtaining method comprises the following steps:
(a) when the reactant of the generation and loss reaction of the negative hydrogen ions is in a vibration combination state, the naAnd nbDensity in a vibrating combined state
Figure BDA0003039982130000033
Density of said vibrational modes
Figure BDA0003039982130000034
Calculated by the formula V:
Figure BDA0003039982130000035
in the formula V, the reaction mixture is shown in the formula V,
Figure BDA0003039982130000036
is in a vibrating combined state giThe flux of (a) is measured,
Figure BDA0003039982130000037
in order to vibrate the density of the combined state,
Figure BDA0003039982130000038
in order to be the thermal velocity,
Figure BDA0003039982130000039
is in a vibrating combined state giMass of (k)BIs the boltzmann constant, and is,
Figure BDA00030399821300000310
is in a vibrating combined state giThe temperature of (a);
Figure BDA00030399821300000311
v is the area of the open boundary, V is the volume of the chamber;
Figure BDA00030399821300000312
showing the vibrational composition g due to the collision reaction l inside the chamberiThe generation or loss of the source term, wherein,
Figure BDA00030399821300000313
klis a complex reaction coefficient, naAnd nbDensity of reactants, respectively;
Figure BDA00030399821300000314
represents a vibration combination g caused by a surface reaction s inside the chamberiThe generation or loss of the source term, wherein,
Figure BDA00030399821300000315
ksis a complex reaction coefficient, naIs the density of the reactants;
(b) when the reactant of the generation and loss reaction of negative hydrogen ions is positive ions, n isaAnd nbIs the density n of positive ionsiDensity n of said positive ionsiObtained by formula VI:
Figure BDA00030399821300000316
in the formula VI, niIs the density of positive ions, uB,iBohm velocity of a positive ion, Aeff,iEffective area for positive ion loss, V is chamber volume, RV,iRepresenting the generation and loss source terms of positive ions due to the collision reaction of the body region;
(c) when the reactant of the generation and loss reaction of negative hydrogen ions is neutral particles, n isaAnd nbDensity n of neutral particlesnDensity n of said neutral particlesnObtained by formula VII:
Figure BDA0003039982130000041
in the formula VII, niIs the density of positive ions, uB,iBohm velocity of a positive ion, Aeff,nDevice for indicating positive ionsEffective area of the wall surface for generating neutral particles, V is the volume of the chamber, and gamma isnIs the flux of the neutral particles and is,
Figure BDA0003039982130000042
nnis the density of the neutral particles and is,
Figure BDA0003039982130000043
is the thermal velocity, mnMass of neutral particles, kBIs the Boltzmann constant, TnThe temperature of the neutral particles; a. thenIs the area of the open boundary, RV,nRepresents the generation and loss source term of neutral particles due to the collision reaction of the body region, Rs,nRepresenting the generation and loss source terms of neutral particles due to collision reaction of the surface;
(d) when the reactant of the generation and loss reaction of negative hydrogen ions is an electron, n isaAnd nbDensity n of electronseDensity n of said electronseObtained by formula VIII:
Figure BDA0003039982130000044
in the formula VIII, neIs the density of the electrons and is,
Figure BDA0003039982130000045
represents H3 +The density of the ions,
Figure BDA0003039982130000046
Represents H2 +The density of the ions,
Figure BDA0003039982130000047
Represents H+The density of the ions;
Figure BDA0003039982130000048
represents H-The density of the ions.
Preferably, the negative hydrogen ion generation and loss reaction j comprises:
reaction j1：e+H2(v)→H+H-；
Reaction j2：e+H2→H+H-；
Reaction j3：
Figure BDA0003039982130000049
Reaction j4：
Figure BDA00030399821300000410
Reaction j5：e+H-→H+2e；
Reaction j6：H++H-→2H；
Reaction j7：H++H-→H+H(n＝2)；
Reaction j8：H++H-→H+H(n＝3)；
Reaction j9：
Figure BDA00030399821300000411
Reaction j10：
Figure BDA0003039982130000051
Reaction j11：
Figure BDA0003039982130000052
Reaction j12：
Figure BDA0003039982130000053
Reaction j13：H-+H→e+H2。
Preferably, the collision reaction/comprises:
reaction by collision l1：
Figure BDA0003039982130000054
Reaction by collision l2：
Figure BDA0003039982130000055
Reaction by collision l3：e+H2(v)→e+2H,v∈gi；
Reaction by collision l4：e+H2(v)→H+H-,v∈gi；
Reaction by collision l5：e+H2(v)→H+H++2e,v∈gi；
Reaction by collision l6：
Figure BDA0003039982130000056
Reaction by collision l7：
Figure BDA0003039982130000057
Reaction by collision l8：
Figure BDA0003039982130000058
Reaction by collision l9：
Figure BDA0003039982130000059
Preferably, the surface reaction s comprises:
H2(v)+wall→H2(w)
surface reaction s1：v∈gi,w＝0orw∈gj,i＞j。
Preferably, the collision reaction of the bulk region in (b) comprises:
Figure BDA00030399821300000510
Figure BDA00030399821300000511
Figure BDA00030399821300000512
Figure BDA00030399821300000513
Figure BDA00030399821300000514
Figure BDA00030399821300000515
Figure BDA0003039982130000061
Figure BDA0003039982130000062
Figure BDA0003039982130000063
Figure BDA0003039982130000064
Figure BDA0003039982130000065
Figure BDA0003039982130000066
Figure BDA0003039982130000067
Figure BDA0003039982130000068
Figure BDA0003039982130000069
Figure BDA00030399821300000610
Figure BDA00030399821300000611
e+H2→2e+H++H；
e+H→2e+H+；
e+H(n＝2)→2e+H+；
e+H(n＝3)→2e+H+；
e+H2(v)→H+H++2e,v∈gi；
H++H-→2H；
H++H-→H+H(n＝2)；
H++H-→H+H(n＝3)。
preferably, the collision reaction of the body region in (c) comprises:
Figure BDA00030399821300000612
Figure BDA00030399821300000613
Figure BDA00030399821300000614
Figure BDA00030399821300000615
Figure BDA00030399821300000616
Figure BDA00030399821300000617
Figure BDA00030399821300000618
Figure BDA0003039982130000071
Figure BDA0003039982130000072
Figure BDA0003039982130000073
Figure BDA0003039982130000074
Figure BDA0003039982130000075
Figure BDA0003039982130000076
Figure BDA0003039982130000077
Figure BDA0003039982130000078
e+H2→2e+H++H；
e+H→2e+H+；
e+H(n＝2)→2e+H+；
e+H(n＝3)→2e+H+；
e+H2(v)→H+H++2e,v∈gi；
H++H-→2H；
H++H-→H+H(n＝2)；
H++H-→H+H(n＝3)；
e+H2→e+2H；
e+H2→e+H+H(n＝2)；
e+H2→e+H+H(n＝3)；
e+H2→H-+H；
e+H-→H+2e；
H(n＝2)+H2→3H；
H(n＝3)+H2→3H；
e+H2(v)→e+2H,v∈gi；
e+H2(v)→H+H-,v∈gi；
Figure BDA0003039982130000079
e+H→e+H(n＝2)；
e+H→e+H(n＝3)；
H+H-→e+H2；
H(n＝3)→H(n＝2)+hν；
e+H(n＝2)→e+H(n＝3)。
preferably, the collision reaction of the surface in (c) comprises:
H(n＝2)+wall→H；
H(n＝3)+wall→H；
2H+wall→H2。
has the advantages that:
the efficiency is high: generally, in the simulation of a negative hydrogen ion source, 23 kinds of particles need to be considered, including charged particles: electron e, positive ion H3 +Cationic H2 +Cationic H+And negative ion H-(ii) a Neutral particles: ground state H2Vibrational excited state H of molecule, ground state H atom, 14 hydrogen molecules2(v ═ 1 to 14) and excited state H of 2 hydrogen atoms (n ═ 2, 3). For each particle, a separate particle number conservation equation is required to determine its density. In addition, collisions occur between various particles, where the chemical reactions involved are more than one thousand or two hundred. If the negative hydrogen ion density is to be accurately simulated, the chemical reaction is not satisfactory, and therefore the simulation efficiency of the conventional model is low. In view of the chamber structure of the negative hydrogen ion source, two-dimensional or even three-dimensional models are often required. Due to computational efficiency limitations, it is almost impossible to achieve in two-or three-dimensional models if one wants to include all of the particles and chemical reactions described above. The simulation method provided by the invention is to excite the vibration excited state H of 14 hydrogen molecules2(v 1-14), i.e. several adjacent excited states are treated as one particle. By doing so, not only can the number of particles contained in the model (i.e., the number of particle number conservation equations) be reduced, but the reactions between the particles in the group can be ignored (i.e., the number of chemical reactions contained in the model also drops significantly).
The precision is high: the negative hydrogen ion density calculated by adopting a grouping model has a difference of less than 6% with the original model, and particularly has a difference of less than 1% when the air pressure is higher. In addition, relative differences are kept at a low level for other positive ion densities, H atom densities and electron temperatures, which fully indicates that the simulation method provided by the invention has high precision.
Drawings
FIG. 1 is a vibration distribution function of hydrogen molecules;
FIG. 2 is a comparison graph of the negative hydrogen ion density results calculated by the grouping model and the original model in example 1;
FIG. 3 is a comparison graph of the negative hydrogen ion density results calculated by the grouping model and the original model of comparative example 1.
Detailed Description
The invention sets the discharge conditions: the power is 1kW to 30kW, and preferably 10 kW; the pressure is 1-30 Pa, preferably 15 Pa. The invention groups 14 vibration excited states of hydrogen molecules according to the slope of the vibration distribution function of the hydrogen molecules under the set discharge condition, and the group is named as a vibration combination state giWherein i is 1, 2, 3 … … i.
The present invention does not specifically limit the acquisition of the vibration distribution function of the hydrogen molecules, and the acquisition may be performed by a method known to those skilled in the art.
