WO2021073056A1 - 一种测量等离子体电子非广延参数的方法 - Google Patents

一种测量等离子体电子非广延参数的方法 Download PDF

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WO2021073056A1
WO2021073056A1 PCT/CN2020/084082 CN2020084082W WO2021073056A1 WO 2021073056 A1 WO2021073056 A1 WO 2021073056A1 CN 2020084082 W CN2020084082 W CN 2020084082W WO 2021073056 A1 WO2021073056 A1 WO 2021073056A1
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extensive
plasma
probe
parameter
single probe
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PCT/CN2020/084082
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French (fr)
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邱慧斌
肖东华
彭行坤
朱宇晴
张显阳
袁尤龙
蔡奇龙
胡天一
高玥
明智毅
周金茂
周振宇
刘三秋
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南昌大学
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    • H—ELECTRICITY
    • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
    • H05H—PLASMA TECHNIQUE; PRODUCTION OF ACCELERATED ELECTRICALLY-CHARGED PARTICLES OR OF NEUTRONS; PRODUCTION OR ACCELERATION OF NEUTRAL MOLECULAR OR ATOMIC BEAMS
    • H05H1/00—Generating plasma; Handling plasma
    • H05H1/0006—Investigating plasma, e.g. measuring the degree of ionisation or the electron temperature
    • H—ELECTRICITY
    • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
    • H05H—PLASMA TECHNIQUE; PRODUCTION OF ACCELERATED ELECTRICALLY-CHARGED PARTICLES OR OF NEUTRONS; PRODUCTION OR ACCELERATION OF NEUTRAL MOLECULAR OR ATOMIC BEAMS
    • H05H1/00—Generating plasma; Handling plasma
    • H05H1/0006—Investigating plasma, e.g. measuring the degree of ionisation or the electron temperature
    • H05H1/0081—Investigating plasma, e.g. measuring the degree of ionisation or the electron temperature by electric means
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J37/00—Discharge tubes with provision for introducing objects or material to be exposed to the discharge, e.g. for the purpose of examination or processing thereof
    • H01J37/32—Gas-filled discharge tubes
    • H01J37/32917—Plasma diagnostics
    • H01J37/32926—Software, data control or modelling

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  • the invention relates to the field of plasma non-extensive parameter diagnosis, in particular to a method for measuring plasma electron non-extensive parameters.
  • Plasma exists widely in the universe, and is often regarded as the fourth state of matter in addition to solid, liquid, and gas.
  • the average kinetic energy of the particles exceeds the binding energy of the lattice, and the solid becomes liquid; when the liquid is heated to the boiling point, the kinetic energy of the ions exceeds the binding energy between the particles, and the liquid becomes a gas.
  • the gas If the gas is further heated, the gas will be partially or completely ionized, that is, the outer electrons of the atom will get rid of the bondage of the nucleus and become free electrons, and the atoms that have lost the outer electrons will become charged ions.
  • the proportion of charged particles exceeds a certain level, the ionized gas will exhibit obvious electromagnetic properties, and the number of positive ions and negative ions (electrons) is equal, so it is called plasma.
  • the present invention provides a method for measuring the plasma electron non-extensive parameter.
  • a method for measuring plasma electron non-extensive parameters using non-extensive statistical mechanics and electrical probes to measure plasma non-extensive parameters.
  • the first step is to describe the plasma by non-extensive statistical mechanics, and obtain the formula of the IV curve of the non-extensive electric single probe;
  • the second step is to collect the experimental data of the electric single probe IV, and the third step is to use the first step to obtain
  • the IV curve formula of the non-extensive electric single probe is used for nonlinear fitting of the IV experimental data of the electric single probe collected in the second step, and the fourth step is the goodness of fit Curve, the fifth step, find the electronic non-extensive parameter value corresponding to the minimum SSE, the sixth step, make the goodness of fit Curve, the seventh step, obtain the electronic non-extensive parameter value corresponding to the maximum R 2 , the eighth step, compare the electronic non-extensive parameters obtained in the seventh step and the fifth step, the ninth step, see the eighth step Check whether the two results are consistent, the tenth step, if the ninth step is consistent, it is confirmed as the optimal electronic non-extensive parameter, the eleventh step,
  • the formula for collecting current by the probe in the first step is:
  • V bias voltage V bias voltage
  • ⁇ p the plasma potential
  • ⁇ B Boltzmann's constant
  • e the electron charge
  • T e the electron temperature
  • n e the electron density of the undisturbed zone
  • a p the collection probe Area
  • a q is the normalization constant of non-extensive distribution Is the non-extensive parameter of electrons in the plasma
  • mi is the ion mass
  • me is the electron mass.
  • plasma is described by non-extensive statistical mechanics, and a non-extensive electric single probe (measurement) theory is established on this basis.
  • a non-extensive electric single probe we measured the electronic non-extensive parameters that cannot be measured by the traditional electric single probe, and obtained more accurate electron temperature, plasma potential, electron density and suspension potential than the traditional single probe.
