CN104216000B - It is a kind of to be used for neutron Soller collimators divergent angle test method - Google Patents
It is a kind of to be used for neutron Soller collimators divergent angle test method Download PDFInfo
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Abstract
The invention discloses a kind of be used for neutron Soller collimators divergent angle test method, comprise the steps:Choose Gaussian function to be used for describing neutron source angular divergence distribution function and neutron transmission collimator angular divergence receptance function, neutron source angular divergence distribution function and neutron transmission collimator angular divergence receptance function are carried out into mathematic integral and forms shake curve representation formula;Then experiment measurement obtains the neutron shake curve experiments data that neutron intensity changes with waving angle by neutron Soller collimators to be measured, after with reference to neutron Soller collimators;Data fitting is carried out to shake curve experiments data followed by shake curve representation formula to obtain shaking curve standard error;It is calculated the angle of divergence of neutron Soller collimators to be measured.The present invention need not limit the spread angle range of neutron source, can be optional with reference to the collimator angle of divergence in test process, relative to 5 order polynomials of 6 undetermined parameters, and convenient in the range of certain error can estimate the collimator angle of divergence to be measured.
Description
Technical field
The present invention relates to Neutron scattering technology, is used for neutron Soller collimators angle of divergence test side more particularly, to a kind of
Method.
Background technology
Neutron Soller collimators are a kind of dispersion angles for being mainly used in restriction neutron streaming so as to collimated neutron bean stream
Instrument, need in use its angle of divergence is tested and analyzed during sub- Soller collimators.
The method for testing and analyzing of the existing neutron Soller collimators angle of divergence sets up mathematical modulo according to experimental configuration first
Type, then carries out Theoretical Calculation and obtains describing the shake curve receptance function of experimental data, finally using theoretical shake curve letter
Number fitting experimental data obtains the angle of divergence exact numerical of collimator;Its Theoretical Calculation part is based primarily upon two models, neutron
Source is described using parabolic function, and collimator angular divergence function is described using symmetrical linear distributed function, and final fitting is real
The shake curve theory function for testing data is quintic algebra curve.
The method needs the spread angle range in certain neutron source, so needing to be limited in necessarily the neutron source angle of divergence
In the range of could use, and with reference to collimator the angle of divergence need it is consistent with the collimator angle of divergence to be measured can just carry out test point
Analysis, the shake curve theory function of final fitting experimental data is quintic algebra curve, so test result is more complicated, and nothing
Method estimates the collimator angle of divergence to be measured in the range of certain error, so with certain room for improvement.
In view of drawbacks described above, creator of the present invention passes through prolonged research and practice obtains this creation finally.
The content of the invention
It is an object of the present invention to provide a kind of be used for neutron Soller collimators divergent angle test method, its feature exists
In:Comprise the steps:
Step 1, using Gauss type function describing neutron source angular divergence distribution function and neutron transmission collimator angular divergence
Then the neutron source angular divergence distribution function and the neutron transmission collimator angular divergence receptance function are carried out by receptance function
Mathematic integral forms shake curve representation formula formula;
Step 2, experiment measurement obtain shake curve experiments data, and according to shake curve representation formula formula to being shaken
Moving curve experimental data is fitted, and obtains shake curve standard error;
Step 3, curve standard error, neutron source standard error and neutron Soller collimators are referred to using the shake
Angle of divergence standard error, is calculated neutron Soller collimators standard error to be measured;
Step 4, using the neutron Soller collimators standard error to be measured, be calculated neutron Soller to be measured collimation
The angle of divergence of device.
