An analysis method based on the number of pulse cycles dominant laser tail wave field electron acceleration

Abstract

The application provides an analysis method based on a pulse period number dominant laser wake field electron acceleration, comprising the following steps: fixing an initial laser normalized intensity, a laser pulse width and changing a laser wavelength, obtaining that different period number laser pulses excite electron density bubble structure in plasma and form a wake field capable of accelerating electrons; starting a laser wake field acceleration simulation, linearly polarized laser excites a bubble structure in plasma, multiple snapshots are taken for the evolution of the bubble structure, and bubble structure diagrams at different times are obtained; statistically analyzing the bubble structure diagrams at different times, obtaining the change of the bubble structure centroid transverse coordinate Δz c ; when the bubble centroid transverse coordinate change Δz c ≥0.01λ p0 , the laser carrier effect is dominant in the laser wake field acceleration process at this moment; otherwise, the mass dynamic effect is dominant. The method can provide analysis guidance for the wake field acceleration research driven by laser of different period numbers, has small calculation amount, is fast in calculation, and can provide a judgment result in real time.

Description

Technical Field

[0001] This invention relates to the fields of novel particle acceleration technology and space radiation environment technology, and in particular, to an analytical method for electron acceleration based on the pulse cycle number-dominated laser wakefield. Background Technology

[0002] Laser wakefield accelerators utilize ultra-intense, ultra-short lasers to excite wakefields in plasma that accelerate electrons. Their acceleration gradients are not limited by the ionization threshold and can reach over 100 GeV / m, exceeding the limit of traditional accelerators by 1000 times. Crucially, the laser excites a wakefield in the plasma that accelerates electrons. Current mainstream theories analyzing cavitation structures primarily rely on the average mass-dynamic model. However, this model is based on the average envelope of multi-period lasers, which fails for wakefield acceleration driven by few-period lasers. The influence of the laser carrier effect must be considered, and these two factors compete in the evolution of cavitation structures, a competition related to the number of laser cycles.

[0003] Existing techniques for analyzing wakefield acceleration processes driven by multi-period laser pulses using mass dynamics models are relatively mature and provide good experimental guidance. Research on wakefield acceleration driven by few-period laser pulses is also gaining momentum, and there are already many theories that can analyze the few-period laser wakefield acceleration process dominated by the carrier effect. However, research on the competition and transition relationship between mass dynamics and the carrier effect during the transition from multi-period to few-period lasers is basically lacking. Furthermore, selecting lasers with a medium number of periods to drive wakefield acceleration is of great significance for improving the quality of the accelerating electron beam.

[0004] Therefore, there is an urgent need for a new technology based on the pulse period number-dominated method for electron acceleration analysis of laser wakefield. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides an analytical method for laser wakefield electron acceleration based on pulse period number dominance. Under the condition that the initial mass dynamics and other parameters are the same, the influence of mass dynamics and carrier effect on the cavitation evolution process in laser-driven wakefield acceleration with different period numbers is studied. A method for determining whether the laser wakefield acceleration process with different period numbers is dominated by the laser carrier is obtained, filling the gap in related research and providing some guidance for the selection of theoretical analysis models for subsequent laser wakefield acceleration experiments.

[0006] To achieve the above objectives, this invention provides an analysis method for electron acceleration in a laser wakefield based on the pulse period number, comprising:

[0007] By fixing the initial laser normalized intensity, pulse width, and focal spot radius to ensure that the initial mass dynamic force is the same, changing the laser wavelength to obtain laser pulses with different number of cycles can excite electron density cavitation structures in the plasma, thereby forming a wake field that can accelerate electrons.

[0008] When a laser wake field acceleration simulation is initiated, after the linearly polarized laser excites a cavitation structure in the plasma, multiple snapshots of the evolution of the cavitation structure are taken to obtain cavitation structure diagrams at different times.

[0009] Statistical analysis of the cavitation structure diagrams at different times yielded the change Δz in the transverse coordinate of the centroid of the cavitation structure. c ;

[0010] When the change in the lateral coordinate of the centroid of the cavitation structure is Δz c ≥0.01λ p0 When λ is at that moment, the dominant effect in the laser wake acceleration process is the laser carrier effect; where λ p0 The initial plasma wavelength;

[0011] Conversely, the dominant effect in the laser wake acceleration process at that moment is a mass dynamic effect.