  • the non-extensive electrical probe plays a role in plasma diagnosis, will measure the plasma non-extensiveness, and improve the diagnostic accuracy of other plasma parameters.
  • Figure 1 is a schematic diagram of an electric single probe test device; 1-electric single probe, 2-vacuum chamber wall;
  • Figure 2 is the curve diagram of the experimental data of the electric single probe (I-V) according to three processing methods (ESP formula, ESP fitting, NSP fitting);
  • the abscissa is the bias voltage V applied to the single probe, and the ordinate is the total current I collected by the single probe.
  • the ESP formula line is an intuitive curve corresponding to the results measured by the traditional electric single probe using the formula method.
  • the ESP fitting line is the measurement result obtained by nonlinear fitting under the assumption that the plasma composition satisfies the Maxwell (extensive) distribution.
  • the corresponding intuitive curve, the NSP fitting line is an intuitive curve corresponding to the measurement result obtained by nonlinear fitting under the assumption that the plasma composition satisfies the non-extensive distribution.
  • Figure 3 is the I-V characteristic curve of a non-widespread electric single probe.
  • Figure 4 is the curve of the nonlinear fitting residual sum of squares with the variation of the electronic non-extensive parameter when the value of the electronic non-extensive parameter is accurate to 0.001.
  • the ordinate SSE is the sum of squared residuals.
  • Figure 5 is the curve of the nonlinear fitting determination coefficient with the electronic non-extensive parameter when the value of the electronic non-extensive parameter is accurate to 0.001.
  • the ordinate R 2 is the nonlinear fitting determination coefficient.
  • a method for measuring plasma electron non-extensive parameters using non-extensive statistical mechanics and electrical probes to measure plasma non-extensive parameters.
  • the first step is to describe the plasma by non-extensive statistical mechanics, and obtain the formula of the IV curve of the non-extensive electric single probe;
  • the second step is to collect the experimental data of the electric single probe IV, and the third step is to use the first step to obtain
  • the IV curve formula of the non-extensive electric single probe is used for nonlinear fitting of the IV experimental data of the electric single probe collected in the second step, and the fourth step is the goodness of fit The curve is shown in Figure 4.
  • the fifth step is to obtain the electronic non-extensive parameter value corresponding to the minimum SSE, and the sixth step is to determine the goodness of fit The curve is shown in Figure 5.
  • the seventh step is to obtain the electronic non-extensive parameter value corresponding to the maximum R 2.
  • the eighth step is to compare the electronic non-extensive parameters obtained in the seventh step and the fifth step.
  • the ninth step see the two results of the eighth step Check whether it is the same. Step 10. If the result of Step 9 is consistent, it is confirmed as the optimal electronic non-extensive parameter.
  • the eleventh step use the optimal electronic non-extensive parameter obtained in the tenth step and substitute it in the third step.
  • the data set in the step is to obtain the data set corresponding to the optimal electronic non-extensive parameters.
  • the measurement result report is output.
  • the probe potential When the probe potential is less than the plasma sheath potential, that is, V ⁇ p -( ⁇ B T e /2e), a positively charged sheath will be formed around the probe.
  • the current collected by the probe is the current formed by the random thermal motion of charged particles entering the sheath.
  • the electron current I e at this time is the random thermal motion current multiplied by the non-extensive exponential factor (instead of the Boltzmann factor):
  • V bias voltage ⁇ p is the plasma potential
  • ⁇ B Boltzmann's constant
  • e is the electron charge
  • T e is the electron temperature
  • n e is the electron density of the undisturbed zone
  • a p is the collection probe Area
  • a q is the normalization constant of non-extensive distribution
  • Is the non-extensive parameter of electrons in the plasma Is the average thermal movement rate of electrons in non-extensive plasma.
  • the collection of ions is based on Bohm’s sheath formation theory. There is a pre-sheath area outside the sheath.
  • the ions flowing to the probe are accelerated through the pre-sheath area from the undisturbed plasma area and reach the ion sound velocity at the edge of the sheath.
  • a s is the surface area of the sheath, when the thickness of the shell is negligible Therefore, the total current collected by the probe at this time is
  • m i is the ion mass
  • m e is the electron mass
  • the IV experimental data collected in step two is collected by a commonly used electric single probe device.
  • the electric single probe test device includes the electric single probe 1 and the vacuum chamber wall 2.
  • the surface of the electric single probe is slightly shorter.
  • An insulating tube made of ceramic, quartz or glass is wrapped, and the right end of the probe passes through the wall of the vacuum chamber to directly contact the plasma represented by random scattered points in Figure 1.
  • the invention collects I-V experimental data through the electric single probe.
  • the left end of the probe is connected to the probe circuit, and the variable power supply with the positive electrode upward is connected in series with an ammeter.
  • the ammeter measures the collected current I of the probe (the positive direction of the current is set to the direction from the probe surface to the plasma, from the electron current and the ion current It can be seen that the electron current is in the positive direction, while the ion current is in the negative direction).
