CN104216000A - Method for testing divergence angle of neutron Soller collimator - Google Patents

Method for testing divergence angle of neutron Soller collimator Download PDF

Info

Publication number
CN104216000A
CN104216000A CN201410443111.XA CN201410443111A CN104216000A CN 104216000 A CN104216000 A CN 104216000A CN 201410443111 A CN201410443111 A CN 201410443111A CN 104216000 A CN104216000 A CN 104216000A
Authority
CN
China
Prior art keywords
neutron
mrow
collimator
msub
divergence
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201410443111.XA
Other languages
Chinese (zh)
Other versions
CN104216000B (en
Inventor
陈东风
刘蕴韬
高建波
孙凯
王洪立
韩松柏
刘新智
李玉庆
郝立杰
李峻宏
肖红文
李眉娟
李天富
王子军
吴立齐
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
China Institute of Atomic of Energy
Original Assignee
China Institute of Atomic of Energy
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by China Institute of Atomic of Energy filed Critical China Institute of Atomic of Energy
Priority to CN201410443111.XA priority Critical patent/CN104216000B/en
Publication of CN104216000A publication Critical patent/CN104216000A/en
Application granted granted Critical
Publication of CN104216000B publication Critical patent/CN104216000B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Landscapes

  • Analysing Materials By The Use Of Radiation (AREA)

Abstract

The invention discloses a method for testing divergence angle of a neutron Soller collimator. The method includes the steps of selecting a Gaussian function to describe an angular divergence distribution function of a neutron source and an angular divergence response function of a neutron transmission collimator, subjecting the angular divergence distribution function of the neutron source and the angular divergence response function of the neutron transmission collimator to mathematical integration to form a rocking curve expression; performing experimental measurement to obtain experimental data of rocking curves of neutron intensity changing with the rocking angle after neutrons pass the to-be-tested neutron Soller collimator and a reference neutron Soller collimator; subjecting the experimental data of the rocking curves to data fitting through the rocking curve expression so as to obtain a rocking curve standard error; calculating a divergence angle of the to-be-tested neutron Soller collimator. The method has the advantages that the divergence angle range of a neutron source need not be limited, the divergence angle of the reference collimator is optional in the testing process, relative to a quantic polynomial of 6 undetermined parameters, and the divergence angle of the to-be-tested collimator can be conveniently estimated in a certain error range.