In the present invention, the grouping is preferably performed in such a manner that the grouping is performed according to the slope of the vibration distribution function of the hydrogen molecules. In a specific embodiment of the present invention, the vibration distribution function of the hydrogen molecules is shown in fig. 1; thus, the 14 vibrational excited states H of the hydrogen molecule2(v 1-14) into three groups, i.e. H2(v 1-4) is a first vibration combination g1，H2(v 5-9) is a second vibration combination g2，H2(v 10-14) is a third vibration combination g3。
After grouping is finished, the negative hydrogen ion density is obtained by utilizing a particle number conservation equation of the negative hydrogen ions shown in a formula I based on the generation and loss reaction of the negative hydrogen ions:
Figure BDA0003039982130000091
in the present invention, in the formula I,
Figure BDA0003039982130000092
a source term representing the negative hydrogen ion generation and loss reaction j inside the chamber. In the present invention, the generation and loss reaction j of negative hydrogen ions preferably includes:
reaction j1：e+H2(v)→H+H-；
Reaction j2：e+H2→H+H-；
Reaction j3：
Figure BDA0003039982130000093
Reaction j4：
Figure BDA0003039982130000094
Reaction j5：e+H-→H+2e；
Reaction j6：H++H-→2H；
Reaction j7：H++H-→H+H(n＝2)；
Reaction j8：H++H-→H+H(n＝3)；
Reaction j9：
Figure BDA0003039982130000101
Reaction j10：
Figure BDA0003039982130000102
Reaction j11：
Figure BDA0003039982130000103
Reaction j12：
Figure BDA0003039982130000104
Reaction j13：H-+H→e+H2。
In the present invention, in the case of the present invention,
Figure BDA0003039982130000105
obtained using formula II:
Figure BDA0003039982130000106
in the present invention, in formula II, kjThe reaction coefficients are: k is a radical ofjThe obtaining method comprises the following steps:
(i) when the generation and loss reaction of negative hydrogen ions is in the vibration combination statejIs a complex reaction coefficient kgi(ii) a The complex reaction coefficient kgiObtained using formula III:
Figure BDA0003039982130000107
in the formula III, kgiIs a complex reaction coefficient, kvIs in a vibrating combined state giIncluding vibrational excited states H2(v) The reaction coefficient of (a); k isvAs a function or constant of electron temperature. In the present invention, when electrons in the generation and loss reaction j of negative hydrogen ions are added as a reactant, k isvAs a function of electron temperature, e.g. negative hydrogen ion generation and loss reaction j1(ii) a When the electronic temperature is used for the first time, the electronic temperature preferably adopts a set initial value, and when the electronic temperature is not used for the first time, the latest electronic temperature obtained by calculation is adopted; the initial value of the electron temperature is preferably 1 eV. In the present invention, when no electron is added as a reactant in the generation and loss reaction j of negative hydrogen ion, k isvIs constant, said kvPreferably by reference to the literature; such as the generation and loss reaction of negative hydrogen ions j4。
In the present invention, in the formula III,
Figure BDA0003039982130000108
obtained by the formula IV:
Figure BDA0003039982130000109
in the formula IV, EvIs a vibrational excited state H2(v) Energy of kBIs the boltzmann constant, and is,
Figure BDA00030399821300001010
is in a vibrating combined state giOf said temperature of
Figure BDA0003039982130000111
The slope of the vibration distribution function is used for solving the problem.
(ii) When the negative hydrogen ion generation and loss reaction has no vibrational combination but has electrons involved, kjAs a function of electron temperature; when the electronic temperature is used for the first time, the electronic temperature preferably adopts a set electronic temperature initial value, and when the electronic temperature is not used for the first time, the latest electronic temperature obtained by calculation is adopted. In the present invention, the initial electron temperature value is preferably 1 eV.
(iii) When the generation and loss reaction of negative hydrogen ions has neither vibrational combination nor participation of electrons, kjIs a constant; k isjPreferably by reference to the literature.
In the present invention, in formula II, naAnd nbDensity of reactants, respectively; n isaAnd nbThe obtaining method comprises the following steps:
(a) when the reactant of the generation and loss reaction of the negative hydrogen ions is in a vibration combination state, the naAnd nbDensity in a vibrating combined state
Figure BDA0003039982130000112
Density of said vibrational modes
Figure BDA0003039982130000113
Calculated by the formula V:
Figure BDA0003039982130000114
in the formula V, the reaction mixture is shown in the formula V,
Figure BDA0003039982130000115
is in a vibrating combined state giThe flux of (a) is measured,
Figure BDA0003039982130000116
in order to vibrate the density of the combined state,
Figure BDA0003039982130000117
in order to be the thermal velocity,
Figure BDA0003039982130000118
is in a vibrating combined state giMass of (k)BIs the boltzmann constant, and is,
Figure BDA0003039982130000119
is in a vibrating combined state giThe temperature of (a); the T isgiPreferably by the slope of the vibration distribution function,
Figure BDA00030399821300001110
v is the volume of the chamber, the area of the open boundary.
In the present invention, in the formula V,
Figure BDA00030399821300001111
showing the vibrational composition g due to the collision reaction l inside the chamberiThe generation or loss of the source term, wherein,
Figure BDA00030399821300001112
klis the composite reaction coefficient; the method for obtaining the composite reaction coefficient is the same as that of (i), and is not described herein again; n isaAnd nbDensity of reactants, respectively; when n isaAnd nbDensity of vibrating composition state, ngiIt is sufficient to set it as unknown. In the present invention, when naAnd nbIs density of negative hydrogen ion
Figure BDA00030399821300001113
Neutral particles nnAnd density n of electronseIn this case, it is preferable to obtain the compound according to formula I and the subsequent steps (c) and (d).