[0012] Further statistical analysis of the cavitation structure diagrams at different times revealed that under mass-driven dynamics, the cavitation centroid is relatively stable, and its lateral oscillations are negligible. However, under laser carrier-driven dynamics, the cavitation centroid exhibits a larger lateral vibration amplitude, and the vibration frequency is the same as the variation frequency of the laser carrier. For cavitation driven by laser propagation along the x-direction with linear polarization in the z-direction, significant lateral oscillations will occur due to the influence of laser carrier evolution in the polarization direction. Conversely, in the y-direction perpendicular to polarization, the cavitation is not affected by laser carrier evolution and does not exhibit significant oscillations in the y-direction. Statistical analysis of the lateral coordinate changes of the cavitation structure centroid on the xz-section of the cavitation can determine the amplitude of the cavitation oscillations. The lateral coordinate changes of the cavitation structure centroid are expressed as follows:

[0013]

[0014] Where n e (x,0,z,t) represents the electron density at coordinates (x,0,z) at time t, and n0 represents the background electron density. Since the cavitation structure is a high-density electron sheath, cases with electron densities lower than the background electron density n0 are invalid. T CEP This indicates the period of the laser carrier wave change.

[0015] Furthermore, λ p0 The initial plasma wavelength is approximately equal to the initial longitudinal length of the cavitation bubble.

[0016] Furthermore, the laser wake field acceleration simulation experiment specifically involves: a femtosecond laser system generating a linearly polarized femtosecond laser beam, the wavelength, focal spot, and angle of which are modulated by an optical system. The modulated femtosecond laser is then injected into a gas target, ionizing the gas molecules in the gas target into plasma and exciting plasma waves to form an electron density cavitation structure, thereby driving the wake field to accelerate electrons.

[0017] Furthermore, multiple snapshots of the cavitation structure were obtained in the experiment using a high-speed camera, and can be quickly exported in numerical simulation experiments.

[0018] Furthermore, the number of pulse cycles ranges from few to many cycles, and the analysis criteria are applicable to any period range of linearly polarized lasers.

[0019] Furthermore, the plasma is a hydrogen plasma target with a density rise gradient.

[0020] Furthermore, the electron number density of the hydrogen plasma target is n0 = 5 × 10⁻⁶. 19 cm -3 The density rise length is 20μm.

[0021] Furthermore, setting the initial laser normalized intensity a0 = 4, the incident laser propagates along the x-axis and is polarized along the z-axis, with Gaussian pulses in both the transverse and longitudinal directions. The expression for the laser field intensity is:

[0022]

[0023] Where ξ = x - ct is the co-moving coordinate, r is the lateral distance from the optical axis, the laser pulse width τ0 = 10 fs, and the focal spot radius σ0 = 3 μm.

[0024] The present invention has the following beneficial effects:

[0025] This invention proposes an analytical method for laser wakefield electron acceleration based on pulse cycle number dominance. Under the condition that the initial mass dynamics and other parameters are the same, the influence of mass dynamics and carrier effect on the cavitation evolution process in laser-driven wakefield acceleration with different cycle numbers is studied. A method for determining whether the laser wakefield acceleration process with different cycle numbers is dominated by the laser carrier is obtained, filling the gap in related research and providing some guidance for the selection of theoretical analysis models for subsequent laser wakefield acceleration experiments.

[0026] For multi-period cases, mass dynamics dominate; for few-period cases, carrier effects dominate; and for medium-period cases, there is a transition from mass dynamics dominance to carrier effect dominance. Identifying the dominant factor in cavitation evolution during laser wakefield acceleration is crucial for selecting appropriate theoretical tools to correctly analyze this physical process. This invention combines theory and three-dimensional particle simulation experiments to propose an analytical method for laser wakefield electron acceleration based on pulse period number dominance. This method obtains the evolution of the cavitation structure by taking multiple snapshots of the wakefield acceleration process at different laser period numbers and statistically analyzing the change in the cavitation centroid position as a criterion, thereby determining the dominant factor in cavitation structure evolution during laser wakefield acceleration at different period numbers.

[0027] This invention allows for the generation of femtosecond laser pulses of different wavelengths by selecting different lasers and configuring the optical system. Furthermore, it enables the creation of gas targets of various shapes using supersonic gas nozzle technology. The electron beam accelerated by the laser incident beam is then focused by a magnetic focusing system and subsequently incident into a radiation effect testing system, allowing for the analysis of information such as the energy spectrum and angular divergence of the electron beam.