Description

Method for testing divergence angle of neutron Soller collimator
Technical Field
The invention relates to a neutron scattering technology, in particular to a method for testing a divergence angle of a neutron Soller collimator.
Background
The neutron Soller collimator is an instrument mainly used for limiting the divergence angle of a neutron beam so as to collimate the neutron beam, and the divergence angle of the neutron Soller collimator needs to be tested and analyzed when the neutron Soller collimator is used.
The existing method for testing and analyzing the divergence angle of the neutron Soller collimator comprises the steps of firstly establishing a mathematical model according to experimental configuration, then carrying out theoretical calculation to obtain a rocking curve response function for describing experimental data, and finally fitting the experimental data by using the theoretical rocking curve function to obtain an accurate numerical value of the divergence angle of the collimator; the theoretical calculation part is mainly based on two models, a neutron source is described by adopting a parabolic function, an angle divergence function of a collimator is described by adopting a symmetrical linear distribution function, and a rocking curve theoretical function for finally fitting experimental data is a quintic polynomial.
The method needs to be within a certain neutron source divergence angle range, so the neutron source divergence angle needs to be limited within a certain range to be used, the divergence angle of the reference collimator needs to be consistent with the divergence angle of the collimator to be tested to perform test analysis, and finally the rocking curve theoretical function of fitting experimental data is a quintic polynomial, so the test result is relatively complex, the divergence angle of the collimator to be tested cannot be estimated within a certain error range, and a certain improvement space is provided.
In view of the above-mentioned drawbacks, the present inventors have finally obtained the present creation through a long period of research and practice.
Disclosure of Invention
The invention aims to provide a method for testing the divergence angle of a neutron Soller collimator, which is characterized by comprising the following steps of: the method comprises the following steps:
step 1, describing a neutron source angle divergence distribution function and a neutron transmission collimator angle divergence response function by adopting a Gaussian function, and then performing mathematical integration on the neutron source angle divergence distribution function and the neutron transmission collimator angle divergence response function to form a general formula of a rocking curve expression;
step 2, obtaining shaking curve experimental data through experimental measurement, and fitting the obtained shaking curve experimental data according to a shaking curve expression formula to obtain a shaking curve standard error;
step 3, calculating to obtain the standard error of the Soller collimator of the neutrons to be detected by utilizing the standard error of the rocking curve, the standard error of the neutron source and the standard error of the divergence angle of the reference Soller collimator of the neutrons;
and 4, calculating to obtain the divergence angle of the neutron Soller collimator to be detected by using the standard error of the neutron Soller collimator to be detected.
Preferably, in step 1, the neutron source angular divergence distribution functionWherein x is the angle of divergence, I0When the divergence angle x is equal to 0, IS(x) A value of (d);
the neutron transmission collimator angular divergence response functionWherein x is the divergence angle and T is the transmittance of the neutron Soller collimator;
the general expression formula of the rocking curve is as follows:
<math> <mrow> <msub> <mi>I</mi> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&Integral;</mo> <msub> <mi>I</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>T</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>T</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mi>d&gamma;</mi> <mo>=</mo> <mi>A exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mi>x</mi> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
when the divergence angle x is 0, measuring the obtained neutron beam intensity;
wherein, T1(x-γ,σ1) The method is a neutron transmission collimator angle divergence response function to be measured, and specifically comprises the following steps:T10the transmittance of the Soller collimator of the neutron to be measured;
wherein, T2(γ,σ2) The method is a reference neutron transmission collimator angle divergence response function, and specifically comprises the following steps:T20is the transmission of a reference neutron Soller collimator;