In the present invention, the collision reaction l preferably includes:
reaction by collision l1：
Figure BDA00030399821300001114
Reaction by collision l2：
Figure BDA00030399821300001115
Reaction by collision l3：e+H2(v)→e+2H,v∈gi；
Reaction by collision l4：e+H2(v)→H+H-,v∈gi；
Reaction by collision l5：e+H2(v)→H+H++2e,v∈gi；
Reaction by collision l6：
Figure BDA0003039982130000121
Reaction by collision l7：
Figure BDA0003039982130000122
Reaction by collision l8：
Figure BDA0003039982130000123
Reaction by collision l9：
Figure BDA0003039982130000124
In the present invention, in the formula V,
Figure BDA0003039982130000125
represents a vibration combination g caused by a surface reaction s inside the chamberiOf (2)The source term is generated or lost, wherein,
Figure BDA0003039982130000126
ksfor the complex reaction coefficient, the method for obtaining the complex reaction coefficient is the same as that of (i), and is not repeated herein; n isaThe density of the vibration combination state is set as an unknown number ngiAnd (4) finishing.
In the present invention, the surface reaction s preferably includes:
H2(v)+wall→H2(w)
surface reaction s1：v∈gi,w＝0orw∈gj,i＞j。
In the present invention, the density n of the vibration combination state is calculated by using the formula VgiFor the density n of the vibration-divided combination state appearing in formula VgiAnd the other parameters adopt set initial values when used for the first time and adopt calculated numerical values when not used for the first time. Thus, formula V is a function of ngiA linear equation of a unit of (1) to calculate ngiAnd (4) finishing.
(b) When the reactant of the generation and loss reaction of negative hydrogen ions is positive ions, n isaAnd nbIs the density n of positive ionsiDensity n of said positive ionsiObtained by formula VI:
Figure BDA0003039982130000127
in the formula VI, niDenotes the density of positive ions, uB,iDenotes the Bohm velocity of the positive ion, Aeff,iRepresents the effective area of positive ion loss, V represents the chamber volume, RV,iRepresenting the generation and loss of source terms of positive ions due to the collision reaction of the bulk region.
In the present invention, the collision reaction of the body region includes:
Figure BDA0003039982130000131
Figure BDA0003039982130000132
Figure BDA0003039982130000133
Figure BDA0003039982130000134
Figure BDA0003039982130000135
Figure BDA0003039982130000136
Figure BDA0003039982130000137
Figure BDA0003039982130000138
Figure BDA0003039982130000139
Figure BDA00030399821300001310
Figure BDA00030399821300001311
Figure BDA00030399821300001312
Figure BDA00030399821300001313
Figure BDA00030399821300001314
Figure BDA00030399821300001315
Figure BDA00030399821300001316
Figure BDA00030399821300001317
e+H2→2e+H++H；
e+H→2e+H+；
e+H(n＝2)→2e+H+；
e+H(n＝3)→2e+H+；
e+H2(v)→H+H++2e,v∈gi；
H++H-→2H；
H++H-→H+H(n＝2)；
H++H-→H+H(n＝3)。
in the present invention, said RV,iIs calculated as the product of the reaction coefficient and the reactant density. In the present invention, R is calculatedV,iMeanwhile, the method for obtaining the reaction coefficient is the same as (i), (ii) and (iii), and is not described herein again; the density of the reactants is obtained in the same manner as in formulas I, (a), (b), (c) and (d), and is not described herein.
In the present invention, the positive deviation is calculated by using formula VIDensity n of seedsiFor the density n of the counterions appearing in formula VIiAnd the other parameters adopt set initial values when used for the first time and adopt calculated numerical values when not used for the first time. Thus, formula VI is a number related to niA linear equation of a unit of (1) to calculate niAnd (4) finishing.
(c) When the reactant of the generation and loss reaction of negative hydrogen ions is neutral particles, n isaAnd nbDensity n of neutral particlesnDensity n of said neutral particlesnObtained by formula VII:
Figure BDA0003039982130000141
in the formula VII, niIs the density of positive ions, uB,iBohm velocity of a positive ion, Aeff,nDenotes the effective area of the positive ions to generate neutral particles on the wall surface, V is the volume of the chamber, and gammanIs the flux of the neutral particles and is,
Figure BDA0003039982130000142
nnis the density of the neutral particles and is,
Figure BDA0003039982130000143
is the thermal velocity, mnMass of neutral particles, kBIs the Boltzmann constant, TnThe temperature of the neutral particles; a. thenIs the area of the open border.
In the present invention, in formula VII, R isV,nRepresenting the generation and loss source terms of neutral particles caused by the collision reaction of the body area; the collision reaction of the body region comprises:
Figure BDA0003039982130000144
Figure BDA0003039982130000145
Figure BDA0003039982130000146
Figure BDA0003039982130000147
Figure BDA0003039982130000148
Figure BDA0003039982130000149
Figure BDA00030399821300001410
Figure BDA00030399821300001411
Figure BDA00030399821300001412
Figure BDA0003039982130000151
Figure BDA0003039982130000152
Figure BDA0003039982130000153
Figure BDA0003039982130000154
Figure BDA0003039982130000155
Figure BDA0003039982130000156
e+H2→2e+H++H；
e+H→2e+H+；
e+H(n＝2)→2e+H+；
e+H(n＝3)→2e+H+；
e+H2(v)→H+H++2e,v∈gi；
H++H-→2H；
H++H-→H+H(n＝2)；
H++H-→H+H(n＝3)；
e+H2→e+2H；
e+H2→e+H+H(n＝2)；
e+H2→e+H+H(n＝3)；
e+H2→H-+H；
e+H-→H+2e；
H(n＝2)+H2→3H；
H(n＝3)+H2→3H；
e+H2(v)→e+2H,v∈gi；
e+H2(v)→H+H-,v∈gi；
Figure BDA0003039982130000157
e+H→e+H(n＝2)；
e+H→e+H(n＝3)；
H+H-→e+H2；
H(n＝3)→H(n＝2)+hν；
e+H(n＝2)→e+H(n＝3)。
in the present invention, said RV,nThe obtaining method of (1) is the product of the reaction coefficient and the density of the reactant; wherein the method for obtaining the reaction coefficient is the same as (i), (ii) and (iii), and is not described herein again; the density of the reactants is obtained in the same manner as in formulas I, (a), (b), (c) and (d), and is not described herein.
