A method and system for measuring a plasma density gradient

Abstract

The application discloses a method and system for measuring plasma density gradient, and belongs to the technical field of plasma physics diagnosis, which comprises the following steps: a femtosecond laser pulse with wide spectrum characteristics and an initial pulse width is incident to a to-be-measured plasma; the pulse width of the femtosecond laser pulse reflected by the to-be-measured plasma is measured; according to a preset mapping relationship between the pulse width of the reflected femtosecond laser pulse and the plasma density gradient and the pulse width of the femtosecond laser pulse reflected by the to-be-measured plasma measured at present, the density gradient of the to-be-measured plasma is determined. The application overcomes the limitation of insufficient time resolution of traditional methods such as the interference method and the shadow method, does not need complex density distribution reconstruction algorithms or model assumptions, can directly obtain gradient information according to the preset mapping relationship between the reflected pulse width and the density gradient, and reduces the data processing complexity and inversion error.

Description

Technical Field

[0001] This invention relates to the field of plasma physics diagnostics, and in particular to a method and system for measuring plasma density gradient. Background Technology

[0002] Plasma density gradient is one of the key physical parameters characterizing plasma state. It directly affects laser energy coupling efficiency, plasma instability development, and energy transfer processes during laser-plasma interaction. Particularly in inertial confinement fusion (ICF), the distribution of the coronal plasma density gradient formed by laser irradiation of a target pellet plays a crucial role in suppressing laser-plasma instabilities such as stimulated Raman scattering and stimulated Brillouin scattering. Therefore, achieving rapid and accurate measurement of this gradient has significant scientific value and application prospects.

[0003] Currently, the diagnosis of plasma density gradients mainly relies on indirect inversion or model-dependent measurement methods of plasma density distribution, including laser interferometry, Thomson scattering, Stark broadening, and shading and schlieren methods. Laser interferometry, by measuring the phase change of a probe laser after passing through the plasma, inverts the electron density distribution and then calculates the density gradient. This method is suitable for low-density plasmas, but in high-density regions near the critical density, the laser cannot penetrate, leading to measurement failure. Furthermore, interferometry requires complex optical systems and phase reconstruction algorithms, and its time resolution is typically limited to the nanosecond scale, making it difficult to capture the rapid evolution of the plasma. Thomson scattering analyzes the spectral characteristics of the incident laser after being scattered by electrons in the plasma, simultaneously obtaining electron density and temperature information. However, this method has a weak signal, requires high-power lasers and high-sensitivity spectrometers, and is complex and costly. In high-density plasmas, collective scattering effects interfere with spectral analysis, affecting the accuracy of gradient inversion. The Stark broadening method utilizes the broadening effect of atomic or ion spectral lines under an electric field to invert electron density. However, this method relies on the assumption that the plasma is in a local thermodynamic equilibrium state, limiting its applicability in non-equilibrium and transient plasmas. Furthermore, spectral line broadening is susceptible to interference from Doppler effects and instrument broadening, leading to significant uncertainties in the inversion results. The shading and schlieren methods invert density distribution by recording the deflection information of probe light in the plasma. However, these methods also face challenges such as complex reconstruction algorithms, limited temporal resolution, and high requirements for optical system stability. They typically assume plasma axisymmetry or a specific distribution model, resulting in significant errors under non-ideal conditions.

[0004] In summary, existing methods for measuring plasma density gradients suffer from low temporal resolution, making them unsuitable for diagnosing transient plasma processes in the femtosecond to picosecond range. Furthermore, these methods are complex, costly, and reliant on large optical platforms or high-power laser systems. The measurement process is also highly invasive or dependent on model assumptions, affecting the actual plasma state or introducing inversion errors. They cannot directly and instantly obtain density gradient information, typically requiring indirect derivation from density distribution, a cumbersome process that accumulates errors. Therefore, current technology lacks a direct method for measuring plasma density gradients with high temporal resolution, non-invasiveness, single-measurement capability, and a simple system structure to meet the needs of high-energy-density physics, laser fusion, and other fields for rapid and accurate diagnosis of plasma states.

[0005] Therefore, existing technologies still need further development. Summary of the Invention

[0006] The main objective of this invention is to provide a method and system for measuring plasma density gradient, aiming to solve the technical problems of complex measurement equipment, low time resolution, indirect measurement process, and easy introduction of errors in the prior art.

[0007] To achieve the above objectives, according to a first aspect of the present invention, the present invention provides a method for measuring plasma density gradient, comprising: S100. A femtosecond laser pulse with broad spectral characteristics and initial pulse width is incident onto the plasma to be tested. S200. Measure the pulse width of the femtosecond laser pulse after it is reflected by the plasma under test; S300. Determine the density gradient of the plasma under test based on the pre-established mapping relationship between the pulse width of the reflected femtosecond laser pulse and the plasma density gradient, and the pulse width of the femtosecond laser pulse reflected by the plasma under test currently measured.

[0008] Specifically, the preset mapping relationship is a preset mapping relationship between the pulse width of the reflected femtosecond laser pulse and the plasma density gradient, which is established in advance through theoretical numerical simulation or experimental calibration methods.

[0009] Specifically, when establishing the preset mapping relationship through the experimental calibration method, the method for establishing the preset mapping relationship includes: By changing the center wavelength of the femtosecond laser pulse, the plasma density gradient of the plasma under test at different critical density values ​​can be measured. The pulse width of the femtosecond laser pulse after reflection from the plasma under different plasma density gradients is obtained; and Based on the obtained pulse width and the corresponding plasma density gradient, a correlation curve between the pulse width and the plasma density gradient is fitted to establish the preset mapping relationship.