[0028] The present invention proposes an analytical method for electron acceleration in laser wakefields based on pulse cycle number. This method can not only provide analytical guidance for the study of wakefield acceleration driven by lasers with different cycle numbers and help to determine the dominant effect in order to select appropriate theoretical analysis tools, but also has low computational cost, fast calculation speed, and can provide judgment results in real time.

[0029] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0030] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0031] Figure 1 This is a flowchart of an analytical method for electron acceleration in a laser wake field based on the number of pulse cycles, according to the present invention.

[0032] Figure 2 This is a schematic diagram of the experimental apparatus used in the method of this invention;

[0033] Among them, 1 is the femtosecond laser system; 2 is the optical system; 3 is the supersonic gas nozzle; 4 is the gas target; 5 is the focusing magnetic field; 6 is the accelerating electron beam; 7 is the radiation effect testing system; and 8 is the high-speed camera system. Detailed Implementation

[0034] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways as defined and covered by the claims.

[0035] This invention provides an analytical method for electron acceleration in a laser wakefield dominated by pulse cycle number. With a fixed pulse width, the pulse cycle number can be controlled by changing the laser wavelength. By fixing the initial normalized laser intensity and pulse width, the initial longitudinal mass dynamic force is controlled to be the same. Changing the laser wavelength allows for the study of the changing dominance between the mass dynamic effect and the laser carrier effect under different cycle numbers. This invention investigates the process of electron acceleration in a wakefield formed by laser-injected plasma with different cycle numbers through three-dimensional particle simulation experiments. Combined with theoretical analysis, it is found that for multi-cycle cases, the mass dynamic effect dominates; for few-cycle cases, the laser carrier effect dominates; and for medium-cycle cases, there is a transition from mass dynamic effect dominance to carrier effect dominance. Through multiple snapshots of the cavitation structure during wakefield acceleration, it is found that when the cavitation structure continuously oscillates laterally, a criterion for determining the dominant effect is derived based on the change in the cavitation centroid position. When the cavitation centroid position changes by Δz... c ≥0.01λ p0 (λ p0 When the plasma wavelength at the initial moment is 0, the carrier effect dominates; otherwise, the mass-dynamic effect dominates. In practical experiments, multiple snapshots of cavitation structures can be obtained using a further developed high-speed camera.

[0036] like Figure 1 As shown, this invention provides an analysis method for electron acceleration in a laser wake field based on the pulse period number, specifically including the following steps:

[0037] Step 1: By fixing the initial laser normalized intensity, pulse width, and focal spot radius to ensure that the initial mass dynamic force is the same, the laser wavelength is changed to obtain laser pulses with different number of cycles to excite electron density cavitation structures in the plasma, thereby forming a wake field that can accelerate electrons.

[0038] Because the dominant effects on electron density cavitation differ under different pulse cycle numbers, the mass dynamics effect dominates in the multi-cycle case, while the laser carrier effect dominates in the few-cycle case. This invention aims to use reasonable criteria to analyze the changes in the dominant effects of mass dynamics and laser carrier under different pulse cycle numbers.

[0039] The structural changes of cavitation bubbles under different effects are primarily reflected in the transverse oscillation amplitude of the centroid. Under the influence of mass dynamics, cavitation bubbles propagate stably with slight transverse oscillations. Under the influence of laser carrier effects, cavitation bubbles oscillate transversely at the same frequency as the carrier wave periodically, with larger oscillation amplitudes leading to earlier bubble breakage. Based on these phenomena, this invention proposes using the transverse coordinate change of the cavitation bubble's centroid as a criterion to determine which effect dominates the cavitation bubble. This method is particularly applicable to linearly polarized lasers.

[0040] Step 2: When a laser wake field acceleration simulation is started, after the linearly polarized laser excites a cavitation structure in the plasma, multiple snapshots are taken of the evolution of the cavitation structure to obtain cavitation structure diagrams at different times.

[0041] Step 3: Perform statistical analysis on the cavitation structure diagrams at different times. Since the carrier effect of linearly polarized lasers is mainly reflected in the polarization direction, the cross-section formed by the polarization direction and the propagation motion direction is selected to analyze the changes in the cavitation structure, and the change Δz of the centroid of the cavitation structure is obtained. c .

