A terahertz radiation generation device based on nonlinear electron beam compression

Abstract

The application provides a terahertz radiation generation device based on nonlinear electron beam compression, comprising an injector, an electron beam modulation system, an electron beam acceleration system, a radiation system and a laser beat frequency system; the laser beat frequency system is configured to generate double-pulse beat frequency laser with constant beat envelope frequency; the electron beam modulation system modulates the initial energy of the electron beam; the electron beam acceleration system performs incomplete linear polarization and nonlinear compression on the electron beam, and converts the electron beam into unequal interval electron beam bunch string; the radiation system makes each micro beam bunch in the unequal interval electron beam bunch string coherently superimposed to synthesize terahertz radiation through the magnetic field taper thereof, and the pulse width of the terahertz radiation is less than one period or one period. The device of the application utilizes beat frequency laser seeding and nonlinear manipulation of the longitudinal phase space of high-energy electron beam, realizes precise shaping of the longitudinal phase space of the electron beam, and thus generates superfast terahertz radiation with adjustable center frequency and pulse width limit compression of at least one period or one period.

Description

Technical Field

[0001] This invention belongs to the field of free-electron laser and terahertz technology, specifically relating to a device for generating extreme light fields through longitudinal phase space manipulation, and more particularly to a terahertz radiation generating device based on nonlinear electron beam compression. Background Technology

[0002] Terahertz radiation refers to the frequency band in the electromagnetic spectrum between microwaves and infrared light. In recent years, with the rapid development of strong-field ultrafast terahertz science, strong-field ultrafast terahertz radiation sources with extremely high peak electric fields and extremely short pulse widths (few periods or even single periods) have demonstrated irreplaceable application value in cutting-edge interdisciplinary research. These extreme light fields can not only effectively drive the nonlinear response of materials, but also play a crucial role in areas such as non-equilibrium ultrafast dynamics detection, coherent control of matter quantum states, and the study of strong-field physics mechanisms.

[0003] On the other hand, strong-field ultrafast terahertz pulses provide an important means of exploring extreme physical processes in condensed matter. For example, strong-field ultrashort terahertz pulses can be used to achieve coherent excitation of lattice vibrations, ultrafast control of spin dynamics, and transient induction of electronic phase transitions in topological materials. Combining such high-energy ultrafast terahertz sources with advanced detection techniques with extremely high time resolution is expected to reveal transient dynamic evolution characteristics at the atomic and molecular scales. However, existing benchtop strong-field terahertz sources, such as optical rectification techniques based on nonlinear optical crystals, while capable of generating short-period pulses, generally suffer from core bottlenecks such as limited pulse energy, difficulty in tuning the center frequency over a wide range, and limitations imposed by the dielectric damage threshold when attempting to break through to higher peak electric fields.

[0004] Particle accelerators and free-electron lasers based on high-energy electron beams can generate high-power, continuously tunable coherent radiation over an extremely wide frequency band by coupling relativistic electron beams with electromagnetic fields. Based on longitudinal phase space manipulation of the electron beam and coherent radiation technology using micro-bundles, this field has successfully achieved high-power output of ultrashort pulses and even attosecond pulses in the X-ray and extreme ultraviolet bands. These breakthroughs provide an important technological path for generating ultra-high-power ultrashort pulses in the terahertz band. Currently, there are related schemes for imprinting equally spaced periodically modulated micro-bundle sequences longitudinally along the electron beam using laser seeding, which holds promise for coherently synthesizing terahertz radiation with extremely high peak electric fields and ultrashort time-domain characteristics in undulators. However, traditional external laser seeding typically involves using a linearized radio frequency cavity to eliminate higher-order energy distributions to generate equally spaced micro-bundles, requiring further improvements to introduce higher-order nonlinear energy chirps to achieve gradually varying spacing.

[0005] Furthermore, the generation of ultrashort terahertz radiation in current accelerators mainly relies on the initial density modulation of the electron gun cathode laser or the space charge oscillation effect in the low-energy transmission section. However, these methods have significant drawbacks. In the extremely low-energy stage, the space charge effect severely damages the bundle microstructure. The strong space charge force leads to severe nonlinear degradation of the longitudinal microstructure of the electron beam, making it difficult to achieve high-purity, high-precision initial phase space modulation, which in turn greatly limits the spectral purity and pulse-limited compression capability of the final terahertz radiation. Direct seeding with an external laser holds promise for achieving highly stable and extremely coherent terahertz coherent radiation. However, overcoming the interference of the space charge effect, obtaining extremely high-purity initial modulation in the terahertz band on the electron beam, and perfectly transforming it into a micro-bundle structure capable of generating ultrafast terahertz radiation through long-distance high-energy acceleration and nonlinear compression still lacks an effective system-level solution. This has become a core technical obstacle restricting the development of strong-field ultrafast terahertz accelerator light sources. Summary of the Invention

[0006] The purpose of this invention is to provide a strong-field ultrafast terahertz radiation generation device based on nonlinear electron beam compression, so as to overcome the phase space degradation caused by the space charge effect of traditional low-energy modulation, and generate strong-field ultrafast terahertz radiation with a wide range of adjustable center frequency, pulse width limited compression of at least periodic or single periodic, and extremely high peak electric field.

[0007] To achieve the above objectives, the present invention provides a terahertz radiation generation device based on nonlinear electron beam compression, comprising an injector, an electron beam modulation system, an electron beam acceleration system, and a radiation system arranged sequentially along the electron beam transmission direction; and a laser beat frequency system; the laser beat frequency system is configured to generate a double-pulse beat frequency laser with a constant beat frequency envelope frequency, and to guide the double-pulse beat frequency laser into the electron beam modulation system; the electron beam modulation system is configured to enable the electron beam to obtain initial energy modulation through the interaction between the electron beam and the beat frequency laser; the electron beam acceleration system is configured to perform incomplete linear polarization and nonlinear compression on the electron beam, converting it into a unequally spaced electron beam cluster; the radiation system receives the unequally spaced electron beam cluster and uses its magnetic field taper to coherently superimpose the micro-clusters in the unequally spaced electron beam cluster to synthesize the desired terahertz radiation, wherein the pulse width of the terahertz radiation is a few-period or single-period.

[0008] The injector is configured to generate an electron beam and accelerate it to an energy suitable for external laser modulation before feeding it into the electron beam modulation system.

[0009] The electron beam modulation system includes at least a modulation segment undulator; the modulation segment undulator is configured to coherently interact with the electron beam and the dual-pulse beat laser during co-linear propagation, and the dual-pulse beat laser and the modulation segment undulator are matched in terms of lateral position, arrival time, polarization direction and resonance conditions, so that the initial energy obtained by the electron beam is modulated as periodic energy modulation.

[0010] The electron beam acceleration system includes a first acceleration structure, a second acceleration structure, a magnetic compression section, and a third acceleration structure arranged sequentially along the electron beam transmission direction. The first and second acceleration structures are used to accelerate the electron beam with initial energy modulation and perform nonlinear correction of the longitudinal phase space. The magnetic compression section is used to convert the energy modulation of the nonlinearly corrected electron beam into density modulation, achieving longitudinal nonlinear compression, so that the electron beam is converted into an unequally spaced electron beam cluster upon emission. The third acceleration structure is used to further accelerate or maintain the energy of the unequally spaced electron beam cluster compressed by the magnetic compression section and introduce it into the radiation system, so that the peak electric field intensity is on the order of hundreds of mV / m to GV / m.

[0011] The nonlinear compression factor of the electron beam acceleration system The nonlinear compression factor varies with the vertical coordinate z. The definition is the first derivative of the slowly varying longitudinal mapping. The reciprocal of the absolute value, a slowly varying longitudinal mapping Based on the longitudinal coordinates of the electron beam after longitudinal nonlinear compression in the magnetic compression section The target terahertz radiation is obtained by retaining only the relevant portion of the slowly varying relative energy deviation; the radiation system outputs target terahertz radiation, and the target terahertz center frequency is obtained by using the beat frequency envelope frequency and / or the nonlinear compression factor of the electron beam acceleration system. To adjust.

[0012] The second acceleration structure is an X-band harmonic linearization cavity, which is configured to operate in an incompletely compensated phase to actively introduce high-order nonlinear chirps into the longitudinal phase space of the electron beam. This results in different compression ratios at the head and tail of the electron beam when it passes through the magnetic compression section, forming the unequally spaced electron beam bunches with gradually changing micro-bundle spacing.

[0013] The radiation system includes a radiation section undulator, a bent iron, and a beam bin arranged sequentially along the transmission direction of the unequally spaced electron beam string; the radiation section undulator is used to generate the terahertz radiation by passing the unequally spaced electron beam string through a magnetic field; the bent iron is used to spatially separate the radiated electron beam from the generated terahertz radiation, so that the terahertz radiation is emitted in a straight line, and the electron beam is deflected and guided into the beam bin.

[0014] The undulator in the radiation section is a conical undulator; the magnetic field taper of the conical undulator along the electron beam propagation direction matches the gradient rate of the bunch spacing of the unequally spaced electron beam bunches. Thus, the radiation phase shift provided by the conical undulator can compensate for the inherent chirp of each micro bunch in the unequally spaced electron beam bunch, so that the radiation fields generated by each micro bunch are aligned and coherently superimposed in the time domain, and finally synthesized into a terahertz radiation pulse with a pulse width of few periods or a single period.

[0015] No. oscillator parameters for each cycle for:

[0016] ,

[0017] in, where is the Lorentz factor corresponding to the electron, and c is the speed of light. For the first The smoothing matching time interval corresponding to each oscillator cycle , For the first The spatial geometric spacing of micro-clusters corresponding to each undulator period position This is the resonant wavelength of the modulation segment undulator.

[0018] The dual-pulse beat frequency laser output by the laser beat frequency system is formed by the coherent superposition of two laser pulses.

[0019] The present invention relates to a high-field ultrafast terahertz radiation generation device based on nonlinear electron beam compression. This device achieves deterministic shaping of the beam phase space through a combination of beat-frequency laser seeding and nonlinear manipulation of the longitudinal phase space of the high-energy electron beam. Specifically, the beat-frequency laser provides high-purity initial energy modulation for the 100 MeV electron beam in the modulation section undulator, perfectly avoiding the damage to the microstructure caused by the space charge effect in the low-energy stage. Subsequently, in the acceleration system, the active nonlinear introduction of the X-band harmonic linearization cavity and the high-order nonlinear compression of the magnetic compression section perfectly transform the energy modulation into a nonlinearly distributed, unequally spaced micro-beam array.

[0020] Furthermore, this unequally spaced micro-bundle array enters a radiating section undulator with a specific magnetic field taper. Through precise geometric matching of the bundle spacing evolution and the undulator's magnetic field parameters, perfect phase synchronization of the terahertz radiation field in the time domain is achieved. The final center frequency of the radiation is determined by the product of the initial frequency difference of the beat-frequency laser and the nonlinear compression factor of the electron beam acceleration system. Adjusting these two factors allows for wide-range continuous tuning of the radiation center frequency.

[0021] Therefore, the device of this invention can generate strong-field ultrafast terahertz radiation with a wide range of continuously adjustable center frequencies, pulse width compression on the order of at least a period or a single period, and extremely high peak power. The device has a simple layout, extremely flexible tuning, and precisely controllable output time-domain characteristics, and can be used for a series of advanced scientific experiments requiring extreme ultrafast terahertz light fields, such as non-equilibrium ultrafast dynamics detection, strong-field physics mechanism research, coherent control of matter quantum states, and high-sensitivity terahertz sensing. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the overall structure of a terahertz radiation generating device based on nonlinear electron beam compression according to an embodiment of the present invention.

[0023] Figure 2 This is a partial structural schematic diagram of the electron beam modulation system and its interacting optical path of the terahertz radiation generating device of the present invention.

[0024] Figure 3 This is a partial structural schematic diagram of the electron beam acceleration system of the terahertz radiation generating device of the present invention.

[0025] Figure 4 This is a partial structural schematic diagram of the radiation system of the terahertz radiation generating device of the present invention.

[0026] Figure 5 This is a schematic diagram illustrating the physical mechanism of the terahertz radiation generating device of the present invention, which utilizes the inherent chirp of unequally spaced micro-bundles and the taper matching of the undulator to coherently synthesize ultrafast terahertz waveforms.

[0027] Figure 6A , Figure 6B and Figure 6C These are numerical simulation results of the phase space (energy-time) evolution and flux distribution of the electron beam in different longitudinal manipulation stages of the device of the present invention; wherein, Figure 6A The longitudinal phase space distribution and current intensity evolution of the electron beam after initial periodic energy modulation is obtained by passing through an electron beam modulation system and seeding with beat frequency lasers are demonstrated. Figure 6B The longitudinal phase space evolution and distribution characteristics of the electron beam after it undergoes nonlinear trimming in the X-band harmonic linearization cavity and passes through the magnetic compression section, and is transformed into an array of unequally spaced micro-beams are demonstrated. Figure 6C The diagram illustrates the longitudinal phase space and flux distribution of the electron beam string after it passes through the final acceleration section exit of the subsequent electron beam acceleration system, and after the energy chirp is eliminated by the beam wake field to reach the final high-energy state.

[0028] Figure 7AThis is a numerical simulation result of the longitudinal current distribution of the unequally spaced micro-bundles formed by the electron beam after high-order nonlinear magnetic compression and subsequent longitudinal phase space evolution before entering the radiating section undulator in this invention. It shows the gradual change in the spacing between the micro-bundles from the head to the tail.

[0029] Figure 7B This is a graph showing the magnetic field parameters (K value) of the radiating section undulator in this invention and their precise matching relationship with the spacing of the unequal-pitched electron beam strings as a function of the number of periods.

[0030] Figure 8A This is a time-domain electric field waveform diagram of the strong field ultrafast terahertz radiation generated by the final coherent superposition of the device of the present invention.

[0031] Figure 8B yes Figure 8A Broadband spectral distribution diagram corresponding to the ultrafast terahertz radiation generated in the process. Detailed Implementation

[0032] The present invention will be further described below with reference to embodiments and accompanying drawings, but this should not be construed as limiting the scope of protection of the present invention. The electron beam energy, beat frequency envelope frequency, acceleration gradient, compression intensity, undulator period, and magnetic field taper used in this embodiment can all be equivalently adjusted according to the target terahertz radiation frequency band and actual device conditions.

[0033] This invention provides a terahertz radiation generator based on nonlinear electron beam compression, which is an ultrafast strong-field terahertz radiation generator. "Ultrafast" refers to the pulse width being compressed to the order of at least one or a few periods, with "few periods" meaning less than five oscillation periods. The specific pulse width is typically in the range of tens of femtoseconds (fs) to a few picoseconds (ps). In the embodiment, the full width at half maximum (FWHM) of the main peak reaches 30 fs. "Strong field" refers to an extremely high peak electric field strength, typically in the range of hundreds of mV / m or even as high as GV / m. In the embodiment, the peak field strength reaches 4000 mV / m (i.e., 4 GV / m).

[0034] The terahertz radiation generation device based on nonlinear electron beam compression of this invention is mainly based on the following principle: Currently, there are related schemes that use laser seeding to imprint equally spaced periodically modulated and induced equally spaced micro-bundle sequences along the longitudinal direction of the electron beam, which generates multi-period non-ultrafast terahertz radiation. This invention utilizes the existing layout of conventional free-electron laser devices and constructively employs an X-band harmonic linearization cavity that actively operates under incompletely compensated phase, allowing it to actively retain or reshape specific secondary energy correlations. Related to tertiary energy This actively introduces the required high-order nonlinear chirp into the longitudinal phase space of the electron beam, ultimately enabling the generation of ultra-short, ultra-intense terahertz radiation (short-period or even single-period) using unequally spaced electron cluster sequences. Furthermore, a key challenge in manipulating the generation of micro-clusters at extremely low energies is the space charge effect. The extremely strong Coulomb repulsion at low energies leads to severe nonlinear degradation of the longitudinal microstructure of the micro-clusters. This invention utilizes an injector to first accelerate the electron beam to the "hundred megaelectron volts energy level." The space charge effect is suppressed at relativistically high energies, and then external seeding is performed using beat-frequency lasers, thus fundamentally avoiding structural damage.

[0035] Figure 1 This is a schematic diagram of the overall structure of a terahertz radiation generating device based on nonlinear electron beam compression according to an embodiment of the present invention. Figure 2 This is a partial structural schematic diagram of the electron beam modulation system and its interacting optical path of the terahertz radiation generating device of the present invention; Figure 3 This is a partial structural schematic diagram of the electron beam acceleration system (including a high-energy acceleration structure, an X-band harmonic linearization cavity, and a magnetic compression section) of the terahertz radiation generating device of the present invention. Figure 4 This is a partial structural schematic diagram of the radiation system (including a conical undulator and a beam separation structure) of the terahertz radiation generating device of the present invention. Figure 5 This is a schematic diagram illustrating the principle of unequally spaced micro-beam strings matching the magnetic field taper of the undulator and coherently synthesizing ultrafast terahertz radiation. Figures 6A to 6C The longitudinal phase space and current intensity evolution of the electron beam after energy modulation, nonlinear compression, and terminal acceleration are shown respectively. Figure 7A The current distribution of the unequally spaced microbeam strings before radiation is shown. Figure 7B This shows the matching relationship between the micro-bundle spacing and the undulator K value; Figure 8A and Figure 8B The time-domain electric field and spectrum of the final terahertz radiation are shown respectively. The strong-field ultrafast terahertz radiation generating device of the present invention is based on nonlinear electron beam compression technology.

[0036] like Figure 1 As shown, the strong field ultrafast terahertz radiation generating device of the present invention includes an injector 1, an electron beam modulation system 2, an electron beam acceleration system 3 and a radiation system 4 arranged sequentially along the electron beam transmission direction, and a laser beat frequency system 5 coupled to the electron beam modulation system 2 in the optical path.

[0037] The laser beat frequency system 5 is configured to generate a dual-pulse beat frequency laser with a constant beat frequency envelope frequency, and to guide the dual-pulse beat frequency laser into the electron beam modulation system 2. The electron beam modulation system 2 is configured to enable the electron beam to obtain initial energy modulation through the interaction between the electron beam and the beat frequency laser. The electron beam acceleration system 3 is configured to perform incomplete linear polarization and nonlinear compression on the electron beam, converting it into a string of unequally spaced electron beams. The radiation system 4 receives the string of unequally spaced electron beams and uses its magnetic field taper to coherently superimpose the micro-beams in the string of unequally spaced electron beams to synthesize the desired terahertz radiation.

[0038] Injector 1 is configured to generate an electron beam and accelerate it to an energy suitable for external laser modulation before feeding it into the electron beam modulation system 2. Injector 1 can be a photocathode injector, which includes a photocathode electron gun, a focusing element, and an accelerating structure. Thus, the photocathode electron gun of injector 1 generates an electron beam by irradiating the photocathode with a driving laser. After being accelerated and laterally matched by the accelerating structure and focusing element, the electron beam reaches an energy in the hundreds of megaelectron volts range, thereby reducing the damage to the longitudinal microstructure caused by low-energy space charge effects during subsequent beat-frequency laser modulation.

[0039] The laser beat frequency system 5 is configured to generate a dual-pulse beat frequency laser with a constant beat frequency envelope frequency, and to guide the dual-pulse beat frequency laser into the electron beam modulation system 2. Specifically, by adjusting the beat frequency envelope frequency of the dual-pulse beat frequency laser and / or changing the nonlinear compression factor of the electron beam, a wide range of continuously adjustable terahertz radiation center frequencies can be achieved.

[0040] The dual-pulse beat-frequency laser output by the laser beat-frequency system 5 is formed by the coherent superposition of two laser pulses. In one embodiment, the two laser pulses have the same center angular frequency. and optical linear chirp coefficient It also has an adjustable relative time delay. The phase of two laser pulses can be expressed as:

[0041] ,

[0042] ,

[0043] The phase difference between the two laser pulses after coherent superposition is:

[0044] ,

[0045] Therefore, beat frequency envelope frequency for:

[0046] ,

[0047] in, The internal time coordinate of the laser pulse. The laser's central angular frequency, The linear chirp coefficient, The relative time delay between the two laser beams is given. This is the beat frequency envelope frequency.

[0048] In other embodiments, the relative time delay between the two laser beams Replace with delay parameters in length form hour, , The speed of light in a vacuum. This refers to a relative time delay.

[0049] By adjusting the relative time delay of the two laser beams and / or linear chirp coefficient It can change the beat frequency envelope frequency. .

[0050] Beat frequency envelope frequency The beat frequency is the frequency generated on the envelope of the beat laser after it has been beat. Its value is typically set in the range of hundreds of GHz to several THz. Beat envelope frequency. By combining the nonlinear compression factor of the electron beam acceleration system 3, the center frequency of the output terahertz covers the frequency band of 0.1~30 THz.

[0051] In other embodiments, the laser beat frequency system 5 may employ dual-wavelength pulses with different center wavelengths, dual pulses with adjustable higher-order dispersion, or other optical structures capable of generating a target beat frequency envelope, as long as they generate a nearly equidistant periodic beat frequency structure within the effective region of the electron beam.

[0052] like Figure 2 As shown, the electron beam modulation system 2 includes at least a modulation segment undulator 21. The electron beam modulation system 2 is configured to interact with a dual-pulse beat-frequency laser during co-linear propagation. The dual-pulse beat-frequency laser and the modulation segment undulator are matched in lateral position, arrival time, polarization direction, and resonance conditions, resulting in initial energy modulation of the electron beam as periodic energy modulation. That is, during the lateral oscillation of the undulator, electrons exchange energy with the laser electric field, thereby writing equidistant periodic energy modulations corresponding to the beat frequency envelope into the longitudinal phase space of the electron beam.

[0053] Among them, resonance condition matching refers to the carrier wavelength of the dual-pulse beat frequency laser. satisfy: ,in, The resonant wavelength of the modulation segment undulator. The Lorentz factor is the corresponding electron. These are the parameters for the modulation section undulator. Lateral position matching means that the mode field waist of the dual-pulse beat laser and the electron beam are fully overlapped in lateral space; arrival time matching means that the dual-pulse beat laser and the electron beam are strictly synchronized at the undulator inlet; polarization matching means that the linear polarization direction of the dual-pulse beat laser is consistent with the swing direction of the electrons in the modulation section undulator.

[0054] The electron beam modulation system 2 also includes a first magnetic compressor located downstream of the modulation section undulator 21. To facilitate the description of the longitudinal compression process, a common reference section is selected upstream of the inlet of the first magnetic compressor, and the longitudinal coordinates are... Total relative energy deviation of the reference energy relative to the common reference section Decompose the data using fast and slow scales:

[0055] ,

[0056] in, The longitudinal coordinate of the magnetic compression input side; Longitudinal coordinates of the magnetic compression input side The total relative energy deviation of the reference energy relative to the common reference section; To represent the slow-scale (gradually varying) energy deviation, it is the baseline of the macroscopic energy distribution after removing high-frequency modulation, which is related to the gradually varying energy formed by the fundamental frequency acceleration structure, the X-band harmonic linearization cavity, and the beam collective effect. It represents the rapid relative energy change obtained after laser modulation, which is the rapid laser energy modulation transmitted from the modulation section undulator to the common reference section. For rapidly modulated, slowly varying amplitude envelope; To quickly modulate the phase.

[0057] When there is no significant nonlinear distortion in the transmission of the laser-modulated phase from the modulation section undulator 21 to the inlet of the first magnetic compressor, the phase is rapidly modulated. It can be approximated as ,in , The period length of the initial energy modulation on the common reference section. This is the initial modulation phase. The beat frequency envelope frequency is changed. The period length of the initial energy modulation at the common reference section can be changed. .

[0058] Electron beam acceleration system 3 is configured to perform incomplete linear polarization and nonlinear compression on the electron beam, transforming it into unequally spaced electron beam bundles. For example... Figure 3As shown, the electron beam acceleration system 3 includes a first acceleration structure 31, a second acceleration structure 32, a magnetic compression section 33, and a third acceleration structure 34 arranged along the electron beam transmission direction. The first acceleration structure 31 and the second acceleration structure 32 are used to accelerate the electron beam with initial energy modulation and perform nonlinear correction of the longitudinal phase space; the magnetic compression section 33 is used to convert the energy modulation of the nonlinearly corrected electron beam into density modulation, realizing longitudinal nonlinear compression, so that the electron beam is converted into an unequally spaced electron beam string when emitted; the third acceleration structure 34 is used to further accelerate or maintain the energy of the unequally spaced electron beam string compressed by the magnetic compression section 33, and introduce it into the radiation system 4, so that the peak electric field intensity is on the order of hundreds of mV / m to GV / m.

[0059] The first accelerating structure 31 primarily enhances the electron beam energy and establishes an overall linear energy chirp. The first accelerating structure 31 typically employs existing S-band (e.g., 2.856 GHz) or C-band (e.g., 5.712 GHz) RF linear accelerator tubes, as detailed in the literature Fang W, Tan J, Li L, et al. RF System for SXFEL: C-band, X-band and S-band[J]. Proceedings of the IPAC2018, Vancouver, Canada, 2018: 4446-4448. The design of the first accelerating structure 31 is entirely consistent with existing technologies, enabling it to operate at an off-crest microwave phase. As the electron beam passes through, not only is an overall energy boost achieved, but the different RF electric fields at the head and tail of the electron beam also introduce a first-order linear energy chirp into the longitudinal phase space of the electron beam. .

[0060] The second accelerating structure 32 is preferably an X-band harmonic linearization cavity, and its operating mode is a key innovation of this invention. The X-band harmonic linearization cavity is configured to operate in a partially compensated phase to actively introduce higher-order nonlinear chirps (such as second- and third-order energy curvature coefficients) into the longitudinal phase space of the electron beam. , This results in the electron beam head and tail receiving different compression ratios when passing through the magnetic compression section 33, forming the unequal-spacing electron beam clusters with gradually changing micro-cluster spacing.

[0061] The X-band harmonic linearization cavity is not a completely new invention in terms of hardware structure; it is a conventional RF acceleration structure already existing in the field of free-electron lasers. The innovation of this invention lies in the configuration of its operating mode. In existing technologies, X-band cavities are designed to "fully compensate for phase" to eliminate curvature; however, in this invention, it is intentionally configured to "operate with incomplete phase compensation." By adjusting the RF power and phase, it actively preserves or reshapes a specific second-order energy curvature. and third-order energy curvature This allows for the active introduction of the required higher-order nonlinear energy chirp into the longitudinal phase space of the electron beam. For details, see Fang W, Tan J, Li L, et al. RF System for SXFEL: C-band, X-band and S-band[J]. Proceedings of the IPAC2018, Vancouver, Canada, 2018: 4446-4448.

[0062] Gradually varying relative energy deviation near the common reference section Taylor expansion can be performed along the vertical axis:

[0063] ,

[0064] Where z is the longitudinal coordinate of the magnetic compression input side, It is a first-order linear energy chirp coefficient, which mainly determines the average compression; and These are the second- and third-order energy curvature coefficients, respectively, which primarily determine the variation in compressibility along the longitudinal position of the bundle. The sinusoidal curvature of the fundamental radio frequency field naturally generates higher-order energy correlations. The phase and voltage of the X-band harmonic linearization cavity are used to compensate for, reshape, or intentionally preserve the second- and third-order energy curvature coefficients. and .

[0065] The magnetic compression section 33 is used to convert the energy modulation of the nonlinearly modified electron beam into density modulation, thereby achieving longitudinal nonlinear compression of the electron beam and transforming it into an unequally spaced electron beam cluster upon emission. Specifically, the magnetic compression section 33 utilizes the correlation between electron energy and path length to convert energy modulation into density modulation.

[0066] Longitudinal coordinate of magnetic compression output side It can be represented as:

[0067] ,

[0068] Where z is the longitudinal coordinate of the magnetic compression input side, , and These are the first, second, and third order longitudinal dispersion coefficients, respectively.

[0069] To illustrate the variation in the spacing between the main micro-bundles, only the slowly varying relative energy deviation is retained (to ignore high-frequency details), and the slowly varying longitudinal mapping is obtained. That is, slowly varying longitudinal mapping Based on the longitudinal coordinates of the electron beam after longitudinal nonlinear compression in magnetic compression section 33 This is obtained by retaining only the relevant portion of the slowly varying relative energy deviation. Slowly varying longitudinal mapping. for:

[0070] ,

[0071] Where z is the longitudinal coordinate of the magnetic compression input side, , These are the first-order and second-order longitudinal dispersion coefficients, respectively. This refers to the gradually varying relative energy deviation.

[0072] First derivative of a slowly varying longitudinal mapping Indicates the local longitudinal magnification, and the nonlinear compression factor of electron beam acceleration system 3. Defined as local longitudinal magnification The reciprocal of the absolute value, that is Therefore, the nonlinear compression factor Variation with the vertical coordinate z. Nonlinear compression factor. The physical meaning is the factor by which the initial period length is shortened.

[0073] Local vertical magnification When constant, the period length of each initial energy modulation Shrinking or lengthening by the same proportion will still result in equal spacing; when the vertical magnification of the region is... With vertical coordinate When the structure changes, different longitudinal positions experience different compressions, and the equidistant modulation is converted into an unequal-spacing structure.

[0074] The actual density peak is generated by a complete mapping that includes rapid modulation. The total relative energy deviation of the electron beam is then considered. Substituting the longitudinal mapping, while retaining the second-order longitudinal dispersion coefficients... In the case of full longitudinal mapping of electron longitudinal position transformation for:

[0075] ,

[0076] Where z is the longitudinal coordinate of the magnetic compression input side, It is a slowly varying longitudinal mapping (only looking at the macroscopic envelope); The first-order longitudinal dispersion coefficient, It is the second-order longitudinal dispersion coefficient. For slowly varying relative energy deviation, The rapidly varying energy modulation component introduced for dual-pulse beat-frequency lasers has a frequency that matches the beat-frequency envelope frequency.

[0077] Rapid periodic energy modulation This causes the flux intensity to periodically form local maxima within each sowing cycle, i.e., to form micro-cluster density peaks; gradually varying baselines. This determines that these principal density peaks are subjected to different compressions at the bundle head, bundle middle, and bundle tail.

[0078] Finally, the localized micro-beam spacing of the terahertz radiation output by radiation system 4 It can be approximated as:

[0079] ,

[0080] = ,

[0081] in, The spacing between localized micro-beam clusters of terahertz radiation. The initial spatial spacing of the micro-bundles For local vertical magnification, Here, c represents the local micro-clustering frequency, and c represents the speed of light. Where z is the beat frequency envelope frequency, and z is the longitudinal coordinate on the magnetic compression input side. This represents the longitudinal coordinate of the magnetic compression output side.

[0082] The final The spatial geometric spacing of the micro-clusters corresponding to each undulator period position satisfy , For the first The longitudinal coordinates of the magnetic compression input side at each undulator cycle position. Therefore, the average compression determines the center position of the final micro-group frequency, and... The spacing chirp is determined by the change in the position of the bundle. Ultimately, by adjusting the initial energy modulation and average compression, a wide range of continuous tuning of the radiation center frequency can be achieved.

[0083] when And retain and At that time, it was preserved near the center of the bundle until The first-order result is the local longitudinal magnification. for:

[0084] .

[0085] Therefore, the aforementioned The first term represents the second-order energy curvature coefficient. The first-order dispersion is converted into a longitudinal compression gradient, and the second term represents the first-order linear energy chirp coefficient. Coupling with second-order dispersion. First-order linear energy chirp coefficient. and second-order energy curvature coefficient Provided by the microwave phase and voltage of the first and second accelerating structures; first-order longitudinal dispersion coefficient and second-order longitudinal dispersion coefficient The deflection magnetic field of the magnetic compression section 33 determines this. These parameters work together to satisfy the local longitudinal magnification. The target envelope equation.

[0086] The third acceleration structure 34 is used to further accelerate or maintain the energy of the unequally spaced electron bundles compressed by the magnetic compression section 33, and then introduce them into the radiation system 4. Specifically, the third acceleration structure 34 is used to further accelerate the unequally spaced micro-bundles formed after compression to the target energy, and to reduce the unfavorable residual average energy chirp by configuring radio frequency phase, longitudinal tail field or other longitudinal phase space compensation methods, while maintaining the micro-bundle spacing and peak current envelope as much as possible. Among them, the third acceleration structure 34 eliminates the residual chirp by configuring a radio frequency phase with a backward peak or by using a longitudinal tail field; in addition, since the electrons reach extremely high energies of gigaelectronvolts (without deflection dispersion), their speed approaches the speed of light, and their relative positions are naturally "frozen," thereby maintaining the micro-bundle spacing.

[0087] like Figure 6A As shown, the electron beam exhibits nearly equidistant periodic energy modulation at the exit of electron beam modulation system 2, while the flux intensity has not yet formed the desired unequal-spacing, high-contrast micro-beam clusters. Figure 6B As shown, after passing through the X-band harmonic linearization cavity (i.e., the second accelerating structure 32) and the magnetic compression section 33, the periodic energy modulation conversion of the electron beam forms a density peak, and due to position-dependent compression, it forms a continuously varying adjacent spacing. Figure 6C As shown, after passing through the third accelerating structure 34, the electron beam reaches the final energy required by the radiation system 4 while maintaining the unequally spaced micro-beam cluster structure.

[0088] The radiation system 4 receives the unequally spaced electron beam strings and uses its magnetic field taper to coherently superimpose the individual micro-beam strings within them to synthesize the desired terahertz radiation. For example... Figure 4 As shown, the radiation system 4 includes a radiation section undulator 41, a bent iron 42, and a beam trash can 43 arranged sequentially along the electron beam transmission direction. The radiation section undulator 41 is preferably a planar tapered undulator with a period of... The dimensionless undulator parameters can remain unchanged. The magnetic field taper of the conical undulator along the electron beam propagation direction varies periodically, and the gradient rate of the bunch spacing of the unequally spaced electron beam bunches matches the gradient rate of the magnetic field taper along the electron beam propagation direction.

[0089] Figure 7A This is a numerical simulation result of the longitudinal current distribution of the unequally spaced micro-bundles formed after the electron beam undergoes high-order nonlinear magnetic compression and subsequent longitudinal phase space evolution before entering the radiating section undulator in this invention. It shows the gradual change in the spacing between the micro-bundles from the head to the tail. The time interval between adjacent micro-bundles is extracted from this longitudinal current distribution, and the spacing sequence is sequentially mapped to each period of the radiating section undulator 41 according to the direction in which the radiation relative to the electron beam slides from the tail to the head.

[0090] Record No. The smoothing matching time interval corresponding to each oscillator cycle is: ,in, For the first The spatial geometric spacing of the micro-clusters corresponding to the periodic positions of the undulators. Therefore, the first Local resonant wavelength per undulator cycle The following conditions must be met for a local resonance relationship to be satisfied:

[0091] ,

[0092] in, For the first The local resonant wavelength of one oscillator cycle The Lorentz factor is the corresponding electron. For the first The oscillator parameters for each cycle.

[0093] No. oscillator parameters for each cycle The magnetic field taper used to define the conical undulator along the electron beam propagation direction. The inverted first... oscillator parameters for each cycle satisfy:

[0094] ,

[0095] in, where is the Lorentz factor corresponding to the electron, and c is the speed of light. For the first The smoothing matching time interval corresponding to each oscillator cycle , For the first The spatial geometric spacing of micro-clusters corresponding to each undulator period position This represents the resonant wavelength of the modulation segment undulator. This relationship transforms the position-varying bunch spacing into periodically varying undulator parameters. This allows for the matching of the magnetic field taper.

[0096] It should be noted that the gradient rate of the bunch spacing in unequally spaced electron bundle strings is not a fixed constant. (Refer to the instruction manual.) Figure 7B For example, the spacing between the micro-clusters is approximately 40 cm from the tail. Gradually shrink to about 15% of the head The gradient rate and its range can be flexibly adjusted according to the specific compression level and target frequency band (e.g., 0.1–30 THz).

[0097] With the first The smoothing matching time interval corresponding to each oscillator cycle The sequence changes continuously along the micro-beam cluster, the first... oscillator parameters for each cycle The magnetic field taper of the conical undulator along the electron beam propagation direction is matched with the gradient rate of the bunch spacing of the unequally spaced electron beam bunches. Thus, the radiation phase shift provided by the conical undulator can compensate for the inherent chirp of each micro bunch in the unequally spaced electron beam bunch, so that the radiation fields generated by each micro bunch are aligned and coherently superimposed in the time domain.

[0098] Specifically, local resonance relationship This ensures that the radiation slides forward relative to the electron beam by one local resonant wavelength within one undulator cycle, i.e., the slide time is... Simultaneously, local angular frequency .

[0099] like Figure 5 As shown, after a matching period, the radiation generated by the rear micro-beam cluster has its wave packet center and carrier phase aligned with the radiation generated by the front micro-beam cluster, thus achieving time-domain alignment and coherent superposition of the radiation fields generated by each micro-beam cluster. The carrier phases of the broadband wave packets are completely aligned and converged into a final synthesis to obtain a terahertz radiation pulse with a pulse width of few periods or a single period.

[0100] The transverse Laplace term in the complete field equations describes radiation diffraction. This embodiment does not solve for this term directly on the transverse grid; instead, it assumes that each local frequency component propagates approximately as a fundamental Gaussian beam, and uses an on-axis electric field amplitude diffraction correction factor. Corrected cumulative radiation field ,in The modified cumulative radiation field is used to introduce diffraction corrections for three-dimensional transverse Gaussian beams into the theoretical one-dimensional model, making the results closer to real physical experiments.

[0101] On-axis electric field amplitude diffraction correction factor for:

[0102] , ,

[0103] in, For the first The on-axis electric field amplitude diffraction correction factor for each period. The lateral overlap factor between the electron beam and the radiation mode. Rayleigh length, For equivalent radiation mode waist, For the first The oscillator cycle entry position. The correction is for the field amplitude, therefore the corresponding power correction is approximately: .

[0104] like Figure 7A As shown, the spacing between the micro-clusters at the entrance of the radiation system varies orderly along the cluster position; as Figure 7B As shown, the K value obtained by inverting the spacing sequence changes smoothly along the oscillator period. Figure 8A The image shows the ultrafast terahertz time-domain electric field after slip coherent superposition, where the main peak is formed by the constructive superposition of wide frequency components, with a peak field strength of 4000 MV / m and a full width at half maximum (FWHM) of 30 fs. Figure 8B The corresponding broadband spectrum is shown.

[0105] After the electron beam generates terahertz radiation through the radiation section undulator 41, the bent iron 42 deflects the electron beam and spatially separates it from the terahertz radiation that is propagating in a straight line. The electron beam then enters the beam garbage bin 43, and the terahertz radiation is output to the user's experimental station via vacuum transmission, focusing, or diagnostic optical path.

[0106] Based on the above-described apparatus of the present invention, the method for generating terahertz radiation includes the following steps:

[0107] Step S1: The relativistic electron beam is generated and accelerated by injector 1. The charge, beam length, transverse dimension, energy dispersion and arrival time of the electron beam are adjusted to meet the requirements of beat frequency laser modulation and subsequent compression.

[0108] The electron beam must meet conditions such as hundreds of megaelectron volts, low energy dissipation, and picosecond-level beam length. The lateral dimension of the electron beam is adjusted by the focusing solenoid, the beam length is adjusted by the driving laser pulse width, and the energy / energy dissipation is adjusted by the electron gun radio frequency power / phase.

[0109] Step S2: Two laser pulses with predetermined linear chirps and relative time delays are generated by the laser beat frequency system 5 and interact with the electron beam in the modulation segment undulator 21 of the electron beam modulation system 2 to write nearly equidistant periodic energy modulation into the electron beam.

[0110] Step S3: The electron beam with periodic energy modulation is passed sequentially through the first accelerating structure 31 and the second accelerating structure 32, and a predetermined first-order linear energy chirp coefficient is formed by setting the radio frequency phase and voltage. Second-order energy curvature coefficient and third-order energy curvature coefficient .

[0111] First-order linear energy chirp coefficient and second-order energy curvature coefficient and third-order energy curvature coefficient Predetermine in advance using the following methods:

[0112] 1) Target Determination: Based on the requirements, pre-set the time interval sequence of micro-beam clusters arriving at the undulator. ;

[0113] 2) Calculate the magnetic field taper: Calculate the required taper sequentially (offline, cycle-by-cycle). sequence;

[0114] 3) Derivation of nonlinear compression: from Reverse spatial spacing Combined with the initial Calculate the corresponding local vertical magnification. .

[0115] 4) Solving for slowly varying correlations: According to the formula After selecting the dispersion parameters, the predetermined values ​​are solved. .

[0116] 5) Hardware parameter settings: Convert the inverse solution values ​​into physical settings for the acceleration structure and X-band cavity.

[0117] Step S3 further includes: passing the electron beam through the magnetic compression section 33, using first-order and higher-order longitudinal dispersion to convert periodic energy modulation into density modulation, and using position-dependent compression ratio to convert the initial equidistant structure into unequal-spacing micro-beam clusters; then using the third acceleration structure 34 to complete energy enhancement and residual energy chirp compensation.

[0118] Step S4: Extract the unequally spaced micro-bundle sequence from the final current intensity distribution, calculate the target resonant wavelength and K-value taper of each undulator period according to the sequence, so that the micro-bundle string enters the radiation section undulator 41, and uses the period-by-period slip and phase closure coherent synthesis required for terahertz radiation.

[0119] As mentioned above, calculating the target resonance wavelength and K-value taper specifically includes: determining the target terahertz radiation index (source origin), deriving the micro-beam cluster spacing sequence (obtaining...). and ), and then calculate the target resonance wavelength and K-value taper (to obtain and ).

[0120] The electron beam is a non-uniformly spaced sequence, with the spacing gradually decreasing from the tail to the head. Here, "sequence" refers to the physical sequence in spatial order (i.e., the path along the electron beam). Axial direction, oscillator period number Calculate the undulator K-value corresponding to each micro-bundle spacing. Because the spacing needs to be gradually varied, the magnetic field of the undulator is different in each cycle. During design, it is necessary to start from the undulator inlet (the first cycle) and calculate the parameters for the second, third, and so on, sequentially along the longitudinal axis until the last cycle. This method of labeling along the undulator cycle... The process of calculating step by step is called sequential computation.

[0121] Step S4 further includes: using a bent iron 42 to separate the radiated electron beam from the terahertz radiation; the electron beam enters the beam trash can 43; and the terahertz radiation is output in a straight line for focusing, transmission, or experimental application. Ultimately, the center frequency of the strong-field ultrafast terahertz radiation is continuously adjustable over a wide range, and the pulse width is compressed to at least the order of a period or a single period.

[0122] The present invention relates to a high-field ultrafast terahertz radiation generation device based on nonlinear electron beam compression. This device achieves deterministic shaping of the beam phase space through a combination of beat-frequency laser seeding and nonlinear manipulation of the longitudinal phase space of the high-energy electron beam. Specifically, the beat-frequency laser provides high-purity initial energy modulation for the 100 MeV electron beam in the modulation section undulator, perfectly avoiding the damage to the microstructure caused by the space charge effect in the low-energy stage. Subsequently, in the acceleration system, the active nonlinear introduction of the X-band harmonic linearization cavity and the high-order nonlinear compression of the magnetic compression section perfectly transform the energy modulation into a nonlinearly distributed, unequally spaced micro-beam array.

[0123] Furthermore, this unequally spaced micro-bundle array enters a radiating section undulator with a specific magnetic field taper. Through precise geometric matching of the bundle spacing evolution and the undulator's magnetic field parameters, perfect phase synchronization of the terahertz radiation field in the time domain is achieved. The final center frequency of the radiation is determined by the product of the initial frequency difference of the beat-frequency laser and the nonlinear compression factor of the electron beam acceleration system. Adjusting these two factors allows for wide-range continuous tuning of the radiation center frequency.

[0124] Therefore, the device of this invention can generate strong-field ultrafast terahertz radiation with a wide range of continuously adjustable center frequencies, pulse width compression on the order of at least a period or a single period, and extremely high peak power. The device has a simple layout, extremely flexible tuning, and precisely controllable output time-domain characteristics, and can be used for a series of advanced scientific experiments requiring extreme ultrafast terahertz light fields, such as non-equilibrium ultrafast dynamics detection, strong-field physics mechanism research, coherent control of matter quantum states, and high-sensitivity terahertz sensing.

[0125] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Equivalent substitutions and modifications made by those skilled in the art to the device structure, optical layout, radio frequency band, compression stage, undulator period, magnetic field taper, and control method without departing from the concept of the present invention should all fall within the scope of protection of the present invention. Parts of the present invention not described in detail can be implemented using conventional techniques in the art.

Claims

1. A terahertz radiation generating device based on nonlinear electron beam compression, characterized in that, It includes an injector (1), an electron beam modulation system (2), an electron beam acceleration system (3), and a radiation system (4) arranged sequentially along the electron beam transmission direction; and a laser beat frequency system (5). The laser beat frequency system (5) is configured to generate a double-pulse beat frequency laser with a constant beat frequency envelope frequency, and to introduce the double-pulse beat frequency laser into the electron beam modulation system (2); the electron beam modulation system (2) is configured to enable the electron beam to obtain initial energy modulation by interacting with the double-pulse beat frequency laser. The electron beam acceleration system (3) is configured to perform incomplete linear polarization and nonlinear compression on the electron beam, converting it into an unequally spaced electron beam string; the radiation system (4) receives the unequally spaced electron beam string and uses its magnetic field taper to coherently superimpose the micro-beams in the unequally spaced electron beam string to synthesize the required terahertz radiation, the pulse width of the terahertz radiation being either a few periods or a single period.

2. The terahertz radiation generating device according to claim 1, characterized in that, The injector (1) is configured to generate an electron beam and accelerate it to an energy suitable for external laser modulation, and then feed it into the electron beam modulation system (2).

3. The terahertz radiation generating device according to claim 1, characterized in that, The electron beam modulation system (2) includes at least a modulation segment undulator (21); the modulation segment undulator (21) is configured to coherently interact with the electron beam and the dual-pulse beat laser in the same direction and collinear transmission, and the dual-pulse beat laser and the modulation segment undulator are matched in terms of lateral position, arrival time, polarization direction and resonance condition, so that the initial energy obtained by the electron beam is modulated as periodic energy modulation.

4. The terahertz radiation generating device according to claim 1, characterized in that, The electron beam acceleration system (3) includes a first acceleration structure (31), a second acceleration structure (32), a magnetic compression section (33), and a third acceleration structure (34) arranged sequentially along the electron beam transmission direction. The first acceleration structure (31) and the second acceleration structure (32) are used to accelerate the electron beam with initial energy modulation and to perform nonlinear trimming of the longitudinal phase space. The magnetic compression section (33) is used to convert the energy modulation of the nonlinearly modified electron beam into density modulation, thereby achieving longitudinal nonlinear compression and converting the electron beam into an unequally spaced electron beam cluster when it is emitted. The third acceleration structure (34) is used to further accelerate or maintain the energy of the unequally spaced electron beams compressed by the magnetic compression section (33) and introduce them into the radiation system (4) so ​​that the peak electric field intensity is on the order of hundreds of MV / m to GV / m.

5. The terahertz radiation generating device according to claim 4, characterized in that, The nonlinear compression factor of the electron beam acceleration system (3) The nonlinear compression factor varies with the vertical coordinate z. The definition is the first derivative of the slowly varying longitudinal mapping. The reciprocal of the absolute value, a slowly varying longitudinal mapping Based on the longitudinal coordinates of the electron beam after longitudinal nonlinear compression in the magnetic compression section (33) Only the relevant part of the slowly varying relative energy deviation is retained; the radiation system (4) outputs target terahertz radiation, the target terahertz center frequency is obtained by the beat frequency envelope frequency and / or the nonlinear compression factor of the electron beam acceleration system. To adjust.

6. The terahertz radiation generating device according to claim 4, characterized in that, The second acceleration structure (32) is an X-band harmonic linearization cavity, which is configured to operate in an incompletely compensated phase to actively introduce high-order nonlinear chirps into the longitudinal phase space of the electron beam, thereby causing the head and tail of the electron beam to obtain different compression ratios when passing through the magnetic compression section (33), forming the unequal-spacing electron beam clusters with gradually changing micro-bundle spacing.

7. The terahertz radiation generating device according to claim 1, characterized in that, The radiation system (4) includes a radiation segment undulator (41), a bent iron (42), and a beam trash can (43) arranged sequentially along the transmission direction of the unequally spaced electron beam bundles. The radiation segment undulator (41) is used to generate the terahertz radiation by passing the unequally spaced electron beam bunches through a magnetic field; The bent iron (42) is used to spatially separate the radiated electron beam from the generated terahertz radiation, so that the terahertz radiation is emitted in a straight line and the electron beam is deflected and guided into the beam garbage bin (43).

8. The terahertz radiation generating device according to claim 7, characterized in that, The radiating section undulator (41) is a conical undulator; The magnetic field taper of the conical undulator along the electron beam propagation direction is matched with the gradient rate of the bunch spacing of the unequally spaced electron beam bunches. Thus, the radiation phase shift provided by the conical undulator can compensate for the inherent chirp of each micro bunch in the unequally spaced electron beam bunch, so that the radiation fields generated by each micro bunch are aligned and coherently superimposed in the time domain, and finally synthesized into a terahertz radiation pulse with a pulse width of few periods or a single period.

9. The terahertz radiation generating device according to claim 8, characterized in that, No. oscillator parameters for each cycle for: ， in, where is the Lorentz factor corresponding to the electron, and c is the speed of light. For the first The smoothing matching time interval corresponding to each oscillator cycle , For the first The spatial geometric spacing of micro-clusters corresponding to each undulator period position This is the resonant wavelength of the modulation segment undulator.

10. The terahertz radiation generating device according to claim 1, characterized in that, The dual-pulse beat frequency laser output by the laser beat frequency system (5) is formed by the coherent superposition of two laser pulses.

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