[0010] Specifically, the method for determining the density gradient of the plasma to be measured includes: The pulse width of the femtosecond laser pulse after reflection from the plasma under test is substituted into the function or lookup table determined by the preset mapping relationship to obtain the corresponding density gradient value of the plasma under test.

[0011] According to a second aspect of the present invention, a system for measuring plasma density gradients is provided, the system comprising: Femtosecond laser module, used to provide femtosecond laser pulses with broad spectral characteristics; A laser transmission and focusing module is used to transmit and focus the femtosecond laser pulse onto the plasma under test, and to collect the laser pulse reflected back from the plasma under test; A laser pulse width measurement module is used to measure the pulse width of the laser pulses collected and reflected back from the plasma under test; The processing module is used to determine the density gradient of the plasma under test based on the pulse width measured by the laser pulse width measurement module and a preset mapping relationship between the pulse width of the reflected femtosecond laser pulse and the plasma density gradient.

[0012] Specifically, the laser transmission and focusing module is a single integrated module that combines the functions of transmitting and focusing incident laser light and collecting reflected laser light.

[0013] Specifically, the laser transmission and focusing module includes a first laser transmission and focusing module and a second laser transmission and focusing module. The first laser transmission and focusing module is used to transmit and focus the femtosecond laser pulse onto the plasma to be tested, and the second laser transmission and focusing module is used to collect the laser pulses reflected back from the plasma to be tested.

[0014] Specifically, the laser pulse width measurement module is at least one of a single autocorrelation meter, a frequency-resolved optical switch, or a spectral phase interferometer.

[0015] Specifically, the laser wavelength of the femtosecond laser module is adjustable; The processing module stores multiple preset mapping relationships corresponding to multiple different laser wavelengths, and is configured to call the corresponding preset mapping relationship according to the currently selected laser wavelength to determine the density gradient of the plasma to be tested.

[0016] Beneficial effects: This invention provides a plasma density gradient measurement system and method. Utilizing the wide-spectrum characteristics of femtosecond lasers and the principle of critical reflection in plasma, the density gradient is inverted by directly measuring the pulse width change of the reflected laser pulse. This achieves non-invasive, single-shot, and rapid direct measurement, avoiding interference with the plasma state and eliminating the need for multiple scans or signal accumulation. Furthermore, by using a femtosecond laser as the probe, the method possesses high time resolution on the femtosecond scale, enabling the capture of the rapid evolution of transient plasma density gradients. This overcomes the limitations of insufficient time resolution in traditional interferometry and shadowing methods. It eliminates the need for complex density distribution reconstruction algorithms or model assumptions; gradient information can be directly obtained based solely on a pre-defined mapping relationship between the reflected pulse width and the density gradient, reducing data processing complexity and inversion errors. This invention is easily integrated and applied in large-scale laser devices, providing a reliable and efficient technical means for online diagnostics in fields such as inertial confinement fusion and laser plasma acceleration. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a method for measuring plasma density gradient provided in a specific embodiment of the present invention; Figure 2 This is a schematic diagram of the composition of the system for measuring plasma density gradient provided in a specific embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the measurement principle of measuring plasma density gradient provided in a specific embodiment of the present invention; Figure 4 This is a schematic diagram of the preset mapping relationship curve between the reflected laser pulse width and the plasma density scale provided in a specific embodiment of the present invention; Figure 5 This is a schematic diagram of the numerical simulation results provided in a specific embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. The described embodiments should not be considered as limitations on this application. All other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this application. Unless otherwise defined, all technical and scientific terms used in the embodiments of this application have the same meaning as commonly understood by those skilled in the art. The terminology used in the embodiments of this application is for the purpose of describing the embodiments of this application only and is not intended to limit this application.

[0020] It should be noted that in the description of this application, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. Furthermore, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance. Unless otherwise specified, the meanings of relevant terms and specific implementations can be found in well-known technologies in the art.

[0021] This invention addresses the urgent need for rapid, accurate, and direct measurement of density gradients near the critical surface of plasma in the field of plasma physics diagnostics, particularly in cutting-edge research areas such as inertial confinement fusion, laser particle acceleration, and high-energy-density physics. Traditional diagnostic methods, such as laser interferometry, shadowing, Thomson scattering, and Stark broadening, while providing plasma information under specific conditions, generally suffer from inherent limitations, including limited temporal resolution, complex and expensive equipment, highly invasive measurement processes or reliance on strong theoretical assumptions, and the inability to directly acquire gradient information in a single measurement. For example, interferometry fails when the plasma density approaches the critical value because the laser cannot penetrate; Thomson scattering signals are weak and subject to collective effects; and spectral methods are limited by model assumptions and the superposition of multiple broadening mechanisms. These limitations make capturing the rapid evolution of transient plasma density gradients within femtosecond to picosecond timescales extremely difficult, failing to meet the ultra-high temporal resolution diagnostic requirements of modern high-power laser-matter interaction research.

[0022] Before providing a further detailed description of the embodiments of this application, some of the nouns and terms involved in the embodiments of this application will be explained. The nouns and terms involved in the embodiments of this application are subject to the following interpretations.

[0023] (1) Plasma density gradient: refers to the physical quantity that describes the rate of change of plasma electron density in space. It usually refers to the density change rate along the laser incident direction. In fields such as inertial confinement nuclear fusion, this parameter directly affects the absorption efficiency of laser energy and the development of various instabilities, and is a key physical parameter.