wherein, Is(γ,σs) The method is characterized in that the angle divergence distribution function of the neutron source is as follows: <math> <mrow> <msub> <mi>I</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mi>&gamma;</mi> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&sigma;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
wherein σs+1+2Standard error for the rocking curve.
Preferably, in step 3, the shaking curve standard error expression is as follows: <math> <mrow> <msubsup> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msubsup> <mi>&sigma;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>&sigma;</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>&sigma;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>;</mo> </mrow> </math>
σ1the standard error of the neutron Soller collimator to be detected is obtained; sigmasIs the standard error of the divergence angle of the neutron source; sigma2Is the standard error of the reference neutron Soller collimator;
by usingExpression and known standard error sigma of neutron sourcesReference neutron Soller collimator divergence angle standard error sigma2And calculating to obtain standard error sigma of the Soller collimator of the neutron to be measured1
Preferably, in the step 4, the divergence angle of the neutron Soller collimator to be measured is calculated by using the full width at half maximum formula and the obtained standard error of the neutron Soller collimator to be measured, where the full width at half maximum formula is:
Γ=2.355σ1
wherein gamma is the divergence angle of the Soller collimator of the neutron to be measured.
Preferably, the rocking curve measuring process is as follows: changing a horizontal included angle between the central axis of the neutron Soller collimator to be tested and the central line of the neutron beam, recording beam intensity values of neutrons corresponding to different included angles after the neutrons pass through the neutron Soller collimator to be tested and the reference neutron Soller collimator, and obtaining a distribution curve of the neutron intensity along with the shaking angle, namely the shaking curve.
Preferably, the standard error of the neutron source divergence angle is determined by the performance of the neutron source emitter itself, and the standard error of the reference neutron Soller collimator is determined by the performance of the reference neutron Soller collimator.
Preferably, the divergence angle x in the expression can be any real number, and a value interval is not required to be limited.
Compared with the prior art, the invention has the beneficial effects that: the divergence angle range of a neutron source does not need to be limited, the divergence angle of a reference collimator can be selected optionally in the test process, and compared with a 5-degree polynomial of 6 undetermined parameters, the rocking curve expression obtained by the invention is further simplified into a Gaussian function of 2 undetermined parameters, the expression is simpler and more visual, and the divergence angle of the collimator to be tested can be conveniently estimated in a certain error range.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of the test of the present invention.
Detailed Description
The above and further features and advantages of the present invention are described in more detail below with reference to the accompanying drawings.
As shown in fig. 1 and 2, according to the experimental configuration, a reasonable mathematical model is selected to describe a neutron source angle divergence distribution function and a neutron transmission collimator angle divergence response function, wherein the neutron source angle divergence distribution function and the neutron transmission collimator angle divergence response function are both described by adopting gaussian functions; and (4) performing mathematical calculation analysis based on the selected mathematical model and the specific experimental scheme configuration to obtain a theoretical mathematical expression of the final rocking curve, and then obtaining a theoretical function of the rocking curve.
The shaking curve obtained by the analysis of the invention is a Gaussian function; carrying out actual measurement according to the experimental scheme to obtain experimental data of the rocking curve, and carrying out data fitting with a theoretical mathematical expression to obtain a standard error of the rocking curve; calculating to obtain the standard error of the collimator to be measured by using a rocking curve standard error expression, the known standard error of the neutron source and the known standard error of the divergence angle of the reference collimator; calculating to obtain the divergence angle gamma of the collimator to be measured by utilizing a mathematical relation between the divergence angle of the collimator and a standard error; the specific process is as follows:
1. the angle divergence distribution function of the neutron source is described by adopting a Gaussian function with the formulaWherein x is the angle of divergence, I0When the divergence angle x is equal to 0, IS(x) The value of (3) can be any real number in the expression, and the value interval is not required to be limited.
2. The angular divergence response function of the neutron transmission collimator is also described by adopting a Gaussian function with the formulaWherein x is a divergence angle, and T is the transmissivity of a neutron Soller collimator (hereinafter referred to as a collimator), that is, the transmission is determined by the performance parameters of the collimator, and the divergence angle x in the expression can be any real number without limiting a value interval.
3. The neutron passes through the collimator to be measured, refers to the collimator, and the shaking curve expression finally obtained through mathematical calculation processing is as follows: (obtaining a distribution curve of neutron intensity along with shaking angle, i.e. a shaking curve)
<math> <mrow> <msub> <mi>I</mi> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&Integral;</mo> <msub> <mi>I</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>T</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>T</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mi>d&gamma;</mi> <mo>=</mo> <mi>A exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mi>x</mi> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>
Wherein, <math> <mrow> <msub> <mi>I</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mi>&gamma;</mi> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&sigma;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
<math> <mrow> <msub> <mi>T</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>T</mi> <mn>10</mn> </msub> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <mi>&gamma;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mrow> <mn>2</mn> <mi>&sigma;</mi> </mrow> <mn>1</mn> <mn>2</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> T10the transmittance of the collimator to be measured;
T20is the transmittance of the reference collimator;
when A is divergence angle x ═ 0, Is+1+2The beam intensity of (a);
σ1fitting the standard error of the collimator to be measured by a computer; sigmasStandard error of divergence angle of neutron source, sigma2The standard error of the collimator is taken as a reference, and is determined by the performance of the instrument.
<math> <mrow> <msubsup> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msubsup> <mi>&sigma;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>&sigma;</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>&sigma;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>
4. Obtaining actual shaking curve experimental data by experimental measurement, and utilizing Is+1+2(x) Fitting the experimental data by the expression (1) to obtain a standard error sigma of the rocking curves+1+2(ii) a The rocking curve measurement procedure was: changing a horizontal included angle between the central axis of the collimator to be tested and the central line of the neutron beam, recording beam intensity values of corresponding neutrons under different included angles after the neutrons pass through the collimator to be tested and the reference collimator, and obtaining a distribution curve of the neutron intensity along with the shaking angle, namely a shaking curve.
5. By usingExpression (2) and standard error sigma of known neutron sourcesReference collimator divergence angle standard error σ2And calculating to obtain standard error sigma of the collimator to be measured1
6. And calculating the divergence angle gamma of the collimator to be measured by using the full width at half maximum formula gamma of the rocking curve FWHM 2.355 sigma.
The following table shows two mathematical models comparing the method of the invention with the conventional method:
wherein:
<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msubsup> <mrow> <mo>[</mo> <msub> <mi>I</mi> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mrow> <mo>-</mo> <mn>2</mn> <mi>&Gamma;</mi> </mrow> <mrow> <mo>-</mo> <mi>&Gamma;</mi> </mrow> </msubsup> <mo>=</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <msup> <mrow> <mo>(</mo> <mi>T</mi> <mo>/</mo> <mi>&Gamma;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>[</mo> <msup> <mrow> <mn>4</mn> <mi>&Gamma;</mi> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>4</mn> <mi>c</mi> <msup> <mi>&Gamma;</mi> <mn>5</mn> </msup> <mo>/</mo> <mn>15</mn> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <mi>x</mi> <mrow> <mo>(</mo> <mn>2</mn> <msup> <mi>&Gamma;</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <mi>c</mi> <msup> <mi>&Gamma;</mi> <mn>4</mn> </msup> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>&Gamma;</mi> <mo>-</mo> <msup> <mi>c&Gamma;</mi> <mn>3</mn> </msup> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mo>+</mo> <msup> <mi>x</mi> <mn>3</mn> </msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>/</mo> <mn>6</mn> <mo>-</mo> <mn>5</mn> <mi>c</mi> <msup> <mi>&Gamma;</mi> <mn>2</mn> </msup> <mo>/</mo> <mn>6</mn> <mo>)</mo> </mrow> <mo>-</mo> <msup> <mi>x</mi> <mn>4</mn> </msup> <mi>c&Gamma;</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <msup> <mi>x</mi> <mn>5</mn> </msup> <mi>c</mi> <mo>/</mo> <mn>20</mn> <mo>]</mo> </mtd> <mtd> <mo>-</mo> <mn>2</mn> <mi>&Gamma;</mi> <mo>&le;</mo> <mi>x</mi> <mo>&le;</mo> <mo>-</mo> <mi>&Gamma;</mi> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math>