[0042] Step 4: When the lateral coordinate of the centroid of the cavitation structure changes by Δz c ≥0.01λ p0 At that moment, the dominant effect in the laser wake acceleration process is the laser carrier effect; where λ p0 The initial plasma wavelength is equivalent to the initial longitudinal length of the cavitation bubble, and can also be calculated using a formula based on the initial laser normalized intensity and plasma density conditions.

[0043] Conversely, the dominant effect in the laser wake acceleration process at this moment is a mass dynamic effect.

[0044] Statistical analysis of the cavitation structure diagrams at different times revealed that under mass-driven dynamics, the cavitation centroid is relatively stable, and its transverse oscillations are negligible. However, under laser carrier-driven dynamics, the cavitation centroid exhibits a large transverse vibration amplitude, and the vibration frequency is the same as the frequency of the laser carrier. For cavitation driven by a laser propagating along the x-direction with linear polarization in the z-direction, significant transverse oscillations occur due to the influence of laser carrier evolution in the polarization direction. Conversely, in the y-direction perpendicular to polarization, the cavitation is not affected by laser carrier evolution and does not exhibit significant oscillations in the y-direction. Therefore, by selecting the xz section where transverse oscillations are significant, statistical analysis of the transverse coordinate changes of the cavitation structure centroid can determine the amplitude of the cavitation oscillations. The transverse coordinate changes of the cavitation structure centroid are expressed as:

[0045]

[0046] Where n e(x,0,z,t) represents the electron density at coordinates (x,0,z) at time t, and n0 represents the background electron density. Since the cavitation structure is a high-density electron sheath, cases with electron densities lower than the background electron density n0 are invalid. T CEP This indicates the period of the laser carrier wave change.

[0047] The laser wake field acceleration experiment in this invention is specifically as follows: a femtosecond laser system generates a linearly polarized femtosecond laser beam. The wavelength, focal spot and angle of the femtosecond laser are modulated by an optical system. The modulated femtosecond laser is injected into a gas target, ionizing the gas molecules in the gas target into plasma and exciting plasma waves to form an electron density cavitation structure, driving the wake field to accelerate electrons.

[0048] The cavitation structure described in this invention can be obtained through multiple snapshot experiments using a high-speed camera and can be quickly derived in numerical simulation experiments. The number of pulse cycles ranges from few to many cycles, and the analysis criteria are applicable to any period range of linearly polarized lasers.

[0049] Figure 2 This is a schematic diagram of the experimental setup used in the method of this invention. The setup includes a femtosecond laser system 1, an optical system 2, a supersonic gas nozzle 3, a gas target 4, a focusing magnetic field 5, a radiation effect testing system 7, and a high-speed camera system 8; the radiation effect testing system 7 includes a test target and a computer electrically connected to the test target.

[0050] The femtosecond laser system 1 is used to provide femtosecond lasers with different wavelengths, intensities, and pulse widths; the optical system 2 is used to modulate the laser, control laser transmission and focusing, etc.; the supersonic gas nozzle 3 is used to eject gas in a timely manner to form a gas target 4; the gas target 4 is a plasma gas target with a density rise gradient, which will form a cavitation structure to accelerate the injected electrons after laser incident; the focusing magnetic field 5 is used to focus the electron beam accelerated from the tail field; the radiation effect testing system 7 is used to analyze the energy spectrum and divergence of the emitted electron beam, etc.; the high-speed camera system 8 is used to provide snapshots of the cavitation evolution.

[0051] A femtosecond laser system 1 generates a femtosecond laser beam. The transmission and focusing of this laser are modulated by an optical system 2 located within a vacuum chamber. The modulated femtosecond laser then enters a gas target 4, ionizing gas molecules into plasma. This plasma wave excites electron cavitation structures, and electrons from the dense shell of the cavitation flow back to the tail of the cavitation and are injected into the interior, forming an accelerated electron beam 6. This electron beam, after passing through a focusing magnetic field 5, acts on a test target of a radiation effect testing system 7. The interaction between the electron beam and the test target yields experimental results of the interaction between the space electron beam and matter. A high-speed camera system 8 takes multiple snapshots of the cavitation structure's evolution, providing images of the cavitation structure at different times, which can be quickly exported in numerical simulation experiments.

[0052] This invention provides an analytical method for electron acceleration in laser wakefields dominated by pulse number. By capturing multiple snapshots of the wakefield acceleration process at different laser cycle numbers, the evolution of the cavitation structure is obtained, and the change in the cavitation centroid position is statistically analyzed as a criterion to determine the dominant factor in the evolution of the cavitation structure during wakefield acceleration at different cycle numbers. This method can help determine the dominant effect of wakefield acceleration driven by lasers of different cycle numbers at a given moment, guiding the selection of appropriate theoretical analysis tools and obtaining a clearer physical picture.

[0053] The present invention will be further explained and described below with reference to specific embodiments.

[0054] The method of this invention is based on the study of the competitive relationship between laser carrier effect and mass dynamics effect in the evolution of cavitation structure under different laser cycle numbers using the 3D particle simulation software Epoch3d. To control variables, the same hydrogen plasma target can be set with a density n0 = 5 × 10⁻⁶. 19 cm -3 The rise time is 20 μm, and the same initial laser normalized intensity a0 = 4 is set to ensure the same initial mass dynamics. The incident lasers all propagate along the x-axis and are polarized along the z-axis. They are Gaussian in both the transverse and longitudinal directions. The expression for the laser field intensity is:

[0055]

[0056] Where ξ = x - ct is the co-moving coordinate, r is the lateral distance from the optical axis, the laser pulse width τ0 = 10 fs, and the focal spot radius σ0 = 3 μm.

[0057] Since the current laser wavelength is generally 0.8 μm, frequency-doubled lasers can be obtained through modulation. Therefore, with a fixed pulse width, different laser wavelengths λ0 = 0.4 μm, 0.8 μm, and 1.2 μm are set to change the number of laser pulse cycles, and then each pulse is incident on the same plasma target. The simulation window is selected as 20 μm × 20 μm × 20 μm to reduce unnecessary calculations. The grid is divided into 800 × 100 × 100 grids, with each grid containing 10 macroparticles. Each macroparticle represents 5000 electrons or ions, and the electron-ion mass ratio is 1 / 1836.

[0058] By taking multiple snapshots of the cavitation structure, we can observe the cavitation structure excited by lasers of different period numbers in plasmas with the same structure. First, we determined that the case with the most period number, λ0 = 0.4 μm, is dominated by mass-dynamic forces, and its cavitation structure and accelerating electron beam are stable and symmetrical. In the case with the fewest period number, λ0 = 1.2 μm, the laser carrier wave dominates. With the continuous change of the laser carrier wave on the laser polarization plane (xz) during laser transmission, the plasma response to the laser pulse becomes asymmetrical, and the cavitation and electron beam oscillate severely in the transverse direction on the polarization plane. Newly injected particles at the tail end have a large transverse momentum. In the case with a moderate period number, λ0 = 0.8 μm, mass-dynamic forces initially dominate, but then the laser carrier wave evolution becomes increasingly intense, the cavitation oscillation gradually intensifies, and the laser carrier wave eventually dominates. Analysis revealed that the transverse coordinate change of the cavitation structure's centroid can be used to identify whether the tail-field acceleration process is dominated by the laser carrier wave. The transverse coordinate change of the cavitation structure's centroid is expressed as:

[0059]

[0060] Where n e (x,0,z,t) represents the electron density at coordinates (x,0,z) at time t, and n0 represents the background electron density. Since the cavitation structure is a high-density electron sheath, cases with electron densities lower than the background electron density n0 are invalid. T CEP This indicates the period of the laser carrier wave change.

[0061] Under the influence of isotropic dynamics, the centroid of the cavitation bubble changes identically across different cross-sections, with oscillation amplitudes less than one-hundredth of the wake wavelength. However, under laser carrier-dominated conditions, the centroid of the cavitation bubble on the laser polarization plane continuously oscillates up and down, with the oscillation period synchronized with the carrier wave's period. Combined with numerical simulation results, when Δz... c ≥0.01λ p0 (λ p0When the initial wavelength of the wake wave is 9.33 μm (in this simulation experiment), it can be seen that the change in the position of the centroid exceeds the scale dominated by mass dynamics. At this time, the laser carrier dominates. Conversely, it can be considered that the change in the centroid is not obvious and the cavitation bubble propagates smoothly forward. The mass dynamics approximation can be used for analysis.

[0062] Based on the flowchart, this analytical method can be described as follows: When a femtosecond laser beam is incident on plasma, driving a wake field to accelerate electrons, we take multiple snapshots of the cavitation evolution to obtain cavitation structure diagrams at different times. Using the centroid statistical formula, we statistically analyze the cavitation structure diagrams, select the laser polarization section, obtain the lateral coordinate changes of the cavitation centroid, and combine this with the centroid change judgment criteria to determine the dominant effect of the laser wake field acceleration process at that moment.

[0063] This analytical method is readily applicable in numerical simulation experiments. Numerical simulations provide a rapid snapshot of the cavitation structure during laser wake acceleration, allowing for near real-time determination of the dominant effect of wake acceleration at that moment. In actual experiments, femtosecond laser pulses with varying period numbers can be obtained by selecting different lasers and configuring the optical system. Gas targets of different shapes can be obtained using supersonic gas nozzle technology, and then ionized into plasma by a pre-laser pulse. The electron beam accelerated by the laser incident beam is then focused by a magnetic focusing system and incident on a radiation effect testing system, allowing for analysis of its energy spectrum and angular divergence. This invention proposes an analytical method for electron acceleration in laser wake fields based on pulse period number dominance. This method not only provides analytical guidance for studying wake acceleration driven by lasers with different period numbers, helping to determine the dominant effect and select appropriate theoretical analysis tools, but also requires minimal computation, is fast, and provides real-time results.

[0064] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An analytical method for electron acceleration in a laser wakefield dominated by pulse period number, characterized in that, include: By fixing the initial laser normalized intensity, pulse width, and focal spot radius to ensure that the initial mass dynamic force is the same, changing the laser wavelength to obtain laser pulses with different number of cycles can excite electron density cavitation structures in the plasma, thereby forming a wake field that can accelerate electrons. When a laser wake field acceleration simulation is initiated, after the linearly polarized laser excites a cavitation structure in the plasma, multiple snapshots of the evolution of the cavitation structure are taken to obtain cavitation structure diagrams at different times. Statistical analysis of the cavitation structure diagrams at different times yielded the changes in the lateral coordinates of the centroid of the cavitation structure. ; When the lateral coordinate of the centroid of the cavitation structure changes When the laser wake acceleration process occurs, the dominant effect at that moment is the laser carrier effect; among which, The initial plasma wavelength; Conversely, the dominant effect in the laser wake acceleration process at that moment is a mass dynamic effect. Among them, for those along Directional transmission, linear polarization direction is A cavitation bubble driven by a laser in the polarization direction will exhibit significant transverse oscillations due to the evolution of the laser carrier wave in the polarization direction, while in the vertical polarization direction... The direction is unaffected by the evolution of the laser carrier wave, and the cavitation will not be affected. Significant oscillations occur in the direction; select samples with obvious transverse oscillations of the cavitation bubble. The amplitude of cavitation oscillation is determined by statistically analyzing the lateral coordinate change of the centroid of the cavitation structure. The lateral coordinate change of the centroid of the cavitation structure is expressed as: in Indicates in Time coordinates are electron density at that location, The density represents the background electron density. Since the structure of a vacuole is a high-density electron sheath, its statistical value is lower than the background electron density. The situation is invalid. Indicates the period of laser carrier wave variation; The laser wake field acceleration simulation experiment is as follows: A femtosecond laser system generates a linearly polarized femtosecond laser beam. The wavelength, focal spot and angle of the femtosecond laser are modulated by an optical system. The modulated femtosecond laser is injected into a gas target, ionizing the gas molecules in the gas target into plasma and exciting plasma waves to form an electron density cavitation structure, driving the wake field to accelerate electrons. The plasma is a hydrogen plasma target with a density rise gradient; the initial laser is set to normalized intensity. The incident laser beams all follow the direction of the incident laser beams. x Axial propagation, z Axially polarized, with Gaussian pulses in both the transverse and longitudinal directions, the laser field intensity expression is: in For co-moving coordinates, The lateral distance from the optical axis, and the laser pulse width. Focal spot radius .

2. The analytical method for electron acceleration in a laser wakefield based on pulse period number as described in claim 1, characterized in that, The cavitation structure was captured using a high-speed camera in multiple snapshot experiments and can be quickly exported in numerical simulation experiments.

3. The analytical method for electron acceleration in a laser wakefield based on pulse period number as described in claim 1, characterized in that, The number of pulse cycles ranges from few to many cycles, and the analysis criteria are applicable to any period range of linearly polarized lasers.

4. The analytical method for electron acceleration in a laser wakefield based on pulse period number as described in claim 1, characterized in that, Electron number density of the hydrogen plasma target Density rises along length .

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