In the present invention, in formula VII, R iss,nRepresenting the generation and loss source terms of neutral particles due to collision reaction of the surface; the collision reaction of the surface comprises:
H(n＝2)+wall→H；
H(n＝3)+wall→H；
2H+wall→H2。
in the present invention, said Rs,nThe obtaining method of (1) is the product of the reaction coefficient and the density of the reactant; wherein the reaction coefficient is preferably obtained by consulting literature; the density of the reactant is obtained in the same manner as in (c), and will not be described in detail.
In the present invention, the density n of neutral particles is calculated using formula VIInFor the density n of the neutrals-removing particles appearing in formula VIInAnd the other parameters adopt set initial values when used for the first time and adopt calculated numerical values when not used for the first time. Thus, formula VII is a radical relating to nnA linear equation of a unit of (1) to calculate nnAnd (4) finishing.
(d) When the reactant of the generation and loss reaction of negative hydrogen ions is an electron, n isaAnd nbDensity n of electronseDensity n of said electronseObtained by formula VIII:
Figure BDA0003039982130000161
in the formula VIII, neIs the density of the electrons and is,
Figure BDA0003039982130000162
represents H3 +The density of the ions,
Figure BDA0003039982130000163
Represents H2 +The density of the ions,
Figure BDA0003039982130000164
Represents H+The density of the ions;
Figure BDA0003039982130000165
represents H-The density of the ions. In the present invention, the method for obtaining the density of the positive ions and the density of the negative ions in the formula VIII is the same as that in the formula I, (c), and is not described herein again.
The following describes a simulation method for estimating the negative hydrogen ion density provided by the present invention in detail with reference to the following examples, but they should not be construed as limiting the scope of the present invention.
Example 1
Step 1: vibration excited state grouping
Setting the discharge condition to 10kW and 15Pa, obtaining the vibration distribution function of hydrogen molecules under the discharge condition, and obtaining the result as shown in FIG. 1; according to the gradient of the hydrogen molecule vibration distribution function shown in figure 1, the vibration excited state H of the hydrogen molecule2(v 1-14) into three groups, i.e. H2(v 1-4) is a first vibration combination g1，H2(v 5-9) is a second vibration combination g2，H2(v 10-14) is a third vibration combination g3。
Step 2: initialization
Density of charged particles (including electron e, positive ion H)3 +、H2 +、H+Anion H-) Electron temperature, neutral particle density (including ground state H)2Molecules, ground-state H atoms, vibrational combination states of 3 hydrogen molecules, and excited states H (n is 2, 3)) of 2 hydrogen atoms are assigned initial values, which are: density of charged particles (including electron e, positive ion H)3 +、H2 +、H+Anion H-) Has an initial value of 1e17m-3Initial value of electron temperature of 1eV, ground state neutral particle density (including ground state H)2Molecular, ground state H atom) of 1e20m-3The initial value of the vibrational combination of 3 hydrogen molecules and the excited state H (n ═ 2, 3)) of 2 hydrogen atoms is 1e18m-3。
And step 3: obtaining the composite reaction coefficient of the vibration combination state
After the vibrational excited states of the hydrogen molecules are grouped, the reactions between the excited states need not be considered, but the reactions of the respective vibrational combined states need to be considered. That is, when the reactant and the product belong to the same vibration combination state, the reaction is ignored; the reaction is taken into account only if the reactants and the products belong to different vibrational combinations. For example: for reaction H2(v)→H2(w) only if v ∈ giAnd w is e gjThis reaction is taken into account. Therefore, with such a grouping model, not only the number of particles to be considered in the model but also the number of chemical reactions involved in the model can be greatly reduced.
The reactions in which the vibration excited state participates in the above-described grouping model are listed in table 1.
TABLE 1 reaction of vibrational excitation participation in the group model
Figure BDA0003039982130000171
Figure BDA0003039982130000181
With R in Table 11Reaction as an example, when v ∈ giAnd w is e gjFrom a vibrating combination giTo a vibrating combined state gjThe reaction source term is
Figure BDA0003039982130000182
Wherein k isR1Is the complex reaction coefficient of the reaction, neAs the density of the electrons, the electron density,
Figure BDA0003039982130000183
is in a vibrating combined state giThe density of (c). Let R be1Has a coefficient of kv→wCoefficient of the recombination reaction kR1And is not equal to all excited states v ∈ giK of (a)v→wInstead, the reaction coefficients between each excited state need to be multiplied by a partition function, as shown in equation IV:
Figure BDA0003039982130000184
in the formula IV, EvIs a vibrational excited state H2(v∈gi) Energy of kBIs the boltzmann constant, and is,
Figure BDA0003039982130000185
is in a vibrating combined state giThe temperature of (a); the above-mentioned
Figure BDA0003039982130000186
The slope of the vibration distribution function is used for solving the problem.