[0024] (2) Pre-defined mapping relationship: This refers to a definite, monotonic functional relationship between the pulse width of the reflected laser pulse and the density gradient of the plasma under known and defined incident laser parameters. This relationship can be established in advance through theoretical numerical simulation or experimental calibration and stored as a database or calibration curve, such as... Figure 4 As shown, this is used for subsequent queries and inversions, thereby enabling direct quantitative measurement of the density gradient.

[0025] (3) Broad spectrum characteristics: refers to the characteristic that the femtosecond laser pulse covers a wide frequency range (or wavelength range) in the frequency domain. This characteristic is the physical basis of the present invention, which enables different frequency components in the laser pulse to be reflected at different critical density spatial positions in the plasma, thereby causing the reflected pulse to be broadened in the time domain.

[0026] (4) Single autocorrelation meter: It is a precision optical instrument used to measure the width of ultrashort laser pulses, such as femtosecond or picosecond pulses. Its feature is that it can complete a complete pulse width measurement with a single laser emission. It is particularly suitable for the diagnosis of non-repetitive or transient events, ensuring the high time resolution of the method of the present invention.

[0027] The present invention will be further described below with reference to the accompanying drawings and preferred embodiments.

[0028] Example 1 Please see Figure 1 This application provides a method for measuring plasma density gradient, which aims to address the shortcomings of existing measurement methods, such as complex equipment, low time resolution, indirect processes, and the need for complex reconstruction algorithms. The method includes: first, incidenting a femtosecond laser pulse with broad spectral characteristics and an initial pulse width onto the plasma to be measured; then measuring the pulse width of the femtosecond laser pulse after reflection from the plasma; and finally, determining the density gradient of the plasma to be measured based on a pre-established mapping relationship between the pulse width of the reflected femtosecond laser pulse and the plasma density gradient, and the currently measured pulse width of the reflected femtosecond laser pulse from the plasma.

[0029] In this embodiment, the aforementioned preset mapping relationship is a preset mapping relationship between the pulse width of the reflected femtosecond laser pulse and the plasma density gradient, which is established in advance through theoretical numerical simulation methods or experimental calibration methods.

[0030] It is understandable that the essence of the above-mentioned pre-defined mapping relationship is to establish a quantitative correspondence between the reflected laser pulse width and the plasma density gradient through theoretical simulation or experimental calibration under the condition of a known incident laser parameter. This mapping relationship is based on the dispersive reflection mechanism of femtosecond lasers near the critical density surface of plasma. The gentler the density gradient, the greater the difference in reflection depth of different frequency components, and the more significant the pulse width broadening. The steeper the density gradient, the less significant the broadening. Numerical methods such as particle simulation and fluid simulation, or experimental measurements using a calibrated plasma source with a known density gradient, can be used to obtain a series of reflection pulse width data corresponding to density gradient values. Based on the calibration data of an initial pulse width, the calibration relationship of reflection pulse width under other initial incident pulse widths can be obtained through theoretical calculations. Then, a functional relationship or a lookup table-like mapping relationship can be established by fitting. This pre-defined mapping relationship can transform the complex spatial density gradient measurement problem into a simple time-domain pulse width measurement problem, realizing the direct inversion from measurable time-domain parameters to the physical parameters to be measured. In actual measurement, the density gradient value near the critical surface of the plasma to be measured can be obtained quickly and accurately simply by substituting the measured reflection pulse width into this mapping relationship. The whole process is simple, direct, and repeatable, fully demonstrating the advantages of non-invasiveness, high temporal resolution, and ease of integration of this invention.

[0031] Furthermore, when establishing the preset mapping relationship through the experimental calibration method, the method for establishing the preset mapping relationship includes: (1) By changing the center wavelength of the femtosecond laser pulse, the plasma density gradient of the plasma under test at different critical density values ​​is measured; (2) Obtain the pulse width of the femtosecond laser pulse after reflection by the plasma under different plasma density gradients; (3) Based on the obtained pulse width and the corresponding plasma density gradient, the correlation curve between the pulse width and the plasma density gradient is fitted to establish the preset mapping relationship.

[0032] It is understandable that the mapping relationship established in the above manner not only covers the gradient measurement requirements of different critical density regions, but also, because it is based on actual experimental data, can effectively avoid model errors that may exist in theoretical simulations, further improving the measurement accuracy and reliability of the method in practical applications. When actually measuring the plasma to be measured, it is only necessary to select the corresponding mapping relationship according to the laser wavelength used, substitute the measured reflection pulse width into the mapping relationship, and the density gradient value of the plasma to be measured at the corresponding critical density can be quickly obtained.

[0033] In this embodiment, the method for determining the density gradient of the plasma to be tested includes: substituting the pulse width of the femtosecond laser pulse reflected by the currently measured plasma into a function or lookup table determined by the preset mapping relationship to obtain the corresponding density gradient value of the plasma to be tested.

[0034] It should be noted that, in the practical application of the above scheme to measure the density gradient of the plasma under test, the specific steps for determining the density gradient of the plasma under test are as follows: First, following the aforementioned measurement procedure, a femtosecond laser pulse is incident on the plasma under test, the femtosecond laser pulse after reflection from the plasma is collected, and its reflected pulse width is accurately measured through a pulse width measurement module. At the same time, the center wavelength of the femtosecond laser pulse used in this measurement is recorded. Then, based on the center wavelength, a preset mapping relationship corresponding to it is selected from a set of pre-established mapping relationships. This preset mapping relationship can be in the form of a function or a discrete lookup table. Finally, the measured reflected pulse width value is substituted into the preset mapping relationship. If the mapping relationship is in the form of a function, the corresponding density gradient value is directly calculated through the function. If the mapping relationship is in the form of a lookup table, the density gradient value that best matches the measured pulse width is obtained from the lookup table through linear interpolation or spline interpolation methods. This achieves rapid and accurate inversion from directly measurable time-domain parameters to the physical parameters under test. The entire process does not require complex phase reconstruction or spectral analysis, significantly simplifying the measurement process and improving measurement efficiency.