<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msubsup> <mrow> <mo>[</mo> <msub> <mi>I</mi> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mrow> <mo>-</mo> <mi>&Gamma;</mi> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <msup> <mrow> <mo>(</mo> <mi>T</mi> <mo>/</mo> <mi>&Gamma;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>[</mo> <mn>2</mn> <msup> <mi>&Gamma;</mi> <mn>3</mn> </msup> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mi>c</mi> <msup> <mi>&Gamma;</mi> <mn>5</mn> </msup> <mo>/</mo> <mn>15</mn> <mo>-</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mi>&Gamma;</mi> </mtd> </mtr> <mtr> <mtd> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mo>-</mo> <msup> <mi>x</mi> <mn>3</mn> </msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>-</mo> <mi>c</mi> <msup> <mi>&Gamma;</mi> <mn>2</mn> </msup> <mo>/</mo> <mn>6</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>x</mi> <mn>4</mn> </msup> <mi>c&Gamma;</mi> <mo>/</mo> <mn>3</mn> <mo>+</mo> <msup> <mi>x</mi> <mn>5</mn> </msup> <mn>3</mn> <mi>c</mi> <mo>/</mo> <mn>20</mn> <mo>]</mo> </mtd> <mtd> <mo>-</mo> <mi>&Gamma;</mi> <mo>&le;</mo> <mi>x</mi> <mo>&le;</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math>
angular divergence of the inventive neutron sourceThe distribution function is described as a gaussian, x is the divergence angle,in the expression, the divergence angle x can be any real number without limiting a value interval; in the traditional method, a neutron source angle divergence distribution function I is givens=I0(1-cx2) In the case of a parabolic distribution, since the neutron intensity cannot be negative, the angular range in this expression must be limited to a reasonable range, i.e. to a range where the neutron intensity is not negativeDerived from thisThat is, when the theoretical model of the traditional method is used to analyze the measured data, the divergence of the neutron source and the divergence of the collimator to be measured are required to meet the conditionIf the divergence of the neutron source is too small, the theoretical model is not applicable, whereas the method of the present invention does not have this limitation.
It can be seen from the above implementation process that the divergence angle of the reference collimator can be selected optionally in the test process, and the theoretical expression of the conventional method requires that the divergence angle of the reference collimator must be consistent with the divergence angle of the collimator to be measured, so that in the actual measurement process, the method of the invention is more flexible in selecting the reference collimator, and is convenient for experimental measurement; for example, only one collimator to be measured is provided, and no additional collimator is used as a reference, so that the measurement analysis cannot be performed by using the conventional method, and the method of the present invention is not limited by this condition.
Compared with two mathematical models of the traditional method, the method has the advantages that compared with a 5-degree polynomial with 6 undetermined parameters, the rocking curve expression is further simplified into a Gaussian function with 2 undetermined parameters, the divergence angle and the full width at half maximum directly correspond to each other, and the expression result is more concise and visual.
The invention can conveniently estimate the divergence angle of the collimator to be measured in a certain error range, and the divergence angle of the neutron source, the divergence angle of the collimator to be measured and the divergence angle of the reference collimator have a fixed relation according to the analysis of the implementation process, wherein the specific relation is thatIn general, the divergence angle Γ of the neutron sourcesThe rocking curve has a relatively large full width at half maximum (FWHM) of 2.355 sigma, for example, when the divergence angle of the neutron source is 3 times that of the reference collimator, i.e., gammas2If the influence of the neutron source is neglected when the final rocking curve full width at half maximum Γ is calculated as 3 and FWHM is calculated as 2.355 σ, the expression can be simplified asThe relative deviation of the simplified calculation result and the calculation result considering the influence of the neutron source is 2.60 percent, and other similar calculation results are shown in the following table; when gamma iss2And (2) not less than 5, neglecting the influence of the divergence angle of the neutron source, wherein the relative deviation of the calculation result is within 1%, and when the measurement analysis is actually carried out, if the numerical value of the divergence angle of the neutron source is generally known, the measurement result can be reasonably estimated within a certain error.