Then the complex reaction coefficient kR1Is represented by formula III:
Figure BDA0003039982130000187
in the formula III, kv→wThe function or constant of the electron temperature is adopted when the electron temperature is used for the first time.
And 4, step 4: solving the density of the vibration combination state
Figure BDA0003039982130000191
For each vibration mode giCan be regarded as a new particle, the density of which
Figure BDA0003039982130000192
The particle number conservation equation can be adopted for calculation, as shown in formula V;
Figure BDA0003039982130000193
in formula V:
Figure BDA0003039982130000194
is in a vibrating combined state giThe flux of (a) is measured,
Figure BDA0003039982130000195
in order to be the thermal velocity,
Figure BDA0003039982130000196
is in a vibrating combined state giThe mass of (c);
Figure BDA0003039982130000197
v is the volume of the chamber, the area of the open boundary.
In formula V:
Figure BDA0003039982130000198
and
Figure BDA0003039982130000199
respectively, the collision reaction l (R in Table 1) due to the inside of the chamber1-R9) And surface reaction s (R in Table 1)10) Induced vibration combination giGenerating or losing a source term, klAnd ksFor the complex reaction coefficient, n, calculated in step 3aAnd nbThe densities of the reactants, respectively. When the reactant is electron (R in Table 1)1-R6) Or H atom (R in Table 1)7) Its density is solved by step 6. When the reactant is negative ion H-(R in Table 1)9) Its density is solved by step 5. The initial value set in step 2 may be used for the first time.
In the method, the particle number conservation equation does not need to be solved aiming at a single vibration state, so that the number of equations to be solved in the model is greatly reduced (14 vibration states originally and 3 combination states now). Table 2 lists the number of particles and the number of reactions involved in the grouping model (the method proposed in this patent) and the original model (the original method).
Table 2 population and reaction numbers included in the group model and the original model.
Figure BDA00030399821300001910
And 5: solving for negative hydrogen ion density nH-
In order to obtain the density of the negative hydrogen ions, the negative hydrogen ions H need to be solved-The conservation of population equation of (a) is shown in formula I:
Figure BDA00030399821300001911
in the formula I, the compound is shown in the specification,
Figure BDA00030399821300001912
represents a negative hydrogen ion H due to a collision reaction j inside the chamber-Specific reaction types are shown in table 3; wherein k isjThe reaction coefficient is shown.
TABLE 3 production and loss reaction of negative hydrogen ions
Figure BDA0003039982130000201
For reactions involving vibrational excited states (j in Table 3)1，j4)，kjThe complex reaction coefficient calculated for step 3.
For other reactions with electron participation (j in Table 32，j3，j5)，kjAs a function of electron temperature. The electron temperature, which will be calculated in step 6, may be the initial value set in step 2 when first used.
For reactions with neither vibrational excited states nor electron participation (j in Table 36-j13)，kjIs constant and can be obtained by consulting literature.
naAnd nbThe densities of the reactants, respectively.
When the reactants are in the vibrational combination (j in Table 3)1，j4) Density n of vibrating combined stategiGiven by step 4;
when the reactant is other kinds of particles, e.g. electrons, H2Molecule, H atom, H3 +Ion, H2 +Ion, H+The ion and density are solved through the step 6, and the initial value set in the step 2 can be adopted when the ion and density are used for the first time.
When the reactant contains negative hydrogen ion H-When (j in Table 3)4-j13) Source item
Figure BDA0003039982130000211
I.e. the density n of negative hydrogen ionsH-As a function of (c). Thus, the unknown variable in formula I is nH-N is obtained by solving formula IH-The value of (c).
Step 6: solving for the density of other particles (for step 4 solving for
Figure BDA0003039982130000212
And for step 5 solving
Figure BDA0003039982130000213
) And electron temperature (for solving k in step 3)v→wAnd reaction coefficient k for solving other electron participation in step 5j)。
Calculating conservation of population and energy of other particles including electron density and positive ion H3 +Density, H2 +Density, H+Density, ground state H2Molecular density, ground state H atom density, excited state H (n ═ 2) density of hydrogen atoms, excited state H (n ═ 3) density of hydrogen atoms, and electron temperature. (the equations in this step are complete with the original methodAnd consistency is not described in detail. )
And 7: and judging whether the density increment of all the particles is smaller than a set value. If so, the operation ends. If not, substituting all the physical quantities into the step 3, and repeating the steps 3-6 until iteration converges.
In order to verify the accuracy of the simulation method provided by the invention, the negative hydrogen ion densities calculated by the grouping model and the original model when the input power is fixed to 10kW and the air pressure is in the range of 1-30 Pa are respectively compared, and the result is shown in FIG. 2.
In addition, the relative differences between the negative hydrogen ion density and other physical quantities calculated by the two models under the corresponding discharge conditions are listed in table 4. As can be seen from table 4 and fig. 2: the negative hydrogen ion density calculated by adopting a grouping model has a difference of less than 6% with the original model, and particularly has a difference of less than 1% when the air pressure is higher. In addition, relative differences are kept at a low level for other positive ion densities, H atom densities and electron temperatures, which fully indicates that the simulation method provided by the invention has high precision.