[0035] Preferably, the initial pulse width of the femtosecond laser pulse can be set to 30 fs. Firstly, a pulse width of 30 fs is a mature and easily achievable typical parameter in the current femtosecond laser technology field. It ensures a sufficiently wide spectral width (according to the Fourier transform limit, a 30 fs pulse width corresponds to a spectral width of approximately 30-40 nm, depending on the pulse shape), providing good frequency resolution for the dispersive reflection of different frequency components in the plasma. Secondly, it avoids introducing complex dispersion effects or placing excessively high demands on the dispersion control of the optical system due to an excessively narrow pulse width (e.g., <10 fs). Furthermore, a 30 fs pulse width is compatible with currently commercially available autocorrelators... Matching the optimal measurement range of pulse width measurement equipment such as frequency-resolved optical switches is beneficial for improving measurement accuracy. In addition, the stability of the pulse width output by the femtosecond laser should be ensured during the measurement process. If necessary, the pulse width of the incident laser can be monitored in real time to eliminate the influence of the laser's own fluctuations on the measurement results and further improve the measurement accuracy. It should be noted that the present invention does not further limit the initial pulse width of the incident femtosecond laser pulse. In addition to setting it to 30fs, it can also be set to 25fs, 35fs, 40fs, etc., which can be further set according to the user's actual needs.

[0036] Example 2 Please see Figure 2To implement the above method, this application also provides a system for measuring plasma density gradient. This system includes a femtosecond laser module, a laser transmission and focusing module, a laser pulse width measurement module, and a processing module. These modules work together to accurately measure the plasma density gradient. Specifically, the femtosecond laser module provides femtosecond laser pulses with broad spectral characteristics; the laser transmission and focusing module transmits and focuses the femtosecond laser pulses onto the plasma under test and collects the laser pulses reflected back from the plasma; the laser pulse width measurement module measures the pulse width of the collected laser pulses reflected back from the plasma; and the processing module determines the density gradient of the plasma under test based on the pulse width measured by the laser pulse width measurement module and a pre-established mapping relationship between the pulse width of the reflected femtosecond laser pulses and the plasma density gradient.

[0037] Specifically, the femtosecond laser module is used to provide femtosecond laser pulses with broad spectral characteristics and specific initial pulse width and center wavelength as probe light for diagnostic purposes.

[0038] The laser transmission and focusing module is used to transmit and focus the femtosecond laser pulses generated by the femtosecond laser module onto the plasma under test, and is responsible for collecting the laser pulses reflected back from the plasma under test. In one embodiment, such as Figure 2 As shown, the module can be composed of two separate parts: a laser transmission and focusing module is responsible for the transmission and focusing of incident light, and the other laser transmission and focusing module is responsible for the collection and transmission of reflected light.

[0039] The optical input of the laser pulse width measurement module is connected to the optical output of the laser transmission and focusing module to accurately measure the pulse width of the collected reflected laser pulses. The processing module, which can be a general-purpose computer, a dedicated digital signal processor (DSP), or a field-programmable gate array (FPGA), has pre-stored the aforementioned preset mapping relationship. This processing module is electrically connected to the laser pulse width measurement module to receive the measured pulse width data and, based on the pre-stored mapping relationship, calculate and output the density gradient value of the plasma under test.

[0040] In one specific embodiment, the laser transmission and focusing module is a single integrated module that combines the functions of transmitting and focusing incident laser light with collecting reflected laser light.

[0041] In another specific embodiment, the laser transmission and focusing module includes a first laser transmission and focusing module and a second laser transmission and focusing module. The first laser transmission and focusing module is used to transmit and focus the femtosecond laser pulse onto the plasma to be tested, and the second laser transmission and focusing module is used to collect the laser pulses reflected back from the plasma to be tested.

[0042] Preferably, the laser pulse width measurement module is at least one of a single autocorrelation meter, a frequency-resolved optical switch, or a spectral phase interferometer.

[0043] Preferably, the laser wavelength of the femtosecond laser module is adjustable; the processing module stores multiple preset mapping relationships corresponding to multiple different laser wavelengths, and is configured to call the corresponding preset mapping relationship according to the currently selected laser wavelength to determine the density gradient of the plasma to be tested.

[0044] Understandably, the femtosecond laser module can employ a wavelength-tunable femtosecond laser source, such as a Ti:sapphire tunable laser, an optical parametric amplifier, or a wavelength-tunable system based on nonlinear frequency conversion, capable of outputting femtosecond laser pulses with a center wavelength that is continuously or discretely tunable within a certain range. It should be noted that the data processing module pre-stores multiple preset mapping relationships corresponding to various laser wavelengths. Since different laser wavelengths correspond to different plasma critical densities, for each available laser wavelength, a specific mapping relationship between its reflection pulse width and plasma density gradient needs to be established. These mapping relationships can be a family of curves calculated separately for different wavelengths through theoretical numerical simulations, or a set of lookup tables or fitting functions obtained through experimental calibration methods at different wavelengths. In actual measurement, the operator first selects a suitable operating wavelength by adjusting the femtosecond laser module according to the expected density range of the plasma to be measured and the measurement requirements. Then, the data processing module reads the laser settings through the communication interface, or automatically identifies the wavelength through real-time monitoring by a wavelength meter, or allows the operator to input the currently selected laser wavelength. It then calls up the mapping relationship corresponding to that wavelength from multiple preset mapping relationships stored internally. Finally, the reflected laser pulse width value measured by the pulse width measurement module is substituted into the called mapping relationship to quickly invert the density gradient value of the plasma at the critical density corresponding to the current laser wavelength. This optimized configuration enables the measurement of a single density region. Through simple wavelength tuning, it allows for flexible scanning and measurement of the density gradient distribution at different depths from low to high density in the plasma, thereby obtaining more complete plasma density gradient profile information and greatly expanding the application scope and measurement capabilities of this invention.

[0045] The following is combined Figures 2-5 The working principle and process of this embodiment will be further described, such as... Figure 2 As shown: Step 1: A femtosecond laser module generates an incident laser pulse with an initial pulse width, which is then guided and focused onto the plasma to be tested by the laser transmission and focusing module. The plasma to be tested has a density distribution that varies along the laser incident direction, forming a plasma density gradient region. The core physical principle of this method is as follows Figure 3 As shown, the upper left figure represents the time-domain waveform (including chirp) of the incident femtosecond laser pulse. The horizontal axis represents time (fs), ranging from -50fs to 50fs, and the vertical axis represents the normalized electric field strength, ranging from -1 to 1. It exhibits a centrally symmetric oscillating wave packet with a Gaussian envelope. The oscillation frequency changes with time, gradually becoming denser from left to right, i.e., the frequency chirps upward, indicating that this is a typical ultrashort femtosecond pulse. The lower left figure represents the time-domain waveform of the reflected laser pulse, which still has a Gaussian envelope. The horizontal axis represents time (fs), ranging from -50fs to 50fs, and the vertical axis represents the normalized electric field strength, ranging from -1 to 1. However, the shape is significantly asymmetrical. Compared to the incident pulse, the pulse width is significantly broadened, and the alternation of positive and negative polarities is more complex. This indicates that the reflected pulse is no longer the original narrow pulse. The pulse width broadening is due to the different positions of the different frequency components reflected in the plasma. Therefore, the reflected pulse exhibits a temporal frequency ordering. Figure 3 The right figure shows a schematic diagram of plasma density distribution and reflection paths of different frequency components, where the horizontal axis represents spatial location. The vertical axis represents the plasma electron density, and its density distribution curve is a monotonically increasing curve. This indicates that the plasma density increases with increasing spatial location, i.e., a density gradient exists. and Indicates two reference density values, Among them, low-frequency components correspond to lower critical densities, and therefore will be present in shallower locations (such as...). The high-frequency components are reflected, and their corresponding high-critical-density components need to propagate deeper to encounter sufficiently high-density regions (such as...). Only when the low-frequency components are reflected can they be reflected. The dashed arrows in the figure represent the propagation paths of different frequency components. Low-frequency components are reflected near the surface, while high-frequency components are reflected after penetrating deeper. Figure 3 This indicates that because femtosecond lasers have broadband characteristics, their different frequency components propagate to different depths in the plasma before being reflected, resulting in time broadening and frequency separation of the reflected pulse, which allows for the inversion of plasma density gradient information.

[0046] according to Figure 3 Because femtosecond laser pulses have broad spectral characteristics, they possess a spectral width of tens of nanometers in the frequency domain, containing optical components of different frequencies (or wavelengths). According to plasma physics, the critical reflection density of a laser... Its frequency (or wavelength) The relationship between them can be approximated as follows: ; in, This represents the critical reflectance density, expressed in cubic centimeters (cm²).-3 ); The wavelength of a laser is expressed in micrometers (μm). This means that different frequency components in an incident laser pulse will travel to different spatial locations in the plasma density gradient region before being reflected. It can be seen that the longer the wavelength, the lower the corresponding critical plasma density; the shorter the wavelength, the higher the corresponding critical plasma density. Specifically, components with lower frequencies and longer wavelengths will be reflected in regions with lower density, such as the low-frequency component reflection path, while components with higher frequencies and shorter wavelengths will penetrate deeper and be reflected in regions with higher density, such as the high-frequency component reflection path.

[0047] Therefore, for plasmas with gradually increasing density distribution, as the laser propagates through them, the plasma density sensed by the laser also gradually increases. Near the critical surface, the relatively long wavelength components in the laser pulse will be reflected by the critical surface corresponding to the wavelength, and the relatively short wavelength components will subsequently be reflected by the corresponding critical surface. Thus, the relatively long wavelength low-frequency components have a short path in the plasma, while the relatively short wavelength high-frequency components have a long path in the plasma.

[0048] Understandably, the separation of different frequency components at their spatial reflection positions leads to differences in the optical path lengths they experience in the plasma. Therefore, the incident laser pulse, which was originally very narrow in the time domain, becomes a reflected laser pulse that is significantly broadened in the time domain after being reflected by the plasma density gradient region. The degree of pulse broadening is directly related to the steepness of the density gradient in the plasma density gradient region. That is, the gentler the density gradient, the greater the difference in reflection positions between different frequency components, the greater the optical path difference, and ultimately the more significant the pulse width broadening of the reflected laser pulse. Conversely, if the density gradient is steeper, the pulse width broadening is smaller.

[0049] For a femtosecond laser pulse that is close to the Fourier transform limit upon incident, it is dispersion-free. After reflection by the critical plasma, the head of the reflected laser pulse mainly consists of low-frequency components with relatively long wavelengths, while the tail consists of high-frequency components with relatively short wavelengths. The reflected laser pulse is stretched in the time domain and its pulse width is broadened compared to the incident laser pulse. Due to the broadband characteristics of femtosecond lasers, the pulse width variation of the reflected laser is essentially due to the different dispersion of different frequency components in the plasma, and specifically, it is mainly related to the steepness of the plasma density gradient at the critical surface. Therefore, the change in the pulse width of the reflected laser is essentially a reflection of the steepness of the plasma density gradient. After establishing the mapping relationship between the change in the pulse width of the reflected laser and the plasma density gradient, the density gradient level at the plasma critical surface can be measured by the change in the pulse width of the reflected laser.

[0050] Step 2: The reflected laser pulse is collected by the laser transmission focusing module and imported into the laser pulse width measurement module to accurately measure its pulse width, such as... Figure 5 As shown, Figure 5 This figure illustrates the temporal evolution of a femtosecond laser pulse during reflection at a critical plasma interface. The horizontal axis represents time (fs), ranging from 0 to 900 fs, and the vertical axis represents the laser electric field intensity in normalized units. The blue dashed line represents the incident laser pulse, and the orange solid line represents the reflected laser pulse. The first figure shows that the initial incident pulse is an ultrashort pulse close to the Fourier transform limit, exhibiting a very narrow and symmetrical spike structure centered at approximately 50 fs. The waveform is almost Gaussian or an ultrashort pulse, with no chirp or broadening, indicating that the incident light is a dispersion-free, broadband, ultrashort femtosecond pulse. The second figure shows that the reflected pulse lags significantly behind the incident pulse, reflecting optical path delay. In the third figure, the reflected pulse is no longer a single spike, but rather... The pulse is composed of multiple superimposed small pulses. The first half is a small positive pulse, and the second half is a larger negative pulse. This indicates that different frequency components experience different phase accumulation and group velocities in the plasma. The low-frequency components (long waves) are reflected first, but with smaller amplitudes, while the high-frequency components (short waves) are reflected later with larger amplitudes. Therefore, the reflected pulse exhibits frequency chirp and pulse width broadening. The steeper the plasma density gradient, the more significant this frequency separation and the greater the pulse width broadening. The fourth figure only shows the orange solid line (reflected light), and the blue dashed line has been removed. The pulse width is significantly increased, and there is a slight oscillation near the center of the waveform, which may be the result of multi-frequency interference. The pulse width broadening directly reflects the density gradient information at the plasma interface. The steeper the density gradient, the stronger the dispersion, the more severe the frequency separation, and the greater the pulse width broadening. In summary, the initial incident pulse is an ultrashort pulse close to the Fourier transform limit. After plasma reflection, due to the difference in group velocities of different frequency components in the density gradient region, the reflected pulse is significantly broadened and exhibits frequency chirp characteristics, with the low-frequency components leading and the high-frequency components lagging. This pulse width broadening phenomenon can be used as a sensitive probe of the plasma density gradient; by measuring the reflected pulse width, the density gradient level at the interface can be retrieved. Figure 5 The numerical simulation results visually demonstrate this process: an incident pulse with a very narrow initial time-domain waveform forms a reflected pulse with a significantly wider time-domain waveform after interacting with the plasma. Step 3: After receiving the pulse width value measured by the laser pulse width measurement module, the processing module compares it with a pre-established preset mapping relationship to determine the density gradient of the plasma to be measured, such as... Figure 4As shown, the preset mapping relationship is represented by a monotonically changing curve. Its horizontal axis is the plasma density scale length, i.e., the length of the plasma density gradient (cm), which is inversely proportional to the density gradient. The vertical axis is the reflected laser pulse width (fs). By referring to this curve, the corresponding density gradient value can be uniquely determined from the measured pulse width value. This method directly inverts the density gradient by measuring a single time-domain parameter (pulse width), avoiding the complex reconstruction algorithm of traditional methods, and realizing direct, simple and high time resolution measurement.

[0051] In a preferred embodiment, the aforementioned preset mapping relationship is established in advance through theoretical numerical simulation or experimental calibration. In the theoretical numerical simulation, a particle simulation (PIC) program can be used to set up a series of plasma models with different density gradients and simulate the interaction between femtosecond laser pulses with specific parameters and these models. The pulse width of the reflected pulse under each gradient is recorded, thereby constructing a mapping relationship as described above. Figure 4 The database or calibration curve shown can be used in experimental calibration with a known plasma source that can precisely adjust the density gradient. The system described in this invention can be used for measurement, while another calibrated method, such as interferometry, is used as a reference to establish the experimental calibration relationship between pulse width and gradient. This pre-established mapping relationship ensures the accuracy and reliability of subsequent measurement results.

[0052] Furthermore, to achieve the aforementioned physical principles, the femtosecond laser pulses provided by the femtosecond laser module preferably possess broad spectral characteristics. A typical Ti:sapphire femtosecond laser can meet this requirement, with a spectral width reaching tens of nanometers, sufficient to generate significant dispersive reflection effects in plasma. This ensures that the broadening of the reflected pulse has sufficiently high sensitivity to density gradients, a characteristic that forms the physical basis for achieving high-precision measurements.

[0053] In one specific implementation, the femtosecond laser pulse generated by the femtosecond laser module has a center wavelength of 800 nm and an initial pulse width of 30 fs. 800 nm is the most commonly used and stable output wavelength for commercial Ti:sapphire femtosecond lasers. The initial pulse width of 30 fs falls within the ultrashort pulse category, providing extremely high temporal resolution to capture instantaneous changes in plasma state. Under these parameters, the corresponding critical density is approximately... Experiments show that when the density gradient of the plasma under test near the critical surface is... At that time, the measured width of the reflected pulse broadened to 66.7 fs; while when the density gradient became more gradual, it was... At that time, the measured reflection pulse width increased significantly to 122.3 fs. This result clearly shows that there is a strong correlation between the change in reflection pulse width and density gradient, and that the method has high sensitivity to changes in density gradient, thus verifying the feasibility and effectiveness of the scheme.

[0054] In another preferred embodiment, the laser pulse width measurement module can specifically be a single-shot autocorrelator. Since many plasma physics processes are transient and non-repeatable, such as the implosion process of a target pellet in inertial confinement fusion, single-shot measurement capability is crucial. A single-shot autocorrelator can accurately measure the femtosecond pulse width in a single laser emission event, meeting the requirements of the present invention for transient process diagnosis, thereby ensuring the high temporal resolution of the method and its practical value in single-event diagnosis.

[0055] In another parallel implementation, to detect gradients in different density regions, the center wavelength of the femtosecond laser pulses generated by the femtosecond laser module can be 351nm. Through frequency doubling technology, 800nm ​​laser light can be easily converted into 351nm ultraviolet laser light. According to the aforementioned formula, the critical density corresponding to 351nm laser light is increased to approximately [missing value]. This means that by changing the wavelength of the incident laser, gradient information in different density regions of a plasma can be selectively diagnosed. For example, when using a 351 nm laser with an initial pulse width of 30 fs, the density gradient near the new critical surface can be measured. When the plasma is in the plasma, the reflected pulse width can be measured to be 66.8 fs. By comparing this value with the mapping relationship curve established in advance for 351 nm laser, its density gradient can be determined. This tunability greatly expands the scope of application of the present invention, enabling it to flexibly meet the diagnostic needs in different experimental scenarios.

[0056] Furthermore, to optimize the system structure and improve stability and integration, the laser transmission and focusing module can be designed as a single integrated module. In this embodiment, Figure 2 The first and second laser transmission and focusing modules are integrated into a single, functionally unified optical path module. This integrated module utilizes a polarization beam splitter (PBS) and a Faraday rotator to achieve co-path transmission and separation of the optical path. Specifically, the linearly polarized incident laser pulse from the femtosecond laser module passes through the polarization beam splitter, and after passing through the Faraday rotator, its polarization plane is rotated by 45 degrees. It is then focused onto the plasma under test by focusing elements such as an off-axis parabolic mirror (OAP). The reflected laser pulse from the plasma passes through the Faraday rotator again, and its polarization plane is rotated by another 45 degrees in the same direction, resulting in a total polarization rotation angle of 90 degrees for the reflected light, with its polarization direction orthogonal to the incident light. When the reflected light returns to the polarization beam splitter, due to the orthogonality of the polarization directions, it is completely reflected into another optical path and guided to the laser pulse width measurement module. This integrated design not only makes the optical path more compact and reduces the number of optical components, but also greatly improves the system's anti-interference capability and alignment stability due to the co-path design.

[0057] The following describes a specific embodiment integrating the aforementioned preferred technical features to demonstrate the comprehensive performance of the invention. In this embodiment, the measurement system adopts an integrated design, with its laser transmission and focusing module being a single integrated module. The femtosecond laser module provides a femtosecond laser pulse with a center wavelength of 800 nm, an initial pulse width of 30 fs, and broad spectral characteristics. The laser pulse width measurement module is a high-precision single-shot autocorrelator. The processing module pre-stores preset mapping relationship curves for pulse width-gradient of 800 nm and 30 fs incident lasers, established through theoretical numerical simulation, such as... Figure 4 As shown.

[0058] The complete workflow of this specific embodiment is as follows: First, before the measurement begins, an 800nm, 30fs laser is calculated and generated at different density gradients (e.g., from...) using a particle simulation program. arrive The database of pulse widths reflected from the plasma is used to form a precise calibration curve, which is then stored in the processing module. During measurement, the femtosecond laser module emits a single 30 fs laser pulse, which is focused onto the plasma under test via an integrated laser transmission and focusing module. After interacting with the plasma, the broadened reflected laser pulse is collected by the same integrated module and, through polarization separation, is fed into a single autocorrelator. The single autocorrelator captures and measures the width of the reflected pulse on a femtosecond timescale and sends this measurement to the processing module. The processing module immediately searches the pre-stored calibration curve and matches the density gradient value corresponding to a pulse width of 122.3 fs. And finally output the result.

[0059] This embodiment achieves beneficial technical effects through the synergistic combination of several preferred features. First, the use of an 800nm, 30fs laser and a single-shot autocorrelator ensures high time resolution and single-shot diagnostic capability at the femtosecond level. Second, the pre-establishment of precise mapping relationships through numerical simulation guarantees high accuracy in quantitative measurements. Third, the use of an integrated optical path module significantly improves the system's stability and compactness, reducing the impact of environmental vibrations and other factors on the measurement. In summary, this embodiment provides a plasma density gradient measurement scheme that combines high time resolution, high accuracy, high stability, directness, simplicity, and suitability for transient event diagnosis.

[0060] The measurement method and system provided in this application have broad application prospects. In inertial confinement fusion research, the density gradient distribution of the coronal plasma directly affects the coupling efficiency of laser energy and the growth of hydrodynamic instabilities. This invention can be used to perform real-time, high-resolution diagnosis of the density gradient during target compression, providing crucial experimental data for optimizing driving laser parameters and target design. In the field of laser wakefield electron acceleration, the plasma density profile has a decisive influence on electron injection and acceleration processes. This invention can be used to accurately characterize and optimize the density gradient of gas targets to generate higher-quality electron beams. Furthermore, in cutting-edge scientific research such as high-harmonic generation and astrophysical plasma simulation, this invention can also serve as an effective diagnostic tool to reveal the evolution laws of key parameters in various ultrafast physical processes.

[0061] Example 3 In a preferred embodiment, this application also provides an electronic device, the electronic device comprising: The computer device includes a memory and a processor, the memory storing computer-readable instructions that, when executed by the processor, implement the method for measuring plasma density gradients. This computer device can be broadly categorized as a server, terminal, or any other electronic device with the necessary computing and / or processing capabilities. In one embodiment, the computer device may include a processor, memory, network interface, communication interface, etc., connected via a system bus. The processor of the computer device can be used to provide the necessary computing, processing, and / or control capabilities. The memory of the computer device may include a non-volatile storage medium and internal memory. The non-volatile storage medium may store an operating system, computer programs, etc. The internal memory can provide an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface and communication interface of the computer device can be used to connect and communicate with external devices via a network. When the computer program is executed by the processor, it performs the steps of the method of the present invention.

[0062] This invention can be implemented as a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, causes the steps of the methods of embodiments of the invention to be performed. In one embodiment, the computer program is distributed across multiple network-coupled computer devices or processors, such that the computer program is stored, accessed, and executed in a distributed manner by one or more computer devices or processors. A single method step / operation, or two or more method steps / operations, may be executed by a single computer device or processor or by two or more computer devices or processors. One or more method steps / operations may be executed by one or more computer devices or processors, and one or more other method steps / operations may be executed by one or more other computer devices or processors. One or more computer devices or processors may execute a single method step / operation, or execute two or more method steps / operations.

[0063] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0064] The technical features described above can be combined arbitrarily. Although not all possible combinations of these technical features are described, any combination of these technical features should be considered to be covered by this specification, provided that such combination does not contain contradictions.

[0065] The specific embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made in accordance with the technical concept of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for measuring plasma density gradient, characterized in that, include: S100. A femtosecond laser pulse with broad spectral characteristics and initial pulse width is incident onto the plasma to be tested. S200. Measure the pulse width of the femtosecond laser pulse after it is reflected by the plasma under test; S300. Determine the density gradient of the plasma under test based on the pre-established mapping relationship between the pulse width of the reflected femtosecond laser pulse and the plasma density gradient, and the pulse width of the femtosecond laser pulse reflected by the plasma under test currently measured.

2. The method for measuring plasma density gradient according to claim 1, characterized in that, The preset mapping relationship is a preset mapping relationship between the pulse width of the reflected femtosecond laser pulse and the plasma density gradient, which is established in advance through theoretical numerical simulation or experimental calibration methods.

3. The method for measuring plasma density gradient according to claim 2, characterized in that, When the preset mapping relationship is established using the experimental calibration method, the method for establishing the preset mapping relationship includes: By changing the center wavelength of the femtosecond laser pulse, the plasma density gradient of the plasma under test at different critical density values ​​can be measured. The pulse width of the femtosecond laser pulse after reflection from the plasma under different plasma density gradients is obtained; and Based on the obtained pulse width and the corresponding plasma density gradient, a correlation curve between the pulse width and the plasma density gradient is fitted to establish the preset mapping relationship.

4. The method for measuring plasma density gradient according to claim 1, characterized in that, The method for determining the density gradient of the plasma to be measured includes: The pulse width of the femtosecond laser pulse after reflection from the plasma under test is substituted into the function or lookup table determined by the preset mapping relationship to obtain the corresponding density gradient value of the plasma under test.

5. A system for measuring plasma density gradient, characterized in that, include: Femtosecond laser module, used to provide femtosecond laser pulses with broad spectral characteristics; A laser transmission and focusing module is used to transmit and focus the femtosecond laser pulse onto the plasma under test, and to collect the laser pulse reflected back from the plasma under test; A laser pulse width measurement module is used to measure the pulse width of the laser pulses collected and reflected back from the plasma under test; The processing module is used to determine the density gradient of the plasma under test based on the pulse width measured by the laser pulse width measurement module and a preset mapping relationship between the pulse width of the reflected femtosecond laser pulse and the plasma density gradient.

6. The system for measuring plasma density gradient according to claim 5, characterized in that, The laser transmission and focusing module is a single integrated module that combines the functions of transmitting and focusing incident laser light with collecting reflected laser light.

7. The system for measuring plasma density gradient according to claim 5, characterized in that, The laser transmission and focusing module includes a first laser transmission and focusing module and a second laser transmission and focusing module. The first laser transmission and focusing module is used to transmit and focus the femtosecond laser pulse onto the plasma to be tested, and the second laser transmission and focusing module is used to collect the laser pulses reflected back from the plasma to be tested.

8. The system for measuring plasma density gradient according to claim 5, characterized in that, The laser pulse width measurement module is at least one of a single autocorrelation meter, a frequency-resolved optical switch, or a spectral phase interferometer.

9. The system for measuring plasma density gradient according to claim 5, characterized in that, The laser wavelength of the femtosecond laser module is adjustable; The processing module stores multiple preset mapping relationships corresponding to multiple different laser wavelengths, and is configured to call the corresponding preset mapping relationship according to the currently selected laser wavelength to determine the density gradient of the plasma to be tested.

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