Free electron laser and miniature undulator

Abstract

The present invention relates to a micro-undulator of a free electron laser, wherein the free electron laser includes an optical processing unit capable of outputting laser polarized in the X direction and a micro-undulator for generating a periodically varying transverse deflection electric field to deflect an electron beam incident in the Z direction. The micro-undulator includes a reflective layer, a base layer located above the reflective layer, and a grating located on the base layer, and the gratings are arranged in the incident direction of the electron beam. The free electron laser of the present invention adopts a micro-undulator. Due to the adoption of optical confinement instead of the conventional magnetic confinement, the size of the micro-undulator can be made very small, thereby reducing the size of the free electron laser. Moreover, the period of the micro-undulator is smaller than that of the undulator composed of conventional magnetic elements, and when generating coherent radiation light, the requirement for the energy of the electron beam can be reduced.

Description

Technical Field

[0001] The present invention relates to a free electron laser and its miniature undulator. Background Art

[0002] The free electron laser light source is a new type of coherent light source, which has many advantages such as a wide working wavelength range, pure spectrum, and high power, and has significant application requirements in the fields of biology, materials, medicine, etc. Therefore, since the invention of the free electron laser theory in the 1970s, the free electron laser technology has developed rapidly. In 1971, John Madey proposed a free electron laser (FEL) device that uses a relativistic electron beam to generate relevant radiation in an undulator. Subsequently, the amplifier and oscillator principles of the FEL were experimentally verified at Stanford University, achieving a gain of 7% at a wavelength of 10 μm. Since then, many research institutions worldwide have also carried out research on FEL oscillators in the infrared and terahertz bands. With the development of the photocathode microwave electron gun and bunch compression technology, the beam quality of linear accelerators has been continuously improved, laying the foundation for free electron lasers with short wavelengths (nm) and ultra-short wavelengths (less than 0.1 nm). In 1983, Bonifacio, Narducci, and Pellegrini proposed using the spontaneous radiation at the tail of the electron beam as the seed laser to interact with the head electron beam, thereby realizing the self-amplified spontaneous radiation (SASE) scheme of X-ray coherent radiation in a high-gain manner. In 1992, Pellegrini proposed using the Stanford Linear Accelerator to generate high-quality electron beams to achieve SASE. In 2009, the first X-ray free electron laser - Linac Coherent Light Source (LCLS) was born in the United States. After 2010, a wave of free electron laser light source construction has swept the world, and many high-performance free electron laser devices have been successively debugged to emit light, such as PAL-XFEL in South Korea, Swiss-FRL in Switzerland, and European-XFEL in Europe. In a free electron laser, a high-energy electron beam passes through a periodically arranged magnetic field (undulator) to generate laser gain. Therefore, the undulator is an essential device in a free electron laser, and the currently built free electron lasers all use undulators composed of periodic magnets.

[0003] However, the existing undulators are very large in size, so it is necessary to provide an undulator with a smaller size. Summary of the Invention

[0004] The object of the present invention is to provide a free electron laser with a micro-undulator and its micro-undulator.

[0005] Define an XYZ space rectangular coordinate system. A free electron laser includes an optical processing unit and a micro-undulator. Among them, the optical processing unit is used to perform preset optical processing on the incident laser to output X-direction polarized light. The micro-undulator is used to generate a periodically changing transverse deflection electric field to deflect the electron beam incident along the Z direction. Among them, the micro-undulator includes a reflective layer parallel to the plane defined by the X axis and the Z axis, a base layer located above the reflective layer, and a grating located on the base layer. The grating is distributed along the incident direction of the electron beam, and the grating grooves are parallel to the X axis.

[0006] As an implementation manner, the tooth thicknesses of the two grating protrusions at both ends of the grating are both d, the tooth thicknesses of the grating protrusions between the two grating protrusions at both ends of the grating are both 2d, the widths of the grating grooves are both 2d, and the number of grating protrusions with a tooth thickness of 2d is odd, where d is a number greater than zero.

[0007] As an implementation manner, the wavelength of the laser is equal to the period of the grating, and the tooth thickness of the grating is half of the period of the grating.