TABLE 4 relative differences between the various physical quantities calculated by the group model and the original model
Figure BDA0003039982130000221
Comparative example 1
Similar to example 1, except that the vibrational excited state H of the hydrogen molecule2(v 1-14) is divided into three groups, H2(v 1-4) is a first vibration combination g1，H2(v 5-8) is a second vibration combination g2，H2(v 9-14) is a third vibration combination g3。
The results of comparing the negative hydrogen ion densities calculated by the above grouping model and the original model when the input power is fixed at 10kW and the air pressure is in the range of 1 to 30Pa are shown in FIG. 3.
As can be seen from fig. 3: with the grouping scheme of comparative example 1, the negative hydrogen ion density was severely overestimated, i.e., the grouping scheme did not accurately reproduce the characteristics of the plasma.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (7)

1. A simulation method for estimating negative hydrogen ion density is characterized by comprising the following steps:
setting a discharge condition: the power is 1 kW-30 kW, the pressure is 1-30 Pa, 14 vibration excited states of the hydrogen molecules are grouped according to the slope of the vibration distribution function of the hydrogen molecules under the set discharge condition, and the group is named as a vibration combination state giWherein i is 1, 2, 3 … … i;
based on the generation and loss reaction of the negative hydrogen ions, the particle number conservation equation of the negative hydrogen ions shown in the formula I is utilized to obtain the density of the negative hydrogen ions:
Figure FDA0003039982120000011
in the formula I, the compound is shown in the specification,
Figure FDA0003039982120000012
a source term representing the negative hydrogen ion generation and loss reaction j inside the chamber,
Figure FDA0003039982120000013
obtained using formula II:
Figure FDA0003039982120000014
in the formula II, kjThe reaction coefficients are: k is a radical ofjThe obtaining method comprises the following steps:
(i) when the negative hydrogen ions are generated and lost, the reaction has vibrationWhen the combination state participates, kjIs a complex reaction coefficient kgi(ii) a The complex reaction coefficient kgiObtained using formula III:
Figure FDA0003039982120000015
in the formula III, kgiIs a complex reaction coefficient, kvIs in a vibrating combined state giIncluding vibrational excited states H2(v) The coefficient of reaction of, said kvThe function or constant of the electronic temperature is adopted, when the electronic temperature is used for the first time, the electronic temperature adopts a set initial value, and when the electronic temperature is not used for the first time, the latest electronic temperature obtained by calculation is adopted;
in the formula (III), the reaction solution is prepared,
Figure FDA0003039982120000016
obtained by the formula IV:
Figure FDA0003039982120000017
in the formula IV, EvIs a vibrational excited state H2(v) Energy of kBIs the Boltzmann constant, TgiIs in a vibrating combined state giTemperature of said TgiObtaining the slope of the vibration distribution function;
(ii) when the negative hydrogen ion generation and loss reaction has no vibrational combination but has electrons involved, kjThe method comprises the following steps that the function of the electronic temperature is adopted, when the electronic temperature is used for the first time, the electronic temperature adopts a set initial value, and when the electronic temperature is not used for the first time, the latest electronic temperature obtained through calculation is adopted;
(iii) when the generation and loss reaction of negative hydrogen ions has neither vibrational combination nor participation of electrons, kjIs a constant;
in formula II: n isaAnd nbRespectively, the density of the reactants, said naAnd nbThe obtaining method comprises the following steps:
(a) when the reactant of the generation and loss reaction of the negative hydrogen ions is in a vibration combination state, the naAnd nbDensity n as a vibrational compositiongiDensity n of said vibrational compositiongiCalculated by the formula V:
Figure FDA0003039982120000021
in the formula V, the reaction mixture is shown in the formula V,
Figure FDA0003039982120000022
is in a vibrating combined state giFlux of (2), ngiIn order to vibrate the density of the combined state,
Figure FDA0003039982120000023
is the thermal velocity, mgiIs in a vibrating combined state giMass of (k)BIs the Boltzmann constant, TgiIs in a vibrating combined state giThe temperature of (a); a. thegiV is the area of the open boundary, V is the volume of the chamber;
Figure FDA0003039982120000024
showing the vibrational composition g due to the collision reaction l inside the chamberiThe generation or loss of the source term, wherein,
Figure FDA0003039982120000025
klis a complex reaction coefficient, naAnd nbDensity of reactants, respectively;
Figure FDA0003039982120000026
represents a vibration combination g caused by a surface reaction s inside the chamberiThe generation or loss of the source term, wherein,
Figure FDA0003039982120000027
ksis a complex reaction coefficient, naIs the density of the reactants;
(b) when the reactant of the generation and loss reaction of negative hydrogen ions is positive ions, n isaAnd nbIs the density n of positive ionsiDensity n of said positive ionsiObtained by formula VI:
Figure FDA0003039982120000028
in the formula VI, niIs the density of positive ions, uB,iBohm velocity of a positive ion, Aeff,iEffective area for positive ion loss, V is chamber volume, RV,iRepresenting the generation and loss source terms of positive ions due to the collision reaction of the body region;
(c) when the reactant of the generation and loss reaction of negative hydrogen ions is neutral particles, n isaAnd nbDensity n of neutral particlesnDensity n of said neutral particlesnObtained by formula VII:
Figure FDA0003039982120000031
in the formula VII, niIs the density of positive ions, uB,iBohm velocity of a positive ion, Aeff,nDenotes the effective area of the positive ions to generate neutral particles on the wall surface, V is the volume of the chamber, and gammanIs the flux of the neutral particles and is,
Figure FDA0003039982120000032
nnis the density of the neutral particles and is,
Figure FDA0003039982120000033
is the thermal velocity, mnMass of neutral particles, kBIs the Boltzmann constant, TnThe temperature of the neutral particles; a. thenIs the area of the open boundary, RV,nRepresents the generation and loss source term of neutral particles due to the collision reaction of the body region, Rs,nRepresenting the generation and loss source terms of neutral particles due to collision reaction of the surface;
(d) when the reactant of the generation and loss reaction of negative hydrogen ions is an electron, n isaAnd nbDensity n of electronseDensity n of said electronseObtained by formula VIII:
Figure FDA0003039982120000034
in the formula VIII, neIs the density of the electrons and is,
Figure FDA0003039982120000035
represents H3 +The density of the ions,
Figure FDA0003039982120000036
Represents H2 +The density of the ions,
Figure FDA0003039982120000037
Represents H+The density of the ions;
Figure FDA0003039982120000038
represents H-The density of the ions.
