CN114739641A - Method for manufacturing reflection cone for high-energy laser beam expansion and reflection cone - Google Patents
Method for manufacturing reflection cone for high-energy laser beam expansion and reflection cone Download PDFInfo
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Abstract
The invention relates to a laser parameter measuring method, in particular to a reflecting cone manufacturing method for high-energy laser beam expansion and a reflecting cone, and solves the technical problem that the reflecting cone of a full-absorption energy meter cannot meet the beam expansion requirements of high-energy lasers with light spots of different sizes under the limitation of a certain absorption cavity size structure. The invention relates to a method for manufacturing a reflection cone for expanding high-energy laser beams, which adopts a sectional structure and can meet the beam expanding requirements of high-energy lasers with different spot sizes; then, establishing a constraint equation set of a reflection cone surface type function f (x) according to a light constraint condition, and finally calculating the surface type function of the reflection cone by using a numerical iteration solving algorithm; the beam expanding requirements of high-energy lasers with different sizes of light spots are met under the condition of a certain absorption cavity size structure; the invention also provides a reflecting cone which can meet the requirements of different reflecting cones in practical application.
Description
Technical Field
The invention relates to a laser parameter measuring method, in particular to a reflecting cone manufacturing method and a reflecting cone for high-energy laser beam expansion.
Background
The high-energy laser has wide application prospect in the fields of national defense, industry, energy sources and the like, and the energy/power parameter of the high-energy laser is an important technical index for evaluating the quality and development level of a laser system. The measurement of energy/power of high-energy lasers has been challenging due to the strong destructive nature of these lasers.
Among the high-energy laser energy/power measurement methods, the full absorption type measurement method is one of the most reliable measurement means. The full-absorption high-energy laser energy/power measuring device generally adopts a cylindrical absorption cavity, a high-temperature-resistant absorption coating is sprayed on the inner surface of the absorption cavity, and a beam expanding reflection cone is arranged at the center of the bottom of the absorption cavity. After the high-energy laser is expanded by the beam expanding reflection cone, the high-energy laser is reflected to the inner wall surface of the absorption cavity and absorbed, so that the temperature of the absorption cavity and the cooling medium outside the absorption cavity is increased, and the energy and the power of the incident laser are inverted by measuring the temperature rise condition of the absorption cavity or/and the cooling medium outside the absorption cavity.
In summary, the beam expanding reflection cone is a core component of the total absorption type high-energy laser energy and power measuring device, and needs to directly endure the irradiation of the high-energy laser and reasonably distribute the laser energy to the absorption cavity, so the surface structure of the beam expanding reflection cone is the key of the total absorption type energy meter. Currently, the spot distribution of high-energy laser is generally gaussian, and the near-field spot size and the far-field spot size of high-energy laser with the same light output power are greatly different. If a single-surface type reflection cone structure is adopted, the heat exchange area of the absorption cavity cannot be effectively utilized under the incidence of small-size light spots, and the size of the full-absorption type laser energy measuring device is larger and larger in order to avoid the damage of the absorption cavity. Therefore, under the limitation of a certain absorption cavity size structure, the reflection cone of the full absorption type energy meter needs to meet the beam expanding requirements of high-energy lasers with different sizes of light spots.
Disclosure of Invention
The invention aims to solve the technical problem that a reflecting cone of a full-absorption energy meter is difficult to meet the beam expanding requirements of high-energy lasers with different sizes under the limitation of a certain absorption cavity size structure, and provides a method for manufacturing the reflecting cone for expanding the high-energy lasers and the reflecting cone, so that the beam expanding requirements of the high-energy lasers with different sizes are met under the condition of a certain absorption cavity size structure.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a method for manufacturing a reflecting cone for expanding high-energy laser is characterized by comprising the following steps:
step 1: defining a surface type function f (x) of the reflection cone, wherein x is more than or equal to 0 and less than or equal to r;
wherein: r is the radius of the bottom of the reflection cone, x is the independent variable of f (x), and x is 0 at the center of the reflection cone and r at the edge of the reflection cone;
step 2: according to the power P of the incident laser, the maximum spot size Z of the incident laser, the convective heat transfer coefficient Hr of the absorption cavity and the maximum tolerance temperature T of the inner wall surface of the absorption cavitymaxCalculating the numerical values of the radius R of the bottom of the reflection cone, the radius R of the absorption cavity and the height L of the absorption cavity;
and step 3: defining a light constraint condition of the reflection cone, and obtaining a light constraint equation set of a surface type function f (x) of the reflection cone; the light constraint condition is a propagation path of light expanded by the reflection cone;
and 4, step 4: solving an analytical expression of a surface type function f (x) of the reflection cone according to the light ray constraint equation set in the step 3;
and 5: calculating temperature distribution T (y) of different positions y of the inner wall surface of the absorption cavity in a thermal equilibrium state according to an analytical expression of f (x), a power density distribution function I (x) of incident laser and a convective heat transfer coefficient Hr of the absorption cavity;
step 6: according to the maximum tolerance temperature T of the inner wall surface of the absorption cavitymaxAnd the temperature distribution T (y) is judged whether T (y) < Tmax；
If yes, outputting a surface type function f (x) of the reflection cone, and finishing the manufacturing of the reflection cone according to an analytical expression of the f (x);
if not, returning to the step 2 until T (y) < Tmax。
Further, step 1 specifically comprises: the surface type function f (x) of the reflecting cone is in two segments, and the surface type function of the reflecting cone is
In the formula: f. of1(x) Is a surface type function of the first section of the reflecting cone;
f2(x) Is the surface type function of the second segment of the reflecting cone;
r1 is the radius of the bottom of the first section of the reflection cone;
r1+ r2 is the radius of the bottom of the second section of the reflecting cone;
Further, step 2 specifically comprises:
according to the power P of the incident laser, the maximum spot size Z of the incident laser, the convective heat transfer coefficient Hr of the absorption cavity and the maximum tolerance temperature T of the inner wall surface of the absorption cavitymaxThe bottom segment sizes R1 and R2 of the reflection cone, the radius R of the absorption cavity, R1+ R2+ b, and the height L of the absorption cavity are determined, wherein b represents the distance from the bottom edge of the reflection cone to the inner wall surface of the absorption cavity.