Preferably, in the step 1, the neutron source angular divergence distribution functionWherein x
For the angle of divergence, I0For the angle of divergence x=0 when ISThe value of (x);
The neutron transmission collimator angular divergence receptance functionWherein x is the angle of divergence, and T is
The absorbance of neutron Soller collimators;
It is described shake curve representation formula formula be:
Wherein, when A is angle of divergence x=0, measure the neutron streaming intensity for obtaining;
Wherein, T1(x- γ, σ1) for neutron transmission collimator angular divergence receptance function to be measured, specially:T10For the absorbance of neutron Soller collimators to be measured;
Wherein, T2(γ, σ2) it is with reference to neutron transmission collimator angular divergence receptance function, specially:T20It is the absorbance with reference to neutron Soller collimators;
Wherein, Is(γ, σs) for the neutron source angular divergence distribution function, specially:
Wherein, σs+1+2To shake curve standard error.
Preferably, in the step 3, shake curve standard error expression is:
σ1For the standard error of the neutron Soller collimators to be measured;σsFor the neutron source angle of divergence standard error;σ2
For the standard error of the reference neutron Soller collimators;
UtilizeExpression formula and known neutron source standard error σs, with reference to neutron Soller collimators dissipate footmark
Quasi- error σ2, it is calculated neutron Soller collimators standard error σ to be measured1。
Preferably, the step 4 is specifically, using the halfwidth formula and the neutron Soller described to be measured for trying to achieve
Collimator standard error is calculated the angle of divergence of the neutron Soller collimators to be measured, and the halfwidth formula is:
Γ=2.355 σ1;
Wherein, Γ is the angle of divergence of neutron Soller collimators to be measured.
Preferably, the shake curved measurement process is:Change neutron Soller collimators axis to be measured and neutron beam
The horizontal sextant angle of stream centrage, under the different angles of record, corresponding neutron passes through neutron Soller collimators to be measured and refers to neutron
Beam intensity value after Soller collimators, obtains neutron intensity with the distribution curve between waving angle, as described shake
Curve.
Preferably, the neutron source angle of divergence standard error is determined by neutron source emitter performance itself, and the ginseng
The standard error for examining neutron Soller collimators is determined by the reference neutron Soller collimators performance.
Preferably, angle of divergence x can use any real number in the expression formula, interval need not be limited.
Compared with the prior art the beneficial effects of the present invention is:The spread angle range of neutron source need not be limited, was tested
Can be optional with reference to the collimator angle of divergence in journey, relative to 5 order polynomials of 6 undetermined parameters, the shake that the present invention is obtained is bent
Line expression formula is further simplified as the Gaussian function of 2 undetermined parameters, and expression formula is more succinct directly perceived, and necessarily can miss
It is convenient in difference scope to estimate the collimator angle of divergence to be measured.
Description of the drawings
Fig. 1 is the flow chart of the present invention;
Fig. 2 is the test schematic diagram of the present invention.
Specific embodiment
It is below in conjunction with accompanying drawing, above-mentioned to the present invention to be described in more detail with other technical characteristic and advantage.
As shown in Figure 1 and Figure 2, according to experimental configuration, rational mathematical model is chosen, for describing neutron source angular divergence point
Cloth function and neutron transmission collimator angular divergence receptance function, wherein, neutron source angular divergence distribution function and neutron transmission are accurate
Straight device angular divergence receptance function is described using Gauss type function;Matched somebody with somebody based on the mathematical model and specific experimental program chosen
Put, carry out mathematical calculation analysis, obtain the pure mathematics expression formula of final shake curve, then obtain shaking curve theory letter
Number.
The shake curve that present invention analysis is obtained is Gauss type function;Actual measurement is carried out according to experimental program, is shaken
The experimental data of moving curve, carries out data fitting with pure mathematics expression formula, obtains shake curve standard error;It is bent using shake
Line standard error expression and known neutron source standard error and collimator angle of divergence standard error is referred to, be calculated to be measured
Collimator standard error;Using the collimator angle of divergence and the relationship of standard error, collimator diverging to be measured is calculated
Angle Γ;Detailed process is as follows:
1st, neutron source angular divergence distribution function is that describing, its formula is using Gauss type function
Wherein x be the angle of divergence, I0For the angle of divergence x=0 when ISX the value of (), in the expression formula, angle of divergence x can use any real number, without the need for limiting
Interval.