  • a voltmeter connected to the wall of the grounded vacuum chamber measures the variable bias voltage applied to the single probe. Adjust the bias voltage applied by the power supply to obtain the data of the current collected by the probe under different bias voltages.
  • FIG. 2 it is a comprehensive effect diagram obtained by processing the IV experimental data of the electric single probe collected in the second step according to three methods (ESP formula, ESP fitting, NSP fitting).
  • the abscissa is the bias voltage V applied to the single probe.
  • the value range is [-39.8582,9.1489] (V).
  • the minimum value of V in the original data is -39.8582V. This minimum value determines the allowable electronic non-extension
  • the maximum value of the parameter is 1.164, and the maximum value of V is 9.1489V ( ⁇ s ), which is obtained by the method of "taking half the logarithm to see the turning point".
  • the ordinate is the total current I collected by a single probe, and the value range is -18.98, 29.97 (mA).
  • the dots are the IV experimental data used in the present invention. All data satisfying V ⁇ s are selected, and there are 50 data points in total. The other data are not the processing objects of the theory proposed by the present invention.
  • the ESP formula line is an intuitive curve corresponding to the results measured by the traditional electric single probe using the formula method.
  • the ESP fitting line is the measurement result obtained by nonlinear fitting under the assumption that the plasma composition satisfies the Maxwell (extensive) distribution.
  • the corresponding intuitive curve, the NSP fitting line is the intuitive curve corresponding to the measurement result obtained by nonlinear fitting under the assumption that the plasma composition satisfies the non-extensive distribution.
  • the three curves all conform to the single-probe measurement curve trend.
  • Fig. 3 it is the IV characteristic curve of a non-extensive electric single probe.
  • the abscissa is the variable bias voltage V applied to the single probe, and the range is (- ⁇ , + ⁇ ).
  • the present invention takes [ ⁇ p- 10 ⁇ B T e /e, ⁇ s ], where ⁇ p is the plasma potential in the undisturbed region, and the reason why the V> ⁇ p region is not selected is that "the electron saturation flow obtained in specific experiments is often not saturated, and it is difficult to rely on saturated electrons.
  • the measured value of the current is used to obtain the plasma parameters"; ⁇ p -10 ⁇ B T e /e ⁇ p belongs to the ion saturation current region; ⁇ s is the boundary potential of the ion sheath, when the bias voltage applied to the single probe drops to ⁇ At s , the surface of the probe begins to form an ion sheath; the probe bias voltage V ⁇ p -5 ⁇ B T e /e and smaller areas, most of the electrons are repelled by the probe surface electric field.
  • the ordinate is the collected current I of the probe (flowing from the surface of the probe to the plasma is the positive direction of the current), the actual situation (under the non-thin sheath approximation) value range is [I si ,+ ⁇ ), this article takes [I si , I s current collection probe], where I s is the variable bias voltage applied to the probe is single when ⁇ s, I si is the ion saturation current, corresponding to a large absolute value of negative bias voltage probe .
  • the three curves in the figure are the electronic non-extensive parameters.
  • Probe characteristic curve at 0.8, 1.0 and 1.1.
  • the curve starts from a large negative probe bias voltage and increases monotonically with the increase of the probe bias voltage, and the increasing speed is getting faster and faster.
  • there is a floating potential point ( ⁇ f , 0) in which the probe collects current I 0.
  • the current collected by the probe is the sum of the electron current and the ion current.
  • the electric field around the probe reduces the degree of suppression of the electron current in the positive direction, and suppresses the ion current in the opposite direction.
  • the nonlinear fitting residual square sum SSE varies with the electronic non-extensive parameter Curve.
  • SSE is the residual sum of squares
  • ⁇ i represents the weight of the i-th data point
  • y i represents the ordinate of the i-th data point
  • the ordinate SSE is the residual sum of squares, and its value range is [303.9174,4537.5306]au; That is, under the extended limit, the residual sum of squares (non-linear fitting) obtained by the single probe theory based on non-extensive statistical mechanics and the residual sum of squares obtained by the traditional single probe theory (non-linear fitting) Similarly, this proves that the non-extensive electric single probe theory proposed by the present invention is correct at the limit of extension.
  • the ordinate R 2 is the coefficient of determination of non-linear fitting (coefficient of determination), where its value range is [-0.2519,0.93229].
  • the non-linear fitting determination coefficient obtained by the single probe theory based on non-extensive statistical mechanics is the same as the nonlinear fitting determination coefficient obtained by the traditional single probe theory, which proves that the present invention proposes The correctness of the non-extensive electric single-probe theory at the limit of extension.
  • the curve of the non-extensive coefficients of non-extensive fitting and the variation of the electronic non-extensive parameters increases first and then decreases as a whole (with fluctuations in very few places).