2. The simulation method of claim 1, wherein the negative hydrogen ion generation and loss reaction j comprises:
reaction j1：e+H2(v)→H+H-；
Reaction j2：e+H2→H+H-；
Reaction j3：
Figure FDA0003039982120000039
Reaction j4：
Figure FDA00030399821200000310
Reaction j5：e+H-→H+2e；
Reaction j6：H++H-→2H；
Reaction j7：H++H-→H+H(n＝2)；
Reaction j8：H++H-→H+H(n＝3)；
Reaction j9：
Figure FDA00030399821200000311
Reaction j10：
Figure FDA00030399821200000312
Reaction j11：
Figure FDA00030399821200000313
Reaction j12：
Figure FDA0003039982120000041
Reaction j13：H-+H→e+H2。
3. The simulation method of claim 1, wherein the collision reaction/, comprises:
reaction by collision l1：
Figure FDA0003039982120000042
Reaction by collision l2：
Figure FDA0003039982120000043
Reaction by collision l3：e+H2(v)→e+2H,v∈gi；
Reaction by collision l4：e+H2(v)→H+H-,v∈gi；
Reaction by collision l5：e+H2(v)→H+H++2e,v∈gi；
Reaction by collision l6：
Figure FDA0003039982120000044
Reaction by collision l7：
Figure FDA0003039982120000045
Reaction by collision l8：
Figure FDA0003039982120000046
Reaction by collision l9：
Figure FDA0003039982120000047
4. The simulation method of claim 1, wherein the surface reaction s comprises:
surface reaction s1：
Figure FDA0003039982120000048
5. The simulation method of claim 1, wherein the collision reaction of the body region in (b) comprises:
Figure FDA0003039982120000049
Figure FDA00030399821200000410
Figure FDA00030399821200000411
Figure FDA00030399821200000412
Figure FDA00030399821200000413
Figure FDA00030399821200000414
Figure FDA0003039982120000051
Figure FDA0003039982120000052
Figure FDA0003039982120000053
Figure FDA0003039982120000054
Figure FDA0003039982120000055
Figure FDA0003039982120000056
Figure FDA0003039982120000057
Figure FDA0003039982120000058
Figure FDA0003039982120000059
Figure FDA00030399821200000510
Figure FDA00030399821200000511
e+H2→2e+H++H；
e+H→2e+H+；
e+H(n＝2)→2e+H+；
e+H(n＝3)→2e+H+；
e+H2(v)→H+H++2e,v∈gi；
H++H-→2H；
H++H-→H+H(n＝2)；
H++H-→H+H(n＝3)。
6. the simulation method of claim 1, wherein the collision reaction of the body region in (c) comprises:
Figure FDA00030399821200000512
Figure FDA00030399821200000513
Figure FDA00030399821200000514
Figure FDA00030399821200000515
Figure FDA00030399821200000516
Figure FDA00030399821200000517
Figure FDA0003039982120000061
Figure FDA0003039982120000062
Figure FDA0003039982120000063
Figure FDA0003039982120000064
Figure FDA0003039982120000065
Figure FDA0003039982120000066
Figure FDA0003039982120000067
Figure FDA0003039982120000068
Figure FDA0003039982120000069
e+H2→2e+H++H；
e+H→2e+H+；
e+H(n＝2)→2e+H+；
e+H(n＝3)→2e+H+；
e+H2(v)→H+H++2e,v∈gi；
H++H-→2H；
H++H-→H+H(n＝2)；
H++H-→H+H(n＝3)；
e+H2→e+2H；
e+H2→e+H+H(n＝2)；
e+H2→e+H+H(n＝3)；
e+H2→H-+H；
e+H-→H+2e；
H(n＝2)+H2→3H；
H(n＝3)+H2→3H；
e+H2(v)→e+2H,v∈gi；
e+H2(v)→H+H-,v∈gi；
Figure FDA0003039982120000071
e+H→e+H(n＝2)；
e+H→e+H(n＝3)；
H+H-→e+H2；
H(n＝3)→H(n＝2)+hν；
e+H(n＝2)→e+H(n＝3)。
7. the simulation method of claim 1, wherein the collision reaction of the surface in (c) comprises:
H(n＝2)+wall→H；
H(n＝3)+wall→H；
2H+wall→H2。
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