[0008] As an implementation manner, the center of the electron beam is close to the surface of the grating.

[0009] As an implementation manner, the distance between the center of the electron beam and the surface of the grating is λ / 4, where λ is the wavelength of the laser, and then the grating satisfies the following relationship:

[0010]

[0011] Where n is the refractive index of the grating, H is the grating tooth height, W is the thickness of the base layer, and N and m are positive integers.

[0012] A micro-undulator includes a reflective layer parallel to the plane defined by the X axis and the Z axis, a base layer located above the reflective layer, and a grating located on the base layer.

[0013] As an implementation manner, the tooth thicknesses of the two grating protrusions at both ends of the grating are both d, the tooth thicknesses of the grating protrusions between the two grating protrusions at both ends of the grating are both 2d, the widths of the grating grooves are both 2d, and the number of grating protrusions with a tooth thickness of 2d is odd.

[0014] As an implementation manner, the grating is a silicon grating.

[0015] As an implementation, it is defined that an electron beam passes above the grating, and a laser irradiates the grating in a direction parallel to the grating lines, where the arrangement direction of the grating is parallel to the incident direction of the electron beam, and the distance between the center of the electron beam and the grating surface is λ / 4, where λ is the wavelength of the laser. Then, the grating satisfies the following relationship:

[0016]

[0017] where n is the refractive index of the grating, H is the height of the grating teeth, W is the thickness of the base layer, and N and m are positive integers.

[0018] As an implementation, the material of the reflective layer is silver, and the material of the base layer is the same as that of the grating.

[0019] Compared with the prior art, the free electron laser of the present invention adopts a micro-undulator. Since the micro-undulator uses optical confinement instead of traditional magnetic confinement, its size can be made very small, thereby reducing the size of the free electron laser. Moreover, the period of the micro-undulator is smaller than that of the undulator composed of conventional magnetic elements. When generating coherent radiation light, it can reduce the requirement for the energy of the electron beam. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the structure and electron beam trajectory of the free electron laser of the present invention.

[0021] Figure 2 It is a schematic diagram of the structure, parameters and laser optical path of the grating of the micro-undulator of the free electron laser of the present invention.

[0022] Figure 3 It is a distribution diagram of the transverse deflection electric field Ex at the center (y = 1.875um) of the electron beam trajectory in the electromagnetic field simulation of an embodiment.

[0023] Figure 4 It is a distribution diagram of the transverse deflection electric field Ex in the electromagnetic field simulation of an embodiment.

[0024] Figure 5 It is a distribution diagram of the electron beam in the initial state when the electron beam tracking calculation is performed by the GPT software in an embodiment.

[0025] Figure 6 It is a bunching distribution diagram of the electron beam after experiencing multiple grating periods when the electron beam tracking calculation is performed by the GPT software in an embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0026] The following will further describe in detail a free electron laser and a micro-undulator of the present invention in conjunction with specific embodiments and the accompanying drawings.

[0027] The free electron laser mainly includes a radiation source for generating laser light, an optical processing unit for performing preset optical processing on the laser light generated by the radiation source, an electron beam generator for generating an electron beam, a linear accelerator, a microwave device, a vacuum system, and a miniature undulator. Please refer to Figure 1 , for the convenience of observation in this embodiment, the radiation source, the electron beam generator, the linear accelerator, the microwave device, and the vacuum system are omitted, the structure of the optical processing unit is simplified, only a lens is shown schematically, and an XYZ space rectangular coordinate system is defined to assist in explaining the specific structures of the free electron laser and the miniature undulator. It can be understood that the radiation source, the electron beam generator, the linear accelerator, the microwave device, the vacuum system, and the optical processing unit can adopt the existing ones.

[0028] The optical processing unit is used to select the linearly polarized laser in the X direction from the femtosecond laser pulse with short pulses and irradiate the miniature undulator from the +Y direction side of the miniature undulator.

[0029] The electron beam output by the electron beam generator is emitted from the -Z direction side to the +Z direction side of the miniature undulator.

[0030] When the miniature undulator is irradiated by the femtosecond laser pulse, a transverse deflection electric field with a sinusoidal periodic change in the Z direction will be generated, so that the electron beam incident in the Z direction is deflected by the modulation of the periodic change of the transverse deflection electric field, generating a periodic oscillation and radiating coherent electromagnetic waves outward, increasing the laser gain. In this embodiment, the miniature undulator mainly includes a reflective layer, a base layer, and a grating.

[0031] Among them, the reflective layer is parallel to the plane defined by the X axis and the Z axis and can be made of a reflective material such as silver.

[0032] The base layer is located above the reflective layer, that is, on the +Y direction side of the reflective layer. Its material is the same as that of the grating and is used to cooperate with the grating to form a preset optical path difference.

[0033] The grating is formed on the base layer, that is, on the +Y direction side of the base layer.

[0034] To obtain better laser gain, the period of the grating should be equal to the wavelength λ of the laser, that is, A + B = λ, where A and B are the dimensions of the two parts (grating protrusions and grating grooves) in one period of the grating respectively. A is the width of the grating protrusion part in the Z-axis direction (tooth thickness), and B is the width of the grating groove in the Z-axis direction (spacing between grating protrusions). In addition, the tooth thickness of the grating can be half of the period of the grating. In this way, when the electron beam passes through half of the grating period length, the surface electric field formed by the laser just reverses. At this time, if the phase slip caused by the transverse velocity is not considered (when the number of undulator periods is small), within one grating period length, the work done by the electric field force on the electron beam is zero. After passing through two grating period lengths, the electron beam returns to the trajectory center (please refer to Figure 1 the electron beam trajectory in

[0035] In this embodiment, the tooth thickness of the grating protrusion closest to the electron beam generator and the farthest from the electron beam generator is set as d, the tooth thickness of the grating protrusions between them is 2d, and the width of the grating groove is 2d. And the number of grating protrusions with a tooth thickness of 2d is odd. In this way, the length of the entire grating is an integer multiple of the grating period, and the grating period A + B = 4d = λ. Such a configuration can ensure that the electron beam has a sinusoidal trajectory along the Z direction during movement. d is a number greater than zero.

[0036] The gratings are distributed along the incident direction of the electron beam. The center of the electron beam is close to the grating surface, and the mutually parallel slits (grooves, or grating lines) between the gratings are also parallel to the X-axis. In this way, the electron beam can be subjected to a relatively large transverse deflection electric field. In this embodiment, the distance between the center of the electron beam and the grating surface is h = λ / 4, and the grating satisfies the following conditions:

[0037]

[0038] where n is the refractive index of the grating, H is the grating tooth height, W is the thickness of the base layer, and N and m are positive integers. When the condition of the first formula in the formula is satisfied, a coherently enhanced electric field can be generated at the electron beam trajectory position (y = 1.875um). When the condition of the second formula in the formula is satisfied, opposite phases can be generated in adjacent half-grating periods.

[0039] According to the above formula, the dielectric constant can be determined based on the grating refractive index n, and then the materials of the grating and the base layer of the micro-undulator can be determined. The material used in this embodiment is silicon dioxide (SiO 2 )

[0040] In this way, when the X-direction polarized light irradiates the grating surface from the Y-axis direction, a sinusoidal periodic transverse electric field distribution can be formed along the Z-axis direction on the grating surface and is also correlated with time, where E inis the maximum amplitude of the electric field, ω is the angular frequency of the electric field, ω 0 is the initial angular frequency of the electric field, t and z are time, ψ 0 and φ 0 are the initial phases of the electric field. Since the polarization characteristics of the incident laser and the grating groove direction are both along the X-axis direction, the electric fields in the Z-axis direction and the Y-axis direction are both zero, that is, E z = E y = 0. According to the electron beam motion equation (where γ is the Lorentz factor (relativistic energy factor), m e is the electron rest mass, is the electron velocity, is the electric field, q is the charge quantity), substituting the electric field expression into this equation, the second-order differential of x with respect to time t can be obtained: Furthermore, the electron beam trajectory equation in the X-axis direction can be obtained:

[0041]

[0042] Let c is the speed of light, β represents the ratio of the electron beam particle velocity to the speed of light, βx represents the ratio of the particle velocity in the x direction to the speed of light, and βy represents the ratio of the particle velocity in the y direction to the speed of light, then there is:

[0043]

[0044] According to the velocity synthesis relationship and performing Taylor expansion on it, retaining the first-order approximation, then there is

[0045]

[0046] In order to enhance the radiation correlation of the electron beam, the grating period λ u = A + B and the coherent radiation wavelength λ s should satisfy where θ is the radiation angle of the free electron laser. Generally, θ is a minimum value, and cosθ is approximately equal to 1, that is, the radiation of the electron beam at intervals of λ u has an integer multiple relationship of the wavelength. From this, it can be obtained (paraxial approximation, taking the radiation angle as zero). Combining equations (1) and (2), the analytical formula for the coherent radiation wavelength can be obtained:

[0047]

[0048] Comparing with the radiation resonance formula of the free electron laser, it can be found that the micro-undulator of the present invention has a similar analytical form but has more higher-order harmonic terms. In the existing conventional undulators, high-energy electron beams (γ >> 1) can be used to generate radiation wavelengths λ s much smaller than the undulator period λu For a free electron laser, for a micro-undulator, since its undulator period is much smaller than that of existing conventional undulators, from the form of its radiation wavelength, it can be known that for generating a free electron laser with the same wavelength, the electron beam energy required by the micro-undulator of the present invention is lower.

[0049] In a specific embodiment, the laser and grating parameters in Table 1 are selected, and using an electromagnetic field simulation software, such as ANSYS Lumerical FDTD or COMSOL or CST, the electric field distribution on the grating surface is simulated. Figure 3-4 The simulation results are shown. It can be seen that at the center of the electron beam trajectory (y = 1.875um), the Ex component is larger and shows a periodic change, while the Ez component is close to zero, meeting the expected design requirements.

[0050] Table 1 Laser and grating parameters

[0051]

[0052] Based on the electric field on the grating surface obtained from the previous simulation, and then using GPT (General Particle Tracking) software for electron beam tracking calculation (parameters are shown in Table 2), setting the beam current of the electron beam to 10 mA, the energy to 10 MeV, and the electron beam starting with a uniform distribution, it is observed that after experiencing 6 grating periods, the electron beam shows obvious bunching, and the relativistic factor of the electron beam drops by 0.15 (refer to Figure 5-6 shown).

[0053] According to the Madey theorem in the free electron laser theory:

[0054] where γ f 、γ i are the energies of the electrons before and after the interaction respectively, the subscripts 1 and 2 represent the first and second order perturbation terms in the power expansion of the optical field respectively, and <> represents the average over the initial phases of all electrons relative to the optical field. Since this theorem starts from the energy change of electron interaction and does not involve the magnetic vector operation of the undulator, it can also be used for the micro-undulator of the present invention. The left side of the equation is the average energy loss of the electron beam, and the right side of the equation is the discretization of the energy change. Also, according to the spontaneous radiation intensity formula: Combined with energy conservation, the small-signal gain of the optical field can be obtained: Substituting the relativistic factor obtained from the simulation and other parameters, the normalized energy gain is about 0.3. Where P is the power, Ω is the solid angle, Es is the electric field strength of the radiation field, and δ is used to represent the change in γ.

[0055] Table 2 Electron beam tracking calculation parameters

[0056]

[0057] In the above embodiments, the tooth thickness of the two grating protrusions at both ends of the grating is d, the tooth thickness of all the grating protrusions in the middle is 2d, and the width of the grating grooves is 2d. And the number of grating protrusions with a tooth thickness of 2d is odd. It can be understood that in other embodiments, the tooth thicknesses of all the grating protrusions can be the same, for example, all 2d, the widths of the grating grooves are also all 2d, and the number of grating protrusions is even. At this time, the electric field deflection causes the electron beam to have a transverse velocity, and the electron beam is a sine trajectory that deflects from the Z-axis to the +X-axis direction or the -X-axis direction during the movement. As long as the position of the product element is adjusted according to the electron beam trajectory.

[0058] In summary, the free electron laser of the present invention uses a micro-undulator, which deflects the electron beam by the electric field of the femtosecond laser on the grating surface instead of the traditional magnetic confinement. Since the laser wavelength is in the order of um, the size of the micro-undulator is extremely small, thus reducing the size of the free electron laser. And the period of the micro-undulator is smaller than that of the undulator composed of conventional magnetic elements. When generating coherent radiation light, it can reduce the requirement for the electron beam energy. In addition, the present invention also provides an analytical expression for the coherent radiation wavelength of the electron beam, which can accurately solve the relationship between the electron beam energy, structure and wavelength, and establish parameters such as the laser frequency and electron beam energy required for the micro-undulator. Those skilled in the art can determine the dielectric material and corresponding size required for the micro-undulator according to the central position of the electron beam trajectory and the laser wavelength, based on the equations.

[0059] Although the description of the present invention is made in combination with the above specific embodiments, it is obvious that those skilled in the art can make many substitutions, modifications and changes according to the above content. Therefore, all such substitutions, improvements and changes are included within the spirit and scope of the appended claims.

Claims

1. A free electron laser, characterized in that, a rectangular coordinate system of XYZ space is defined, including: an optical processing unit for performing a preset optical processing on the incident laser to output a linearly polarized light in the X direction; and a micro undulator for generating a periodically varying transverse deflection electric field to deflect the electron beam incident along the Z direction; wherein, the micro undulator includes: a reflective layer parallel to the plane defined by the X axis and the Z axis; a base layer located above the reflective layer; and a grating located on the base layer, the grating being distributed along the incident direction of the electron beam, and the grating grooves being parallel to the X axis; wherein, the linearly polarized light in the X direction irradiates the surface of the grating from the Y axis direction.

2. The free electron laser according to claim 1, characterized in that, the tooth thicknesses of the two grating protrusions at both ends of the grating are both d, the tooth thicknesses of the grating protrusions between the two grating protrusions at both ends of the grating are both 2d, the widths of the grating grooves are both 2d, and the number of the grating protrusions with a tooth thickness of 2d is odd, where d is a number greater than zero.

3. The free electron laser according to claim 1, characterized in that, the wavelength of the laser is equal to the period of the grating, and the tooth thickness of the grating is half of the period of the grating.

4. The free electron laser according to claim 1, characterized in that, the center of the electron beam is close to the surface of the grating.

5. The free electron laser according to claim 1, characterized in that, the distance between the center of the electron beam and the surface of the grating is λ / 4, where λ is the wavelength of the laser, and then the grating satisfies the following relationship: wherein, n is the refractive index of the grating, H is the height of the grating tooth, W is the thickness of the base layer, and N and m are positive integers.

6. A micro undulator, characterized in that, including: a reflective layer parallel to the plane defined by the X axis and the Z axis; a base layer located above the reflective layer; and a grating located on the base layer; it is defined that an electron beam passes above the grating, and a laser irradiates the grating from a direction perpendicular to the grating lines, wherein the arrangement direction of the grating is parallel to the incident direction of the electron beam, the distance between the center of the electron beam and the surface of the grating is λ / 4, where λ is the wavelength of the laser, and then the grating satisfies the following relationship: wherein, n is the refractive index of the grating, H is the height of the grating tooth, W is the thickness of the base layer, and N and m are positive integers.

7. The micro undulator according to claim 6, characterized in that, the tooth thicknesses of the two grating protrusions at both ends of the grating are both d, the tooth thicknesses of the grating protrusions between the two grating protrusions at both ends of the grating are both 2d, the widths of the grating grooves are both 2d, and the number of the grating protrusions with a tooth thickness of 2d is odd.

8. The micro undulator according to claim 6, characterized in that, the grating is a silicon grating.

9. The micro undulator according to claim 6, characterized in that, the material of the reflective layer is silver, and the material of the base layer is the same as that of the grating.

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