The result statistical table of the corresponding rocking curves of the divergence angles of different neutron sources is as follows:
compared with the traditional method, the error analysis of the method is as follows;
1. considering no influence of a neutron source, assuming that the divergence angle of the neutron source is far larger than the divergence angle gamma of the collimator, two transmission angle distribution functions of the collimator in triangular distribution used in the conventional method have a rocking curve function which is the convolution of the two distribution functions, and the result is as follows:
<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>I</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <msup> <mi>T</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mn>4</mn> <mi>&Gamma;</mi> <mo>/</mo> <mn>3</mn> <mo>+</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>/</mo> <mi>&Gamma;</mi> <mo>+</mo> <msup> <mi>x</mi> <mn>3</mn> </msup> <mo>/</mo> <msup> <mrow> <mn>6</mn> <mi>&Gamma;</mi> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>2</mn> <mi>&Gamma;</mi> <mo>&le;</mo> <mi>x</mi> <mo>&le;</mo> <mo>-</mo> <mi>&Gamma;</mi> </mtd> </mtr> </mtable> </mfenced> </math>
<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>I</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <msup> <mi>T</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>&Gamma;</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>/</mo> <mi>&Gamma;</mi> <mo>-</mo> <msup> <mi>x</mi> <mn>3</mn> </msup> <mo>/</mo> <mn>2</mn> <msup> <mi>&Gamma;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mi>&Gamma;</mi> <mo>&le;</mo> <mi>x</mi> <mo>&le;</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </math>
the numerical calculation method gives that the full width at half maximum is 1.44 gamma;
the method is adopted for analysis, the rocking curve is the convolution of two Gaussian functions, and the result is also a Gaussian function; the half height width of the rocking curve isCompared with the traditional method, the relative deviation is 1.81%.
2. The traditional method gives specific experimental parameters of gamma 2.94 multiplied by 10-3=10.11',c=1.8×104Calculated according to the theoretical formula introduced therein, rocking curve Is+1+2(x) The full width at half maximum measurement results are: FWHM 14.43 ═ 1.43 Γ;
according to the formula of the invention, the half height width of the neutron source distribution is calculatedRocking curve Is+1+2(x) Full width at half maximum results FWHM 14.03' ═ 1.39 Γ; the method of the invention is divided intoThe analysis results deviate by 2.77% from the literature results.
3. The measurement and analysis result of a rocking curve of a collimator based on the theory of the traditional method, wherein c is 1.34 multiplied by 104R 10.72' neutron source distribution half-height widthCalculated according to a formula disclosed in the conventional method, rocking curve Is+1+2(x) The full width at half maximum measurement results are: FWHM 15.35 ═ 1.43 Γ.
Calculated according to the formula of the invention, the rocking curve Is+1+2(x) The full width at half maximum measurement result is FWHM 14.93 ═ 1.39 Γ, and the deviation of the analysis result of the method of the invention from the literature result is 2.73%.
4. The following table shows the calculation results of the half-height width of the rocking curve of the method and the conventional method and the relative deviation, gamma, of the rocking curve of the method and the conventional method under the condition that the common collimator divergence angle diverges from different neutron sourcess+1+2New is the calculation result of the full width at half maximum of the rocking curve of the method, gammas+1+2Ref is the shaking curve full width at half maximum calculation result of the conventional method;
a common collimator divergence angle is shown in a statistical table of divergence conditions of different neutron sources:
as can be seen from the data in the table, in most cases, the relative deviation of the two methods is below 4%; under the condition that the divergence angle of the neutron source is fixed, the smaller the divergence angle of the collimator is, the smaller the relative deviation is; when the collimator divergence angle is constant, the relative deviation becomes smaller as the neutron source divergence angle becomes larger.
The foregoing is merely a preferred embodiment of the invention, which is intended to be illustrative and not limiting. It will be understood by those skilled in the art that various changes, modifications and equivalents may be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (7)