2nd, neutron transmission collimator angular divergence receptance function is also that describing, its formula is using Gauss type functionWherein x is the angle of divergence, and T is the absorbance of neutron Soller collimators (hereinafter referred to as collimator),
Determined by the performance parameter of collimator itself, angle of divergence x can use any real number in the expression formula, interval need not be limited.
3rd, neutron processes the shake curve table for finally giving by mathematical calculation through collimator to be measured with reference to collimator
Up to formula it is:(obtaining neutron intensity with the distribution curve between waving angle, as shake curve)
Wherein,
T10For the absorbance of collimator to be measured;
T20It is the absorbance with reference to collimator;
When A is angle of divergence x=0, Is+1+2Beam intensity;
σ1For the standard error of collimator to be measured, computer fitting need to be passed through;σsFor neutron source angle of divergence standard error, σ2
It is the standard error with reference to collimator, which is determined by instrument performance itself.
4th, experiment measurement obtains actual shake curve experiments data, using Is+1+2X () expression formula (1) is carried out to experimental data
Fitting, obtains shake curve standard error σs+1+2;Shaking curved measurement process is:Change collimator axis to be measured and neutron beam
The horizontal sextant angle of stream centrage, under the different angles of record, corresponding neutron passes through collimator to be measured and with reference to the line after collimator
Intensity level, obtains neutron intensity with the distribution curve between waving angle, as shakes curve.
5th, utilizeExpression formula (2) and known neutron source standard error σs, with reference to collimator angle of divergence standard error
σ2, it is calculated collimator standard error σ to be measured1。
6th, using the halfwidth formula Γ=FWHM=2.355 σ of shake curve, it is calculated collimator angle of divergence Γ to be measured.
Following table is two kinds of mathematical model contrasts of the method for the invention and traditional method:
Wherein:
Neutron source angular divergence distribution function of the present invention is described using Gauss type function, and x is the angle of divergence,In the expression formula, angle of divergence x can use any real number, need not limit interval;And traditional method
In provide neutron source angular divergence distribution function Is=I0(1-cx2), it is parabola shaped distribution, as neutron intensity can not possibly be negative
Value so that in the reasonable scope, i.e., angular range must limit in the expression formulaThus derive and can obtainDuring i.e. using the theoretical model of traditional method come analysis measurement data, it is desirable to the divergence of neutron source with treat
Survey collimator divergence and need to meet conditionIf the divergence of neutron source is too little, the theoretical model is just not
It is suitable for, and the method for the present invention then not no restrictive condition.
The present invention be can be seen that by above-mentioned implementation process can be optional with reference to the collimator angle of divergence in test process, and
The theoretical expression of traditional method is required must be consistent with the collimator angle of divergence to be measured with reference to the collimator angle of divergence, so in reality
In measurement process, the inventive method is just relatively more flexible in the selection with reference to collimator, convenient experiment measurement;Collimation such as to be measured
Device only has one, does not have an extra same collimator to refer to, just can not measure analysis using traditional method, and
The inventive method is not then limited by this condition.
As can be seen that undetermined relative to 6 from the method for the invention with the two of traditional method kinds of mathematical model contrasts
5 order polynomials of parameter, shake the Gaussian function that curve representation formula is further simplified as 2 undetermined parameters, the angle of divergence and half height
Wide directly correspondence, expression formula result are more succinct directly perceived.