  • the nonlinear fitting determination coefficient obtained by the electric single probe theory based on non-extensive statistical mechanics is the smallest in When using the electric single probe theory based on non-extensive statistical mechanics, the nonlinear fitting determination coefficient increases with the increase of the electronic non-extensive parameter, but it is less than the nonlinear fitting determined by the traditional single probe theory.
  • the nonlinear fitting determination coefficient obtained by the electric single probe theory based on non-extensive statistical mechanics is equal to the nonlinear fitting determination coefficient obtained by the traditional single probe theory;
  • the electronic non-extensive parameter increases from 0.506, and the non-linear fitting determination coefficient becomes larger and larger (there are fluctuations in very few places), until Reach the maximum certainty factor That is to say, at this time, the nonlinear fitting determination coefficient obtained by the electric single probe theory based on non-extensive statistical mechanics is the largest (closest to 1), and the fitting result is the closest to the truth; then as the electronic non-extensive parameter increases, The coefficient of determination of nonlinear fitting is getting smaller and smaller; until When the nonlinear fitting determination coefficient is the same as the nonlinear fitting determination coefficient obtained by the traditional single-probe theory, the non-extensive statistical mechanics is reduced to Boltzmann-Gibbs statistical mechanics, which is When using the non-linear fitting determination coefficient obtained from the
  • Boltzmann-Gibbs statistical mechanics is not an optimal statistical mechanics to describe the plasma system, but non-extensive statistical mechanics can be adjusted due to its one more non-extensive parameter.
  • the theory can better describe the real plasma system; here, the real plasma system is described by the non-extensive statistical mechanics with a non-extensive parameter of 0.775, which is the same as the result of the fitting method using SSE as a measure of goodness of fit (0.775 is the optimal non-extensive parameter value), which confirms the reliability of our fitting results.
  • Table 1 shows various plasma parameters obtained by the method of the present invention, which not only measures the plasma non-extensibility, but also improves the diagnostic accuracy of other plasma parameters.