1. A method for testing the divergence angle of a neutron Soller collimator is characterized by comprising the following steps: the method comprises the following steps:
step 1, describing a neutron source angle divergence distribution function and a neutron transmission collimator angle divergence response function by adopting a Gaussian function, and then performing mathematical integration on the neutron source angle divergence distribution function and the neutron transmission collimator angle divergence response function to form a general formula of a rocking curve expression;
step 2, obtaining shaking curve experimental data through experimental measurement, and fitting the obtained shaking curve experimental data according to a shaking curve expression formula to obtain a shaking curve standard error;
step 3, calculating to obtain the standard error of the Soller collimator of the neutrons to be detected by utilizing the standard error of the rocking curve, the standard error of the neutron source and the standard error of the divergence angle of the reference Soller collimator of the neutrons;
and 4, calculating to obtain the divergence angle of the neutron Soller collimator to be detected by using the standard error of the neutron Soller collimator to be detected.
2. The method for testing the divergence angle of a neutron Soller collimator, as set forth in claim 1, wherein:
in the step 1, the neutron source angle divergence distribution functionWherein x is the angle of divergence, I0When the divergence angle x is equal to 0, IS(x) A value of (d);
the neutron transmission collimator angular divergence response functionWherein x is the divergence angle and T is the transmittance of the neutron Soller collimator;
the general expression formula of the rocking curve is as follows:
<math> <mrow> <msub> <mi>I</mi> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&Integral;</mo> <msub> <mi>I</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>T</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>T</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mi>d&gamma;</mi> <mo>=</mo> <mi>A exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mi>x</mi> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
when the divergence angle x is 0, measuring the obtained neutron beam intensity;
wherein, T1(x-γ,σ1) The method is a neutron transmission collimator angle divergence response function to be measured, and specifically comprises the following steps:T10the transmittance of the Soller collimator of the neutron to be measured;
wherein, T2(γ,σ2) The method is a reference neutron transmission collimator angle divergence response function, and specifically comprises the following steps:T20is the transmission of a reference neutron Soller collimator;
wherein, Is(γ,σs) The method is characterized in that the angle divergence distribution function of the neutron source is as follows: <math> <mrow> <msub> <mi>I</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>&gamma;</mi> <mo>,</mo> <msub> <mi>&sigma;</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mi>&gamma;</mi> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&sigma;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
wherein σs+1+2Standard error for the rocking curve.
3. The method for testing the divergence angle of the neutron Soller collimator, as set forth in claim 1 or 2, wherein in the step 3, the rocking curve standard error expression is: <math> <mrow> <msubsup> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msubsup> <mi>&sigma;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>&sigma;</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>&sigma;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>;</mo> </mrow> </math>
σ1the standard error of the neutron Soller collimator to be detected is obtained; sigmasIs the standard error of the divergence angle of the neutron source; sigma2Standard error of Soller collimator for the reference neutron;
By usingExpression and known standard error sigma of neutron sourcesReference neutron Soller collimator divergence angle standard error sigma2And calculating to obtain standard error sigma of the Soller collimator of the neutron to be measured1
4. The method for testing the divergence angle of the neutron Soller collimator according to claim 1 or 2, wherein the step 4 is specifically to calculate the divergence angle of the neutron Soller collimator to be tested by using the half-width formula and the obtained standard error of the neutron Soller collimator to be tested, and the half-width formula is as follows:
Γ=2.355σ1
wherein gamma is the divergence angle of the Soller collimator of the neutron to be measured.
5. The method for testing the divergence angle of a neutron Soller collimator as claimed in claim 1 or 2, wherein: the shaking curve measuring process comprises the following steps: changing a horizontal included angle between the central axis of the neutron Soller collimator to be tested and the central line of the neutron beam, recording beam intensity values of neutrons corresponding to different included angles after the neutrons pass through the neutron Soller collimator to be tested and the reference neutron Soller collimator, and obtaining a distribution curve of the neutron intensity along with the shaking angle, namely the shaking curve.
6. The method for testing the divergence angle of a neutron Soller collimator, as set forth in claim 3, wherein: the standard error of the neutron source divergence angle is determined by the performance of the neutron source emitter, and the standard error of the reference neutron Soller collimator is determined by the performance of the reference neutron Soller collimator.
7. The method for testing the divergence angle of a neutron Soller collimator, as set forth in claim 3, wherein: the divergence angle x in the expression can be any real number without limiting the value interval.
CN201410443111.XA 2014-09-02 2014-09-02 It is a kind of to be used for neutron Soller collimators divergent angle test method Active CN104216000B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201410443111.XA CN104216000B (en) 2014-09-02 2014-09-02 It is a kind of to be used for neutron Soller collimators divergent angle test method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201410443111.XA CN104216000B (en) 2014-09-02 2014-09-02 It is a kind of to be used for neutron Soller collimators divergent angle test method