And the present invention convenient in the range of certain error can estimate the collimator angle of divergence to be measured, according to implementation process point
Analysis, the neutron source angle of divergence and the collimator angle of divergence to be measured and has fixed relationship with reference to the collimator angle of divergence, and physical relationship isIn general, angle of divergence Γ of neutron sourcesIt is relatively large, it is contemplated that collimator to be measured and ginseng
Examine the collimator angle of divergence it is consistent in the case of analytical calculation shake curve halfwidth Γ=FWHM=2.355 σ, such as neutron source send out
When scattered angle is with reference to 3 times of sizes of the collimator angle of divergence, i.e. Γs/Γ2=3, final shake curve halfwidth Γ=FWHM=2.355
If σ ignores the impact of neutron source when calculating, its expression formula can be reduced toResult of calculation and consideration after simplification
The impact result of calculation relative deviation of neutron source is 2.60%, and other similar result of calculations see the table below;Work as Γs/Γ2>=5, ignore
The impact of the neutron source angle of divergence, within 1%, reality is measured when analyzing result of calculation relative deviation, if substantially understood
The angle of divergence numerical value of neutron source, it is possible to rationally estimate measurement result in certain error.
Different neutron source angle of divergence correspondence shake Dependence Results statistical tables:
And in the present invention compared with traditional method, its error analysis is as follows;
1st, the impact of neutron source is not considered, it is assumed that the neutron source angle of divergence is much larger than collimator angle of divergence Γ, traditional method institute
The collimator transmission angular distribution function of two triangular shape distributions, its shake curvilinear function is the convolution of two distribution functions,
As a result it is:
Numerical computation method provides its halfwidth for 1.44 Γ;
As a result or Gauss type function analyzed using the inventive method, shake the convolution that curve is two Gaussian functions,;Its
Shaking curve halfwidth isCompared with traditional method, its relative deviation is 1.81%.
2nd, traditional method provides specific experiment parameter Γ=2.94 × 10-3=10.11', c=1.8 × 104, by its introduction
Theoretical formula method, shake curve Is+1+2X () halfwidth measurement result is:FWHM=14.43'=1.43 Γ;
Formula according to the present invention is calculated, and neutron source full width at half maximum isShake curve
Is+1+2X () halfwidth result is FWHM=14.03'=1.39 Γ;The inventive method analysis result with respect to result by references deviation is
2.77%.
3rd, a kind of collimator shake curved measurement analysis result in the conventional way for theoretical foundation, wherein c=1.34 ×
104, Г=10.72 ', neutron source full width at half maximumTraditionally disclosed formula meter
Calculate, shake curve Is+1+2X () halfwidth measurement result is:FWHM=15.35'=1.43 Γ.
Calculate by the formula of the present invention, shake curve Is+1+2X () halfwidth measurement result is FWHM=14.93'=1.39
Γ, the inventive method analysis result are 2.73% with respect to result by references deviation.
4th, following table provides the common collimator angle of divergence under different neutron source transmitting cases, the inventive method and traditional method
Shake curve halfwidth result of calculation and both relative deviation, Γs+1+2- new is that the inventive method shakes curve halfwidth
Result of calculation, Γs+1+2The shake curve halfwidth result of calculations of-ref for traditional method;
The common collimator angle of divergence is in different neutron source transmitting case statistical tables:
Can be seen that in most cases by data in table, the relative deviation of two methods is below 4%;In neutron source
In the case that the angle of divergence is certain, the collimator angle of divergence is less, and relative deviation is less;In the case where the collimator angle of divergence is certain,
The neutron source angle of divergence is bigger, and relative deviation is less.
Presently preferred embodiments of the present invention is the foregoing is only, is merely illustrative for the purpose of the present invention, and it is non-limiting
's.Those skilled in the art understanding, can carry out many changes to which in the spirit and scope limited by the claims in the present invention,
Modification, in addition it is equivalent, but fall within protection scope of the present invention.