Further, step 4 specifically includes:
4.1) setting f1(x) Initial value of (0 < f)1(0)0< L, where superscript 0 represents the 0 th iteration;
4.2) according to the light constraint equation system in the step 3,f is obtained1(x)nAnd f2(x)nThe analytical expression of (3), wherein the superscript n represents the nth iteration calculation;
4.3) judgment
If f2(r1+r2)nIf | < ε, output f1(x)nAnd f2(x)nWherein ε is a small amount greater than zero;
let f1(0)n+1＝f1(0)n-f2(r1+r2)nReturn to step 4.2).
Further, step 5 specifically includes:
5.1) calculating the position y of the inner wall surface of the absorption cavity
In the formula: g1(x) Type f indicating laser irradiation to reflecting cone1(x) When the light source is in the upper position, the incident light is reflected to the position on the inner wall surface of the absorption cavity;
g2(x) Type f indicating laser irradiation to reflecting cone2(x) When the light is emitted, the incident light is reflected to the position on the inner wall surface of the absorption cavity;
f1' (x) is f1(x) The first derivative of (a);
f2' (x) is f2(x) The first derivative of (a);
5.2) defining the area beam expansion ratio E (x) of incident light rays at different radius positions x of the reflecting cone
In the formula: dScavity(x) Showing the area variation projected to the inner wall surface of the absorption cavity when the incident light ray changes dx at the radius x of the reflection cone;
dSbeam(x) Indicating incident light on half of the reflecting coneWhen dx is changed at the position of the x, the area of the light spot is changed;
5.3) according to E in step 5.2)1(x) And E2(x) Calculating the laser power density D (x) of the corresponding absorption cavity at the position x with different radiuses of the reflection cone
5.4) converting the independent variable from different radius positions x of the reflecting cone into the position y of the inner wall surface of the absorption cavity, wherein the conversion relation is as follows:
in the formula:
and
are respectively g1(y) and g2(y) the inverse function of (y);
5.5) calculating the temperature distribution T (y) at different positions y on the absorption cavity under the thermal equilibrium state
In the formula: t is0Indicating the initial temperature of the inner wall of the absorption chamber.
Further, step 6 specifically includes:
according to the maximum tolerance temperature T of the inner wall surface of the absorption cavitymaxAnd the temperature distribution T (y) of the absorption cavity, and whether T (y) is less than Tmax；
If yes, outputting the surface type function f of the reflection cone (1)1(x) And f2(x) According to f1(x) And f2(x) The analytical expression of (2) completes the manufacture of the reflection cone (1);
if not, returning to the step 2 until T (y) < Tmax。
Further, in step 5.2), the area beam expansion ratio e (x) is calculated by the formula:
in the formula: | g1' (x) | denotes g in step 5.1)1(x) The absolute value of the first derivative of (a);
|g1' (x) | denotes g in step 5.1)2(x) The absolute value of the first derivative of (a).
Furthermore, the reflecting cone is a central axis symmetric geometric structure body generated around the central axis of the incident ray;
the surface type of the reflecting cone is an intersecting curve on a geometric plane generated by the intersection of the geometric plane containing the central axis and the reflecting cone;
the thermal equilibrium state is that the energy of the incident laser light is equal to the heat extracted by the absorption cavity.
Furthermore, the value of epsilon is 0.001 mm.
In addition, the invention also provides a reflecting cone, which is characterized in that: the method for manufacturing a reflecting cone for expanding beam of high-energy laser as claimed in any one of claims 1 to 9.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention relates to a method for manufacturing a reflection cone for expanding high-energy laser beams and the reflection cone, which adopt a sectional curved surface structure and can meet the beam expanding requirements of high-energy lasers with different spot sizes. And then establishing a constraint equation set of the reflecting cone surface type function f (x) according to the light constraint condition, and finally calculating the surface type function of the reflecting cone by using a numerical iteration solving algorithm. On the basis, the temperature distribution of the inner wall surface of the absorption cavity under the thermal equilibrium state is calculated according to the spot distribution type of the incident laser and the whole convection heat transfer coefficient of the absorption cavity, and whether the temperature of the inner wall surface of the absorption cavity is lower than the highest tolerance temperature or not is judged, so that different requirements of practical application can be met.
Drawings
FIG. 1 is a schematic diagram of a continuous center cross-sectional structure of a first derivative of a planar reflector according to a first embodiment of the present invention;
FIG. 2 is a flowchart illustrating a method for solving a surface function according to a first embodiment of the reflection cone of the present invention;
FIG. 3 is a schematic diagram of continuous time light confinement of the first derivative of the surface type according to a first embodiment of the reflective cone of the present invention, wherein θ0，θ1,θ2,θ3The included angle between the tangent of any point on the reflecting conical surface and the X axis is respectively, h is the central height of the reflecting conical surface, r1 and r2 are respectively the radius of the bottom of the reflecting conical surface, b is the distance between the edge of the bottom of the reflecting conical surface and the inner wall surface of the absorption cavity, c is the distance between the upper edge of the absorption cavity reflected by the light at the center of the incident laser and the outlet of the absorption cavity, a is the difference between the height of the lower edge of the absorption cavity reflected by the incident laser at the radius r1 of the reflecting conical surface and the central height h of the reflecting conical surface; h is the distance between the upper edge and the lower edge of the absorption cavity body from the incident laser light;
FIG. 4 is a schematic view of the angle θ defined in FIG. 3;
FIG. 5 is a half schematic view of a planar structure of an embodiment of a reflection cone of the present invention;
FIG. 6 is a schematic diagram of a temperature distribution T (y) on an absorption cavity according to an embodiment of the present invention;
FIG. 7 is a schematic diagram of a central cross-sectional structure of a second embodiment of a reflection cone according to the present invention when the first derivative of the profile is suddenly changed;
FIG. 8 is a schematic diagram of light confinement when the first derivative of the profile is suddenly changed according to a second embodiment of the reflective cone of the present invention, wherein θ0，θ1,θ2,θ3The included angles between the tangent line of any point on the reflecting conical surface and the X axis are respectively shown, h is the central height of the reflecting conical surface, r1 and r2 are respectively the radius of the bottom of the reflecting conical surface, b is the distance between the edge of the bottom of the reflecting conical surface and the inner wall surface of the absorption cavity, c is the distance between the upper edge of the absorption cavity reflected by the light at the center of the incident laser and the outlet of the absorption cavity, a is the difference between the height of the lower edge of the absorption cavity reflected by the incident laser at the radius r1 of the reflecting conical surface and the central height h of the reflecting conical surface; h is the distance between the upper edge and the lower edge of the absorption cavity body from the incident laser light;
FIG. 9 is a schematic view of the angle θ defined in FIG. 8;
FIG. 10 is a half schematic view of a two-sided structure of an embodiment of a reflection cone of the present invention;
FIG. 11 is a schematic view of the temperature distribution T (y) on the absorption cavity in the second embodiment of the present invention;
the reference numbers in the figures are:
1-reflection cone, 2-absorption cavity.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the technical solutions of the present invention, belong to the protection scope of the present invention.
Example one
As shown in fig. 1 and fig. 2, a schematic diagram of a central cross-sectional structure of a sectional type reflection cone 1 when a first derivative of the surface type is continuous and a flow chart of solving a surface type function of the sectional type reflection cone 1 according to the present invention are shown; the invention relates to a method for manufacturing a reflecting cone 1 for expanding high-energy laser beams, which comprises the following steps of:
step 1: defining a surface type function f (x) of the reflection cone 1, wherein x is more than or equal to 0 and less than or equal to r;
wherein, the surface function f (x) of the reflection cone 1 is two-stage, and the surface function of the reflection cone 1 is
In the formula: r is the radius of the bottom of the reflection cone 1, x is the independent variable of f (x), and x is 0 at the center of the reflection cone 1 and r at the edge of the reflection cone 1;
f1(x) Is the surface type function of the first section of the reflecting cone 1;
f2(x) Is the surface type function of the second section of the reflecting cone 1;
r1 is the radius of the bottom of the first section of reflection cone 1;
r1+ r2 is the bottom radius of the second section of the reflecting cone 1;
subscript 1 and subscript 2 denote a first segment reflection cone 1 and a second segment reflection cone 1, respectively.
And 2, step: according to the power P of the incident laser, the maximum spot size Z of the incident laser, the convective heat transfer coefficient Hr of the absorption cavity 2 and the maximum tolerance temperature T of the inner wall surface of the absorption cavity 2maxThe bottom segment sizes R1 and R2 of the reflection cone 1, the radius R of the absorption cavity 2, R1+ R2+ b, and the height L of the absorption cavity 2 are determined, wherein b represents the distance from the bottom edge of the reflection cone 1 to the inner wall surface of the absorption cavity 2.
And step 3: defining a light constraint condition of the reflection cone 1, and obtaining a light constraint equation set of a surface type function f (x) of the reflection cone 1; the light constraint condition is that the light is propagated through the propagation path after the light is expanded by the reflecting cone 1
And 4, step 4: solving an analytical expression of a surface function f (x) of the reflection cone 1 according to the light ray constraint equation set in the step 3;
4.1) setting f1(x) Initial value of (0 < f)1(0)0< L, where superscript 0 represents the 0 th iteration;
4.2) solving f according to the light constraint equation set in the step 31(x)nAnd f2(x)nThe analytical expression of (3), wherein the superscript n represents the nth iteration calculation;
4.3) judgment
If f2(r1+r2)nIf | < epsilon, epsilon > 0, then f is output1(x)nAnd f2(x)nWhere ε is a small amount greater than zero;
let f1(0)n+1＝f1(0)n-f2(r1+r2)nReturn to step 4.2).
And 5: calculating temperature distribution T (y) at different positions y on the inner wall surface of the absorption cavity 2 in a thermal equilibrium state according to an analytical expression of f (x), a power density distribution function I (x) of incident laser and a convective heat transfer coefficient Hr of the absorption cavity 2;
5.1) calculating the position y of the inner wall surface of the absorption cavity 2
In the formula: g1(x) Type f representing laser irradiation to reflection cone 11(x) When the light source is in the upper position, the incident light is reflected to the position on the inner wall surface of the absorption cavity 2;
g2(x) Type f representing laser irradiation to reflection cone 12(x) When the light is emitted, the incident light is reflected to the position on the inner wall surface of the absorption cavity 2;
f1' (x) is f1(x) The first derivative of (a);
f2' (x) is f2(x) The first derivative of (a);
subscript 1 and subscript 2 denote a first-stage reflection cone 1 and a second-stage reflection cone 1, respectively;
5.2) defining the area beam expansion ratio E (x) of incident light rays at different radius positions x of the reflecting cone 1
In the formula: dScavity(x) The area variation quantity projected to the inner wall surface of the absorption cavity 2 when the incident light ray changes dx at the radius x of the reflection cone 1 is shown;
dSbeam(x) Showing the variation of the spot area when the incident light changes dx at the radius x of the reflecting cone 1;
in the formula: | g1' (x) | denotes g in step 5.1)1(x) The absolute value of the first derivative of (a);
|g1' (x) | denotes g in step 5.1)2(x) The absolute value of the first derivative of (a).
5.3) according to E in step 5.2)1(x) And E2(x) Calculating the laser power density D (x) on the corresponding absorption cavity 2 at the position x with different radiuses of the reflection cone 1
5.4) converting the independent variable from different radius positions x of the reflection cone 1 into the position y of the inner wall surface of the absorption cavity 2, wherein the conversion relation is as follows:
in the formula:
and
are respectively g1(y) and g2(y) the inverse function of (y);
5.5) calculating the temperature distribution T (y) at different positions y on the absorption cavity 2 in the thermal equilibrium state
In the formula: t is0The initial temperature of the inner wall surface of the absorption chamber 2 is shown.
Step 6: according to the maximum tolerance temperature T of the inner wall surface of the absorption cavity 2maxAnd the temperature distribution T (y) of the absorption cavity 2, and whether T (y) is less than Tmax；
If yes, outputting a surface type function f (x) of the reflection cone 1, and finishing the manufacturing of the reflection cone 1 according to an analytical expression of f (x);
if not, returning to the step 2 until T (y) < Tmax。
In this embodiment, the reflection cone 1 is a central axis symmetric geometric structure generated around the central axis of the incident light; the surface shape of the reflection cone 1 is an intersection curve on a geometric plane generated by the intersection of the geometric plane containing the central axis and the reflection cone 1. The light constraint condition is a propagation path of light after being expanded by the reflecting cone 1; the incident laser power density is the laser power in unit area; the thermal equilibrium state is that the energy of the incident laser light is equal to the amount of heat extracted by the absorption cavity 2. The value of epsilon is 0.001 mm.
For further explanation, this embodiment will be exemplified; as shown in fig. 1 and fig. 2, a schematic diagram of a central cross-sectional structure of a sectional type reflection cone 1 when a first derivative of the surface type is continuous and a flow chart of solving the surface type function of the sectional type reflection cone 1 according to the present invention are shown; at present, the maximum output power of the optical fiber laser used for industrial processing is about 20000W, the light spot distribution is Gaussian distribution, and the power is 1/e2The spot radius ranges from 5mm to 30 mm. The manufacturing method of the reflecting cone 1 for expanding the beam of the high-energy laser comprises the following steps:
step 1: defining the surface type function of the two-section type reflection cone 1 as a second-order polynomial according to the coordinate relation:
wherein k is11，k12，k13All represent a second order polynomial f1(x) Coefficient of (a), k21，k22，k23All represent a second order polynomial f2(x) The coefficient of (a).
Step 2: according to the incident laser power P of 20000W, the maximum spot radius Z of 30mm and the convective heat transfer coefficient Hr of the absorption cavity 2 of 12000W/m2K. Maximum temperature T of the inner wall surface of the absorption cavity 2max＝500℃。
The radius R1 of the bottom of the reflection cone 1 is 12mm, R2 is 18mm, the radius R of the absorption cavity 2 is R1+ R2+ b is 35mm, and the length L of the absorption cavity 2 is 80 mm.
And 3, step 3: as shown in fig. 3 and 4, the light constraint condition of the reflection cone 1 is defined, and a constraint equation set of the two-segment reflection cone 1 surface type function is set;
3.1) the light reflection of incident laser facula center department is to absorbing cavity 2 upper edge, and is 15mm apart from absorbing cavity 2 export distance, obtains the relation:
tanθ0＝-f1'(0)
3.2) the light ray at the radius r1 of the reflection cone 1 is reflected to the lowest edge of the absorption cavity 2, and the height of the lower edge is greater than the central height h of the reflection cone 1, the difference between the two is a is 10mm, and the obtained relation is:
tanθ1＝-f1'(r1)
3.3)f1(x) Is continuous and monotonically decreasing in the range of 0 ≦ x ≦ r1, resulting in the relationship:
tanθ0≤-f1'(x)≤tanθ1
3.4) the incident laser beam with the spot in the range of r1 < x ≤ r1+ r2 sequentially expands the beam from the lower edge of the absorption cavity 2 to the upper edge of the absorption cavity 2, and the relation is as follows:
tanθ2＝-f2'(r1)
tanθ3＝-f2'(r1+r2)
tan2θ3＝(L-c)/b
3.5)f2(x) Is continuous and monotonically increasing over the range r1 ≦ x ≦ r1+ r2, resulting in the relationship:
tanθ2≥-f2'(x)≥tanθ3
3.6) the cone surface of the reflection cone 1 and the first derivative thereof are continuous, and the relation is obtained as follows:
f1(r1)＝f2(r1)
f1'(r1)＝f2'(r1)
and 4, step 4: as shown in fig. 5, the numerical iterative solution algorithm is used to set the light constraint equations from step 3.1) to step 3.6)Initial value f1(0)0F is obtained after 3 iterations, 10mm and 0.001mm1(x) And f2(x) The analytical expression of (a) is:
using derived f1(x) And f2(x) The analytical expression of (2) draws the surface shape of the two-segment type continuous reflection cone 1.
And 5: according to the surface type function f obtained in the step 41(x) And f2(x) The power density distribution function I (x) of the incident laser and the convective heat transfer coefficient Hr of the absorption cavity 2, and the temperature distribution function T (y) of the inner wall surface of the absorption cavity 2 at different positions y under the thermal equilibrium state are calculated.
The incident laser power density distribution function I (x) is a Gaussian function, and the expression is as follows:
wherein P represents the total incident laser power, and P is 20000W; omega 01/e representing Gaussian beam2The radius of the ring.
5.1) calculating the position y of the reflection cone 1 reflecting the light rays with different radii x to the inner wall surface of the absorption cavity 2
In the formula: g1(x) Type f representing laser irradiation to reflection cone 11(x) Up time reflected to the position on the inner wall surface of the absorption cavity 2, g2(x) Type f representing laser irradiation to reflection cone 12(x) Is reflected to the position on the inner wall surface of the absorption cavity 2, f1' (x) is f1(x) First derivative of f2' (x) is f2(x) The first derivative of (1), the subscript 1, and the subscript 2 represent the first segment reflection cone 1 and the second segment reflection cone 1, respectively.
5.2) defining the light area beam expansion ratio of the reflection cone 1 at different radius positions x:
in the formula: dScavity(x) Represents the area variation dS projected onto the inner wall surface of the absorption cavity 2 when the ray is changed by dx at the radius x of the reflection cone 1beam(x) The amount of change in spot area when the light ray changes dx at the radius x of the reflection cone 1.
E (x) the formula:
in the formula: | g1' (x) | denotes g in step 5.1)1(x) Absolute value, | g, of the first-order instructor of1' (x) | denotes g in step 5.1)2(x) The absolute value of the first-order instructor, subscript 1 and subscript 2 denote the first-stage reflection cone 1 and the second-stage reflection cone 1, respectively.
5.3) E calculated according to step 5.2)1(x) And E2(x) Calculating the laser power density D (x) on the corresponding absorption cavity 2 at the position x with different radiuses of the reflection cone 1, wherein the calculation formula is as follows:
in the formula: i (x) represents a power density distribution function of the incident laser light, and subscripts 1 and 2 represent the first stage reflection cone 1 and the second stage reflection cone 1, respectively.
5.4) converting the independent variable from different radius positions x of the reflection cone 1 into a position y on the inner wall surface of the absorption cavity 2, wherein the conversion relation is as follows:
in the formula: y representing an absorption chamber 2The position on the inner wall surface,
And
are respectively g1(y) and g2The inverse function of (y), subscript 1 and subscript 2 denote the first segment reflection cone 1 and the second segment reflection cone 1, respectively.
5.5) calculating the heat convection coefficient Hr of the known absorption cavity 2 to 12000W/m2K, initial temperature T of inner wall surface of absorption cavity 2020 ℃ is set; in the thermal equilibrium state, the temperature distribution t (y) at different positions y on the absorption cavity 2 is calculated by the formula:
as shown in FIG. 6, the 1/e of the Gaussian beam calculated in step 5.5) is used2Radius of circumference omega0Temperature distributions T (y) at different positions y on the absorption cavity 2 under 5mm, 10mm and 15mm respectively.
Step 6: maximum temperature T of the inner wall surface of the absorption cavity 2max500 deg.C, 1/e in the minimum Gaussian beam2The radius of the surrounding is 5mm, the highest temperature of the inner wall of the absorption cavity 2 is about 400 ℃, the highest tolerance temperature is 500 ℃, and the two-section type reflection cone 1 is manufactured continuously.
Example two
The basic concept of the second embodiment is the same as that of the first embodiment, and the specific content is as follows:
step 1: as shown in fig. 7, which is a schematic diagram of a central cross-sectional structure of the two-segment type reflection cone 1 according to the embodiment of the present invention when the first derivative of the surface type changes suddenly, the surface type function of the two-segment type reflection cone 1 when the change suddenly changes is defined as a second-order polynomial according to the coordinate relationship:
wherein k is11，k12，k13All represent a second order polynomial f1(x) Coefficient of (a), k21，k22，k23All represent a second order polynomial f2(x) The coefficient of (a).
Step 2: according to the incident laser power P of 20000W, the maximum spot radius Z of 30mm and the convective heat transfer coefficient Hr of the absorption cavity 2 of 12000W/m2K. Maximum tolerance temperature T of inner wall surface of absorption cavity 2max＝500℃。
The radius R1 of the bottom of the reflection cone 1 is 12mm, R2 is 18mm, the radius R of the absorption cavity 2 is R1+ R2+ b is 35mm, and the length L of the absorption cavity 2 is 80 mm.
And step 3: as shown in fig. 8 and 9, the light constraint condition of the reflection cone 1 is defined, and the constraint equation set of the two-segment reflection cone 1 surface type function during abrupt change is as follows:
3.1) the light reflection of facula center department is to absorbing cavity 2 upper limb, and is 15mm apart from 2 export distances of absorbing cavity, obtains the relational expression:
tanθ0＝-f1'(0)
3.2) the light at the spot radius r1 is reflected to the lower edge of the absorption cavity 2, and the height of the lower edge is greater than the central height of the reflection cone 1, and the difference between the two is that a is 10mm, the relation is obtained as follows:
tanθ1＝-f1'(r1)
3.3)f1(x) Is continuous and monotonically decreasing in the range of 0 ≦ x ≦ r1, resulting in the relationship:
tanθ0≤-f1'(x)≤tanθ1
3.4) the light of the light spot positioned at r1 and x is more than or equal to r1+ r2 is expanded from the upper edge of the absorption cavity 2 to the lower edge of the absorption cavity 2 in sequence, and the relation is obtained as follows:
tanθ2＝-f2'(r1)
tanθ3＝-f2'(r1+r2)
tan2θ3＝b/(h+a)
3.5)f2(x) Is continuous and monotonically decreasing over the range r1 ≦ x ≦ r1+ r2, resulting in the relationship:
tanθ2≤-f2'(x)≤tanθ3
3.6) the cone surface of the reflection cone 1 is continuous, the relation is obtained:
f1(r1)＝f2(r1)
and 4, step 4: as shown in fig. 10, an initial value f is set according to the light constraint equations from step 3.1) to step 3.6) by using a numerical iterative solution algorithm1(0)0F is obtained after 4 iterations, 10mm and 0.001mm1(x) And f2(x) The analytical expression of (a) is:
using derived f1(x) And f2(x) The surface type of the two-section type reflection cone 1 is drawn by the analytical expression of (1).
And 5: according to the surface type function f obtained in the step 41(x) And f2(x) The power density distribution function I (x) of the incident laser and the convective heat transfer coefficient Hr of the absorption cavity 2, and the temperature distribution function T (y) of the inner wall surface of the absorption cavity 2 at different positions y under the thermal equilibrium state are calculated.
The incident laser power density distribution I (x) is a Gaussian function and is expressed as:
wherein P represents the total incident laser power, and P is 20000W; omega 01/e representing Gaussian beam2The radius of the ring.
5.1) calculating the position y of the reflection cone 1 reflecting the light rays with different radii x to the inner wall surface of the absorption cavity 2
In the formula: g1(x) Type f representing laser irradiation to reflection cone 11(x) Up time reflected to the position on the inner wall surface of the absorption cavity 2, g2(x) Type f representing laser irradiation to reflection cone 12(x) Is reflected to the position on the inner wall surface of the absorption cavity 2, f1' (x) is f1(x) First derivative of f2' (x) is f2(x) The first derivative of (1), the subscript 1, and the subscript 2 represent the first segment reflection cone 1 and the second segment reflection cone 1, respectively.
5.2) defining the light area beam expansion ratio of the reflection cone 1 at different radius positions x:
in the formula: dScavity(x) Represents the area variation dS projected onto the inner wall surface of the absorption cavity 2 when the ray is changed by dx at the radius x of the reflection cone 1beam(x) The amount of change in spot area when the light ray changes dx at the radius x of the reflection cone 1.
E (x) the formula is:
in the formula: | g1' (x) | denotes g in step 5.1)1(x) Absolute value of first leading teacher, | g1' (x) | denotes g in step 5.1)2(x) The absolute value of the first-order instructor, subscript 1 and subscript 2 denote the first-stage reflection cone, respectively1 and a second segment reflection cone 1.
5.3) E calculated according to step 5.2)1(x) And E2(x) Calculating the laser power density D (x) on the corresponding absorption cavity 2 at the position x with different radiuses of the reflection cone 1, wherein the calculation formula is as follows:
in the formula: i (x) denotes a power density distribution function of the incident laser light, and subscript 1 and subscript 2 denote first-stage reflection cone 1 and second-stage reflection cone 1, respectively.
5.4) converting the independent variable from different radius positions x of the reflection cone 1 into a position y on the inner wall surface of the absorption cavity 2, wherein the conversion relation is as follows:
in the formula: y represents a position on the inner wall surface of the absorption chamber 2,
And
are respectively g1(y) and g2The inverse function of (y), subscript 1 and subscript 2 denote the first segment reflection cone 1 and the second segment reflection cone 1, respectively.
5.5) calculating the heat convection coefficient Hr of the known absorption cavity 2 to be 12000W/m2K, initial temperature T of inner wall surface of absorption cavity 20At 20 deg.C; in the thermal equilibrium state, the temperature distribution t (y) at different positions y on the absorption cavity 2 is calculated by the formula:
as shown in FIG. 11, the 1/e of the Gaussian beam calculated by step 5.5) is utilized2Radius of circumference omega0Respectively of 5mm, 10mm and 15mm,the temperature distribution t (y) at different locations y on the absorption chamber 2.
Step 6: maximum temperature T of the inner wall surface of the absorption cavity 2max500 deg.C, 1/e of minimum Gaussian beam2The radius of the ring is 5mm, the highest temperature of the inner wall of the absorption cavity 2 is about 400 ℃, the highest tolerance temperature is 500 ℃, and the two-section type reflection cone 1 is manufactured when mutation occurs.
Claims (10)
1. A method for manufacturing a reflecting cone for expanding high-energy laser beams is characterized by comprising the following steps:
step 1: defining a surface type function f (x) of the reflection cone (1), wherein x is more than or equal to 0 and less than or equal to r;
wherein: r is the radius of the bottom of the reflecting cone (1), x is the independent variable of f (x), and x is 0 at the center of the reflecting cone (1) and r at the edge of the reflecting cone (1);
step 2: according to the power P of the incident laser, the maximum spot size Z of the incident laser, the convective heat transfer coefficient Hr of the absorption cavity (2) and the maximum tolerance temperature T of the inner wall surface of the absorption cavity (2)maxCalculating the values of the radius R of the bottom of the reflection cone (1), the radius R of the absorption cavity (2) and the height L of the absorption cavity (2);
and 3, step 3: defining a light constraint condition of the reflection cone (1) and obtaining a light constraint equation set of a surface type function f (x) of the reflection cone (1); the light constraint condition is a propagation path of light after being expanded by the reflection cone (1);
and 4, step 4: solving an analytical expression of a surface function f (x) of the reflection cone (1) according to the light ray constraint equation set in the step 3;
and 5: calculating temperature distribution T (y) of different positions y of the inner wall surface of the absorption cavity (2) in a thermal equilibrium state according to an analytical expression of f (x), a power density distribution function I (x) of incident laser and a convective heat transfer coefficient Hr of the absorption cavity (2);
step 6: according to the maximum tolerance temperature T of the inner wall surface of the absorption cavity (2)maxAnd the temperature distribution T (y) is judged whether T (y) < Tmax；
If yes, outputting a surface type function f (x) of the reflection cone (1), and finishing the manufacturing of the reflection cone (1) according to an analytical expression of f (x);
if not, returning to the step 2 until T (y) < Tmax。
2. The method for manufacturing the reflecting cone for expanding the beam of the high-energy laser as claimed in claim 1, wherein the step 1 specifically comprises: the surface function f (x) of the reflecting cone (1) is two-stage, and the surface function of the reflecting cone (1) is
In the formula: f. of1(x) Is a surface type function of the first section of the reflecting cone (1);
f2(x) Is a surface type function of the second section of the reflecting cone (1);
r1 is the radius of the bottom of the first section of the reflecting cone (1);
r1+ r2 is the bottom radius of the second section of the reflecting cone (1);
subscript 1 and subscript 2 denote a first-stage reflection cone (1) and a second-stage reflection cone (1), respectively.
3. The method for manufacturing a reflection cone for high-energy laser beam expansion according to claim 2, wherein the step 2 specifically comprises:
according to the power P of the incident laser, the maximum spot size Z of the incident laser, the convective heat transfer coefficient Hr of the absorption cavity (2) and the maximum tolerance temperature T of the inner wall surface of the absorption cavity (2)maxAnd determining the bottom section sizes R1 and R2 of the reflecting cone (1), the radius R of the absorption cavity (2) as R1+ R2+ b and the height L of the absorption cavity (2), wherein b represents the distance from the bottom edge of the reflecting cone (1) to the inner wall surface of the absorption cavity (2).
4. The method for manufacturing a reflecting cone for high-energy laser beam expansion according to claim 3, wherein the step 4 specifically comprises:
4.1) setting f1(x) Initial value of (0 < f)1(0)0< L, where superscript 0 represents the 0 th iteration;
4.2) solving f according to the light constraint equation set in the step 31(x)nAnd f2(x)nThe analytical expression of (3), wherein the superscript n represents the nth iteration calculation;
4.3) judgment
If f2(r1+r2)nIf | < ε, output f1(x)nAnd f2(x)nWherein ε is a small amount greater than zero;
let f1(0)n+1＝f1(0)n-f2(r1+r2)nReturn to step 4.2).
5. The method for manufacturing a reflection cone for high-energy laser beam expansion according to claim 4, wherein the step 5 specifically comprises:
5.1) calculating the position y of the inner wall surface of the absorption cavity (2)
In the formula: g1(x) Indicates the surface type f of the laser irradiation to the reflecting cone (1)1(x) When the light source is in use, the incident light is reflected to the position on the inner wall surface of the absorption cavity (2);
g2(x) Indicates the surface type f of the laser irradiation to the reflecting cone (1)2(x) When the light source is used, the incident light is reflected to the position on the inner wall surface of the absorption cavity (2);
f1' (x) is f1(x) The first derivative of (a);
f2' (x) is f2(x) The first derivative of (a);
subscript 1 and subscript 2 denote a first-stage reflection cone (1) and a second-stage reflection cone (1), respectively;
5.2) defining the area beam expansion ratio E (x) of incident light rays at different radius positions x of the reflecting cone (1)
In the formula: dScavity(x) The area variation quantity of the incident light projected to the inner wall surface of the absorption cavity (2) when the radius x of the reflection cone (1) is changed by dx is shown;
dSbeam(x) The change of the spot area is shown when the incident light ray changes dx at the radius x of the reflecting cone (1);
5.3) according to E in step 5.2)1(x) And E2(x) Calculating the laser power density D (x) of the corresponding absorption cavity (2) at different radius positions x of the reflection cone (1)
5.4) converting the independent variable from different radius positions x of the reflection cone (1) into the position y of the inner wall surface of the absorption cavity (2), wherein the conversion relation is as follows:
in the formula:
and
are respectively g1(y) and g2(y) the inverse function of (y);
5.5) calculating the temperature distribution T (y) at different positions y on the absorption cavity (2) in the thermal equilibrium state
In the formula: t is0Indicates the initial temperature of the inner wall surface of the absorption cavity (2).
6. The method for manufacturing a reflection cone for high-energy laser beam expansion according to claim 5, wherein the step 6 specifically comprises:
according to the maximum tolerance temperature T of the inner wall surface of the absorption cavity (2)maxAnd the temperature distribution T (y) of the absorption cavity (2) to judge whether T (y) is less than Tmax；
If yes, outputting the surface type function f of the reflection cone (1)1(x) And f2(x) According to f1(x) And f2(x) The analytical expression of (2) completes the manufacture of the reflection cone (1);
if not, returning to the step 2 until T (y) < Tmax。
7. The method of claim 6, wherein the step of forming the reflecting cone comprises: in step 5.2), the area beam expansion ratio e (x) is calculated by the following formula:
in the formula: | g1' (x) | denotes g in step 5.1)1(x) The absolute value of the first derivative of (a);
|g1' (x) | denotes g in step 5.1)2(x) The absolute value of the first derivative of (a).
8. The method for manufacturing a reflecting cone for expanding high-energy laser beam according to claim 7, wherein: the reflection cone (1) is a central axis symmetric geometric structure body generated around the central axis of the incident ray;
the surface type of the reflecting cone (1) is an intersecting curve on a geometric plane generated by the intersection of the geometric plane containing a central shaft and the reflecting cone (1);
the thermal equilibrium state is that the energy of the incident laser is equal to the heat output of the absorption cavity (2).
9. A method for manufacturing a reflecting cone for expanding beam of high-energy laser according to any one of claims 1 to 8, wherein: the value of epsilon is 0.001 mm.
10. A reflection cone (1), characterized in that: the method for manufacturing a reflecting cone for expanding beam of high-energy laser as claimed in any one of claims 1 to 9.
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