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Abstract

一种测量等离子体电子非广延参数的方法，采用非广延统计力学和电单探针(1)测量等离子体非广延参数。将等离子体由非广延统计力学描述，并在此基础上建立非广延电单探针(1)测量理论，应用非广延电单探针(1)测得传统电单探针(1)无法测得的电子非广延参数，获得更精确的电子温度、等离子体电位、电子密度和悬浮电位，提高了等离子体参数的诊断精度。

Description

一种测量等离子体电子非广延参数的方法 技术领域
本发明涉及等离子体非广延参数诊断领域，具体涉及一种测量等离子体电子非广延参数的方法。
背景技术
等离子体广泛存在于宇宙中，常被视为是除去固、液、气外，物质存在的第四态。将固体加热到熔点时，粒子的平均动能超过晶格的结合能，固体会变成液体；将液体加热到沸点时，离子的动能超过粒子之间的结合能，液体会变成气体。如果进一步对气体加热，气体则部分电离或完全电离，即原子的外层电子会摆脱原子核的束缚变成自由电子，而失去外层电子的原子变成带电的离子。当带电粒子的比例超过一定程度时，电离气体就会呈现出明显的电磁性质，而其中正离子和负离子(电子)的数目相等，因此被称之为等离子体。
在等离子体参数诊断领域，许多等离子体参数(信息)由电探针诊断获得。等离子体中各成分(粒子)预设服从什么分布对电单探针测量至关重要，需要先预设待测等离子体可用什么统计力学来描述。等离子体的统计假说包括玻尔兹曼-吉布斯统计力学，在该假说中，等离子体各成分服从麦克斯韦-玻尔兹曼分布。然而，理论分析和大量实验证明等离子体各成分不满足玻尔兹曼-吉布斯统计。将等离子体视为由麦氏成分和非麦氏成分构成，可由非广延统计力学很好地描述，由此带来的描述等离子体非广延性的新等离子体参数——电子非广延参数
Figure PCTCN2020084082-appb-000001
——还无法诊断。
发明内容
针对上述无法测量等离子体非广延参数的技术问题，本发明提供一种测量等离子体电子非广延参数的方法。
本发明所采用的技术方案为：
一种测量等离子体电子非广延参数的方法，采用非广延统计力学和电探针测量等离子体非广延参数。
进一步地优选，具体步骤为：
第一步，用非广延统计力学描述等离子体，求得非广延电单探针I-V曲线公式；第二步，收集电单探针I-V实验数据，第三步，采用第一步求得的非广延电单探针I-V曲线公式对第二步收集到的电单探针I-V实验数据进行非线性拟合，第四步，作拟合优度
Figure PCTCN2020084082-appb-000002
曲线，第五步，求得最小SSE对应的电子非广延参数值，第六步，作拟合优度
Figure PCTCN2020084082-appb-000003
曲线，第七步，求得最大R 2对应的电子非广延参数值，第八步，将第七步和第五步求得的电子非广延参数对照，第九步，看第八步两结果对照是否一致，第十步，如果第九步结果为一致，则确认为最优电子非广延参数，第十一步，利用第十步求得的最优电子非广延参数，代入第三步中的数据组，得到最优电子非广延参数对应的数据组，第十二步，输出测量结果报告。
进一步地优选，所述步骤一中探针收集电流的公式为：
Figure PCTCN2020084082-appb-000004
其中：V为偏置电压，Φ p为等离子体电位，κ B为玻尔兹曼常数，e是电子电荷，T e是电子温度，n e是未扰区电子密度，A p是探针收集面积，A q为非广延分布归一化常数，
Figure PCTCN2020084082-appb-000005
是等离子体中电子的非广延参数，m i是离子质量，m e是电子质量。
本发明将等离子体由非广延统计力学描述，并在此基础上建立非广延电单探针(测量)理论。应用非广延电单探针我们测得了传统电单探针无法测得的电子非广延参数，并且获得了较传统单探针更精确的电子温度、等离子体电位、电子密度和悬浮电位。通过本发明的技术方案，非广延电探针在等离子体诊断中发挥作用，将测量等离子体非广延性，并提高其它等离子体参数的诊断精度。
附图说明
图1是电单探针测试装置示意图；1-电单探针，2-真空室壁；
图2是电单探针(I-V)实验数据按三种处理方法(ESP公式、ESP拟合、NSP拟合)所得 曲线图；
横坐标是单探针上外加偏置电压V，纵坐标是单探针收集总电流I。ESP公式线是传统电单探针采用公式法所测得的结果对应的直观曲线，ESP拟合线是在等离子体成分满足麦克斯韦(广延)分布的假设下进行非线性拟合得到的测量结果对应的直观曲线，NSP拟合线是在等离子体成分满足非广延分布的假设下进行非线性拟合得到的测量结果对应的直观曲线。
图3是非广延电单探针I-V特性曲线。
图4是电子非广延参数取值精确到0.001时非线性拟合残差平方和随电子非广延参数变化曲线。纵坐标SSE是残差平方和。
图5是电子非广延参数取值精确到0.001时非线性拟合确定系数随电子非广延参数变化曲线。纵坐标R 2是非线性拟合确定系数。
具体实施方式
下面结合附图对本发明作详细说明。
一种测量等离子体电子非广延参数的方法，采用非广延统计力学和电探针测量等离子体非广延参数。
具体步骤为：
第一步，用非广延统计力学描述等离子体，求得非广延电单探针I-V曲线公式；第二步，收集电单探针I-V实验数据，第三步，采用第一步求得的非广延电单探针I-V曲线公式对第二步收集到的电单探针I-V实验数据进行非线性拟合，第四步，作拟合优度
Figure PCTCN2020084082-appb-000006
曲线，如图4所示。第五步，求得最小SSE对应的电子非广延参数值，第六步，作拟合优度
Figure PCTCN2020084082-appb-000007
曲线，如图5所示。第七步，求得最大R 2对应的电子非广延参数值，第八步，将第七步和第五步求得的电子非广延参数对照，第九步，看第八步两结果对照是否一致，第十步，如果第九步结果为一致，则确认为最优电子非广延参数，第十一步，利用第十步求得的最优电子非广延参数，代入第三步中的数据组，得到最优电子非广延参数对应的数据 组，第十二步，输出测量结果报告。
步骤一中所述非广延电单探针I-V曲线公式通过以下过程推导：
当探针电位小于等离子体鞘电位，即V＜Φ p-(κ BT e/2e)时，探针周围将形成正电荷鞘层。探针收集电流是由随机热运动的荷电粒子进入鞘层所形成的电流。在非广延统计框架下，这时电子电流I e为随机热运动电流乘以非广延指数因子(代替玻尔兹曼因子)：
Figure PCTCN2020084082-appb-000008
其中：V为偏置电压，Φ p为等离子体电位，κ B为玻尔兹曼常数，e是电子电荷，T e是电子温度，n e是未扰区电子密度，A p是探针收集面积，A q为非广延分布归一化常数，
Figure PCTCN2020084082-appb-000009
是等离子体中电子的非广延参数，
Figure PCTCN2020084082-appb-000010
是非广延等离子体中电子的平均热运动速率。离子的收集，按Bohm的鞘层形成理论，鞘外有一预鞘区，流向探针的离子从未扰动等离子体区经预鞘区加速，并在鞘边缘达到离子声速
Figure PCTCN2020084082-appb-000011
探针表面收集到的是越过鞘边缘的离子形成的电流，称为离子饱和电流I si(＝-|I si|)。将鞘层形成的Bohm理论推广到非广延情形，有：
Figure PCTCN2020084082-appb-000012
这里A s为鞘层表面积，当壳厚度可以忽略时有
Figure PCTCN2020084082-appb-000013
故此时探针总收集电流为
Figure PCTCN2020084082-appb-000014
m i是离子质量，m e是电子质量。
步骤二中收集I-V实验数据通过常用的电单探针装置收集，如图1所示，电单探针测试装置包括电单探针1和真空室壁2，电单探针表面被略短的陶瓷、石英或玻璃材质的绝 缘管包裹着，探针右端穿过真空室壁与图1中用随机散点表示的等离子体直接接触。本发明通过电单探针收集I-V实验数据。探针左端连接着探针电路，正极向上的可变电源串联着电流表，电流表测量探针的收集电流值I(电流正方向设为从探针表面流向等离子体的方向，从电子电流和离子电流的电荷移动方向可以看出，电子电流是正方向的，而离子电流是负方向的)。与接地的真空室壁相连的电压表测量单探针上外加的可变偏置电压。调节电源所加偏置电压大小，得到不同偏置电压下探针收集电流的数据。
如图2所示，是将第二步收集的电单探针I-V实验数据按三种方法(ESP公式、ESP拟合、NSP拟合)处理所得综合效果图。横坐标是单探针上外加偏置电压V，取值范围为[-39.8582,9.1489](V)，原始数据中V最小值为-39.8582V，这个最小值决定了所允许的电子非广延参数的最大值1.164，V最大值为9.1489V(≈Φ s)，是通过“取半对数看折点”方法获得的。纵坐标是单探针收集总电流I，取值范围为-18.98,29.97(mA)。圆点是本发明中所使用的I-V实验数据，选取了满足的V≤Φ s所有数据，共50个数据点，其它的数据不是本发明提出的理论的处理对象。ESP公式线是传统电单探针采用公式法所测得的结果对应的直观曲线，ESP拟合线是在等离子体成分满足麦克斯韦(广延)分布的假设下进行非线性拟合得到的测量结果对应的直观曲线，NSP拟合线是在等离子体成分满足非广延分布的假设下进行非线性拟合得到的测量结果对应的直观曲线，三条曲线均符合单探针测量曲线趋势，在探针上外加偏置电压V≤Φ s范围内，始终随V增大而增大。从图中容易读出采用ESP公式方法测得的结果与原始数据接近程度最差。我们采用残差平方和SSE以及判定系数R 2来判断三根曲线中谁与原始数据的接近程度最高。
如图3所示，是非广延电单探针I-V特性曲线，横坐标为单探针上外加的变化的偏置电压V，范围为(-∞,+∞)，本发明取[Φ p-10κ BT e/e,Φ s]，其中Φ p是未扰区等离子体电位，未选取V＞Φ p区域的原因是“具体实验中得到的电子饱和流往往并不饱和，难于凭借饱和电子流测量值获得等离子体参数”；Φ p-10κ BT e/e＜＜Φ p属离子饱和流区；Φ s是离子鞘层 边界电位，当单探针上外加的偏置电压降低到Φ s时探针表面开始形成离子鞘层；探针偏置电压V≤Φ p-5κ BT e/e及更小的区域，绝大部分电子被探针表面电场排斥。纵坐标是探针的收集电流I(以从探针表面流向等离子体为电流正方向)，实际情形(非薄鞘近似下)取值范围为[I si,+∞)，本文取[I si,I s]，其中I s为单探针上外加的可变偏置电压为Φ s时探针收集电流，I si是离子饱和电流，对应于绝对值很大的负的探针偏置电压。当探针收集电流I＝0时，流向探针表面的电子和离子电荷通量相等，此时探针偏置电压为悬浮电位Φ f。图中的三条曲线分别是电子非广延参数
Figure PCTCN2020084082-appb-000015
为0.8,1.0和1.1时的探针特性曲线。先关注于三条曲线共有的特征，曲线从很大的负探针偏置电压开始随探针偏置电压增加而单调递增，并且递增的速度也越来越快。在探针偏置电压逐渐增加的过程中其中存在一个悬浮电位点(Φ f,0)，该点探针收集电流I＝0。探针收集电流是电子电流和离子电流之和，在探针偏置电压不断升高的过程中，探针周围的电场对正方向的电子电流的抑制程度减小，对反方向的离子电流抑制逐渐增强，造成了探针收集电流密度j p的递增；由于电子质量m e远小于离子质量m i，Φ s处的电子电流的绝对值明显大于饱和离子电流I si的绝对值，而且偏置电压对电子电流的绝对增长效应较对离子电流的明显，故递增的速度越来越快；容易得出，递增过程中存在某点电子电流与离子电流相等，使得探针收集电流I＝0。对于不同非广延参数的情况，其中非广延参数
Figure PCTCN2020084082-appb-000016
为1时，所有结论回到玻尔兹曼-吉布斯统计框架下的结果；整体无单调性。
如图4所示，是电子非广延参数取值精确到0.001时非线性拟合残差平方和SSE随电子非广延参数
Figure PCTCN2020084082-appb-000017
变化曲线。
Figure PCTCN2020084082-appb-000018
SSE是残差平方和，ω i表示第i个数据点的权重，y i表示第i个数据点的纵坐标，
Figure PCTCN2020084082-appb-000019
表示第i个数据点的横坐标对应的拟合线的纵坐标。横坐标为电子分布函数的非广延参数，取值范围为(-1,+∞)，这里取
Figure PCTCN2020084082-appb-000020
未考虑
Figure PCTCN2020084082-appb-000021
的情况是由于
Figure PCTCN2020084082-appb-000022
时总电流因子为负以及
Figure PCTCN2020084082-appb-000023
出现虚部；电子非广延参数最大值
Figure PCTCN2020084082-appb-000024
从这里可以看出非广延电单探针能处理的电子非广延参数范围(最大值)还依赖于I-V实验数据的最小偏置电压值，此处q Fe,max＝1.164。
Figure PCTCN2020084082-appb-000025
为广延极限，此种情形下的结果都回到玻尔兹曼-吉布斯统计框架下的结果。纵坐标SSE是残差平方和，其取值范围是[303.9174,4537.5306]a.u.；注意到
Figure PCTCN2020084082-appb-000026
即在广延极限下，采用基于非广延统计力学的单探针理论所得的(非线性拟合)残差平方和与采用传统单探针理论所得的(非线性拟合)残差平方和相同，这证明了本发明提出的非广延电单探针理论在广延极限时的正确性。采用基于非广延统计力学的单探针理论所得的(非线性拟合)残差平方和随电子非广延参数变化的曲线整体是先减后增的，也即非广延拟合效果先变优后变差(极个别地方有波动)。具体地说即在
Figure PCTCN2020084082-appb-000027
时取得最大(非线性拟合)残差平方和为
Figure PCTCN2020084082-appb-000028
在
Figure PCTCN2020084082-appb-000029
时，随着电子非广延参数增加，(非线性拟合)残差平方和越来越小(极个别地方有波动)，但大于采用传统单探针理论所得的(非线性拟合)残差平方和，直至
Figure PCTCN2020084082-appb-000030
时，与采用传统单探针理论所得的(非线性拟合)残差平方和313.2270a.u.相等；当
Figure PCTCN2020084082-appb-000031
时，采用基于非广延统计力学的电单探针理论所得的(非线性拟合)残差平方和仍随电子非广延参数增加而变小，直到
Figure PCTCN2020084082-appb-000032
时，(非线性拟合)残差平方和达到最小值303.9174a.u.，也即此时拟合结果最接近真实；之后(非线性拟合)残差平方和随非广延参数增加而递增，但仍小于采用传统单探针理论所得的(非线性拟合)残差平方和；直到
Figure PCTCN2020084082-appb-000033
时，(非线性拟合)残差 平方和与采用传统单探针理论所得的(非线性拟合)残差平方和相同，因为此时非广延统计力学约化为玻尔兹曼-吉布斯统计力学，也即此时采用的是同一种理论，此时两残差平方和自然相同；当
Figure PCTCN2020084082-appb-000034
时，采用基于非广延统计力学的电单探针理论所得的(非线性拟合)残差平方和相较于采用传统单探针理论所得的(非线性拟合)残差平方和要大，且随着电子非广延参数增加，大的程度由零逐渐拉大，一直到非广延参数达到最大值
Figure PCTCN2020084082-appb-000035
此时
Figure PCTCN2020084082-appb-000036
这种变化趋势数学上的原因是(非线性拟合)残差平方和SSE随电子非广延参数
Figure PCTCN2020084082-appb-000037
从0开始增加一直在优化，直至
Figure PCTCN2020084082-appb-000038
时，取得最优值303.9174a.u.，而在达到最优值之后，随着非广延参数增大则非线性拟合结果一直在变差；这种变化趋势物理上的原因：玻尔兹曼-吉布斯统计力学不是一个最优的统计力学来描述等离子体系统，而非广延统计力学由于其多一个非广延参数，从而可以调节，使得理论能更好地描述真实等离子体系统；在这里真实等离子体系统，由非广延参数为0.775的非广延统计力学描述。
如图5所示，是电子非广延参数取值精确到0.001时非线性拟合确定系数R 2随电子非广延参数
Figure PCTCN2020084082-appb-000039
变化曲线，R 2＝1-SSE/SST，SST是实验数据和均值之差的平方和，
Figure PCTCN2020084082-appb-000040
纵坐标R 2是非线性拟合确定系数(coefficient of determination)，这里其取值范围是[-0.2519,0.93229]。
Figure PCTCN2020084082-appb-000041
为广延极限，此种情形下
Figure PCTCN2020084082-appb-000042
即在广延极限下，采用基于非广延统计力学的单探针理论所得的非线性拟合确定系数与采用传统单探针理论所得的非线性拟合确定系数相同，这证明了本发明提出的非广延电单探针理论在广延极限时的正确性。采用基于非广延统计力学的单探针理论所得的非线性拟合 确定系数随电子非广延参数变化的曲线整体是先增后减(极个别地方有波动)。物理上，总体上来说即随着非广延参数从0增大到0.775，非线性拟合确定系数越接近1，拟合结果越接近真实；而随着电子非广延参数从0.775进一步增大时，拟合结果越远离真实。具体地说在q Fe→0时采用基于非广延统计力学的电单探针理论所得的非线性拟合确定系数最小为
Figure PCTCN2020084082-appb-000043
在
Figure PCTCN2020084082-appb-000044
时，采用基于非广延统计力学的电单探针理论所得的非线性拟合确定系数随电子非广延参数增大而增大，但小于采用传统单探针理论所得的非线性拟合确定系数，直到q Fe＝0.506时，采用基于非广延统计力学的电单探针理论所得的非线性拟合确定系数才与采用传统单探针理论所得的非线性拟合确定系数相等；随着电子非广延参数从0.506增加，非线性拟合确定系数越来越大(极个别地方有波动)，直到
Figure PCTCN2020084082-appb-000045
达到最大确定系数
Figure PCTCN2020084082-appb-000046
也即此时采用基于非广延统计力学的电单探针理论所得的非线性拟合确定系数最大(最接近1)，拟合结果最接近真实；之后随着电子非广延参数增大，非线性拟合确定系数越来越小；直到
Figure PCTCN2020084082-appb-000047
时，非线性拟合确定系数与采用传统单探针理论所得的非线性拟合确定系数相同，因为此时非广延统计力学约化为玻尔兹曼-吉布斯统计力学，也即此时采用的是同一种理论所得的非线性拟合确定系数，此时两个确定系数自然相同；当
Figure PCTCN2020084082-appb-000048
时，采用基于非广延统计力学的电单探针理论所得的非线性拟合确定系数相较于采用传统单探针理论所得的非线性拟合确定系数要小(更远离1)，且随着电子非广延参数增加，小的程度由零逐渐拉大，最后在
Figure PCTCN2020084082-appb-000049
时，
Figure PCTCN2020084082-appb-000050
此种变化趋势的原因：玻尔兹曼-吉布斯统计力学不是一个最优的统计力学来描述等离子体系统，而非广延统计力学由于其多一个非广延参数，从 而可以调节，使得理论能更好地描述真实等离子体系统；在这里真实等离子体系统，由非广延参数为0.775的非广延统计力学描述，这与采用SSE为拟合优度衡量的拟合方法所得结果相同(0.775为最优非广延参数值)，确证了我们拟合结果的可靠性。
结果表明采用NSP拟合方法测量到的结果在上述两种指标下都是最接近于I-V实验数据的，这证明了非广延统计力学的优越性。值得一提的是，I-V测量数据蕴含的系统的非广延性可由基于非广延统计力学的NSP拟合方法给出的最优电子非广延参数反映，这正是本发明提出的非广延电单探针的最重要功能，此处我们测得的最优电子非广延参数值为0.775。
以下表1为通过本发明的方法得出的各项等离子体参数，不仅测量了等离子体非广延性，并提高其它等离子体参数的诊断精度。
Figure PCTCN2020084082-appb-000051
表1
以上所述仅表达了本发明的优选实施方式，其描述较为具体和详细，但并不能因此而理解为对本发明专利范围的限制。应当指出的是，对于本领域的普通技术人员来说，在不脱离本发明构思的前提下，还可以做出若干变形、改进及替代，这些都属于本发明的保护 范围。因此，本发明专利的保护范围应以所附权利要求为准。

Claims (3)

  1. 一种测量等离子体电子非广延参数的方法，其特征在于，采用非广延统计力学和电探针测量等离子体非广延参数。
  2. 根据权利要求1所述的一种测量等离子体电子非广延参数的方法，其特征在于，具体步骤为：
    第一步，用非广延统计力学描述等离子体，求得非广延电单探针I-V曲线公式；第二步，收集电单探针I-V实验数据；第三步，采用第一步求得的非广延电单探针I-V曲线公式对第二步收集到的电单探针I-V实验数据进行非线性拟合；第四步，作拟合优度
    Figure PCTCN2020084082-appb-100001
    曲线；第五步，求得最小SSE对应的电子非广延参数值；第六步，作拟合优度
    Figure PCTCN2020084082-appb-100002
    曲线；第七步，求得最大R 2对应的电子非广延参数值；第八步，将第七步和第五步求得的电子非广延参数对照；第九步，看第八步两结果对照是否一致；第十步，如果第九步结果为一致，则确认为最优电子非广延参数；第十一步，利用第十步求得的最优电子非广延参数，代入第三步中的数据组，得到最优电子非广延参数对应的数据组；第十二步，输出测量结果报告。
  3. 根据权利要求1所述的一种测量等离子体电子非广延参数的方法，其特征在于，所述步骤一中探针收集电流的公式为：
    Figure PCTCN2020084082-appb-100003
    其中：V为偏置电压，Φ p为等离子体电位，κ B为玻尔兹曼常数，e是电子电荷，T e是电子温度，n e是未扰区电子密度，A p是探针收集面积，A q为非广延分布归一化常数，q Fe是等离子体中电子的非广延参数，m i是离子质量，m e是电子质量。
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