Claims (5)
- It is 1. a kind of to be used for neutron Soller collimators divergent angle test method, it is characterised in that:Comprise the steps:Step 1, using Gauss type function come describe neutron source angular divergence distribution function and the angular divergence of neutron transmission collimator response Then the neutron source angular divergence distribution function and the neutron transmission collimator angular divergence receptance function are carried out mathematics by function Integration forms shake curve representation formula formula;Step 2, experiment measurement obtain shake curve experiments data, and bent to the shake for obtaining according to shake curve representation formula formula Line experimental data is fitted, and obtains shake curve standard error;Step 3, using it is described shake curve standard error, neutron source standard error and with reference to neutron Soller collimators diverging Angle standard error, is calculated neutron Soller collimators standard error to be measured;Step 4, using the neutron Soller collimators standard error to be measured, be calculated neutron Soller collimators to be measured The angle of divergence;In the step 1, the neutron source angular divergence distribution functionWherein x be the angle of divergence, I0For I during angle of divergence x=0SThe value of (x);The neutron transmission collimator angular divergence receptance functionWherein x is the angle of divergence, and T is neutron The absorbance of Soller collimators;It is described shake curve representation formula formula be:Wherein, when A is angle of divergence x=0, measure the neutron streaming intensity for obtaining;Wherein, T1(x- γ, σ1) for neutron transmission collimator angular divergence receptance function to be measured, specially:T10For the absorbance of neutron Soller collimators to be measured;Wherein, T2(γ, σ2) it is with reference to neutron transmission collimator angular divergence receptance function, specially:T20It is the absorbance with reference to neutron Soller collimators;Wherein, Is(γ, σs) for the neutron source angular divergence distribution function, specially:Wherein, σs+1+2To shake curve standard error;In the step 3, shake curve standard error expression is:σ1For the standard error of the neutron Soller collimators to be measured;σsFor the neutron source angle of divergence standard error;σ2For institute State the standard error with reference to neutron Soller collimators;UtilizeExpression formula and known neutron source standard error σs, with reference to neutron Soller collimators angle of divergence standard error σ2, it is calculated neutron Soller collimators standard error σ to be measured1。
- 2. neutron Soller collimators divergent angle test method is used for as described in claim 1, it is characterised in that the step Rapid 4 specifically, be calculated institute using halfwidth formula and the neutron Soller collimators standard error described to be measured tried to achieve The angle of divergence of neutron Soller collimators to be measured is stated, the halfwidth formula is:Γ=2.355 σ1;Wherein, Γ is the angle of divergence of neutron Soller collimators to be measured.
- 3. neutron Soller collimators divergent angle test method is used for as described in claim 1, it is characterised in that:It is described to shake Moving curve measurement process is:Change the horizontal sextant angle of neutron Soller collimators axis to be measured and neutron streaming centrage, remember Under the different angles of record, corresponding neutron passes through neutron Soller collimators to be measured and with reference to the line after neutron Soller collimators Intensity level, obtains neutron intensity with the distribution curve between waving angle, as described shake curve.
- 4. neutron Soller collimators divergent angle test method is used for as described in claim 1, it is characterised in that:In described Component angle of divergence standard error is determined by neutron source emitter performance itself, and the mark of the reference neutron Soller collimators Quasi- error is determined by the reference neutron Soller collimators performance.
- 5. neutron Soller collimators divergent angle test method is used for as described in claim 1, it is characterised in that:The table Up in formula, angle of divergence x can use any real number, need not limit interval.
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CN105319575A (en) * | 2015-12-04 | 2016-02-10 | 中国原子能科学研究院 | Neutron performance testing device of neutron collimator |
CN109212585B (en) * | 2018-07-26 | 2023-09-01 | 东莞材料基因高等理工研究院 | Testing method and device for detecting embedded angle distribution of neutron monochromator |
CN109659061B (en) * | 2018-12-27 | 2020-06-23 | 中国原子能科学研究院 | Neutron collimator structure with continuously adjustable divergence angle and calibration method thereof |
CN109671513B (en) * | 2018-12-27 | 2020-06-23 | 中国原子能科学研究院 | Neutron collimator structure with continuously adjustable divergence angle and calibration method thereof |
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