Publications (2)

Publication Number Publication Date
CN104216000A true CN104216000A (en) 2014-12-17
CN104216000B CN104216000B (en) 2017-03-29

Family

ID=52097695

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201410443111.XA Active CN104216000B (en) 2014-09-02 2014-09-02 It is a kind of to be used for neutron Soller collimators divergent angle test method

Country Status (1)

Country Link
CN (1) CN104216000B (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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
CN109212585A (en) * 2018-07-26 2019-01-15 东莞材料基因高等理工研究院 It is a kind of for detect neutron monochromator mosaic angle distribution test method and device
CN109659061A (en) * 2018-12-27 2019-04-19 中国原子能科学研究院 The continuously adjustable neutron howitzer structure of the angle of divergence and its scaling method
CN109671513A (en) * 2018-12-27 2019-04-23 中国原子能科学研究院 The continuously adjustable neutron howitzer structure of the angle of divergence and its scaling method

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102288626A (en) * 2011-07-18 2011-12-21 中国原子能科学研究院 Neutron texture testing equipment

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102288626A (en) * 2011-07-18 2011-12-21 中国原子能科学研究院 Neutron texture testing equipment

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
H.MEISTER等: "NEUTRON COLLIMATORS WITH PLATES OF SELF-CONTRACTING FOILS", 《NUCLEAR INSTRUMENTS AND METHODS》 *
刘丽娟等: "蒙特卡罗方法在Soller中子狭缝准直器优化设计中的应用", 《原子能科学技术》 *
谢超美: "高分辨粉末中子衍射谱仪的设计和部分硬件的研制", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 *

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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
CN109212585A (en) * 2018-07-26 2019-01-15 东莞材料基因高等理工研究院 It is a kind of for detect neutron monochromator mosaic angle distribution test method and device
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
CN109659061A (en) * 2018-12-27 2019-04-19 中国原子能科学研究院 The continuously adjustable neutron howitzer structure of the angle of divergence and its scaling method
CN109671513A (en) * 2018-12-27 2019-04-23 中国原子能科学研究院 The continuously adjustable neutron howitzer structure of the angle of divergence and its scaling method
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
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

Also Published As

Publication number Publication date
CN104216000B (en) 2017-03-29

Similar Documents

Publication Publication Date Title
Timmons et al. The importance of temporal design: How do measurement intervals affect the accuracy and efficiency of parameter estimates in longitudinal research?
Ganesan et al. Characterization of uncertainties in atmospheric trace gas inversions using hierarchical Bayesian methods
Boselli et al. Cold gas properties of the Herschel Reference Survey-II. Molecular and total gas scaling relations
Hargreaves et al. Skill and reliability of climate model ensembles at the Last Glacial Maximum and mid-Holocene
US20180321208A1 (en) Determining the net emissions of air pollutants
Schulze et al. Selection effects in the black hole-bulge relation and its evolution
De Smedt et al. Bias due to differential and non-differential disease-and exposure misclassification in studies of vaccine effectiveness
CN104216000B (en) It is a kind of to be used for neutron Soller collimators divergent angle test method
Weißmann et al. Studying the properties of galaxy cluster morphology estimators
Saeki et al. Implications of overestimated anthropogenic CO 2 emissions on East Asian and global land CO 2 flux inversion
Lilow et al. Constrained realizations of 2MRS density and peculiar velocity fields: growth rate and local flow
Winton et al. Climate sensitivity of GFDL's CM4. 0
CN104730025B (en) Mixture quantitative analysis method based on terahertz spectroscopy
Morandi et al. Triaxiality and non-thermal gas pressure in Abell 1689
Bo et al. The accuracy of predicted acoustical parameters in Ancient Open-Air Theatres: A case study in Syracusae
CN107729621A (en) A kind of verification tool of statical model
KR20170033147A (en) Apparatus and method for generating greenhouse gas distribution data across administrative regions
Clyde et al. Organizational commitment as moderating the relationship between professional commitment, locus of control, and professionalism on whistleblowing intention
Stroe-Kunold et al. Estimating long-range dependence in time series: An evaluation of estimators implemented in R
Libardoni et al. Correction to “Sensitivity of distributions of climate system properties to the surface temperature data set”
Baneschi et al. Non-steady-state closed dynamic chamber to measure soil CO2 respiration: A protocol to reduce uncertainty
CN105607123B (en) Method and device for calculating seismic wave characteristic information of random pore medium model
CN104317856A (en) Method for testing and evaluating vocabulary amount
Kovačević-Dojčinović et al. Black Hole Mass Estimation in Type 1 AGN: Hβ vs. Mg II lines and the role of Balmer continuum
He et al. On the prevalence of high climate sensitivity models

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant