Abstract
1 Introduction
Temperature is one of the most important parameters for characterizing the thermodynamic state of matter. Temperature measurements of materials under extreme conditions play an important role in military applications, inertial confinement fusion[
To date, measurements of the mechanical parameters, such as the shock-wave velocity and pressure, of a system have reached a relatively mature state in shock-wave experiments to study the EOS. However, accurately measuring thermodynamic parameters, such as the temperature, remains a difficult task because of the measurement complexity, precision requirements for the instruments, and the establishment of the calculation model[
Although the SOP system has been widely adopted in shock temperature measurements, the reliability of this system has always been questioned. Firstly, the method of temperature measurement based on Planck’s theory has been proposed for decades, but few people have validated the SOP system with more than one standard source to prove its reliability. Secondly, Zeldovich and Raizer[
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Here, we present a method to calibrate and verify the SOP system using two kinds of Planckian radiator standard lamp sources with different color temperatures to calibrate the system. The two lamps are regarded as the standard for each other in the SOP system. The relative deviation between the measured data and the standard value was calibrated for, enabling the SOP system to be used at thousands of kelvin. In addition, a method to analyze the uncertainty and sensitivity of the SOP system is described. A series of laser-induced shock experiments were conducted at a laser facility to verify the reliability of the SOP system for temperature measurements at tens of thousands of kelvin.
2 Verification of the SOP system
2.1 Theoretical basis
The temperature measurement diagnostic system is based on Planck’s black-body theory, which states that all bodies of finite temperature emit with a spectral radiance characteristic of their thermal state[
Two calibrated, Planckian radiator, standard lamps with different color temperatures were used in the calibration and verification of the SOP system, and are regarded as the known standard and unknown source for each other. One of the lamps is a CSTM-USLR-S12F produced by American Labsphere Incorporated, a National Institute of Standards and Technology (NIST)-traceable halogen tungsten lamp
2.2 Experimental configuration
Calibration experiments were conducted at the ‘Shenguang-II’ laser facility platform. The optical path of the calibration is identical to the laser-induced shock experiments. Figure
The outlet of the standard lamp is placed at the object plane of the imaging system. The first part of the imaging system (L1) is composed of several achromatic lenses to produce a magnified real image. This real image is transmitted and collimated by the compound lenses (L2 and L3). After passing through the periscope system, the projection is imaged by L4 at the slit of the SOP streak camera. The specially designed beam splitter (BS) is a dichroic mirror that reflects the probe beam (660 nm) to the VISAR while transmitting the thermal emission to the SOP. A single-channel or multi-channel narrowband filter was placed in front of the slit of the streak camera to allow wavelength-specific light transmission.
When starting the calibrations, the lower-color-temperature lamp (marked as Lamp A) was first placed on the object plane, as shown in Figure
2.3 Multi-channel method
When the filter in front of the streak camera is a multi-channel filter, the temperature of Lamp B can be obtained by fitting several
Similarly, Lamp B was considered as the standard lamp source and Lamp A as the source to be measured. Then, four calculated
No. | MCP | Channel | Standard: Lamp A | Standard: Lamp B | ||
---|---|---|---|---|---|---|
M001 | 850 V | Four-channel | 4893 | 1.3 | 2904 | 1.7 |
M002 | 800 V | Four-channel | 4870 | 1.8 | 2924 | 0.99 |
S001 | 750 V | Single-channel: 442 nm | 4801 | 3.2 | 2981 | 0.94 |
S002 | 800 V | Single-channel: 442 nm | 4818 | 2.9 | 2975 | 0.74 |
S003 | 850 V | Single-channel: 442 nm | 4839 | 2.4 | 2966 | 0.44 |
S0011 | 850 V | Single-channel: 410 nm | 4711 | 5.2 | 2981 | 0.94 |
S0012 | 850 V | Single-channel: 450 nm | 4844 | 2.3 | 2967 | 0.47 |
S0013 | 850 V | Single-channel: 490 nm | 4857 | 2.0 | 2978 | 0.84 |
S0014 | 850 V | Single-channel: 590 nm | 4749 | 4.3 | 3041 | 2.9 |
S0021 | 800 V | Single-channel: 410 nm | 4752 | 4.3 | 2990 | 1.2 |
S0022 | 800 V | Single-channel: 450 nm | 4879 | 1.6 | 2977 | 0.81 |
S0023 | 800 V | Single-channel: 490 nm | 4894 | 1.3 | 2983 | 1.0 |
S0024 | 800 V | Single-channel: 590 nm | 4782 | 3.6 | 3057 | 3.4 |
Table 1. Calibration and verification results (measured temperature
2.4 Single-channel method
If the filter in front of the streak camera is a single-channel filter, the temperature of Lamp B can be obtained from Equation (
3 Uncertainty and sensitivity analysis of the SOP system
For the multi-channel method, the uncertainty of the temperature and emissivity can be calculated by fitting the error from the least squares method[
The relative uncertainty of
The values of
The values of
In calibration experiments,
Therefore, the uncertainty and relative uncertainty of the temperature to be measured,
No. | Sample | ||||||||
---|---|---|---|---|---|---|---|---|---|
(nm) | (nm) | (K) | (K) | ||||||
M001B | Lamp B | Four-channel | 4893 | 226 | |||||
M002B | Lamp B | Four-channel | 4870 | 217 | |||||
S001B | Lamp B | 442 | 20 | 4799 | 121 | ||||
S002B | Lamp B | 442 | 20 | 4817 | 121 | ||||
S003B | Lamp B | 442 | 20 | 4838 | 122 | ||||
S0011B | Lamp B | 410 | 10 | 4711 | 102 | ||||
S0012B | Lamp B | 450 | 10 | 4843 | 113 | ||||
S0013B | Lamp B | 490 | 15 | 4854 | 123 | ||||
S0014B | Lamp B | 590 | 15 | 4747 | 138 | ||||
S0021B | Lamp B | 410 | 10 | 4725 | 103 | ||||
S0022B | Lamp B | 450 | 10 | 4869 | 114 | ||||
S0023B | Lamp B | 490 | 15 | 4880 | 124 | ||||
S0024B | Lamp B | 590 | 15 | 4762 | 139 | ||||
M001A | Lamp A | Four-channel | 2904 | 140 | |||||
M002A | Lamp A | Four-channel | 2924 | 50 | |||||
S001A | Lamp A | 442 | 20 | 2981 | 84 | ||||
S002A | Lamp A | 442 | 20 | 2975 | 84 | ||||
S003A | Lamp A | 442 | 20 | 2967 | 84 | ||||
S0011A | Lamp A | 410 | 10 | 2982 | 56 | ||||
S0012A | Lamp A | 450 | 10 | 2968 | 54 | ||||
S0013A | Lamp A | 490 | 15 | 2977 | 64 | ||||
S0014A | Lamp A | 590 | 15 | 3040 | 64 | ||||
S0021A | Lamp A | 410 | 10 | 2983 | 57 | ||||
S0022A | Lamp A | 450 | 10 | 2976 | 54 | ||||
S0023A | Lamp A | 490 | 15 | 2986 | 64 | ||||
S0024A | Lamp A | 590 | 15 | 3062 | 65 | ||||
D0211 | Quartz | 450 | 10 | 0.707 | 0.109 | 46498 | 7727 | ||
D0212 | Quartz | 590 | 15 | 0.720 | 0.111 | 47710 | 8787 | ||
D0213 | Fused silica | 410 | 10 | 0.534 | 0.082 | 43134 | 6847 | ||
D0214 | Fused silica | 490 | 15 | 0.534 | 0.082 | 61117 | 11836 |
Table 2. Variables and their uncertainties in the calibrations and shock-wave experiments. Samples for the calibrations using a single-channel begin with an S; samples for calibrations using a multi-channel begin with an M; and samples for the shock-wave experiments begin with a D. In particular, the
The precision of the temperature calculation can be improved by analyzing its sensitivity to the variables
For the shock-wave experiments shown in Figures
4 Applications in shock experiments
To verify the reliability of the SOP system for temperature measurements at tens of thousands of kelvin, quartz was selected as the material to be studied, owing to its abundant research data. A series of laser-induced shock experiments were conducted at the ‘Shenguang-II’ laser facility. Decaying shock waves were generated by ablation of the thin plastic layers (CH and CHBr) backing the sample. Laser energies of up to 1000 J were delivered at 351 nm. The temporal profile of the laser was nearly square, with an FWHM of
Standard laser-shock diagnostics, including SOP and VISAR, were employed. The VISAR (660 nm) was applied for simultaneous diagnostics with the SOP for the free surface velocity and optical reflectivity. The diagnostic systems had a temporal resolution of
Figures
5 Conclusions
Two calibrated Planckian radiators with different color temperatures were used for calibration and verification of the SOP system. They are regarded as both the known standard and unknown source for each other in the SOP system. The SOP system was calibrated using both multi-channel and single-channel methods. To verify the reliability of the SOP system, the relative deviation between the measured data and the standard value was calibrated for. Also, a method to analyze the uncertainty and sensitivity of the SOP system was proposed. To verify the reliability of the SOP system for temperature measurements at tens of thousands of kelvin, a series of laser-induced shock experiments were conducted at the ‘Shenguang-II’ laser facility. The measured temperature of quartz in our experiments agreed with previous works fairly well, which could be evidence of the reliability of the SOP system.
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